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University

This is to certify that the
dissertation entitled

ESTIMATING FOREST CANOPY ATTRIBUTES VIA
AIRBORNE, HIGH-RESOLUTION, MULTISPECTRAL
IMAGERY IN MIDWEST FOREST TYPES

presented by
DEMETRIOS GATZIOLIS

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Forestfl

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MS U is an Affirmative Action/Equal Opportunity Institution

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DATE DUE

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(N01! § 31230

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6/01 c:/ClFIC/DateOue.965-p.15

 

ESTIMATING FOREST CANOPY ATTRIBUTES VIA AIRBORNE,
HIGH-RESOLUTION, MULTISPECTRAL IMAGERY
IN MIDWEST FOREST TYPES
By

Demetrios Gatziolis

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Forestry

2003

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ABSTRACT
ESTIMATING FOREST CANOPY ATTRIBUTES VIA AIRBORNE,
HIGH-RESOLUTION, MULTISPECTRAL IMAGERY
IN MIDWEST FOREST TYPES
By

Demetrios Gatziolis

An investigation of the utility of high spatial resolution (sub-meter), 16-bit,
multispectral, airborne digital imagery for forest land cover mapping in the
heterogeneous and structurally complex forested landscapes of northern Michigan is
presented. Imagery frame registration and georeferencing issues are presented and a
novel approach for bi-directional reflectance distribution function (BRDF) effects
correction and between-frame brightness normalization is introduced. Maximum
likelihood classification of five cover type classes is performed over various geographic
aggregates of 34 plots established in the study area that were designed according to the
Forest Inventory and Analysis protocol. Classification accuracy estimates show that
although band registration and BRDF corrections and brightness normalization provide
an approximately 5% improvement over the raw imagery data, overall classification
accuracy remains relatively low, barely exceeding 50%. Computed kappa coefficients
reveal no statistical differences among classification trials. Classification results appear
to be independent of geographic aggregations of sampling plots.

Estimation of forest stand canopy parameter parameters (stem density, canopy
closure, and mean crown diameter) is based on quantz’jying the spatial autocorrelation

among pixel digital numbers (DN) using variogram analysis and slope break analysis, an

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alternative non-parametric approach. Parameter estimation and cover type classification
proceed from the identification of tree apexes. Parameter accuracy assessment is
evaluated via value comparison with a spatially precise set of field observations. In
general, slope-break-based parameter estimates are superior to those obtained using
variograms. Estimated root mean square errors at the plot level for the former average
6.5 % for stem density, 3.5 % for canopy closure and 2.5% for mean crown diameter,
which are less than or equal to error rates obtained via traditional forest stand cruising
by experienced personnel. The employed methodology entails parsimonious
parameterization and is supportive of automation. Overall cover type classification
accuracy increases from approximately 70% when using original imagery DNs to over
85% when band registration problems are corrected and variable brightness regimes
among imagery frames are normalized. Limiting cover type classification to pixels
identified as tree apexes is found to improve traditional classification approaches that
use all pixels by 35%.

Image—texture analysis based on intensity co-occurrence provides a quantitative
evaluation of second order image texture features that carry discriminatory potential for
forest cover type classification purposes. Procedure development and evaluation is based
on two independent data sets. Classification accuracies exceeding 60% can potentially be
achieved by using only image texture information. In its current level of development,

procedure applicability may be limited because of substantial computational cost,

absence of computer software for automation, and the complexity of methodologies

integral to the feature selection process.

Copyright by
DEMETRIOS GATZIOLIS
2003

To my sweetheart and fiancee Evagelia Baros with all my love

ACKNOWLEGEMENTS

Dr. Larry A. Leefers, my major professor, for his guidance and support;

Dr. David P. Lusch, my academic adviser, for stimulating my interest in remote sensing
through his charismatic teaching;

Dr. Jiaguo Qi, for sharing his invaluable insights on analysis methodologies and
techniques;

Dr. Steven K. Friedman, for providing working space and access to computing resources
in his laboratory;

Dr. Jeremy S. Fried, for his long-term commitment to my academic progress;

Frank Sapio, for providing access to the imagery and financially supporting the field data
collection;

Mark Zweifler, for the encouragement and help with research logistics;

The late Dr. Carl W. Ramm, for his mentoring and his contribution towards the
development of critical thinking;

The late Dr. George Bouyoucos, whose fellowship enabled my graduate studies;

My friends, Gem, Joe, and Marcelo, for their encouragement; and

My parents, Georgios and Styliani Gatziolis, for their emotional support and love.

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TABLE OF CONTENTS

CHAPTER 1

INTRODUCTION ............................................................................................................... l
1.1. Background ................................................................................................................. 2
1.2. Dissertation Objectives ............................................................................................... 4
1.3. Formation and Characteristics of Remote Sensing Data ............................................ 4
1.4. Remote Sensing Platforms .......................................................................................... 8
1.5. Imagery Calibration .................................................................................................. 10
1.6. Current and Projected Operational Forestry Remote Sensing Applications ............ 13
1.7. Analysis Methods of Remotely Sensed Data in Forestry ......................................... 13
1.8. Image Information Extraction by Spectral Analysis ................................................ 18
19 Beyond Spectral Analysis ......................................................................................... 20
1.10. Dissertation Outline .................................................................................................. 22
Literature Cited .................................................................................................................. 25
CHAPTER 2

AN EVALUATION OF BAND REGISTRATION, BRIGHTNESS VARIABlLlTY, AND Bl-
DIRECTIONAL REFLECTANCE DISTRIBUTION FUNCTION EFFECTS ON FOREST COVER
TYPE CLASSIFICATION USING HIGH SPATIAL RESOLUTION, MULTISPECTRAL IMAGERY..31

Abstract .............................................................................................................................. 32
2.1. Introduction ............................................................................................................... 32
2.2. Methods .................................................................................................................... 36
2.2.1. Site characteristics ........................................................................................... 36
2.2.2. Description of Imagery Set .............................................................................. 37
2.2.3. Sampling Scheme ............................................................................................ 38
2.2.4. Field Measurements ......................................................................................... 39
2.2.5. Image preprocessing ........................................................................................ 41
2.2.5.1. Band Registration ................................................................................... 41
2.2.5.2. Normalization of spectral frame brightness ............................................ 43

2.2.6. Image Classification ........................................................................................ 47
2.3. Results ...................................................................................................................... 49
2.3.1. Band Registration ............................................................................................ 49
2.3.2. Normalization of Frame Brightness ................................................................. 50
2.3.3. Image Classification ........................................................................................ 52
2.4. Discussion ................................................................................................................. 55
2.4.1. Band Registration ............................................................................................ 55
2.4.2. Normalization of Frame Brightness ................................................................. 57
2.4.3. Image Classification ........................................................................................ 58
2.5. Conclusion ................................................................................................................ 61
Literature Cited .................................................................................................................. 63
Tables ................................................................................................................................. 66

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CHAPTER 3
FOREST STAND CANOPY STRUCTURE PARAMETER VALUE ESTIMATION AND COVER
TYPE CLASSIFICATION VIA DIGITAL NUMBER AUTOCORRELATION TECHNIQUES IN

HIGH-SPATIAL RESOLUTION MULTISPECTRAL DIGITAL IMAGERY .................................. 88
Abstract .............................................................................................................................. 89
3.1. Introduction ............................................................................................................... 90
3.2. Individual Tree Identification ................................................................................... 93

3.2.1. Parametric quantification of image autocorrelation ........................................ 96

3.2.2 Non-parametric quantification of image autocorrelation ................................ 99
3.3 Individual Tree Classification ................................................................................... 99
3.4 Methods .................................................................................................................. 101

3.4.1 Study Site Characteristics and Description of Imagery Set ........................... 101

3.4.2. Field Measurements ....................................................................................... 103

3.4.3. Imagery Processing ........................................................................................ 104

3.4.4. Window Size Computation for LMF Imagery Processing ............................ 104

3.4.5. Tree Apex Identification via LMF Imagery Processing ................................ 109

3.4.6. Computation of Canopy Structure Parameters .............................................. 110

3.4.7. Cover Type Classification of Tree Apexes .................................................... 112
3.5. Results .................................................................................................................... 113

3.5.1. Local Maximum Filtering Methods ............................................................... 113

3.5.2. Stem Density .................................................................................................. 116

3.5.3. Tree apexes .................................................................................................... 117

3.5.4. Canopy Closure ............................................................................................. 118

3.5.5. Crown Diameter ............................................................................................. 119

3.5.6. Crown Delineation ......................................................................................... 120

3.5.7. Cover Type Classification of Tree Apexes .................................................... 121
3.6. Discussion ............................................................................................................... 124
3.7. Conclusion .............................................................................................................. 131
Literature Cited ................................................................................................................ 133
Tables ............................................................................................................................... 139
Figures ............................................................................................................................. 157
CHAPTER 4

AN INVESTIGATION OF THE UTILITY OF SECOND ORDER TEXTURE FEATURES FOR
FOREST COVER TYPE CLASSIFICATION USING HIGH-SPATIAL-RESOLUTION AIRBORNE

DIGITAL IMAGERY ....................................................................................................... 166
Abstract ............................................................................................................................ 167
4.1. Introduction ............................................................................................................. 167
4.2. Digital imagery texture measures ........................................................................... 170

4.2.1. Co-occurrence-based texture measures ......................................................... 171

4.2.2. Gray Level Co-occurrence Matrix features ................................................... 174

4.2.3. Image classification using GLCM features ................................................... 175
4.3. Methods .................................................................................................................. 181

4.3.1. Study Site Characteristics and Imagery Description ..................................... 181

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4.3.3. Image Pre-processing ..................................................................................... 184
4.3.4. Band selection, co-occurrence matrix development, and texture feature
selection ......................................................................................................... 185
4.4. Results and Discussion ........................................................................................... 188
4.5. Conclusion .............................................................................................................. 197
Literature Cited ................................................................................................................ 200
Tables ............................................................................................................................... 204
Figures ............................................................................................................................. 206
CHAPTER 5
SUMMARY ................................................................................................................... 2 13
5.1. A Critique of Analysis Methods ............................................................................. 214
5.2. The Role of Image Segmentation ........................................................................... 219
5.3. Evaluation of Analysis Results ............................................................................... 222
5.4. Evaluation of Field Data Collection Methods ........................................................ 223
5.5. Further Research Opportunities .............................................................................. 225
5.6. Conclusion .............................................................................................................. 226
Literature Cited ................................................................................................................ 227
APPENDIX 1 .................................................................................................................. 228
A.1. Crown delineation ................................................................................................... 229
A2. Crown centroid calculation ..................................................................................... 231
A.3. Crown diameter calculation .................................................................................... 232
AA. Bidirectional Reflectance Distribution Function Model ......................................... 233
A.5. Maximum likelihood classification ........................................................................ 235
A6. Cross-validation and classification accuracy assessment ....................................... 238
Literature Cited ................................................................................................................ 242
Tables ............................................................................................................................... 243
Figures ............................................................................................................................. 245
APPENDIX 2 .................................................................................................................. 252
3.1. Effects of Brightness/BRDF Normalization on Semivariogram Range
Computation. .......................................................................................................... 253
B2. Trend Surface Analysis ........................................................................................... 254
Literature Cited ................................................................................................................ 259
Figures ............................................................................................................................. 260

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LIST OF TABLES

Table 2.1. Cover types and their major species components in the study area. ............ 66

Table 2.2. Spectral registration vector components and length at plot centers
calculated as those that maximized between-band correlation using dark pixels of
the NIR band. Band correlation was evaluated within a 300 x 300 window
centered at respective plot centers. .............................................................................. 67

Table 2.3. Sums of spectral DN value differences between DN means of
overlapping regions of adjacent frames along closed multi-frame paths calculated
before and after BRDF/Brightness adjustment. DN means were computed using
only the portion of overlapping regions occupied by deciduous forests. BRDF
coefficients of the Roujean et a1. model, integral to the normalization process and
optimized to minimize Spectral column sums, are Shown. .......................................... 68

Table 2.4a. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for all subplots with
signatures developed from Sites I and 11 using original DNs ....................................... 69

Table 2.4b. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site I using
original DN Site I Signatures. ....................................................................................... 70

Table 2.4e. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site I using
original DN site II signatures ....................................................................................... 71

Table 2.4d. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site 11 using
original DN Site II signatures ....................................................................................... 72

Table 2.4e. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site 11 using
original DN site I signatures. ....................................................................................... 73

Table 2.4f. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for all subplots using post-
brightness normalization signatures from Site I. .......................................................... 74

Table 2.4g. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site I using
post-brightness normalization Si gnatures from site I. .................................................. 75

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Table 2.4h. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site I using
post-brightness normalization signatures from Site II. ................................................ 76

Table 2.4i. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site [I using
post-brightness normalization signatures from site II. ................................................ 77

Table 2.4j. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site 11 using
post-brightness normalization signatures form Site I ................................................... 78

Table 2.5. Z-scores of subplot classification results for combinations of cross-
validation-based classification choices computed as standardized differences of
respective kappa coefficients and associated p-values. ............................................... 79

Table 2.6. Change in class-conditional kappa coefficients computed before and
after brightness normalization. .................................................................................... 80

Table 2.7. Classification error rates of subplots conditional upon cover type group
(deciduous or coniferous) produced with maximum-likelihood based cross
validation for all plots in the study area before and after brightness normalization....8l

Table 3.1. Parameter values of linear regression models Obtained by fitting plot
stem density values predicted via application of two image LMF processing
techniques on field measurements of stem density. 1 39

Table 3.2. Root Mean Square Errors (RMSE) or discrepancies, between stem
density values predicted via LMF image processing and corresponding field
measurements. Stem density is expressed in trees per hectare. Values in
parentheses represent percent absolute error from observed cover type mean of
stem density. .............................................................................................................. 139

Table 3.3. Parameter values of linear regression models obtained by fitting plot
canopy closure values predicted via tree apex identification using image LMF
processing techniques and crown delineation algorithms on field measurements of
canopy closure. .......................................................................................................... 140

Table 3.4. Root Mean Square Errors (RMSE) between plot canopy closure
predictions obtained using LMF image processing for tree apex identification and
crown delineation algorithms and corresponding field measurements. Canopy
closure is expressed in percent of plot area. Values in parentheses represent
percent absolute error from observed cover type mean of canopy closure. .............. 140

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crown diameter value estimates obtained via variogram and image morphology
analysis to corresponding diameter estimates derived from field observations.

Image crown delineation was based on LMF processing techniques and associated
crown delineation algorithms. ................................................................................... 141

Table 3.6. Root Mean Square Error (RMSE) between plot mean crown diameter
predictions obtained i) via crown delineation based on image LMF processing
using variogram ranges, ii) via crown delineation based on image LMF processing
using directional Slope breaks, and iii) as the mean variogram range among
subplots, and mean crown diameter estimates derived from field Observations.
Values in parentheses represent percent absolute error from observed cover type
mean of mean crown diameter ................................................................................... 142

Table 3.7a. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from pixels identified as representing apexes of individual trees (slope
break method) for subplots in Sites I and II and original pixel DNS .......................... 143

Table 3.7b. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from subplot pixels identified as representing apexes of individual trees
(Slope break method) in Site I for subplots in site I and original DNS. ...................... 144

Table 3.7c. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from subplot pixels identified as representing apexes of individual trees
(slope break method) in site II for subplots in site I and original DNS. .................... 145

Table 3.7d. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from subplot pixels identified as representing apexes of individual trees
(Slope break method) in site II for subplots in site II and original DNS. ................... 146

Table 3.7c. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from subplot pixels identified as representing apexes of individual trees
(slope break method) in Site I for subplots in site II and original DNS. .................... 147

Table 3.7f. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from pixels identified as representing apexes of individual trees (slope
break method) for subplots in sites I and II and brightness-normalized pixel DNS. .148

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associated accuracy assessment parameters obtained by using spectral signatures
developed from subplot pixels identified as representing apexes of individual trees
(slope break method) in site I for subplots in site I and brightness-normalized
pixel DNS. .................................................................................................................. 149

Table 3.7h. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from subplot pixels identified as representing apexes of individual trees
(slope break method) in site II for subplots in Site I and brightness-normalized
pixel DNS. .................................................................................................................. 150

Table 3.7i. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from subplot pixels identified as representing apexes of individual trees
(slope break method) in site II for subplots in Site II and brightness-normalized
pixel DNS. .................................................................................................................. 151

Table 3.7j. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using Spectral signatures
developed from subplot pixels identified as representing apexes of individual trees
(slope break method) in site I for subplots in site II and brightness-normalized
pixel DNS. .................................................................................................................. 152

Table 3.8. Z-scores of subplot classification result comparison for combinations of
cross-validation-based classification scenarios computed as standardized
differences of respective kappa coefficients. Parentheses denote p-values. Scores
in bold and in italics indicate significance at oc=0.05. Scores in bold only indicate
significance at OI=0.01. Classification signatures were developed using pixels
identified as tree apexes via slope break-based imagery LMF processing ................ 153

Table 3.9. Classification error rates of subplots conditional upon cover types group
(deciduous or coniferous) produced with maximum-likelihood based cross
validation for all plots in the study area before and afier brightness normalization
using subplot pixels identified as tree crown apexes. Apex identification was
performed using slope break-based imagery LMF processing. ................................. 154

Table 3.10. Change in class-conditional Kappa coefficients computed before and
after brightness normalization using tree apex signatures. ........................................ 155

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cross-validation-based classification scenarios, computed as standardized
differences of respective kappa coefficients. Associated p-values are in
parentheses. Scores in bold indicate significance at (1:001. Classification
scenarios entailed signature development using 1) all pixels in a subplot, and 2)
pixels corresponding to subplot tree apexes identified via Slope break-based
imagery LMF processing. .......................................................................................... 156

Table 4.1. Commonly-used Gray Level Co-occurrence Matrix features. ................... 204

Table 4.2. Forest cover type classification results and associated accuracy
assessment parameters obtained by using a quadratic discriminant function-based
classifier operating on four imagery texture feature (energy, entropy, inertia, and
homogeneity) derived from Gray Level Co-occurrence matrices and trained with
independent data (112 observations). ........................................................................ 205

Table 4.3. Statistical comparison of texture-based forest cover type classification
accuracy estimates with results obtained by using various spectrally-based,
maximum likelihood classification schemes. Z-statistics correspond to

standardized differences of corresponding kappa coefficient values. ....................... 205
Table A. 1. DAIS technical specifications ..................................................................... 243
Table A2. Coefficient values used in the Roujean et a1. (1992) BRDF model for

deciduous forest and those derived with the brightness normalization process. ....... 244
Table A.3. Standard and actual .................................................................................... 244

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LIST OF FIGURES

Figure 2.1. Study area map portraying hydrological features. ........................................ 82

Figure 2.3. Registration vectors that maximized correlation between the NIR band
and each of the visible bands for the image frame hosting plot 21. Correlation was
calculated using the NIR band dark pixels for every 1/16‘h frame portion. Vector
colors correspond to respective bands. ........................................................................ 86

Figure 2.4. Post-brightness-adjustment mean spectral frame DNS for Site 1 (top) and
Site 11 (bottom) and ensuing between-Site mean spectral brightness differences. ...... 87

Figure 3.1. NIR band variogram ranges and mean slope-break lengths (circles)
and corresponding window sizes (squares) computed along a transect dissecting a
northern hardwoods subplot. Lines serve visualization purposes only. .................... 157

Figure 3.2. Original NIR band Digital Numbers (DN), DN-fit via local regression,
and pixel identified as slope-break-length truncation locations, along a 30-pixel
transect in a Natural Pine subplot. ............................................................................. 158

Figure 3.3. Observed vs. predicted stem density at the plot level for five forest
cover types. Stem density estimates were obtained from tree apexes identified on
NIR-band imagery via local maximum filtering (LMF) with window sizes
conditioned upon (a) computed variogram ranges, and (b) mean slope break
estimates. Plot cover types are color-coded while the LMF techniques employed
are symbol-shape-coded. ........................................................................................... 159

Figure 3.4. NIR band of an aspen subplot and tree apex locations identified by
using local maximum filtering with window Sizes conditioned upon (a) computed
variogram ranges, and (b) mean Slope break estimates. ............................................ 160

Figure 3.5. Observed vs. predicted canopy closure for plots in five forest cover
types. Canopy closure estimates were obtained from crown delineation based on
crown apexes identified on NIR-band imagery by using local maximum filtering
(LMF) with window sizes conditioned upon (a) computed variogram ranges, and
(b) mean slope break estimates. Cover types are color-coded while employed
LMF techniques are symbol-shape-coded. ................................................................ 161

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Figure 3.6. Observed vs. predicted mean crown diameter for plots situated in five
forest cover types. Mean crown diameter estimates were obtained from crown
delineation based on crown apexes identified on NIR-band imagery by using local
maximum filtering (LMF) with window sizes conditioned upon (a) computed
variogram ranges, and (b) mean slope break estimates. Cover types are color-
coded while employed LMF techniques are symbol-shape-coded. ........................... 162

Figure 3.7. Observed vs. predicted mean crown diameter for plots situated in five
forest cover types. Mean crown diameter estimates were calculated as the mean
range of variograms computed using the NIR band Digital Numbers for every
subplot in a plot. Cover types are color-coded. ......................................................... 163

Figure 3.8. Observed and NIR-band-estimated individual tree crown extent of an
oak subplot. Crown apex identification and subsequent crown delineation was
performed by using (a) variogram ranges and (b) slope breaks. Coordinate system
origin is at the subplot’s center and its scale is measured in pixels ........................... 164

Figure 3.9. Percentage of classified pixels for various probability thresholds
imposed on cross-validation-based maximum likelihood classification scenarios
of cover types prior to and after imagery brightness normalization. Development
of classification signatures was based on pixels identified as tree crown apexes via
Slope break-based imagery LMF processing. Lines serve visualization purposes
only. ................................................................................................................. 165

Figure 4.1. (a) A hypothetical 2-bit (4 gray levels) 5x5 image with, (b)
Corresponding general (pre-normalized) GLCM form with gray levels 1-4. (c)
Between-pixel angles used in the computation of GLCM, (d)-(i), GLCM structure
for distance of 1 pixel and choices of angular displacements. .................................. 206

Figure 4.2. Pictorial representation of two classes of GLCM weighting functions:
Weighting dependent on matrix element value (entropy and energy features), and
weighting dependent on an element’s spatial position (remaining features). Darker
shades indicate larger element weighting. ................................................................. 207

Figure 4.3. 4-bit image exhibiting geometric (regular) texture, and Cramer’s V
statistic calculated from image GLCMS as a function of displacement distance d.
Angular pixel displacement (0) used was 0°). .......................................................... 208

Figure 4.4. Pictorial representation of the Hughes phenomenon showing the
decrease in expected feature class probability as data dimensionality increases
from l-D (a) to 2-D (b). 100 realizations were drawn for each feature class from
Gaussian [~N(1,0)], independently and identically distributed data. Probability is
expressed as percentage. ............................................................................................ 208

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Figure 4.5. Decision boundaries for a two-class data set produced by a linear (a)
and quadratic (b) discriminant fimction developed using two object features.
Object class is color-coded. ....................................................................................... 209

Figure 4.6. NIR-band Normalized Gray Level Co-occurrence Matrices of an aspen

subplot produced 0={135+7r, 0, 45, 90} and various pixel displacement distances
d, and values of corresponding Cramer’s V statistic. ................................................ 210

Figure 4.7. NIR-band Normalized Gray Level Co-occurrence Matrices produced
for five subplot, each situated in one of the forest cover types present in the study
area, using d_==_l and 6_=_{l35+7r, 0, 45, 90}. ............................................................ 211

Figure 4.8. Forest cover type classification rules developed via quadratic
discriminant functions for texture feature pairs derived from NIR-band Gray
Level Co-occurrence Matrices calculated using [(1 = l, 61 = {135+7r, O, 45, 90}]

pixel displacement vectors ......................................................................................... 212
Figure A. 1. Spatial arrangement of DAIS image frames for Sites I and II. ................ 245
Figure A.2. Plot design according to the F lA/FHM protocol. .................................... 246

Figure A.3. Vertical tree crown projection map for a northern hardwood subplot
(24B). Crowns correspond to the portion of tree foliage visible from above. Dots
represent tree stems and are of size proportional to stem DBH. ............................... 247

Figure A.4. Illustration of target viewing and illumination geometry, and
associated angular parameters used in BRDF models. The figure, drawn in
perspective, preserves angles but not distances. ........................................................ 248

Figure A.5. Spline-based tree crown delineation using four, projected-to-the-
ground offsets of crown periphery. Offsets are expressed as vectors V1 to V4.
Dashed lines in the bottom part denote circular arc segments for each of the four
quadrants defined by pairs of clockwise adjacent vectors. Solid line Spline
segments S(Sx, Sy) represent the derived horizontal extent of the crown and are
produced by circular arc shifting along the X-axis, proportional to the (R,.-Ry)/Rx
ratio. Rx = |Vil and Ry = lVi+1|. ................................................................................... 249

Figure A.6. Vertical tree crown projection map for a northern hardwood subplot
(24B). Crowns correspond to the portion of tree foliage visible from above. Dots
represent true and pseudo crown centroids ................................................................ 250

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at 10° increments around the crown’s centroid. Dc denotes the diameter of a circle
occupying the same area with the crown. .................................................................. 251

Figure B.l. (a,b) Portrayal of original digital numbers Zoo-J) for row i and column j
indices of the NIR band for a coniferous stand and corresponding omnidirectional
empirical variogram.(c, b) Portrayal of digital numbers after image linear
translation and corresponding empirical variogram. (e, f, g). Portrayal of digital
numbers after processing original imagery with surface D(x;J) approximating an
imaginary anisotropic kernel similar to those typically embedded within BRDF
normalization models, and corresponding empirical variogram. .............................. 260

Figure B.2. NIR band image of a Red Pine subplot and empirical variograms
computed by using the DNS of pixels within the subplot prior to and after
processing for removal of first order autocorrelation. Circle in orange
superimposed on the image denotes the subplot boundary. Lines in the variogram
plot denote a Spline fit on the estimates of semivariance. ......................................... 261

Figure 3.3. Empirical variograms and fitted splines of post-trend-processed
imagery depicting a Red Pine subplot. ...................................................................... 262

xviii

CHAPTER 1

INTRODUCTION

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1.1. Background

Remote sensing has been synoptically defined as the detection, recognition, or
evaluation of objects by means of distant sensing or recording devices. Formally, the
American Society for Photogrammetry and Remote Sensing defined remote sensing as
“the measurement or acquisition of information of some property of an object or
phenomenon, by a recording device that is not in physical or immediate contact with the
object or phenomenon under study” (Colwell, 1983). In forestry, the information that can
be gleaned from visual interpretation of analog aerial photographs is well-understood,
frequently used, and routinely integrated in forest planning and management. Information
extracted from digital remote sensing data, however, is less commonly used. Many forest
managers maintain that the majority of digital remotely sensed data and the methods of
analysis are too complex to be of adequate utility to them. Furthermore, the effective use
of digital imagery often requires substantial investment in technological infrastructure.

Today, more than ever, forest management challenges are multiscale and
intricately linked to society’s need to measure, preserve, and manage for multiple, ofien
incompatible, values. Population growth and climate change are likely to catalyze these
ever increasing pressures on forests. The forest ecosystem itself is complex and
multifaceted. Understanding its functional structure requires information at a range of
spatial and temporal scales. Remote sensing information, integrated with other spatial and
non-spatial data sets, could form the information base upon which sound forest
management decisions can be made.

Remotely sensed imagery on its own is probably of little value to forest managers.

It is rather the interpretation of information extracted from those data that is used to

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address management challenges. Converting data to information is not a straightforward
task. It requires an understanding of the laws of physics and principles that govern the
formulation of remote sensing data and expertise in selecting the appropriate data
analysis methodology. It is ofien assumed that if an element of interest can be “seen” in a
digital remote sensing image, there would shortly be an automated procedure capable of
translating that visual impression into a usable piece of information. Practice has shown
that such optimism if frequently unfounded.

Forestry remote sensing began with manual methods of analysis applied to analOg
aerial photographs (Silva, 1978). Relative to information content, analog aerial
photographs are inexpensive and easy to use (Caylor, 2000). Comprehensibility and
economic considerations make airphotos the most common form of remote sensing in
forestry. As new types of imagery and analyses emerge, digital remote sensing will
become increasingly useful for forest managers (Wynne et al., 2000). Clearly, the onus is
on the remote sensing community to provide forest managers with examples of
applications that are cost-effective and easily implemented. These considerations are the
primary motivation for this dissertation. Using remote sensing data carrying some of the
most advanced characteristics currently available, a series of methodologies were
developed or refined that translated these data into information needed in operational
forest management. The chapter begins with an outline of the dissertation’s objectives.
Then forest attributes retrievable by remote sensing are discussed, and characteristics of
imagery acquisition systems are presented. A brief overview of the current and projected

operational remote sensing applications follows. Finally, image processing and analysis

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methods emphasizing the extraction of forest canopy characteristics and inventory

variables are introduced.

1.2. Dissertation Objectives

The goal of this study was to evaluate the utility of airborne, high resolution,
multispectral digital imagery for forest management decision-making in the structurally
complex forested landscapes of the upper Midwest. To ensure that the findings would be
representative, all dominant cover types in the region were included in the investigation.
Development and testing of methodologies was based on detailed and precise field
Observations. The potential for automation, where promising, guided the methodology
choices.

The three objectives of this dissertation were:

0 Evaluate the influence of airborne image acquisition
characteristics/idiosyncrasies on traditional, spectrally-based forest
classification efforts.

0 Assess the ability of image spatial analysis to reveal the horizontal
structure of the forest canopy and to enhance classification accuracies.

0 Evaluate the role image texture can have in stand classification.

1.3. Formation and Characteristics of Remote Sensing Data

A basic understanding of the characteristics of remote sensing data is essential
when considering its relevance to providing forest information products. In an ideal
world, a remote sensing image would be formed only from the energy reflected from a

target, and received by a perfect sensor. In practice, image formation is a rather

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complicated process. Gerstl (1990), Richard and Jia (1999), and Jensen (2000) offer a
summary of the principles that govern the interaction of light energy with forests, as
those are manifested in digital imagery. Other sources such as the energy reflected by
objects in the vicinity of the target and the contribution from atmospheric constituents are
exogenous to target radiance. The image formation process is also affected by the spectral
(wavelength-range specific) reflectance characteristics of the target, viewing geometry
(which describes the position of the sensor relative to the target), and illumination
geometry (which for optical remote sensing describes the position of the sun in relation to
the target). To complicate the process further, Spectral target reflectance, and viewing and
illumination geometry factors are not independent. Rather, they operate synergistically
and regulate target reflectance in a Spatial pattern referred to as the bi-directional
reflectance distribution function (BRDF). Forests in particular, because of their
complicated structure, cause a strongly directional reflectance. Accounting for the effects
of illumination geometry, atmosphere, and BRDF, would help the interpretation of
remote sensing image in forest applications.

Remotely sensed data are typically presented to the user in the form of digital
numbers (DN). Digital numbers are the quantification of energy recorded by the sensor
via an analog-to-digital converter. Because DNS are consistent within the imagery, in the
sense that higher DNS correspond to a higher amount of energy or density of photons
intercepted in unit time, they can be used in image analysis without further processing
(Franklin and Giles, 1995). The assumption made is that analog-tO-digital converters
translate photon density to DNS monotonically. A more rigorous assumption is that

PhOton density and DNS are related linearly. The coefficient that describes the

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relationship is commonly known as the gain of the sensor. Knowing the gain coefficient
facilitates imagery comparisons acquired using the same or different sensors at different
times, and the comparison between satellite, airborne and field-based sensor
measurements. Most satellite sensors provide calibration information embedded in the
header of the imagery. Digital airborne imagery acquired by commercial vendors ofien
completely lacks information on sensor calibration thereby depriving the user of the
opportunity to fully explore the information content of the imagery. The implications
might be more serious for multispectral array scanners, which are in essence a collection
of theoretically identical detectors arranged on a grid. Many array scanners currently in
use, including those employed in the acquisition of the imagery used in this dissertation,
are equipped with a million or more such detectors across the matrix and the assumption
that all of them are operationally identical is undoubtedly improbable. Calibrating
detector is practically infeasible though, and image analysis usually proceeds assuming
that sensitivity and gain differences among detectors are negligible.

Sensor resolution is a compound term comprising spectral, Spatial, radiometric,
and temporal dimensions. Spectral resolution denotes the number and width of specific
wavelength intervals, known as bands or channels, of the electromagnetic spectrum to
which the sensor is sensitive. Particular intervals, sometimes as narrow as Snm, are
optimal for uncovering certain biophysical information. Broadband multispectral sensors
are designed to detect radiance across a 50 to 100nm, usually non-overlapping, intervals
in a few different areas of the Spectrum. Hyperspectral sensors detect radiance over very

narrow intervals (e.g., 2 to 4 nm wide).

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Spatial resolution is the projection of the detector element through the sensor
Optics onto the landscape forming the instantaneous field of View (IF OV). It corresponds
to the smallest separation distance between objects that can be distinguished by the
sensor. The higher the spatial resolution the smaller the objects that can be detected. The
spatial resolution of airborne platforms is dependent on the flight altitude. Irrespective of
altitude, the energy intercepted by a single detector, is represented, after its quantification
to DN, as an image or picture element (pixel).

Frequently, remote sensing data are distinguished in terms of their spatial
dimension as of L(ow)- or H(igh)-resolution (Strahler, 1986). This characterization is in
reference to the size of the object(s) of interest. It is possible the same imagery set to be
L-resolution for one application and H-resolution for another. In forestry remote sensing,
typical satellite data are L-resolution (2 20-30m pixels). In this case, the dominant scene
objects (trees) are smaller than the pixel size and the sensor records the composite
radiance emanating from a collection of trees within the pixel area. Airborne data are
usually H-resolution (S 2m pixels), with a Single, average-sized tree crown being larger
than the pixel size. Therefore, radiance measured for a given pixel location is likely to be
directly related to the reflectance characteristics of an individual tree crown or portion of
a crown.

Radiometric resolution is related to the sensor’s ability to detect differences in the
Signal strength of intercepted energy in specific wavelengths. Greater radiometric
resolution allows smaller differences in reflectance to be discriminated. Sensor

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radiance increments within its sensitivity range.

With the exception of temporal resolution (the ability to provide repeated
coverage of a particular area), which can be considered as an independent dimension,
there are certain trade-offs among the remaining three imagery resolution dimensions. An
increase in the number of bands or channels is often accompanied by a decrease in spatial
resolution. To acquire more or narrower bands, a sensor must view an area on the ground
for a longer period of time, and therefore, the size of the area viewed increases from a
constant altitude. If the radiometric resolution is increased so that smaller differences in
radiance can be detected, then the spatial resolution, the number of bands, the narrowness
of the bands, or all three, must be reduced. This is because the amount of energy that is
reflected from the area viewed is fixed. If the amount of energy is divided into too many
bands (Spectral resolution) using many increments (radiometric resolution) over too small
an area (spatial resolution), then the energy signal becomes unacceptably weak compared
to the always-present system noise. In sensor design, it is the Signal-to-noise ratio that

should be maximized, rather than any of the spectral, spatial, or radiometric resolutions.

1.4. Remote Sensing Platforms

Digital remote sensing data of forests can be acquired from field-based, airborne,
and satellite platforms and might comprise a variety of imagery types (Chen et al., 1991)
or non-imaging spectroscopy measurements (Miller et al., 1976). Many types of ground
platforms have been used in remote sensing of forest canopy spectral reflectance
(Blackburn and Milton, 1997). Field Spectroscopy can be used in remote sensing in at

least three ways (Milton et al., 1995): l) to provide data for developing and testing of

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models of Spectral reflectance, 2) to collect calibration information for airborne or
satellite image acquisition (Wulder et al., 1996), and 3) as a remote sensing tool of its
own (Blackburn, 2000).

A variety of free-flying airborne platforms have been used in collecting remote
sensing observations. The ones most commonly used include low- and high-altitude
flying aircrafis and satellites. Sensors on airborne platforms typically offer greatly
enhanced spatial and spectral resolution over their satellite counterparts, coupled with the
ability to more closely control experimental design during image acquisition. For
example, they allow control over flight path azimuth or they can operate under clouds
and at different altitudes from low and slow survey flights (McCreight et al., 1994) and to
high-altitude reconnaissance flights (Moore and Pozlin, 1990). Airborne sensors usually
exceed satellite system capabilities in terms of their combined Spatial resolution, spectral
resolution, and signal-to—noise ratio performance (Anger, 1999). AS a result, satellite
imagery cannot be expected to replace digital airborne imagery by providing the same
type of forestry information (Roller, 2000). Basically, airborne data are of higher quality.
Airborne sensors allow longer exposure or dwell times, they often offer a customizable
sampling of the electromagnetic spectrum to fit the needs of the user, and their
measurements can be calibrated and atmospherically corrected by simultaneous ground-
based measurements over deployed reflectance targets. Compared to satellite imagery
however, airborne digital imagery has higher acquisition cost per unit area covered,
inferior sensor calibration, smaller area footprint, ofien ambiguous data documentation,
and only rarely availability of imagery archives at frequencies higher than once in 5-10

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Much of the cost of remote sensing is embedded in the analysis of the imagery to
produce information products. Generally, imagery quality is more important that the
initial acquisition cost, particularly in applications where the final cost of the information
product is critical (Agner, 1999). Often a better quality, and therefore more expensive, set
of images can yield information more economically, simply because it requires less
processing. The challenge is to optimize the choice of an imagery type to meet the needs
of the user (King, 1995). Bergen etal., (2000) presented a list of criteria that can be used
to assess the cost-effectiveness of information using the characteristics of the derived
information and the cost of producing such information. In cases where remotely sensed
information mandatory for the development of management plans can replace what is
typically acquired with field visits, the cost savings can be very significant. Even if
remote sensing information can only partially replace field-collected information, the use

of remote sensing technology could still be economically prudent.

1.5. Imagery Calibration

Remote sensing data contain a series of distortions produced by sensor
imperfections, atmospheric effects, viewing and illumination conditions, and topography.
In general, in digital analysis, failure to normalize these radiometric and geometric
distortions could lead to inaccurate remote sensing output products (Yang and Vidal,
1990), especially in the presence of Significant relief (Sandmeier and Itten, 1997).
Radiometric imagery correction can be a multi-stage process in which DNS are in
succession converted to at-sensor radiances, at-sensor reflectances, and finally to target
reflectances using atmosphere and illumination models (Sandmeier and Itten, 1997). All

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radiances (Wilson et al., 1994; Wolter et al., 1995) is sufficient. In some cases there may
be no need to perform any radiometric correction at all (Cohen et al., 1998). The number
of image radiometric correction stages that should be implemented is a function of the
availability of calibration information, analysis objectives, and the experience of the
analyst.

The complexity of atmospheric and topographic effects increases by the strongly
directional reflectance patterns of forest canopies. Because BRDF effects are target-
specific, information on canopy characteristics is required prior to its correction. At the
same time, extracting canopy information such as cover type requires atmospheric and
BRDF effects to be normalized first, which gives rise to a tautology. To avoid the
tautology, it is common practice to assume that canopies exhibit Lambertian behavior
(Sandmeier and Itten, 1997), which in turn renders topographic and atmospheric
corrections only marginally successful. Geometric distortions are related to sensor and
imaging geometry and topography (Fogel and Tinney, 1996). Corrections can applied to
provide locational accuracy (Burkholder, 1999), but they necessitate image resampling
which is known to alter pixel spectral characteristics proportionally to the spatial relation
between the input and output grids.

The forms of imagery distortions mentioned above are usually more pronounced
in imagery acquired by airborne platforms, especially those flying at low altitudes,
because of the large parallax present and the sometimes substantial variation in platform
altitude, velocity, and attitude. Distortion correction requires a substantial effort
investment by experienced analysts, especially for digital airborne imagery acquired

using array scanners. Contrary to satellite imagery, where each image frame typically

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National Forest, usually comprises several hundred to thousand frames. Such large
imagery frame sets have coordinate systems of variable orientation, are characterized by
varying target reflectance and brightness regimes. In the forests of the upper Midwest in
particular, which are characterized by intense fragmentation and cover type variability,
and by fi'equent presence of swamps, wetlands, and lakes, such brightness variability
even between image frames acquired in sequence is prominent. Although in theory
brightness variability could be easily normalized across the entire imagery set by using
the spectral gain factor effective during each image frame acquisition, practical
limitations originating at the sensor’s sensitivity adjustment at the analog system
component (i.e. prior to signal conversion from analog to digital format), typically result
in imagery sets for which the per-frame gain factor remains unknown. To date, there are
no known examples of research investigations that attempted a Simultaneous correction
of BRDF effects, geometric distortions, and variable brightness regimes using more than
a handful of array scanner imagery frames. Perhaps the difficulty in correcting those
distortions has discouraged such efforts; or perhaps the preoccupation with the relatively
coarse resolution Spatial imagery obtained from satellite platforms has prevented a more
concerted effort in the airborne arena. Those issues are addressed in this dissertation. A
methodology was developed, capable of substantially reducing distortion magnitude and

allowing for significant improvements in the quality of subsequent analysis products.

12

1.6. Current and Projected Operational Forestry Remote
Sensing Applications

Remote sensing has the potential of playing a critical role in forest management in
many different settings - operational forest cover mapping, forest structure and change
analysis, and forest inventory assessment. A minimal list of probable, near-future
operational forest remote sensing applications could include (Wynne and Carter, 1997):
a. Forest cover type characterization, b. Determination of forest stand conditions and
forest health, c. Site characterization, and (1. Fire monitoring. If emphasis is shifted from
applications to the fundamental concepts of digital remote sensing, additional
applications in forestry could be considered operational (Cohen et al., 1996): e. Mapping
forest cover, f. Measuring and monitoring structure, function, and composition of
vegetation, and g. Detecting change in these conditions over time. An additional set of
applications appears to be on the threshold of operational status: landscape structure
modeling, defoliation monitoring, and biophysical forest inventory. It is expected that by
2008 a complete set of operational remote sensing applications in forestry, will become
increasingly apparent, with major contributions primarily from analysis of high-

resolution imagery (Wynne and Oderwald, 1998).

1.7. Analysis Methods of Remotely Sensed Data in Forestry

Most forestry remote sensing analysis methods are either experimental or
normative. The former operate on the assumption that the control of variables influencing
a phenomenon under investigation is feasible. In forest remote sensing applications the
experimental method is used to improve our understanding of the relationship between a

forest condition of interest and the information available about that condition extracted

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from remote sensing data. In this context, the analysis can be viewed as an experiment
where the remote sensing data are the dependent variables and the forest condition(s) of
interest form the independent variables. If control could be exerted on all the independent
variables, then it could be expected that a strong relationship be identified between the
independent and dependent variables. The identified relationship could then be treated as
a precise and accurate predictive model that, when inverted, could provide reliable
estimates of the forest condition under investigation using only remote sensing data
(Bracher and Murtha, 1994).

Controlling all confounding variables is perhaps feasible in a laboratory setting. In
an actual image acquisition mission over a forested area though, it is impossible to know
all the variables that influenced the remote sensing measurements. These influences
cannot be uniquely determined, but can certainly overwhelm the signal from the
condition of interest. Hence, the actual relationship between a forest condition and
remotely sensed data is typically much less predictable than those obtained by standard
experimental methods (Blackburn, 2000). Because of this limitation, the normative
(Haring, 1992) method is often employed.

Under the normative approach there is typically a lack of control of the
independent variables that influence the image characteristics. This makes the
relationships found subject to caveats and constraints that must be carefully documented
and described. Although the normative approach supports the development of
relationships under less than ideal conditions, it suffers from the lack of generality that
could lead to highly Spurious local insights, especially where there is very little

theoretical foundation in support of an identified relationship.

14

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Both experimental and normative remote sensing analysis methodologies are, in
essence, modeling efforts. A unique characteristic of the remote-sensing-based models is
that, in their inverted mode, all their independent variables are derived from sensor
measurements of energy reflected (or backscattered) from an object or condition. The
models operate under the implicit assumption that object or condition variates cause a
predictable variation on sensor measurements. In digital remote sensing over forested
landscapes this assumption may not necessarily hold. For example, the energy reflected
from a forest stand canopy in a leaf-on condition, is basically unaffected by the stand
stem wood mass. If the objective were to estimate wood biomass using remote sensing, it
would seem more reasonable to use one or more surrogate variables (e. g., crown
diameter, tree height, species association) for which more accurate quantitative estimates
can be derived using remote sensing data and then use these surrogate variables to predict
stand woody biomass. Such considerations have raised concerns that perhaps the
application of remote sensing technology to routine forest management is not feasible, at
least in the short term (Battaglia and Sands, 1998). From a remote sensing analyst’s
perspective, it is frequently the absence of explicit and complete problem definition that
has precluded wide acceptance of remote sensing as a forest management tool (English
and Dale, 1999). Despite reservations by certain forest managers, there appears to be a
general consensus that the synoptic and repetitive biophysical vegetation information
requirements for large geographic areas over long periods of time can only be provided
by remote sensing.

Several studies in the 1980s established that low-resolution satellite data can be

classified for forest cover, stand age, and crown closure (Walsh, 1980; Horler and Ahem,

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1986). In most studies Since then, correlations to height, basal area, and biomass were
good to moderate (e.g., Kovats, 1997; Shettigara and Sumerling, 1998); correlations to
density, size diversity, mean diameter, and number of species were moderate (e.g., Roy et
al., 1996; Cohen et al., 2001; Franco-Lopez, 2001); and correlations to understory
measures such as number of seedlings, and understory cover were weak (e.g., Stenback
and Congalton, 1990; Jakubauskas and Price, 1997; Hall et al., 2000). Even the better
correlations though were usually too weak to allow them to be used in forest management
and planning. The main problem is rooted in the fact that the optical sensor only detects
reflectance from the top of the canopy (Holmgren and Thuresson, 1998) effectively
precluding assessment of attributes that are physically demonstrable only beneath the
canopy. In many forests, crown closure will reach a maximum while basal area and
structural complexity will continue to increase, but the optical remotely sensed signal,
particularly from low-resolution imagery, is not significantly affected by these changes
(Franklin, 1986).

High spatial or spectal resolution digital imagery is subject to similar restrictions
in terms of its beneath-canopy, forest-stand structure information content. However, it
offers a much more detailed View of the horizontal structure of the canopy. In particular,
it provides explicit information on the amount and spatial distribution of Shadowing in
the stand, which can exert a dominant influence on the stand’s reflectance (St-Onge and
Cavayas, 1995). A pixel in this type of imagery would characterize only a small part of
the tree crown, shadow, or the understory. The spatial detail present in hi gh-resolution
imagery allows individual tree-crown delineation (Gougeon, 1995; Brandtberg, 1997),

and could improve estimates of crown closure, stem density, and species composition by

16

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exploring image texture (Gerylo et al., 1998). Identification of individual trees has been
successful with images having spatial resolution of 0.6m or smaller, but conceivably will
work well enough with 1m satellite data to justify more extensive use and development
(Wulder, 1999). Most investigations of individual tree identification have been reported
in pure or mixed conifer stands where the conical shape of crowns generates abrupt
distinctions between sunlit and shadowed portions of crowns and facilitates accurate tree
identification. In deciduous stands, tree crowns usually defy formal shape conventions,
have multiple crown maxima and less distinct edges, making tree identification much
more challenging (Warner et al., 1999). Although imagery with 1m or finer spatial
resolution has been available from airborne platforms for decades, and is now becoming
available from satellite platforms, there are very few examples of projects using this type
of imagery for stand structure, Species composition, and crown closure mapping.

In this dissertation the normative analysis approach was used. The concerns
aforementioned and related to the ability of optical remotely sensed imagery to provide
accurate and reliable information on forest structure, even in the presence of high
resolution imagery, guided the early stages of dissertation objective formulation. In
response to those concerns, analyses focused on canopy cover type classification and on
quantifying canopy surface attributes including stem density, canopy closure, and crown
size. Were other types of forest structure information to be pursued (e.g., tree height,
composition of understory vegetation, basal area, etc.), non-optical remotely sensed
imagery (microwave, lidar) would have been explored as more promising for delivering
those types of information (Dubayah and Drake, 2000; Fransson et al., 2000). To improve

the chances of regional methodology applicability, analyses techniques were based on

17

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canopy morphological characteristics extracted from the imagery, rather than, for

example, identified mathematical relationships.

1.8. Image Information Extraction by Spectral Analysis

The extraction of information from remotely sensed data is usually based on
differentiating spectral response patterns in the landscape. The three more common types
of information of interest in forest management applications are: a). Continuous forest
variable estimation, b). Forest classification information, and c). Forest change or
difference information. A plethora of image analysis techniques has been proposed for
deriving such information, and each technique has spawned numerous options, that will
likely continue to evolve. A common characteristic among analysis methods is that they
are oriented towards providing information at the stand level, which Should not come as a
surprise given that most methodologies were developed for L-resolution imagery. Using
essentially those same techniques with H-resolution imagery can potentially be
imprudent, given that the information content in H- and L-resolution imagery is
organized at different spatial levels. To confirm the hypothesis that indeed high spatial
resolution imagery is a unique information source for forestry applications that requires
the use of specific analysis methods, this research investigated the second type of forest
applications mentioned above (forest classification) in a dual spatial scope: at the stand-
level and at the individual tree level.

Continuous variable estimation occurs primarily by one of the few common forms
of inversion modeling, including regression analysis, neural networks, reflectance
modeling, or radiative transfer modeling. These approaches follow traditional, albeit

sometimes unconventional, statistical probability design where two sets of variables, one

18

derived from the imagery and the second from field observations or ancillary
information, are related. Because however, these methods do not account for the position
Of the pixels within the forest stand examined, and offer no theoretical justification for
the form of the models produced, the accuracy of the continuous variables they estimate
is largely dependent on the quality and comprehensiveness of the input training data
(Salvador and Pons, 1998) and tends to drop substantially when used at stand conditions
other than those used to developed the models. To improve the robustness of derived
continuous variable estimates in this research, model formulation was spatially explicit,
in the sense that the spatial relationships among adjacent pixels determined model output.
Positionally explicit information for model development and evaluation, however,
is rather costly, especially at the individual tree level. Very few cases are known (Warner
et al., 1999; Pouliot et al., 2002; Wulder et al., 2002) for which spatially explicit stem
information was used, and all involved a single stand. Tree stem location information
probably suffices for an evaluation of methods aiming at predicting stem density but is
likely inadequate for models developed to estimate canopy structure variables, such as
canopy closure and mean tree diameter. Those concerns led to an ambitious endeavor that
by using survey equipment and methodology mapped precisely the horizontal canopy
structure of plots installed in 34 stands, stratified across major cover types of the Midwest
region. It was assumed that the detailed field observations could lead to interesting
insights related to how canopy structure is manifested in hi gh-resolution imagery and
permit canopy structure model tuning to account for those insights. Whether the expenses

associated with such an endeavor were justified, can be judged by observing associated

19

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research findings, not only in terms of estimate accuracy obtained but also in regard to
the value and generalized applicability of the methodologies employed.

A major trend in remotely sensed data analysis in forestry has been the emphasis
on automation. However, it is still the case that most techniques, even when supported by
software package routines, require substantial human intervention, judgment, and
guidance in order to operate successfully, prerequisites that defy automation. The
importance of automation is more pronounced in the analysis of hi gh-resolution imagery
in part because of the small footprint and therefore the large number of image frames that
need to be processed. Possibly the only area in forestry remote sensing where automation
and standardization has been achieved is the assessment of classification accuracy in the

form of a contingency table or confusion matrix (Congalton and Green, 1999).

1.9. Beyond Spectral Analysis

Despite numerous achievements associated with information product extraction
from digital imagery in forestry, the accuracy of product attributes are usually inferior to
those achieved by experienced interpreters of analog aerial photographs. This might be,
in part, because digital imagery rarely supports stereoscopic View of the forest but
probably also because attribute value estimation is usually based strictly on the per-pixel
spectral response of the forest. Photointerpreters, on the other hand, in addition to tonal
characteristics, are accustomed to using a variety of textural, pattern, Shape, object,
shadow, and topographical evidence. Improvements in the use of these texture/context
descriptors in digital remote sensing analysis may allow canopy structure parameter
estimates obtained from digital imagery to rival the accuracy levels that manual

photointerpretation achieves (Green, 2000). Development of such methodologies is

20

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emphasized by the need for forest classification and inventory parameter product
integration with other forms of digital information usually provided via Geographic
Information Systems, and the steady decline in the number of experienced
photointerpreters available to perform those tasks.

One of the most promising alternatives to spectrally-based analysis of digital
imagery in forestry is to consider classification in a spatial context. The premise is that a
pixel’s most probable classification, when viewed in isolation, may change when viewed
in some context (Haralick and .100, 1986). The simplest context classifiers use
neighboring pixels to decide, confirm, or change the classification or labeling of the pixel
at the center of the neighborhood. Attempts to broaden context classifier algorithms have
included incorporating the spatial correlation function between pixels (Khazanie and
Crawford, 1990) and contextual parameters (Chen, 1999). These concepts are closely
related to image texture analysis. Image texture is the quantification of the spatial
variation of image tones, often referred to as gray levels, that defies precise definition
because of its perceptual character (Hay et al., 1996).

Human vision possesses a powerful innate ability to recognize textural
differences, although the complex neural and psychological processes by which this is
accomplished have so far evaded detailed scientific explanation. The interest in
quantifying texture in digital domains has led analysts to focus on the structural and
statistical properties of textures (Haralick, 1986). It is expected that by combining per-
pixel and area-based texture processing, more accurate classifications of remotely sensed
imagery can be generated (Ryherd and Woodcock, 1997). Parallel to the use of texture in

classification, interest has developed in texture itself as a variable in forest applications

21

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(Coops and Culvenor, 2000). Texture has been Shown to be directly related to different
aspects of forest stand structure, including age, density, and leaf area index (Wulder et
al., 1996; St-Onge and Cavayas, 1997).

Image texture, however, is an abstract term. lts quantification has been attempted
in a variety of disciplines including machine Vision, pattern recognition, and remote
sensing, resulting in a large number of approaches and an even larger number of texture
metrics. Their value for forestry remote sensing applications is, at large, unknown.
Today, there are few guidelines to help analysts decide which of these approaches and
metrics may be better suited, if suited at all, for a particular forestry application. A
chapter of this dissertation is devoted in providing such guidelines towards forest cover
type classification using a branch of texture quantification methods known as gray level
co—occurrence analysis. Instead of simply relaying analysis results for the metrics used in
the investigation, as is the usual case, the chapter provides a detailed presentation of

methodology options encountered at every step of the multistage procedure employed.

1.10. Dissertation Outline

The current chapter described the motivation behind the dissertation research, the
study objectives, and a brief exposure to the factors that affect remote sensing imagery
formation, calibration, and analysis used in forestry applications. Chapter 2 deals the
detection, quantification, and correction of a series of imagery imperfections that are
customarily encountered in a digital airborne imagery set. It presents a novel approach
that allows for a simultaneous correction of BRDF and variable brightness regimes
among imagery frames and a technique for reducing band registration problems. The

impact of geometric and radiometric imperfections on the accuracy of forest cover type

22

classification based on the popular, maximum likelihood method is assessed by
comparing classification results obtained using the original imagery set and one obtained
after correction/ normalization of the imperfections. It is shown that although corrections
do improve classification results, the classification accuracy even for the corrected set
remains too low to be of any utility.

Chapter 3 describes a parametric method known as variogram analysis and the
development of a non-parametric metric, both capable of quantifying pixel brightness
autocorrelation and used for the identification of tree apexes, the number of which is
subsequently converted to an estimate of stand density. Further investigations of canopy
reflectance patterns based on identified tree apexes, yield estimates of canopy closure and
mean crown diameter. Estimate accuracies were found to be comparable, if not superior,
to those obtained with field observations, especially when tree apexes are identified using
the non-parametric approach. The Chapter also describes cover type classification
scenarios involving only pixels identified as tree apexes. It is Shown that a remarkable
accuracy improvement of more than 30 percentage points is achieved compared to the
traditional, non-spatially explicit approach used in Chapter 2. Classification accuracies
achieved using the corrected imagery (>85%) are found to approach operational status.

Chapter 4 describes the use of image texture for forest cover type classification
purposes. It introduces a multistage procedure, which shows that the quantitative
evaluation of texture-related cover type discrimination power associated with image
bands, necessary image pre-processing choices, texture measures, and finally texture
features can provide classification accuracies similar to those obtained using spectral

classification of raw (uncorrected) imagery.

23

Chapter 5 provides a critique of analysis methods used in this dissertation and an
evaluation of analysis results. It also describes a framework that can be used to combine
spectral, textural, and canopy structural characteristics for potential improvements in
cover type classification accuracy. Insights regarding field data collection methodologies

and a projection of additional research investigations in the study area are also presented.

24

Literatur'

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29

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30

CHAPTER 2

AN EVALUATION OF BAND REGISTRATION, BRIGHTNESS VARIABILITY, AND
BI-DIRECTIONAL REF LECTANCE DISTRIBUTION FUNCTION EFFECTS ON
FOREST COVER TYPE CLASSIFICATION USING HIGH SPATIAL RESOLUTION,

MULTISPECTRAL IMAGERY

31

Abstract

An investigation of the utility of high spatial resolution (sub-meter), 1 6-bit, multispectral,
airborne digital imagery for forest land cover mapping in the heterogeneous and
structurally complex forested landscapes of northern Michigan is presented. The Chapter
addresses imagery frame registration and georeferencing issues and introduces a novel
approach for bi-directional reflectance distribution function (BRDF) eflects correction
and between-frame brightness normalization. Maximum likelihood classification of five
cover type classes is performed over various geographic aggregates of 34 plots
established in the study area that were designed according to the Forest Inventory and
Analysis protocol. Classification accuracy estimates derived from confusion matrices
show that although band registration and BRDF corrections and brightness
normalization provide an approximately 5% improvement over the raw imagery data,
overall classification accuracy remains relatively low, barely exceeding 5 0%. Computed
kappa coeflicients reveal no statistical differences among classification trials.
Classification results appear to be independent of geographic aggregations of sampling
plots. The low overall classification accuracies are attributed to the cover type-invariant

spectral properties of crown portions in shadows.

2.]. Introduction

The most common use of digital remote sensing data in forestry is for cover type
classification of forested landscapes. Its importance is demonstrated by the fact that there
are forest classification precedents in virtually all the major biomes of the world
(Darvishsefat, 1995; Foody and Hill, 1996; Hansen et at. 2001). The purpose of the

classification effort is often to allow contiguous areas covered with forests to be depicted

32

in their natural state, thus making a single classification scheme appropriate for these
areas. Level II classification of Anderson et a1. (1976) is an example of a generic scheme
ofien imposed in such cases. In practice though, rarely would a general purpose
classification serve specialized purposes equally well (Bailey, 1996), resulting in forest
cover type classification challenges in certain areas of the world to be better understood
than in others because of the extensive prior work performed there or the presence of
long-term research initiatives (Shoshany, 2000).

Most remote sensing-based forest cover type classification efforts use L-
resolution multispectral satellite imagery (Strahler et al., 1986), in part because of the
reasonable cost and extensive archives many satellite platforms offer (White et al., 1995;
Archard et a1, 2001; Woodcock et al., 2001), and have traditionally been spectrally based.
Pixel values in L-resolution imagery correspond to the composite reflectance of many
objects and therefore mask the spatial arrangement of objects within the pixel and allow
only broader spatial patterns to be identifiable, thereby limiting the utility of spatial and
textural investigations to the stand level or beyond. On the other hand, operational forest
management decisions are almost exclusively based on information extracted from
analog infrared or color infrared aerial photographs (Wynne and Oderwald ,1998). The
use of analog aerial photographs in forest classification, however, is subject to
constraints, including availability of experienced photointerpreters, lack of photographic
enhancement capabilities, and difficulty in photographic reproduction, mosaicing, and
overlay with other forms of spatial data. The increasing popularity of digital airborne
imagery over the last decade can be regarded as an attempt to combine the merits of

satellite L-resolution imagery with the rich information content of large-scale

33

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photography, and the flexibility of processing options characteristic of digital
information. Recent technological advancements have allowed H-resolution imagery
(Strahler et al., 1986) to be available even from satellite platforms (e. g. IKONOS-Space
Imaging, QuickBird—Eurimage), at least at the panchromatic level, thus allowing growing
optimism that improvements in our ability to extract enhanced information on the types
and attributes of forests from airborne digital data could be directly applicable to future,
economical satellite H-resolution data.

In contrast to the popularity of L-resolution satellite imagery for forest cover type
mapping, there is only a handful of examples that have employed airborne, high-spatial-
resolution, multispectral imagery for that purpose (Coulter et al., 2000; Lefsky et al.,
2001) and none of them in the forests of the Midwest region. The few known examples
typically involve a very limited number of cover type classes, often only one coniferous
and one deciduous class, utilize a single image (frame), and use information derived from
large-scale aerial photography for evaluating classification results (Biging et al., 1995).
Little justification is usually offered, other than perhaps financial constraints, for the
tendency to rely upon assessed information as opposed to direct observations when
evaluating classification accuracy. Such practices are likely to foster propagation of
errors and introduce uncertainty in information treated as “ground-truth” which is not
accounted for in derived classification products.

Spectral classifications of airborne, high-spatial resolution, multispectral imagery
are subject to the H—resolution challenge (Hay et al., 1996), which implies that as the
spatial resolution of the sensor increases (i.e. the pixel size becomes smaller), so does the

within-class spectral variability of surface features, resulting in a reduction of class

34

separability and a consequent reduction in classification accuracy. The latter is often
attributed, in part, to the spectral properties of pixels that represent the shadowed portions
of tree crowns (Woodcock and Strahler, 1987; Marceau et al., 1990). However, a few
studies have argued that although shadows mutually cast between tree crowns reduce the
spectral differences between cover types, shadow pixels maintain adequate information
content that would permit cover type classification with reasonable accuracy levels,
especially for 16-bit imagery (Gwinner and Schaale, 1997).

In forest classifications, the H—resolution challenge is further intensified because
of similarities in the spectral reflectance characteristics among forest cover types relative
to non-forested ones. An additional level of complexity is introduced by the strong,
directionally anisotropic reflectance, known as the bi-directional reflectance distribution
function (BRDF) effect, that forests exhibit due to their complex horizontal and vertical
structure and by topographic effects where present. In contrast, Landsat scene (or frame)
which encompasses millions of hectares, a very large number of digital airborne imagery
frames are required to cover even a relatively small sample area, spanning an extensive
range of solar illumination conditions. In geographic regions characterized by forest
cover type variability, such as those typical in upper Midwest, airborne imagery frames
are subject to considerable variation in scene brightness. H-resolution airborne digital
imagery is often delivered to the analyst with substantial georeferencing errors introduced
by imprecise aircraft internal navigation systems, inadequate camera calibration
information, or with noticeable registration discrepancies between bands, especially when
a multi-camera arrangement is used for imagery acquisition. All of these

factors/characteristics of airborne digital imagery operate synergistically and the extent to

35

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which they affect forest cover type classification products is unknown, or at least it is
subject to speculation.

The objectives of this study are to 1) develop a procedure for detecting,
quantifying, and correcting the geometric and spectral distortions that are often present in
airborne, digital imagery (multispectal and multiframe, high spatial resolution), and 2)
evaluate the extent to which camera and sensor-related imperfections and idiosyncracies
affect forest cover type classification while considering frame proximity issues, BRDF
effects, and brightness variations among imagery frames. Evaluation is based on spatially
accurate and precise field observations at the individual tree level for five forest cover

types common in the Great Lakes region.

2.2. Methods

2.2.1. Site characteristics

The study area comprises two sites, the one in the south-central part of Grand
Traverse County (Site I) and the other in the northern part of Wexford County (Site 11),
Michigan (Figure 2.1). Note that figures in this dissertation often contain color. The sites
are separated by about 10km in the northwest-southeast direction and extend over 8,805
and 12,626 hectares of land, respectively. More than half (56%) of the study area is
owned and managed by the Michigan Department of Natural Resources. Most of the
study area consists of forests and wetlands (82%), while agricultural use, mainly row
crops, represents 8%. Other land use classes include orchards (4%) and residential areas
(4%). Residential development is concentrated in the northwestern part of site I.
Geomorphic features include moraines and outwash plains. The average slope, calculated

by using the finite differences algorithm on a 10m, 1:24,000 USGS Digital Elevation

36

Model available for the area is 3.5% and 2.7% for sites I and II respectively. Relief is
more pronounced along the Manistee River, which crosses site II from northeast to
southwest.

The study area is characterized by pronounced spatial heterogeneity of forest
cover types. For that reason, it was selected in 1999 by the Michigan Department of
Natural Resources (MDNR) as one of the pilot areas used for evaluating the utility of
digital remote sensing data for monitoring and mapping state-owned forest resources. The
associated effort is formally known as the Integrated Forest Mapping and Planning
(IF MAP) project. The majority of the forest cover types extant in the northern Lower
Peninsula of Michigan are present in the forested part of the study sites. The five cover
types used in this study are listed in Table 2.1. The study area also contains cedar swamps
dominated by Northern White Cedar (T huja occidentalis).

The primary forest management objectives of the MDNR include timber
production, wildlife habitat enhancement, recreation opportunities, and aspen
preservation. Several private land owners offer seasonal horseback riding and

snowmobiling opportunities.

2.2.2. Description of Imagery Set

The imagery data set used in this study was acquired on August 11, 1999, using
the Digital Airborne Imaging System (DAIS [Space Imaging, 1999]), a sensor which
provides imagery in four bands (three visible and one near infrared) via frame (digital
array) cameras equipped with appropriate band-specific filters mounted in a 2x2
arrangement. Appendix 1, Table A.1 contains detailed information on the technical

specifications of the system. The 394- frame imagery set was delivered by the vendor

37

georeferenced in TIFF uncompressed format and was accompanied by limited, per-frame
metadata on flight direction, acquisition time, and flight height above the ground. The
latter averaged 2,170m (st.dev = 25m) for site I and 2,195m (st.dev = 7m) for site 11.
Average frame endlap was 24.26% (st.dev = 0.74%) along flight lines, sidelap averaged
22.28% (st.dev = 1.41%) between flight lines. Flight line orientation and resulting spatial
arrangement of frames in each of the two study sites are shown in Appendix 1, Figure
A.1. Pixel size ranged from 0.893m to 0.949m (mean = 0.926m, st.dev = 0.018m). 36
frames contained clouds and/or cloud shadows. DAIS automatically adjusts the sensor
sensitivity (sometimes known as sensor “gain”) for each band immediately prior to image
capture in order to prevent saturation or underexposure due to rapid changes in target

reflectance. The system, however, does not record the spectral gain coefficients used for

each frame.

2.2.3. Sampling Scheme

A total of 34 plots, 16 in site I and 18 in site II, were established stratified across
the major forest cover types present in the study area with the exception of cedar swamps
which were excluded due to difficult accessibility. Seven plots were installed in each of
the northern hardwoods, aspen, red pine plantations, and natural pine cover types while 6
plots were located in the oak cover type. Plots were installed on level land, within
homogeneous stands, and away from cover type ecotones. Stand homogeneity was
evaluated by field inspections. A minimum 60% crown closure threshold was imposed by
the MDNR as a selection criterion. Stands in the vicinity of image frame centers were
given sampling priority. All plots were situated within the inner quarter area of the

associated image frame, which resulted in a maximum view angle of 865" at plot-center.

38

2.2.4. Field Measurements

Field observations were obtained in a collaborative effort with the MDNR and the
Forest Health Monitoring (F HM) program during the summer of 2000, exactly one year
after image acquisition. Since its initiation in 1990, FHM has collected an expansive set
of forest attributes (USDA FS, 1997) and it is since May 1998 integrated with the Forest
Inventory and Analysis (FIA) program at the plot level. Adoption of the F IA/FHM field
protocols ensured compatibility of data used in this study with a wealth of archived and
soon-to-be-collected F IA data, greatly enhancing the potential for wide application of the
study findings. Each plot in the F IA/FHM protocol consists of four subplots located at the
center and vertices of an equilateral triangle with side length of 62.18m (Appendix 1,
Figure A.2). The base of the triangle is oriented East-West. Although in the standard
design subplots have a radius of 7.32m, recent protocol modifications have allowed for a
large subplot, for example to increase the number of large trees sampled in oldgrowth
stands. For this study, subplot diameters ranged from 10m to 15m but were consistent for
all subplots belonging to any given plot.

Following the installation of a plot center, which coincides with the center of
subplot 1, center points for subplots 2-4 were located using a theodolite and range finder.
The center of subplot 1 served as the origin of a plot-specific coordinate system oriented
to the cardinal directions. Direction was identified using a tripod-mounted survey
compass adjusted for magnetic declination. Transects were subsequently used to link the
subplot centers to the centroids of small reference objects that were clearly identifiable on
the image frames. These reference points, usually small, short shrubs, had a horizontal

footprint smaller that a pixel, contrasted well with surrounding vegetation, and were

39

selected so as to avoid confusion among reference and non-reference objects. Reference
points were assigned plot coordinates using Euclidean geometry and distance/direction
measurements (in three dimensions) between transect vertices. Subsequently, the plot
coordinates associated with objects on each plot were translated into image frame
coordinates by using these reference point coordinates. The Root Mean Square Error
(RMSE) of plot-to-image coordinate translations calculated using subplot centers for each
of the 34 plots had a mean of 18.2cm (st.dev = 5.3cm), or about 0.2 pixels. The precision
of the theodolite and range finder measurements were evaluated by establishing, ten (two
per cover type), closed transects of considerable total length (> lkrn) with many vertices
(>25) and comparing the positional discrepancy between the first and last vertex, which,
in the absence of any measurement error, should coincide. The RMSE for the 10 trials
was 4.2cm (st.dev = 2.9cm), or 0.045 pixels.

Spatial and attribute data were collected for all trees within each subplot having
diameter at breast height (DBH) of at least 5cm. Spatial data included the azimuth and
distance of the stem center from the subplot center, and the periphery of the visible-from-
above tree crown projected to the ground. Crown portions of trees with stems outside the
subplot were also recorded (Appendix 1, Figure A.3). The horizontal extent of a crown
was projected to the ground using clinometers and measured as distance from the stem
center using a tape. For regularly shaped crowns only four distance measurements along
the cardinal directions were taken. Irregularly shaped crowns necessitated a larger
number of angular and distance measurements. Attribute data included species, DBH,
foliage vigor rating and presence or absence of tree membership in the canopy

dominance/co-dominance class. For two trees in each subplot the total height was

40

measured. Spatial measurements were organized as polygon or point layers in a
geographic information system (GIS) using plot coordinates. The methods used to
delineate crowns from point measurements, and subsequently identify crown centroids
and calculate crown diameters are described in Appendix 1. All GIS crown and tree stem
layers, initially represented in plot coordinates were ultimately translated in image

coordinates.

2.2.5. Image preprocessing

Examination of the spectral properties of pixels on line transects chosen randomly
in image flames revealed imperfections in the geometric alignment (registration) of the
bands. Further, overall brightness differences among image frames were very apparent.
Depending on their magnitude, such image deficiencies could seriously degrade the
quality of the subsequent image analysis products. The steps taken to correct band
registration problems and normalize the spectral brightness among image frames are

outlined below.

2.2.5.1. Band Registration

Transparent materials such as atmospheric gases, refract wavelengths of
electromagnetic radiation to different degrees, such that a point source in the image plane
(i.e., the plane of the object) is recorded as multiple or almost-coalesced points in the
focal plane (i.e., the plane at which the digital camera records the image), thereby
producing band misregistrations. Band misregistration may also occur as the result of
physical misalignment of cameras or their optical components at the focal plane. The
traditional approach for correcting band registration problems is to identify areas of

intense spectral gradient (i.e. edges), and attempt to align them (Tian and Huhns, 1986).

41

The proper displacement (or registration) vector is identified as the one that maximizes
the correlation coefficient between the two bands processed. However, between-band
correlation is strongly affected by the types of objects depicted in the imagery. It is
indeed possible for two bands to be highly collinear for a given combination of surfaces
and practically unrelated for another. Because the reflectance regimes of most natural
objects and surfaces present in the blue, green, and red bands are highly collinear,
correlation-based investigations are expected to reduce the magnitude of registration
problems. Such optimism though cannot be extended to include the near infrared band,
because the abrupt increase in the reflectance of healthy vegetation in that band is not
accompanied by similar reflectance behavior in other types of surfaces.

Spectral correlation computations were restricted to include only the darkest
pixels per frame band. The appropriate digital number (DN) threshold for classifying a
pixel as ‘dark’ was identified by examining the DN histogram for the NIR band. For
unirnodal NIR histograms, the pixels with a DN smaller than the 2nd percentile were
selected. For bimodal histograms, characteristic of frames containing water features, first
the DN corresponding to the trough between histogram modes was identified, and then
the threshold was set to include the 2% of pixels in the frame with UN value larger than
the trough DN (Figure 2.2b). This approach effectively masked all pixels not positioned
in deep shadows or water (Figure 2.2c). Subsequently, with the NIR band kept stationary,
all other bands in a frame were shifted up to 5 pixels, in whole pixel increments, around
the center of an 11x1 1 window. Shorter (subpixel) intervals could be used for frame
shifting, but subpixel intervals would have necessitated pixel interpolation, which is

known'to distort image features and spectral attributes. For each band shift, the

42

correlation coefficient with the ‘dark’ pixels in the NIR band was calculated. The optimal
displacement offset, henceforward known as registration vector, was identified as the one
that maximized this correlation. The NIR band was selected to remain stationary because
of its lower sensitivity to atmospheric refraction of light in comparison to the visible
bands. To evaluate the robustness of this registration vector identification method, the
procedure was repeated for 20 frames, this time keeping the red band stationary.

It was discovered that the presence of large clusters of pixels identified as dark,
might affect the ability of band correlation computations to reveal and correct registration
problems. This can be particularly important in cases where the direction of the
misregistration coincides with the main axis of elongated clusters of dark pixels, such as
those occurring along stand edges or streams. Thus, prior to band shitting, dark pixel
clusters containing more than 10 pixels where eliminated (2.2d). Cluster identification
and membership calculations were performed using the connected components algorithm
(Shapiro and Stockman, 2001) with the four-neighbor option. To investigate the potential
presence of variable registration accuracy across a frame, spectral correlations were
computed for every 1/16th (128 x 128 pixels) of a frame, and, for frames containing a

plot, for a 300 x 300 pixel window centered on each plot center.

2.2.5.2. Normalization of spectral frame brightness

In the absence of 1) the sensor’s spectral gain coefficients per frame and 2) the
spectral reflectance of any targets, between-frame brightness normalization efforts
explored alternative approaches. Preliminary investigations revealed that targets believed
to have invariant reflectance during the course of image acquisition (such as ponds or

unpaved roads on sandy soils), and therefore well suited to the normalization process,

43

were either only sporadically available in the study area (ponds) or had significant
spectral variability (unpaved roads). Because of these limitations, normalization efforts
focused on overlapping regions between adjacent frames. It was assumed that the
difference in the mean DN value of pixels positioned in the overlapping region of a pair
of adjacent frames would be representative of the overall spectral brightness difference
between respective frames.

To determine the spatial extent of overlapping regions, adjacent frames needed to
be properly georeferenced. To improve the poor registration accuracy of the imagery
provided by the commercial vendor, often found to exceed 100m, image frames were
georeferenced manually using leaf-on and leaf-off, 1:12,000-scale Digital Ortho
Quadrangles (DOQs) available for the study area (Michigan Department of Natural
Resources, 2001) and nearest neighbor pixel interpolation. Frame georeferencing using
this method produced an RMSE of 1.9m or approximately two pixels.

Image portions close to the edge of frames are acquired with the largest view
angles in an imagery set, and therefore are susceptible to stronger BRDF effects
compared to other frame portions. Differences in DNs due to BRDF effects are likely to
be further accentuated for overlapping frame regions, since in such circumstances the
difference in relative viewing azimuth angles (Figure A.4, Appendix 1) for pixels in these
regions approaches 180°. Failure to mitigate BRDF effects prior to calculating mean DN
values for the overlapping region between frames would make successful brightness
normalization unlikely.

A semi-empirical model applicable to heterogeneous surfaces, developed by

Roujean et al. (1992), was used for BRDF correction of overlapping frame regions. It

44

considers the surface spectral reflectance to be the outcome of two main processes: a
diffuse reflection component that accounts for the geometric structure of opaque
reflectors on the surface of objects and scattering from the object’s volume. Both
components are represented in the model via three, surface-type-specific parameters, k0,
k,, and k2. BRDF correction coefficients are computed as the fraction of surface
reflectance of standard over actual viewing and illumination geometry. Details on model
structure, and an illustration of viewing and illumination geometry are in Appendix 1.
BRDF corrections were computed for the portion of overlapping frame regions occupied
by deciduous forest. It was assumed that the anisotropic reflectance of coniferous forests
due to BRDF effects was similar to that of deciduous forests. The extent of deciduous
forests was determined by spatial overlays of georeferenced image frames with a beta
version of the IFMAP classification maps. Proper model parameter values were identified
by using a simplistic optimization method to be discussed shortly. Other land use / land
cover types available in the study area such as coniferous forest and grassland were not
considered because they were present in fewer than half of the overlapping frame regions.
The optimization method entailed resolving band misregistration (if any) for each
of the overlapping frame regions, correcting BRDF effects for deciduous forests at those
regions, calculating the region’s mean pixel DN values for the deciduous forest portion of
each We in an adjacent pair, computing the difference of the means for each frame
pair, and finally summing the differences along a closed path that traversed many frames.
The method operated under the assumption that BRDF differences among deciduous
forest cover types were minimal. Since each of the paths originated and terminated at the

same frame, and given that BRDF effects were considered normalized, the sum of mean

45

DN differences between adjacent frames along the path should be close to zero. Any
discrepancies could be attributed to an improper combination of BRDF model parameter
values. Ten closed paths were established, 5 per study site, each originating at different
locations within the respective sites and traversing 15 to 20 frames. Established paths
avoided frames with clouds or cloud shadows. Note that deciduous forests, unlike other
forest cover and land use types, were present in each overlapping frame region along
every path. Using published spectral model parameter values for deciduous forests as
seed values (Table A2, Appendix 1) a large number (> 1,200) of k0, k], and k2 value
combinations were tested for each band, each resulting in pixel-specific spectral
correction coefficients to be used for BRDF normalization. BRDF correction coefficients
are defined as the ratio of model predictions for standard over actual illumination and
viewing conditions (Table A.3, Appendix 1). Smaller increments in the values of k0, k],
and kg were examined as the model-parameter combinations being evaluated produced
progressively smaller sums of DN differences along the paths. The combination that
minimized the differences among all established paths while consistently providing
spectral correction coefficients within the 0.7 to 1.3 range was identified as the one that
provided the optimum BRDF correction and was subsequently used for brightness
adjustment (Table A2, Appendix 1). Spectral correction coefficients outside the 0.7 to
1.3 range were considered improbable. Brightness variation adjustment was also
examined for individual paths. The optimum model coefficient values were used to
determine the spectral brightness difference between a frame and its neighbors based on
the brightness differences detected within the overlapping regions. The effectiveness of

the method in correcting brightness variations among frames was evaluated by comparing

46

the DN difference sums along the established paths after the BRDF normalization to the
DN difference sums obtained using the original DN values.

With the relative brightness difference among adjacent frames known, frame DN
values for each band were adjusted relative to those of a frame in the middle of sites I and
II respectively. Adj ustrnents progressed radially away from the site centers.
Subsequently, the mean per-band value for all frame portions occupied by forest was
computed for each site. It was assumed that the ratio of spectral reflectance between
deciduous and coniferous forests was constant. Finally, spectral DNS for the frames at
site I were adjusted a second time so that their mean value over forested landscapes
would match the mean DN value of forested landscapes in site II. All BRDF corrections
and brightness normalization procedures were performed using Arc Macro Language

(AML) scripts in ArcInfo (ESRI, 2001 ).

2.2.6. Image Classification

As mentioned earlier, all major cover types present in the study area, with the
exception of Cedar swamps, were represented in the field data set. In the presence of a
known forest cover type classification scheme, a supervised classification approach was
selected. The maximum likelihood (ML) option was used primarily because of its
parametric structure. Initial investigations of cover type spectral signatures, both with and
, without registration correction and BRDF/brightness normalization, showed that non-
parametric classification options (e.g., parallelepiped) would result in significant
signature overlaps and greater classification confusion rates.

Classification was conducted on the subplot level. Subplot pixel membership was

determined via spatial overlays of image frames with vector subplot boundaries in image

47

coordinates. Pixels split by a boundary were considered to be subplot members if 50% or
more of their area was within the subplot. In the ML classification process, pixels in each
subplot were assigned to one of the five classes (Aspen, Northern Hardwoods, Oak, Red
Pine Plantations, or Natural Pine). A cross-validation approach (Lachenbruch and
Mickey, 1968) was undertaken for signature development involving two geographic
extents: i) site-specific, and ii) global. A subplot Q2 (belonging to plot Q) in site I for
example, was classified via three sets of spectral signatures developed: 1) using all pixels
in the remaining subplots at site I except those in the related subplots (Q1, Q3, and Q4)
and all the subplots in site II, 2) using the pixels in the remaining (unrelated) subplots of
site I only, and 3) using all pixels in site II subplots but no pixels from site I subplots.
Subplots in site II were classified in a similar fashion for a total of five classification
products. Absent this cross-validation approach, it would be difficult to ensure that the
potentially low spectral variability within a plot compared to the variability among plots
of the same cover type would not inflate classification accuracy estimates. Subplot
classification was applied to both raw DNs and to a dataset that had been corrected for
between-band misregistration and normalized for BRDF/brightness variability, for a total
of 10 classification trials (scenarios).

Classification outputs were post-processed with subplot-specific pixel majority
filters that assigned a single class (cover type) to each subplot. Classification accuracy
estimates were derived from confusion matrices and associated indicators (percent of
subplots correctly classified and kappa coefficients) (Congalton, 1991) computed after
the application of majority filters. Differences in the classification performance were

evaluated using parametric statistical tests. Details on the tests and the computation of

48

confusion matrices and accuracy indicators are provided in Appendix 1. The power of
each classification output was evaluated by imposing several different minimal
probability thresholds (none, 0.1, 0.25, 0.50, 0.75) for class membership. Pixels with all

class conditional probabilities below the imposed threshold remained unclassified.

2.3. Results

2.3.1. Band Registration

Between-band registrations errors (Figure 2.3a) identified by correlation-based
investigations and quantified by using the length of calculated registration vectors
revealed that, in general, the shorter the wavelength of the visible band the larger its
registration discrepancy relative to the near infrared band (Table 2.2). For individual
frames, spectral misregistration was practically random both in magnitude (vector length)
and orientation (vector azimuth) (Figure 2.3b). The absence of any detectable pattern of
misregistration among frames and bands remained even when the frames were arranged
in acquisition time sequence. Spectral registration vectors computed for tiles arranged in
a 4x4, non-overlapping formation within the frame (i.e. each tile covering a unique 1/16th
of the frame), revealed substantial within-frame vector variability and spatially correlated
vector azimuth and length (Figure 2.4). Such variability in spectral registration cannot be
attributed to varying atmospheric optical depth and spectral refraction rates, or to
markedly different spectral reflectances among cover types, especially in the absence of
significant topographic variations. It is, rather, an indication of imperfect alignment of the
focal planes of the cameras used in the acquisition of imagery. The lack of consistent
registration vector attributes (azimuth and length) between corresponding tiles in

sequentially acquired frames could potentially be explained by an unstable mounting of

49

the camera set on the aircraft body, which would leave the alignment of the optical axes
and focal planes of the cameras vulnerable to aircraft fuselage vibration and wind
pressure.

Ranking of the band correlation coefficient values computed for different vectors,
either for an entire frame or for a portion of it, revealed that, for many frames, a single
vector would offer a correlation value clearly larger (by as much as 0.10) than any other
vector. For many other frames, there were two vectors offering high correlation values,
while the next best correlation values were substantially smaller than the two higher ones.
In the latter case, vector length and relative azimuth difference was always one length
unit and 450 respectively thus providing a strong indication that registration discrepancy
for the band pair tested for the frame in question was about half a pixel.

Comparisons of registration vectors computed with the NIR band stationary to
those computed by keeping the red band stationary revealed that vector length and
azimuth convergence for the two alternatives was achieved only when the DN band
histogram threshold used to assign a pixel to the ‘dark’ class was appropriately low.
Eliminating large clusters of ‘dark’ pixels allowed vector attribute convergence even
when the DN histogram threshold was set to the 3rd percentile. Maintaining large clusters

had occasionally necessitated setting the DN threshold to the lSt percentile.

2.3.2. Normalization of Frame Brightness

Brightness variations among frames in the original imagery were found to be
significant. The sums of mean brightness differences (expressed in DNS) for overlapping
regions along each the 10 close multi-frame paths established for testing varied between

—6,3 15 and 4,989 DNs for the NIR band in the original imagery (Table 2.3). When scaled

50

to the number of frames present in the path, brightness variations among all established
paths stretched from —421 to 301 DNs for a range of 722 and a mean of 285 DNS for the
NIR band. The mean per frame brightness variation among paths for the blue, green, and
red bands was 23 8, 319, and 255 DNs, respectively. The latter values could be considered
as systematic errors that would accumulate in the process of adjusting frame spectral
brightness starting from the frame in the center of each site and progressing to the frames
on the periphery. Accordingly, the brightness adjustment for a frame positioned 10
frames from the center of each study site should be expected to sustain an average error
of 2380, 3190, 2550, and 2850 DNs for the blue, green, red, and NIR bands. Those values
correspond to approximately 12%, 15%, 13%, and 9% of the effective DN range for
healthy forest vegetation and therefore should be considered substantial. It should be
noted that these values correspond to the average per frame brightness correction error
and errors in individual frame brightness adjustments could be larger.

Compared to the original imagery spectral DNS, post-normalization brightness
variations calculated along the closed multi-frame paths, were on the average two orders
of magnitude smaller (Table 2.3). For the NIR band, the mean per path brightness
variation among the established paths had a range of 250 DNS or about 1/45th of the same
range without normalization. For the blue, green, and red bands, the reduction in along-
path brightness variation achieved with the normalization process amounted to 93.9%,
93.7%, and 95.0% respectively; when expressed on a per-frame basis, post-adjustment
mean brightness variations were practically absent. For pairs of adjacent frames, the
mean DN difference of their overlapping regions occupied by deciduous forests was

always less than 1% of the effective range for healthy forest vegetation after brightness

51

normalization. Note that if the normalization process involved individual paths,
additional reductions in mean, per path brightness variation are attainable. However, the
optimal BRDF correction coefficients computed for individual paths, would, generally,
produce slightly larger brightness variations when applied to the other paths than those
produced when optimizing simultaneously for all the paths. The differences in the site-
specific, mean spectral brightness of forested land between the two sites ranged from

— 175 for the NIR band to 83 for the green band (Figure 2.5). These differences in the
spectral means were used to adjust the frames of site I to those of site 11. These
discrepancies between site spectral means originated primarily from the mean brightness
difference of the two frames at the respective site centers that were used for brightness
adjustment. Brightness adjustment resulted in leptokurtic distributions of frame means
with a range of about 1,000 DNS for the visible bands. For the NIR band, the distribution
of frame means was approximately Gaussian with a range of 2,500 (Figure 2.5). It should
be noted that some variability in spectral frame means was expected because of

differences in the composition of forest types in each frame (deciduous vs. coniferous).

2.3.3. Image Classification

Classification accuracy estimates derived from computed confusion matrices were
unacceptably low. Overall classification accuracies ranged from 43.1% to 48.4% when
the original imagery was used and from 50.0% to 53.1% after brightness normalization
(Table 2.4a-j). The average improvement in overall classification accuracy offered by
brightness normalization was 5.66% with a coefficient of variation of 0.39, and was
larger within each of the two sites (8.3% for site I and 6.3% for site II) than across them

(6.9% for site I and 3.1% for site 11). Overall kappa coefficients values followed a similar

52

trend, ranging from 0.29 to 0.36 for the original imagery and from 0.38 to 0.41 after
brightness normalization (Table 2.4a-j). Correcting for brightness variations improved the
overall classification kappas by an average of 0.070 with a 0.40 coefficient of variation.
Again, the improvement was larger within sites (0.103 for site I and 0.077 for site 11) than
across sites (0.087 for site I and 0.037 for site II). Classification was significant at a=0.01
(Zk, Z-score of kappa, > 2.576) for all scenarios. However, all pair-wise comparisons of
classification outcomes (overall, within and across sites, pre- and post-brightness
normalization) based on the computation of standardized differences of respective kappa
coefficients showed no statistical significance even at a = 0.10 (Table 2.5).
Class-conditional kappa coefficients computed before and after brightness
normalization showed that correction of brightness variations generally resulted in
increased coefficients (Table 2.6). Averaged across all five classification scenarios, the
improvement was substantial for northern hardwoods subplots (0.150) and about half that
amount for aspen (0.071), oak (0.065) and red pine plantations (0.066). This trend was
absent in natural pine where brightness correction led to decreases in kappa coefficients
for three of the five classification scenarios, however. Within-site brightness correction
for natural pine increased the kappa coefficients. The largest coefficient increases
observed included the classification scenarios of all northern hardwoods subplots from
0.29 to 0.51, of northern hardwoods in site I with signatures developed within the site
from 0.23 to 0.40, of aspen in site I with signatures developed in site II from 0.24 to 0.40;
and of oak in site I with signatures developed in site 1 from 0.14 to 0.30.
Class-conditional kappas computed prior to correcting for brightness variations

among frames did not reveal any patterns related to whether the signatures for subplot

53

classification were developed within the subplot’s site or not. In four scenarios (aspen
and red pine plantations in site I, aspen and northern hardwoods in site II), within-site
signatures yielded larger kappas, but in five others (northern hardwoods and oak in site I,
and oak, red pine plantations and natural pine in site II) the kappas where higher for
signatures from across sites. For one classification scenario (natural pine in site I), the
kappa was the same within and across sites. After brightness normalization, in seven
classification scenarios within and across sites signature development produced the same
kappa. Once kappa was larger across sites (northern hardwoods in site I) and three times
was larger within the site (natural pine in site I, and aspen and natural pine in site II).
Confusion matrices calculated for each of the classification scenarios (Table 2.4a-
j) showed that there were substantial confusion rates among all five cover types.
Confusion rates for aspen, northern hardwoods, and oak were higher within the deciduous
cover type group (i.e. where a deciduous cover type subplot was assigned to a deciduous
cover type other than the correct one) while red pine plantations and natural pine
exhibited comparable error rates between themselves and the deciduous cover types
(Table 2.7). This is an indication of overlapping signatures in the four dimensional
feature space that is not limited to only coniferous or only deciduous cover types, as it is
usually the case in traditional L-resolution imagery classification. Commission and
omission errors calculated from the confusion matrices (Table 2.4a-j) suggested that
signatures developed using all pixels in the training areas do a poor job of capturing the
spectral identity of cover types or cover type groups known to be spectrally discernable in
L-resolution imagery. Further, subplots assigned to the wrong cover type class in each

classification scenario did not, in general, belong to the same plot. For most plots, one

54

and rarely two of its subplots were misclassified. Evidently, the classification errors
observed cannot be solely attributed to the spectral variability between plots of the same
cover type.

Interesting insights into the structure of the spectral signatures were gained by
examining the percentage of pixels that are classified for various maximum likelihood
thresholds (Table 2.4a-j). Even small (<= 0.10) probability thresholds left large
percentages of pixels unclassified. The proportion of unclassified pixels was
approximately 50% for a threshold of 0.25 and exceeded 80% when the threshold was set
to 0.50. Hence, for the majority of pixels in a subplot, pixel assignment to a cover type
was based on a weak association between the pixel’s spectral profile and the structure of
the signature of the assigned cover type class. A maximum likelihood threshold of 0.75
allowed only 2-5% of the pixels in a subplot to be classified, and these were always
positioned approximately half way between the sunlit portion of the crown and the
shadowed areas between crowns. Progressive threshold decreases resulted in a gradual
expansion of classified pixel clusters positioned between the sunlit and shadowed areas;
at very low thresholds, only the center of sunlit areas and deep shadows remained

unclassified.

2.4. Discussion

2.4.1. Band Registration

The proposed method for correction of band registration errors is computationally
efficient when the main cause of misregistration is imperfect alignment of the focal
planes of cameras used in the acquisition of multispectral, low or medium altitude

imagery. In the absence of significant topography, variation in image platform altitude

55

and overly heterogeneous conditions, focal plane misalignment can be expected to
generate a consistent band misregistration among sequentially acquired frames. Under
these circumstances, registration vectors identified for portions of one frame could be
applied to all corresponding frame portions in the same flight path, thereby significantly
reducing the computation load, while permitting reduction in registration errors for
portions of frames in which spectral profiles do not support correlation optimization
computations. When focal plan misalignment varies among fi'ames or when image
acquisition conditions result in variable registration accuracy regimes within frames, the
presence of an adequate number of multispectrally ‘dark’ pixels in all frame regions is
crucial if the correlation-based methodology employed in this study is to produce
satisfactory corrections. The absence of ‘dark’ pixels in a portion of a frame occupied by
forest, and for which registration correction is required, is common in stands with a
smooth canopy surface and high canopy closure. In such cases, increasing the DN
threshold that assigns a pixel to the ‘dark’ class and applying the correlation method
would likely yield satisfactory correction of misregistration for the visible bands, but not
for the infrared band.

Discrepancies in the magnitude and orientation of registration vectors that
maximized band correlations for different choices of stationary bands and DN histogram
thresholds used to identify ‘dark’ pixels emphasize the need for a careful DN threshold
selection. The 2nd DN histogram percentile and the subsequent processing of ‘dark’ pixels
with the connected components algorithm were found to be good choices for the imagery
in this study. Very low DN histogram percentiles, for example 0.5%, would eliminate any

dependencies of the method to differences in reflectance characteristics among objects in

56

a frame. However, they would also reduce the number of ‘dark’ pixels used in the
computation of band correlation thereby increasing the susceptibility of the registration
vectors to errors introduced by the variable, non-linear spectral gain effect that sensors
exhibit at the lower range of their spectral sensitivity.

, Because the method is designed to evaluate band registration only in whole-pixel
increments along the axes of digital arrays, it is incapable of correcting misregistration
caused by relative rotation between the arrays. Further, the proximity or coincidence of
principal points in each spectral component in a frame could, in the presence of band
rotation, lead to gross underestimates of misregistration magnitude because pixels
positioned symmetrically away from the principal points would tend to produce local
registration vectors of similar length but opposite orientation. Therefore, in the presence
of band rotation, registration vectors would vary among different frame portions. The
only realistic option for correcting or reducing such misregistration that does not involve
frame resampling would be to restrict correction to each frame portion separately -- a less
than ideal solution because of ensuing band registration discontinuities at flame
partitioning boundaries. When applied properly, in terms of ‘dark’ pixel identification
and flame portion extent, the method would eliminate any band registration errors larger

than 0.5 pixels, while preserving the spectral profiles of objects of interest.

2.4.2. Normalization of Frame Brightness

BRDF model coefficients optimized during the brightness adjustment procedure
are not necessarily appropriate for any deciduous forest. The Roujean’s et a1. (1992)
model, as well as many others, is designed to standardize reflectance of an object for

various illumination and viewing geometries. Without information on spectral gain

57

coefficients and radiometric field measurements, however, the only alternative is to base
classification on DNS. In this study, thebrightness adjustment operated under the
potentially unrealistic assumption that object reflectance could be approximated as a
linear transformation of DNs intrinsic to the BRDF correction process, with the linearity
assumption imposed by the kemel-based structure of the BRDF model. The fact that
theBRDF model coefficient values converge to minimize brightness differences for the
overlapping regions along frame paths and that the vast variations in brightness among
flames for the original DNs are practically eliminated by the brightness adjustment are
encouraging, albeit qualitative indications that these assumptions are valid. Coefficient
generalization could be further restricted by the fact that optimization was based only on
larger viewing zenith angles (i.e. those that corresponded to overlapping flame regions).
Note that although only deciduous forests were used as a basis for the brightness
adjustment, normalization was based on all forested land. In landscapes where coniferous
stands are ubiquitous in the overlapping regions of frames, a separate, independent
brightness adjustment could be derived, which would permit an assessment of the
method’s dependence on and ability to provide brightness normalization for another class

of vegetation.

2.4.3. Image Classification

The classification approach used in this study, although conceptually similar,
differs flom traditional classifications of L-resolution imagery in the sense that the
classification unit (a single pixel) corresponds to small portions of tree crowns rather than
multiple crown aggregates. The differences in spatial scale between the imagery unit

(pixel) and the classification unit (subplot) have important implications for classification

58

results because, unless a fuzzy classification scheme is employed, it necessitates
elimination of the within-subplot pixel class variability. The classification accuracy
estimates that were derived do not account for the fact that the confusion table entries are
not assigned directly by the ML classifier on a pixel basis, but are in addition post-
processed with a majority filter on the subplot level. As such, the classification accuracy
estimates could be seriously overestimated. Concerns about accuracy estimate bias are
accentuated by the low maximum likelihood probabilities of the most probable class
determined by the classifier.

The observations made on the spatial allocation of classified pixels for various
maximum likelihood thresholds, the variability of assigned classes for subplots in the
same plot, and the analysis of the confusion matrices all suggest that the spectral
signatures for each cover type class are ‘contaminated’ by the presence of a significant
number of spectrally dark pixels with DNs that are not exclusively associated with any
one class. The spectral signature for each of the five cover types classes could be
regarded as approximating a hyperellipse in four-dimensional space in which the dark
pixels that correspond to shadowed crown portions or small canopy openings occupy the
volume around one of the ellipse’s focus while the pixels for the sunlit portions of crowns
are centered around the other focus. The signature mean, positioned approximately half
way between the two foci, corresponds to crown portions located at the flinge of direct
and diffuse illumination. Moreover, the dark foci of ellipses for different cover types tend
to be proximal in four-dimensional space thereby indicating that there is little, if any,
spectral separability between shadowed portions of the five cover types. By contrast, the

bright foci for the five cover type signatures represented in this study tend to exhibit

59

mutual inhibition, thus causing a rotation of the main ellipse axis around its respective
dark focus. Hence, when all cover types are simultaneously considered, only the brighter
components of their ellipsoid volumes do not overlap. Because signature means are
positioned much closer to dark foci rather than bright foci, the relative signature ellipse
rotation produces smaller spectral separation between signature means than the distance
between the bright foci thereby decreasing the accuracy of maximum likelihood
classification, given that the latter is based on the spectral distance of a pixel flom
signature means (Appendix 1, Equation A.19).

While the presence of shadows and resulting spectrally dark pixels in high spatial
resolution digital imagery over forested landscapes affects the means of spectral
signatures, brightness variations and BRDF effects are primarily related to the structure
of covariance matrices (Appendix 1, Equation A.19) and inflate the volume those
signatures occupy in multi-dimensional space and hence the extent of overlap. The
approximately 5% improvement in classification accuracy achieved after BRDF
corrections and brightness adjustments is most likely the result of a reduction in the 4-
dimensional volume of the cover type signatures involved.

The larger variability of classification accuracy estimates for individual cover
type classes compared to the variability of estimates for the pooled subplot set can be
partially attributed to differences in the number of subplots considered in each scenario,
but also to differences in canopy roughness within cover types. Even with invariable
canopy density, foliage composition and orientation of leaves or needle bundles,
differences in canopy surface roughness occasionally present be tween and within plots of

the same cover type will generate variability in the size and darkness of shadows cast

60

between crowns of adjacent trees and hence alter the degree to which dark pixels
influence the composition of respective cover type signatures. Note that the significance
of kappa coefficient differences between the various geographic extents of signature
development and brightness correction alternatives cannot be evaluated at the cover type
level because the kappa coefficient variance estimates necessary for the associated
statistical testing are known to be unstable and biased when the sample size is relatively

small.

2.5. Conclusion

The low overall accuracy of all classification products obtained using all subplot
pixels, found to be considerably inferior to the accuracy traditionally obtained using L-
resolution, mid-summer imagery for similar classification schemes, suggests that their
value for cover type classification and support of forest management decisions is fairly
limited. The spectral profiles of pixels corresponding to shadowed portions of forest
stand canopies are instrumental in minimizing the spectral separability of signatures for
the five forest cover types of this study. At the same time though, they emphasize the
potential of signature development conditional to crown portions to offer significant
improvements in their power to discern cover types. The merits of the latter approach are
investigated in detail in Chapter 3. The approach used in this Chapter, however, is
computationally more efficient and does not require a shift of classification focus flom
the subplot level to individual trees, nor does it necessitate identification of individual
tree crowns.

Signature development based on variable geographic extents was found to have

minimal impact on classification accuracy, but it should be kept in mind that there is only

61

marginal variability in the ecological gradients (edaphic, climatic, and topographic) that
influence forest growth between the two sites used in this study. It was shown that the
noticeable decline in classification accuracy that results flom band misregistration and
variable frame brightness conditions can be avoided, but the associated computation cost,
analyst expertise and time investment, and ancillary information requirements necessary
for error correction and brightness normalization could be prohibitive. Depending on the
type of registration errors, absolute corrections may be impossible unless compromises
related to the objects’ spectral profiles are made (i.e. resampling). However, it should be
expected that the process of correcting band misregistration could be simplified if
technical problems such as camera focal plane alignment imperfections were to be
eliminated. Similarly, simply recording the spectral gain coefficients used for the
acquisition of each image flame would have permitted reflectance- rather than DN-based
classification and would have allowed for theoretically sound BRDF correction rather
than the empirical approximation used. It should be expected that as commercial vendors
of airborne, multispectral, high resolution digital imagery gain experience, such technical
problems would diminish, ultimately increasing the potential utilization of this type of

imagery for forest land cover classification.

62

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65

Tables

Table 2.1. Cover types and their major species components in the study area.

 

Cover Type Major species present

 

Common name Latin name

 

Aspen Big Tooth Aspen (Populus grandidentata), and
Quaking Aspen (Populus tremuloides)
Northern hardwoods Sugar Maple (A cer saccharum),
Red Maple (Acer rubrum),

American Beech (F agus americana),
Black Cherry (Prunus serotina),

 

Basswood (T ilia americana), and
White Ash (F raxinus americana)
Oak White Oak (Quercus alba), and
Red Oak (Quercus rubra)
Red Pine Plantation Red Pine (Pinus resinosa)
Natural Pine White Pine (Pinus strobes)
66

Table 2.2. Spectral registration vector components and length at plot centers calculated
as those that maximized between-band correlation using dark pixels of the NIR band.
Band correlation was evaluated within a 300 x 300 window centered at respective plot
centers.

 

 

 

 

 

 

 

 

NIR-BLUE NIR-GREEN NIR-RED
Vector component 7:123: Vector component £3133: Vector component £233:

00 00 OD

‘5 ‘5 E "a? 5 iii ‘3

'5‘. :33 z m z m z
1 0 -1 1 00 0 0 0.00 0 0 0.00
2 0 -1 1 .00 -1 0 1 .00 0 0 0.00
3 -2 -1 2 24 0 0 0. 00 0 0 0.00
4 0 1 1 .00 -1 0 1.00 0 -1 1 .00
5 0 0 0. 00 0 -2 2. 00 1 1 1 41
6 0 0 0. 00 1 0 1 0.0 -1 0 1.00
7 -1 0 1. 00 2 1 2.24 0 0 0.00
8 -1 1 1.41 0 0 0.00 -1 0 1. 00
9 -2 -1 2. 24 1 1 1.41 1 1 1.41
10 0 1 1. 00 1 0 1.00 1 -1 1.41
11 -1 0 1 0.0 0 1 1.00 0 -1 1.00
12 -1 -1 1.41 0 1 1 .00 0 0 0. 00
13 1 -1 1.41 -2 -1 2.24 1 1 1.41
14 0 0 0.00 0 1 1.00 0 -1 1 .00
15 0 0 0.00 -1 0 1 .00 -1 -1 1 .41
16 1 -1 1.41 0 -1 1 .00 -1 0 1 .00
17 0 0 0.00 -1 -1 1.41 1 1 1 .41
18 1 -1 1.41 1 0 1 .00 0 0 0.00
19 -1 0 1 .00 0 -1 1 .00 -1 0 1.00
20 0 1 1 .00 -1 -2 2. 24 0 1 1 .00
21 0 1 1 .00 -1 -1 1.41 1 1 1 .41
22 0 -1 1.00 -1 0 1.00 0 0 0.00
23 0 0 0.00 -1 1 1.41 0 0 0.00
24 0 -2 2.00 0 0 0.00 1 0 1.00
25 2 0 2.00 0 0 0.00 0 1 1.00
26 -1 1 1.41 2 0 2 00 0 0 0.00
27 2 1 2.24 0 1 1 00 1 0 1.00
23 1 -1 1.41 0 1 1. 00 0 -1 1.00
29 1 -1 1.41 1 0 1 .00 1 0 1.00
30 -2 1 2.24 0 0 0. 00 0 0 0.00
31 -2 -2 2.83 0 1 1.00 0 0 0. 00
32 0 -1 1.00 -1 0 1.00 1 -1 1.41
33 0 2 2 00 1 1 1.41 1 0 1 .00
34 -1 2 2. 24 1 0 1.00 -1 0 1 .00
T°ta1 42.32 35.78 26.31

 

 

 

67

Table 2.3. Sums of spectral DN value differences between DN means of overlapping
regions of adjacent frames along closed multi-frame paths calculated before and after
BRDF/Brightness adjustment. DN means were computed using only the portion of
overlapping regions occupied by deciduous forests. BRDF coefficients of the Roujean et
a]. model, integral to the normalization process and optimized to minimize spectral
column sums, are shown.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Brightness Variability Within a Frame Path (DN)
Blue Green Red NIR
c... 1:: 'o 1:: -o
O C'- — d.) .— d) —. O .— 0
1.. "" “I .§ ‘3 .5 ‘3 .5 ‘3 .5
:13 =5 3 a :9 .5, "a ‘50 '5 ~50 '5 ~50 "a
m 5"; g g a '5: E 8 E '5 E '5 E
z "= 2 2’ 2 2
I 1 16 1279 -44 -2730 54 3460 -98 4813 143
I 2 18 -2384 130 -1238 46 1107 -38 3085 -75
I 3 17 1137 182 -3320 276 1729 212 -4695 -91
I 4 20 -2259 24 -169 30 -3251 30 1926 -28
I 5 20 3720 -192 -2829 -112 -2910 -142 -4166 52
II 6 18 -1252 -6 3774 -56 3778 110 2865 -107
II 7 15 1260 -114 3549 -174 -2323 148 4185 -104
II 8 1 5 3466 80 3542 -24 -508 72 -63 15 6
II 9 15 -2092 -38 2282 42 1466 -128 -975 83
II 10 20 886 44 1350 38 1298 -62 4989 77
Column Sum 3761 66 4211 120 3846 104 5712 -44
Column Range 6104 374 7094 450 7029 354 11304 250
Mean (among paths)
per flame brightness 238 2 319 6 255 8 285 -1
variability
Range (among paths)
of per flame 370 21 432 28 379 21 722 16
brightness variability
.,, k0 0.153 0.183 0.147 0.281
'O H
o G
.51 ‘4‘ .93
g a {5’ k, 0.115 0.147 0.099 0.058
5- ‘” 5
k2 0.036 0.052 0.058 0.301

 

68

 

Table 2.4a. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for all subplots with signatures
developed from sites I and 11 using original DNs.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

69

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 12 5 4 2 2 25
E Northern Hardwoods (NH) 7 13 4 3 30
E Oak 10 2 3 26
5 Red Pine Plantation (RPP) 1 4 16 8 31
Natural Pine (NP) 3 2 5 12 24
Column Total 28 28 24 28 28 136
Accuracy (%) Errors (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 42.86 48.00 46.43 57.14 0.00 0.00
NH 46.43 43.33 60.71 53.57 0.10 21.30
Oak 41.67 38.46 66.67 58.33 0.25 48.20
RPP 57.14 51.61 53.57 42.86 0.50 87.60
NP 42.86 50.00 42.86 57.14 0.75 98.20
Class Conditional Kappa
ASP 0.3452 Overall Accuracy (%) 0.4632
NH 0.2864 Kappa Coefficient 0.3288
Oak 0.2527 52., 0.0019
RPP 0.3907 zk 7.5535‘
NP 0.3704 ' Significant at or = 0.01

 

 

Table 2.4b. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site I using original
DN site I signatures.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 7 2 2 3 1 15
E Northern Hardwoods (NH) 4 5 3 0 2 14
E Oak 3 3 4 2 2 14
.53 Red Pine Plantation (RPP) 0 l 2 8 4 15
Natural Pine (NP) 2 1 1 3 7 14
Column Total 16 12 12 16 16 72
Accuracy (%) EITOTS (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 43.75 46.67 56.25 50.00 0.00 0.00
NH 41.67 35.71 58.33 75.00 0.10 23.50
Oak 33.33 28.57 66.67 83.33 0.25 50.10
RPP 50.00 53.33 50.00 43.75 0.50 86.60
NP 43.75 50.00 56.25 43.75 0.75 97.50
Class Conditional Kappa
ASP 0.3143 Overall Accuracy (%) 0.4306
NH 0.2286 Kappa Coefficient 0.2876
Oak 0.1429 $2k 0.0035
RPP 0.4000 zk 4.8617'
NP 0.3571 ‘ Significant at a = 0.01

 

 

 

70

Table 2.4e. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site I using original
DN site II signatures.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 7 3 3 3 1 17
E Northern Hardwoods (NH) 4 5 2 0 l 12
'9; Oak 3 2 4 2 2 l3
'5 Red Pine Plantation (RPP) l l 1 7 4 14
Natural Pine (NP) 1 l 2 4 8 16
Column Total 16 12 12 16 16 72
Accuracy (%) Errors (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 43.75 41.18 56.25 62.50 0.00 0.00
NH 41.67 41.67 58.33 58.33 0.10 21.30
Oak 33.33 30.77 66.67 75.00 0.25 48.20
RPP 43.75 50.00 56.25 43.75 0.50 87.60
NP 50.00 50.00 50.00 50.00 0.75 98.20
Class Conditional Kappa
ASP 0.2437 Overall Accuracy (%) 0.4306
NH 0.3000 Kappa Coefficient 0.2856
Oak 0.1692 s2k 0.0035
RPP 0.3571 zk 4.8183‘
NP 0.3571 ’ Significant at or = 0.01

 

 

 

71

Table 2.4d. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site II using original
DN site II signatures.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 5 3 2 1 l 12
E Northern Hardwoods (NH) 2 7 3 0 0 12
"'3‘ Oak 3 4 5 0 1 13
5 Red Pine Plantation (RPP) 0 l 1 7 4 13
Natural Pine (NP) 2 1 1 4 6 l4
Column Total 12 16 12 12 12 64
Accuracy (%) Errors (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 41.67 41.67 58.33 58.33 0.00 0.00
NH 43.75 58.33 56.25 31.25 0.10 19.50
Oak 41.67 38.46 58.33 66.67 0.25 47.20
RPP 58.33 53.85 41.67 50.00 0.50 82.80
NP 50.00 42.86 50.00 66.67 0.75 96.40
Class Conditional Kappa
ASP 0.2821 Overall Accuracy (%) 0.4688
NH 0.4444 Kappa Coefficient 0.3366
Oak 0.2426 s2, 0.0040
RPP 0.4320 zk 5.2889‘
NP 0.2967 ’ Significant at at = 0.01

 

 

72

Table 2.4e. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for subplots in site II using original
DN Site I signatures.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 5 4 2 2 1 14
E Northern Hardwoods (NH) 2 6 3 0 0 11
'fi Oak 4 4 6 0 0 14
'8 Red Pine Plantation (RPP) 0 l 0 6 3 10
Natural Pine (NP) 1 1 1 4 8 15
Column Total 12 16 12 12 12 64
Accuracy (%) EITOI’S (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 41.67 35.71 58.33 75.00 0.00 0.00
NH 37.50 54.55 62.50 31.25 0.10 19.10
Oak 50.00 42.86 50.00 66.67 0.25 48.60
RPP 50.00 60.00 50.00 33.33 0.50 83.20
NP 66.67 53.33 33.33 58.33 0.75 95.40
Class Conditional Kappa
ASP 0.2088 Overall Accuracy (%) 0.4844
NH 0.3939 Kappa Coefficient 0.3569
Oak 0.2967 s2k 0.0041
RPP 0.5077 2.. 5.5768'
NP 0.4256 ’ Significant at at = 0.01

 

 

 

73

Table 2.4f. Maximum Likelihood classification results and associated accuracy
assessment parameters obtained with cross validation for all subplots using post-
brightness normalization signatures from site I.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 15 5 4 2 3 29
3 Northern Hardwoods (NH) 5 14 2 l 1 23
E Oak 4 6 11 2 5 28
6 Red Pine Plantation (RPP) l l 4 16 7 29
Natural Pine (NP) 3 2 3 7 12 27
Column Total 28 28 24 28 28 136
Accuracy (%) EITOYS (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 53.57 51.72 46.43 50.00 0.00 0.00
NH 50.00 60.87 50.00 32.14 0.10 18.10
Oak 45.83 39.29 54.17 70.83 0.25 41.20
RPP 57. 14 55.17 42.86 46.43 0.50 83.20
NP 42.86 44.44 57.14 53.57 0.75 94.80
Class Conditional Kappa
ASP 0.3921 Overall Accuracy (%) 0.5000
NH 0.5072 Kappa Coefficient 0.3751
Oak 0.2628 s2. 0.0019
RPP 0.4355 z. 8.5801'
NP 0.3004 ’ Significant at a = 0.01

 

 

 

74

Table 2.4g. Maximum Likelihood classification results and associated accuracy

assessment parameters obtained with cross validation for subplots in site I using post-
brightness normalization signatures from site I.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

75

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 8 2 2 2 1 15
E Northern Hardwoods (NH) 3 7 3 0 l 14
'3‘ Oak 3 2 5 l 1 12
'5 Red Pine Plantation (RPP) l 0 1 9 5 16
Natural Pine (NP) 1 1 l 4 8 15
Column Total 16 12 12 16 16 72
Accuracy (%) Errors (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 50.00 53.33 50.00 43.75 0.00 0.00
NH 58.33 50.00 41.67 58.33 0.10 25.60
Oak 41.67 41.67 58.33 58.33 0.25 50.90
RPP 56.25 56.25 43.75 43.75 0.50 83.40
NP 50.00 53.33 50.00 43.75 0.75 97.50
Class Conditional Kappa
ASP 0.4000 Overall Accuracy (%) 0.5139
NH 0.4000 Kappa Coefficient 0.3907
Oak 0.3000 0.0036
RPP 0.4375 6.5202‘
NP 0.4000 " Significant at a = 0.01

 

 

Table 2.4b. Maximum Likelihood classification results and associated accuracy

assessment parameters obtained with cross validation for subplots in site I using post-
brightness normalization signatures from site II.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

76

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 8 2 2 l 2 15
33 Northern Hardwoods (NH) 2 7 3 0 1 13
'fi Oak 3 3 5 0 1 12
'5 Red Pine Plantation (RPP) 1 0 1 9 5 16
Natural Pine (NP) 2 0 1 6 7 16
Column Total 16 12 12 l6 16 72
Accuracy (%) Errors (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 50.00 53.33 50.00 43.75 0.00 0.00
NH 58.33 53.85 41.67 50.00 0.10 23.50
Oak 41.67 41.67 58.33 58.33 0.25 50.10
RPP 56.25 56.25 43.75 43.75 0.50 86.60
NP 43.75 43.75 56.25 56.25 0.75 97.30
Class Conditional Kappa
ASP 0.4000 Overall Accuracy (%) 0.5000
NH 0.4462 Kappa Coefficient 0.3727
Oak 0.3000 s2k 0.0036
RPP 0.4375 zk 6.1910‘
NP 0.2768 ‘ Significant at a = 0.01

 

 

Table 1.
asessm-
hrighme

J

( 'lussi l'IL-d
All :1

_

 

{7-

EJ

'4’.
—,—¢
U—‘d

03k
RPP

Xi

C135

 

ASP
“1
Oak
RPE

 

Table 2.4i. Maximum Likelihood classification results and associated accuracy

assessment parameters obtained with cross validation for subplots in site 11 using post-
brightness normalization signatures from site II.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

77

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 6 3 2 2 l 14
32 Northern Hardwoods (NH) 2 9 3 0 0 14
'g Oak 3 3 5 0 l 12
'3 Red Pine Plantation (RPP) 0 0 l 7 3 11
Natural Pine (NP) 1 1 1 3 7 l3
Column Total 12 16 12 12 12 64
Accuracy (%) Errors (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 50.00 42.86 50.00 66.67 0.00 0.00
NH 56.25 64.29 43.75 31.25 0.10 19.50
Oak 41.67 41.67 58.33 58.33 0.25 47.20
RPP 58.33 63.64 41.67 33.33 0.50 82.80
NP 58.33 53.85 41.67 50.00 0.75 96.40
Class Conditional Kappa
ASP 0.2967 Overall Accuracy (%) 0.5313
NH 0.5238 Kappa Coefficient 0.4132
Oak 0.2821 s2k 0.0040
RPP 0.5524 zk 6.5028‘
NP 0.4320 ' Significant at a = 0.01

 

 

Table 2.4j. Maximum Likelihood classification results and associated accuracy

assessment parameters obtained with cross validation for subplots in site 11 using post-
brightness normalization signatures form site I.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

78

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 6 4 2 1 2 15
3 Northern Hardwoods (NH) 2 9 3 0 0 14
5 Oak 3 2 5 1 1 12
5 Red Pine Plantation (RPP) 0 0 1 7 3 11
Natural Pine (NP) 1 l 1 3 6 12
Column Total 12 16 12 12 12 64
Accuracy (%) EITOTS (%) ML Probability Unclassified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 50.00 40.00 50.00 75.00 0.00 0.00
NH 56.25 64.29 43.75 31.25 0.10 20.00
Oak 41.67 41.67 58.33 58.33 0.25 48.40
RPP 58.33 63.64 41.67 33.33 0.50 80.90
NP 50.00 50.00 50.00 50.00 0.75 95.10
Class Conditional Kappa
ASP 0.2615 Overall Accuracy (%) 0.5156
NH 0.5238 Kappa Coefficient 0.3936
Oak 0.2821 52.. 0.0041
RPP 0.5524 zk 6.1819‘
NP 0.3846 ’ Significant at a = 0.01

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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79

Table 2.6. Change in class-conditional kappa coefficients computed before and after
brightness normalization.

 

Cover Original Brightness

 

 

 

 

 

 

 

 

Type DNs Corrected AKap pa
ASP 0.3452 0.3921 0.0469
NH 0.2864 0.5072 0.2208
All subplots using signatures from site I and II Oak 0.2527 0.2628 0.0101
RPP 0.3907 0.4355 0.0448
NP 0.3704 0.3004 -0.0700
ASP 0.3143 0.4000 0,0357
NH 0.2286 0.4000 01714
Site I subplots using site I signatures Oak 01429 03000 0.1571
RPP 0.4000 0.4375 0,0375
NP 0.3571 0.4000 0,0429
ASP 0.2821 0.2967 0,0145
NH 0.4444 0.5238 00794
Site 11 subplots using site II signatures Oak 0.2426 0.2821 0.0395
RPP 0.4320 0.5524 0,1204
NP 0.2967 0.4320 0. 13 5 3
ASP 0.2437 0.4000 0.1563
NH 0.3000 0.4462 0.1462
Site I subplots using site II signatures Oak 0.1692 0.3000 0.1308
RPP 0.3571 0.4375 0,0304
NP 0.3571 0.2768 -0.0803
ASP 0.2088 0.2615 0,0527
NH 0.3939 0.5238 01299
Site 11 subplots using site I signatures Oak 02967 02821 -0.0146
RPP 0.5072 0.5529 0,0452
NP 0.4256 0.3846 -00410
ASP 0.0712
NH 0.1495
Average across all five classification scenarios Oak 0.0646
RPP 0.0657
NP -0.0026

 

80

Table 2.7. Classification error rates of subplots conditional upon cover type group
(deciduous or coniferous) produced with maximum-likelihood based cross validation for
all plots in the study area before and after brightness normalization.

 

 

 

 

 

 

As en Northern Oak Red Pine Natural
p Hardwoods Plantation Pine
Deciduous 12(43%) 11 (39%) 8(33%) 7(25%) 8(29%)

Original DNS
Coniferous 404%) 404%) 6(25%) 5(18%) 8(29%)
Brightness Deciduous 902%) 11 (39%) 6(25%) 508%) 902%)
“mnaliza‘im Coniferous 404%) 3 (11%) 7(29%) 7(25%) 7(25%)

 

 

 

 

 

 

 

 

81

Figures

 

   
 
 
  

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/‘. 1

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It 1 SITE P“

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Hydrology
N Streams
- Wetlands

- Lakes .\ _7; l, Wexford County'

l "l ’ a. l‘
. l ,

‘u‘

w’ itzk

 

.r'

 

 
   
    

 

TX 0 5 10 15 Kilometers

 

 

 

Figure 2.1. Study area map portraying hydrological features.

82

 

 

 

Percent of Frame Pixels

 

 

 

 

00 30000

200
UN

Histogram trough DN: 4000
4080 < DN (Non-Water Dark Pixelsf 6383
Non-Water Dark Pixels = 2% of the image

 

 

 

 

(a) (b)

Binary Reclassification of Image Binary Image Processed with the

Based on Histogram Information Connected Components Algorithm

 

 

 

 

 

 

 

(c) (d)

 

 

Figure 2.2. a. Original near infrared image frame, b. Image histogram with
characteristic bimodal form, typical in the presence of water bodies, c. Binary
reclassification of original image produced by using the upper dark pixel range DN as
reclassification threshold, and d. Elimination of dark pixel clusters in the binary image
with processing with the connected components algorithm for clusters with pixel
membership exceeding 10.

83

 

 

Green Band

 

 

 

 

 

 

 

 

 

 

+ + Blue

Green
+ Red

+ NH

 

 

 

 

 

 

 

 

 

 

Figure 2.3a. Spectral frame portions of original imagery featuring a 3x3 pixels square
window superimposed on each frame and corresponding to the same frame row and
column indices. The 3x3 grid shows the location of the darkest pixel within the square
window for each band.

84

 

 

Blue Band Green Band

Red Band

 

 

 

 

 

 

 

 

 

 

All
+ bands

 

 

 

 

 

 

 

 

 

Figure 2.3b. Spectral frame portions of imagery corrected for registration errors featuring
a 3x3 pixels square window superimposed on each frame and corresponding to the same
frame row and column indices. The 3x3 grid shows the location of the darkest pixel
within the square window.

85

 

Spectral Misregistration Vectors
for 256x256 pixel frame portions

 

 

 

A A 4 4
v v V A y A v 4
l l
I
___LLLLLL-1__L_m__meL_
V v A V A v A v v 4

 

 

 

 

A A 4 4
4 1 l4 ' 4 4
>—— _ _—____ iififlp i7_ _ _. ..7 fifi V_. ‘. v___.
, A V A 4
4 4 4 > 4 >

 

 

 

 

 

 

 

Unit (1300) vector

 

 

 

Figure 2.4. Registration vectors that maximized correlation between the NIR band and
each of the visible bands for the image frame hosting plot 21. Correlation was calculated
using the NIR band dark pixels for every 1/16th frame portion. Vector colors correspond
to respective bands.

86

 

 

Mean Frame Spectral Brightness of Forested Land

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Site | (128 Frames)
0 _
('0
0 Blue Band
' Green Band
0 Red Band
§ ~ NIR Band
0
8
O _
E N z e
g e 0
Lu . 0.
LL
0
g .0. O O
E o _ ,
v- . r-
. I O .
O O O O a t
I O O O r i
0 O
O - O
O -t - - -
l I I fl I I I I
4000 6000 8000 10000 12000 14000 16000 18000
DNs
Mean S ectral
p 46
I Site ii (192 Frames)
0 _
('J O
o ' Blue Band
. ° Green Band
' e 0 Red Band
5 o 0 ~ NIFi Band
.
5;
a 8 - :.
q, o o o o
0 I
g I O O
E o a
.— . q
I I O 0 m
. a a
. m
I v -
O O
O O O O
C O I a
o _.
I I I I I I I I
4000 6000 8000 10000 12000 14000 16000 18000
DNs

 

 

Figure 2.5. Post-brightness-adjustment mean spectral frame DNS for Site I (top) and
Site 11 (bottom) and ensuing between-Site mean spectral brightness differences.

87

CHAPTER 3

FOREST STAND CANOPY STRUCTURE PARAMETER VALUE ESTIMATION AND
COVER TYPE CLASSIFICATION VIA DIGITAL NUMBER AUTOCORRELATION
TECHNIQUES IN HIGH-SPATIAL RESOLUTION MULTISPECTRAL DIGITAL

AIRBORNE IMAGERY

88

Abstract

A study of forest stand canopy parameter assessment and cover type classification using
digital, airborne, multispectral imagery is presented. The estimated parameters include
stem density, canopy closure, and mean crown diameter. Parameter estimation is based
on quantifying the spatial autocorrelation among pixel digital numbers (DN) using
variogram analysis and an alternative, non-parametric approach known as slope-break
analysis. Parameter estimation and cover type classification proceed from the
identification of tree apexes. Parameter accuracy assessment is evaluated via value
comparison with a spatially precise set of field observations over 34 plots installed in 5
cover types common in the Midwest region. Results show that, in general, slope-break-
based parameter estimates are superior to those obtained using variograms. Estimated
root mean square errors at the plot level for the former average 6.5 % for stem density,
3.5 % for canopy closure and 2.5 % for mean crown diameter, which are less than or
equal to error rates obtained via traditional forest stand cruising by experienced
personnel. The employed methodology entails parsimonious parameterization and is
supportive of automation. Overall cover type classification accuracy remains stable
among classification scenarios across varying geographic extents and increases from
approximately 70% when using original imagery DNS to over 85 % when band
registration problems are corrected and variable brightness regimes among imagery
frames are normalized. Limiting cover type classification to pixels identified as tree
apexes is found to improve traditional classification approaches that use all pixels by a

remarkable 3 5 %.

89

3.1. Introduction

High spatial resolution digital imagery holds a promising potential for the
extraction of forest inventory and canopy structure information including the delineation
of individual tree crowns, canopy closure, stem density, stand species composition and
crown classification (Franklin and McDermid, 1993; Gougeon, 1995a; Brandtberg, 1997;
Dralle and Rudemo, 1997; Larsen, 1997; Gerylo et al., 1998; Larsen 1998; Quackenbush
et al., 1999; Sheng et a1, 2001). Traditionally, forest canopy structure parameters have
been derived from aerial photographs (King, 2000; Wulder et al., 2002). A series of trials
conducted by the Canadian Forest Management Institute three decades ago revealed that
aerial photographs are rich in information content for individual-tree-based forest
inventory purposes (Aldred and Kippen, 1967; Brun, 1972; Bonnor, 1977; Sayn-
Wittgenstein, 1978). However, information extraction from aerial photographs is based
on manual interpretation, a process known to be time consuming, labor intensive, and
error-prone (Biging et al., 1991). Lately, due to increasing requirements on quantitative
forest inventory information, a decrease in the popularity of aerial photographs for forest
management decision-making has been observed (Hyyppéi et al., 2000). Digital, high-
Spatial-resolution imagery, sometimes known as H-resolution imagery (Strahler eta1.,
1986), acquired from airborne platforms and recently available from satellites (QuickBird
[Aplin et al., 1997] and IKONOS [Mangold, 1999]) is well suited to producing
quantitative estimates of inventory variables and canopy structure attributes, and to
Process automation (Gong et al., 1999). Due to the large geographic extent of forests,

automation is a practical prerequisite for full exploitation of the H-resolution digital

90

imagery in forest applications (Gougeon, 1995b; McGraw etal., 1998; Pouliot et al.,
2002)

In high-spatial-resolution digital imagery of forested landscapes, each tree crown
is represented by multiple pixels. Some of them correspond to the sunlit portion of the
crowns while others represent crown portions in shadow. View and illumination angles,
tree geometry, foliage orientation and bidirectional reflectance operate synergistically to
create a variation of radiance, represented by pixel digital numbers (DN), at different
locations within an individual crown (Leckie et al., 1992). Spectral DN values also vary
as a function of the tree crown depth being greater near the tree center and lessening
towards the crown edges (Li and Strahler, 1992). AS a result, individual trees may be
discerned as localized regions of high DN values. Individual tree identification based on
high-DN-value digital image regions has been accomplished with a variety of techniques
including valley following (Gougeon, 1995a), threshold-based clustering (Culvenor,
2002), template matching (Pollock, 1996; Larsen and Rudemo, 1997; Larsen, 1999),
mathematical morphology (Walsworth and King, 1999), minimum cost route selection
(Warner et al., 2000), maximum filtering (Brandtberg, 1997; Culvenor et al., 1999;
Niemann et al., 1999; Pinz, 1999, Wulder etal., 2000), spatial autocorrelation (Treitz,
2001), or combinations of these approaches (Wulder et al., 2002).

Individual tree identification offers a potentially superior alternative to traditional
per-pixel-based classification of forest cover types Since it allows spectral signature
Construction using only the brightest pixels of a crown, or the average of the sunlit
Portion of a crown, or even the mean value within the identified crown (Gougeon, 1997).

It has also been used for forest stand delineation and to provide estimates of forest stand

91

canopy st
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canopy structure parameters such as crown size, stem density, and canopy closure
(Gougeon, 1997; Gerylo, 1998). These canopy structure parameters are important inputs
to forest models (Sprinz and Burkhart, 1987; Gering and May, 1995; Deutschman etal.,
1997; Pereira et al., 1997; Trichon, 2001) and are critical in modeling forest fires (Keane
et al., 1999).

Individual tree crown identification appears to work best with digital imagery
having a spatial resolution less than 1m, but it is expected to work well enough with 1m
airborne and satellite digital imagery to justify more extensive development and use of
the H-resolution, digital remote sensing technology (Wulder, 1999). Most of the
techniques mentioned above have been tested in pure or mixed coniferous stands, or
stands with only simple combinations of one or two conifer and deciduous species
(Gerylo et al., 1998). In such circumstances, the conical shape of crowns produces a
rough canopy surface with distinct tree apexes and shadowed portions that facilitate
individual crown delineation. Conversely, deciduous tree crowns typically defy
conformal shapes, often have multiple maxima, usually exhibit a relatively smooth
canopy surface and less distinct edges, and thus are more difficult to delineate (Warner et
al., 1999).

Despite sporadic successes in utilizing H-resolution imagery in forest stand
classification and canopy structure parameter estimation, “. .. this area of image analysis
in forestry appears surprisingly poorly developed” (Franklin, 2001, p. 260). The few
studies that have used this technology in forest inventory parameter estimation usually
Operated on a single image (frame) and a single forest stand, or a very small number of,

typically coniferous, adjacent stands. Hence, little is known about whether high-spatial-

92

resolution imagery can reliably be used to predict forest inventory parameter values for
stands of variable, deciduous forest cover types. Spatially extended investigations have
been hindered by 1) frame geometric correction and registration requirements (Franklin,
2001, p.260); 2) logistic concerns related to the acquisition of necessary canopy
parameter information in the field (Gong et al., 1999); 3) brightness variations among
imagery frames (Mikkola and Pellikka, 2002; Chapter 2, this dissertation), and 4) a dearth
of process automation paradigms (McGraw et al., 1998).

The objective of the research presented in this chapter is to investigate the utility
of airborne, hi gh-spatiaI-resolution, multispectral digital imagery for cover type
classification and canopy structure parameter estimation while addressing all of the
aforementioned factors known to hinder information extraction at the multiple stand
scale. Two hypotheses are evaluated: 1) spectral classification of forest cover types based
on signatures derived from selected tree crown portions improves classification accuracy
obtained using spectral Signatures of all pixels in a forest stand (the traditional approach),
and 2) estimates of stand canopy structure parameters (stem density, average crown
diameter, canopy closure) can be reliably obtained via pixel DN spatial autocorrelation
structure analysis. These hypotheses were evaluated for five cover types common in the
Midwest region using a detailed set of field observations obtained from multiple, non-

adjacent stands.

3.2. Individual Tree Identification

At present, algorithms that detect individual trees in H-resolution imagery are
based on the association of a tree apex with a local maximum in image brightness value.

This spectral reflectance pattern of tree crowns constitutes the main structural element for

93

every forest stand canopy and when viewed in three dimensions it can be perceived as a
convex shape. For coniferous species, the shape of individual crowns could be
approximated by a cone. Hence, high-resolution imagery of a forest stand is composed of
contiguous pixel regions, which represent trees or clusters of trees. The variety of
techniques for processing individual trees from high-spatial-resolution imagery
mentioned earlier, all attempt to capture the differing image spatial structure that emerges
from the complex relationships between image Spatial resolution and canopy structural
characteristics. The ratio of crown size to resolution is sometimes used as an indicator
capable of quantifying such relationships and thus for determining the image analysis
technique best suited for individual crown identification (Poulioteta1., 2002). For
example, at ratio values of 30 or larger the morphology of individual trees may be
detected (Brandtberg, 1997). Ratio values between 8 and 30 appear to justify use of the
valley following algorithm, while for ratio values in the range of 2 to 8 the most
appropriate processing technique appears to be local maximum filtering (LMF) (Wulder,
1998). The latter case is typical of imagery sets acquired with a spatial resolution of 0.6-
1.0m.

In medium to densely forested areas on hi gh-spatial-resolution imagery,
individual trees may be discerned as regions of high reflectance (i.e. high DNS). For
conifers, the spatial structure of this reflectance pattern results in a single local maximum
DN value found at or near the center of tree crowns (W ulder et al., 2000). Deciduous
species, on the other hand, generally exhibit larger within-crown brightness variation due
to the effect of branches, branch bundles, and branch shadow patterns on the spectral

response of the crown, which is ofien characterized by multiple maxima and non-

94

monotonic change in brightness from the crown center to its periphery (Franklin et al.,
1996). In the LMF approach for tree identification, a window is passed over all pixels of
a forest stand to determine if a given pixel is of higher DN than all other pixels within the
window (Dralle and Rudemo, 1997). Pixels identified as the largest DN within the
window are noted as stem locations. However, when a window of fixed Size is passed
over a forest stand it does not account for the presence of trees with different crown sizes.
Therefore a fixed sized window is incapable of accounting for the object-resolution
relationship that exists between the trees (objects) and the image spatial resolution
(Franklin, 1996). As a result, the presence of trees with a crown size larger than the fixed
window would tend to inflate the number of trees identified and increase the tree
commission error rate while trees with a crown size smaller than the fixed window would
often be missed thus increasing the omission error rate. In fixed-size windows, a
reduction in the one type of error typically results in an increase in the other error type
(Wulder, 2002). In forest stands characterized by highly variable tree crown sizes, fixed-
size windows were found to perform very poorly, often correctly identifying fewer than
half of the total number of dominant and co—dominant trees present (Wulder, 2000). A
simultaneous reduction in commission and omission error rates of identified trees is
possible when the size of the window used in LMF is adjusted to reflect the brightness
variability in the vicinity of the processed pixel (Pouliot et al., 2002). Such a pixel-
specific conditioning of window size can be accomplished by examining the form of
spatial autocorrelation among pixels. A quantification of spatial autocorrelation can be
performed by several techniques and corresponding measures (Deutsch and Journel,

1992, p.40), including variogram analysis.

95

3.2.1. Parametric quantification of image autocorrelation

Variogram analysis is a well understood and frequently applied image-processing
technique in remote sensing (Curran and Atkinson, 1998). It can be used to provide a
quantitative assessment of spatial dependency for continuously varying phenomena
Warekamp et al., 1996). A variogram describes the magnitude, spatial scale and general
form of the variation among spatially distributed, continuous variables (Matheron, 1963),
but it can be modified to accommodate the analysis of spatial dependency for phenomena
sampled at regular intervals, such as the spectral reflectance or brightness regimes in
digital imagery (Curran and Atkinson, 1998). Variogram analysis entails the computation
of relationships between pixel pairs. The relationship between pairs of pixels found h
pixels apart (the “lag” distance), is quantified as half the average square difference
between pixel pair values and it is known as the semivariance for that lag. Hence the
semivariogram, Kh), is a plot of semivariance as a function of lag and is computed

(Curran, 1988) as
rlh)=-;-E[Z(x)-Z(x-h)]2 (3.1)

where Z denotes a pixel value at location x. When computed on digital imagery, x is a
two element vector of the pixel’s row and column indices. The lag h indexes the distance
between pixel pairs for comparison. The prefix “semi” in semivariance denotes the fact
that each pixel in a pair enters the computation of (1) twice, once as Z(x) (head value) and
once as Z(x-h) (tail value). A division by two is necessary to adjust )(h) to its proper
value. It should be noted that the terms variogram and semivariogram are treated as

equivalent in the literature and are used interchangeably unless specifically mentioned

96

otherwise. When the semivariogram is computed for an imagery region R, its value for a
given lag h is an estimate of the semivariance for that lag and represents a measure of
dissimilarity between spatially separated pixels (Jupp et al., 1988). The lag-specific

semivariance estimate is computed as

m(h)

ilh)= l 212(20- 2(x -h)] (3.2)

2m (h)_

where m(h) is the number of pixels within R separated by h. In the presence of spatial
structure, a semivariogram would reveal that semivariance rises with increasing h, until
reaching an asymptote known as the “sill”, which indicates the maximum variability
between pixels. The “range” of the semivariogram is the number of lags, or distance to
the sill (Curran and Atkinson, 1998). Within the range, Spatial dependence is indicated;
pixels separated by distances larger than the range are understood to be spatially
independent (uncorrelated) (Levesque and King, 1996). The range of semivariograms
computed on digital imagery represents the average size of the structural elements
depicted in the imagery, which, in the case of medium- to high-density forests and H-
resolution, equals the mean crown diameter (Cohen et al., 1990). Therefore, the range of
the semivariogram computed for the neighborhood R around individual pixels might be
useful for determining the appropriate size of the window for identifying individual trees
(Wulder et al., 2000).

Although conceptually, semivariogram range computation is associated with a
number of logistical concerns and theoretical constraints (Daley et al., 1998). It assumes
that the second-order spatial autocorrelation of pixels within R is stationary, and first-

order autocorrelation (trend) is absent. If a trend is indeed present and not accounted for,

97

unbounded or overestimated semivariogram ranges should be expected (Deutsch and
Journel, 1992). Further, because solar illumination is strongly directional, mutual
shadowing between adjacent crowns causes anisotropic reflectance autocorrelation
patterns. Empirical semivariograms computed parallel to the solar plane over forest in H-
resolution digital imagery tend to have shorter ranges than those computed across the
solar plane. To avoid a systematic bias in range value computation, it is important to
either identify the proper orientation for directional semivariogram computation or
equally weight all possible directions, thus producing an omnidirectional semivariogram
(Franklin etal., 1996). In addition, because the reliability of semivariance estimates is
known to decrease with increasing lag (Curran and Atkinson, 1998), the size (largest
dimension) of R around a processed pixel should be at least three times the maximum
expected range value so that an adequate number of pixels pairs contribute to the
computation of semivariance estimates for lag distances that approximate the expected
range (Isaaks and Srivastava, 1989). Assuming a forest stand with dominant and co-
dominant trees of maximum crown diameter of 8m, and with a 1m imagery spatial
resolution, a reliable range estimation would necessitate a region of 24 x 24 = 576 pixels
to be examined for each processed pixel, thereby resulting in substantial computational
cost. A region of such size would allow pixels belonging to crowns non-adjacent to the
crown in which the processed pixel belongs to influence the semivariogram range value
computed for the latter pixel. Semivariograms, therefore, provide a quantification of
autocorrelation that has a regional rather than local scope and may thus be a biased
estimator of the appropriate window size for individual tree identification in stands

characterized by variable crown sizes.

98

3.2.2 Non-parametric quantification of image autocorrelation

Alternative, local estimates of image autocorrelation can be obtained by relaxing
the parametric structure of the variogram, sometimes known as slope breaks (Wulder et
al., 2000). They are a simple means of measuring the region of dependence around a
pixel and their use is based on the assumption that every pixel in the image may
correspond to a local brightness or reflectance maximum and therefore a tree apex. For
each pixel in the imagery an omnidirectional set of transects can be analyzed to assess the
distance (in whole pixel increments) at which a minimum DN is encountered. Slope
breaks may also be described as the first inflection point in the gradient of reflectance or
brightness along a transect. Although a large number of transects can be considered, in
practice slope breaks are computed along the 8 cardinal directions. The appropriate size
of the window for LMF image processing is determined as the average distance from the
center of the processed pixel to the inflection points along all transects. In addition to
providing tree-specific estimates of autocorrelation, slope break computation offers
substantial improvement in computation efficiency when compared to LMF window sizes
estimated via variogram range. However, since fewer pixels are engaged in the
computation of slope breaks it is likely that window size is more susceptible to bias

introduced by random noise embedded in pixel DNS (Pouliot et al., 2002).

3.3 Individual Tree Classification

The variability in reflectance among portions of a single tree crown and, hence, in
the DNS of pixels representing it in H-resolution imagery, has implications on the ability
to accurately classify a particular crown to a cover type class. As demonstrated in

Chapter 2, crown pixels in shadow reduce the separability of cover type signatures while

99

bright pixels located at or near the crown apex tend to improve it. Crown apexes
identified with the LMF approach enable the partitioning of the, usually overlapping,
cover type signatures to include only the brightest pixels, thus contributing to signature
compactness and separability, and increasing the potential of improved classification
accuracy. However, the reduction in the number of pixels that participate in signature
development when only tree apexes are considered may enhance the influence of the
geometric errors and spectral noise often present in H-resolution, digital, airborne
imagery on the resulting classification accuracy.

When signature development is performed in the traditional approach, pixels
contributing to signature development form clusters, each one of which extends over
several trees and is sometimes as large as a forest stand. Even in the presence of
substantial band registration errors, and assuming that the magnitude of the registration
vectors is much smaller than the size of the pixel clusters used for signature development,
there would be major spatial overlap of such clusters for each band in the imagery set.
Therefore, even in the presence of misregistration, all tree crown portions would be
represented equally well in signature development following the traditional approach. In
tree-apex-based signature development, however, band misregistration of a single pixel
could cause inclusion in the signature of pixels in one or more bands that actually
represent crown parts other than the apex, particularly for coniferous species with conical
crowns. Given that reflectance declines rapidly from the tree apex to the crown periphery,
but at directionally variable rates (Pellikka et al., 2000), the classification accuracy of
identified tree apexes in imagery characterized by different spectral registration vectors

than those present at the signature training areas could be substantially inferior to one

100

obtained 1
problems.
a tree ape
al., 1996;
hence. 811
pixels m;
than the

Current a
Surface 1
lllihltol
the 13018
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mear

Olband

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Michtg
are Se;
and 12
Olmed

obtained using signatures generated and used in imagery free of band registration
problems. In addition, for some crown shapes a pixel identified via the LMF approach as
a tree apex, might in reality be the center of the sunlit portion of the crown (Franklin et
al., 1996; Wulder et al., 2000). This problem is a function of illumination direction and,
hence, subject to image acquisition timing. AS a result, signatures developed from such
pixels may have inherited BRDF effects related more to the morphology of the crown
than the relation between illumination and viewing directions. It should be noted that
current algorithms embedded in BRDF correction models do not account for target
surface inclination and thus are incapable of normalizing BRDF effects within a crown
(Mikkola and Pellikka, 2002). To date, the effect of imagery inferiorities and BRDF on
the potential of tree-apex-based classification to provide improved cover type
classification accuracy is Speculative. This study attempts to quantify those effects by
comparing tree-apex-based cover type classification results prior to and afier elimination

of band misregistration and normalization of variable brightness/BRDF regimes.

3.4 Methods

3.4.1 Study Site Characteristics and Description of Imagery Set

The study area comprises two Sites, the one in the south-central part of Grand
Traverse County (Site I) and the other in the northern part of Wexford County (Site 11),
Michigan (Figure 2.1). Note that figures in this dissertation often contain color. The sites
are separated by about 10km in the northwest-southeast direction and extend over 8,805
and 12,626 hectares of land, respectively. More than half (56%) of the study area is
owned and managed by the Michigan Department of Natural Resource. Most of the study

area consists of forests and wetlands (82%), while agricultural use, mainly row crops,

101

represents 8%. Other land use classes include orchards (4%) and residential areas (4%).
Residential development is concentrated in the northwestern part of site I. Geomorphic
features include moraines and outwash. The average slope, calculated by using the finite
differences algorithm on a 10m, 1224,000 USGS Digital Elevation Model available for
the area is 3.5% and 2.7% for sites I and II respectively. Relief is more prominent along
the Manistee River, which crosses site II from northeast to southwest.

The study area is characterized by pronounced spatial heterogeneity of forest
cover types. The majority of the forest cover types extant in the northern Lower
Peninsula of Michigan are present in the forested part of the study sites. These include: 1.
Aspen, consisting of Big Tooth (Populus grandidentata) and Quaking (Populus
tremuloides) aspen; 2. Northern hardwoods, consisting primarily of Sugar Maple (Acer
saccharum), Red Maple (Acer rubrum), American Beech (Fagus americana), Black
Cherry (Prunus serotina), Basswood (T ilia americana) and White Ash (F raxinus
americana); 3. Oak, consisting of White (Quercus alba) and Red (Quercus rubra) oak; 4.
Natural Pine, mainly White Pine (Pinus strobus); 5. Pine plantations consisting primarily
of Red Pine (Pinus resinosa); and 6. Cedar swamps dominated by Northern White Cedar
(T huja occidentalis). The main forest management objectives of the MDNR include
timber production, enhancement of wildlife habitat, recreation, preservation of aspen, and
riparian best management practices. Several private land owners offer a network of tracts
used seasonally for horseback riding and snowmobiling.

The imagery data set used in this study was acquired on August 11, 1999, using
the Digital Airborne Imaging System (DAIS [Space Imaging, 1999]). It contains four

bands, three in the visible and one near infrared that were acquired by frame (digital

102

array) cameras equipped with appropriate band-specific filters in a 2x2 arrangement.
Appendix 1 contains detailed information on the technical specifications of the system
(Table A.1), flight line orientation, and the spatial arrangement of frames in each study

site (Figure A.1).

3.4.2. Field Measurements

A total of 34 plots, 16 in site I and 18 in site II, were established stratified across
the major forest cover types present in the study area with the exception of cedar swamps
that were excluded due to accessibility issues. Plots were allocated on level land, within
homogeneous stands, and away from cover type ecotone zones. Stand homogeneity was
evaluated with field inspections. A minimum 60% canopy closure threshold was imposed
by the MDNR as a selection criterion. All plots were Situated within the inner quarter
area of the associated image frame, resulting in plot-center view angles less than 10°.

Field measurements were obtained in the summer of 2000, exactly a year after the
acquisition of imagery, following the F IA/F HM field protocols (Appendix 1, Figure A.2).
To ensure an adequate number of trees within a subplot, its radius was increased from the
standard 7.32m, proportional to the size of trees present. Subplot diameter was kept equal
within plots, but ranged from 10m to 15m between plots. Subsequent to plot center
allocation, canopy structure parameters including the horizontal extent of individual tree
crowns and stem locations were recorded using field survey techniques. All spatial and
tabular data on tree crowns and stem locations were organized as geographic information
system (GIS) layers translated into the image coordinate system. Details on the

methodologies employed are available in Chapter 2.

103

3.4.3. Imagery Processing

Preliminary examinations of the 394-frame imagery set Showed apparent variation
in brightness, even among adjacent frames. Further investigations revealed imperfections
in the geometric alignment (registration) of the frame bands and a non-stationary spatial
distribution of registration vectors. In addition, BRDF effects were detected, principally
along frame edges. A pair of novel techniques was developed to correct these imagery
imperfections. The first was used to correct for band misregistration by using information
extracted from spectral histograms of frames, and then by examining the magnitude of
autocorrelation among the spectrally darkest pixels in a frame. The second technique,
aimed at a simultaneous correction of BRDF effects and brightness variability, optimized
the parameters of a popular BRDF model applied to the overlapping regions between

adjacent frames. Both techniques are described in detail in Chapter 2.

3.4.4. Window Size Computation for LMF Imagery Processing

The computation of variable, locally adjusted window sizes for LMF processing
of multispectral, H-resolution imagery and the subsequent identification of pixels
believed to represent tree apexes are processes with many embedded parameters. In the
interest of reducing the analysis load to manageable levels in this research, choices were
made regarding the version of imagery to be used (original vs. corrected for band
misregistration and variable brightness), and the bands to be considered.

Because window size computation is in essence an effort to quantify the extent of
reflectance or DN autocorrelation, and hence of local, sub-frame scope, it is unlikely that
it would be affected by BRDF effects or brightness variability, given that both of those

phenomena are governed by processes with large, frame or multi-frame scope. It is

104

evident from a careful evaluation of equation (3.2) that the addition or subtraction of a
constant (similar to the average brightness difference among two image frames) from
each pixel DN value would not affect the Shape, and therefore the range, of the computed
empirical variograms. It can be shown (Appendix 2) that imagery processing with a
kernel function similar to those employed in popular BRDF effect correction models
(including the one by Roujean et al. (1992) used in Chapter 2), would not affect the range
of variograms computed for the same image region before and after processing with the
kernel. Window size computation via Slope breaks, a spatial operation with even
narrower spatial scope compared to the variogram, would be expected to produce the
same window sizes regardless of the presence or absence of brightness variations and
BRDF effects. However, to eliminate discrepancies in the position of identified tree
apexes among different bands (later used in tree-apex cover type classification) due to
registration problems, it was decided to proceed with the brightness/BRDF-normalized
version of the imagery.

Visual inspection of empirical variograms computed for each of the four bands
and every subplot revealed that the variogram ranges were often either unbounded (i.e.
increased monotonically with lag distance, never reaching an asymptote) or were
substantially larger than the mean tree crown diameter in corresponding subplots. Those
observations were consistent with findings reported by Treitz (2001) using H-resolution,
airborne, digital imagery of boreal forests in northern Ontario. Similar observations were
made by Franklin and Wulder (1996) in British Columbia. They decided to truncate the
range of unbounded variograms to a predefined maximum value in order to avoid

unrealistically large window sizes. In addition, the assessed range of computed

105

variograms were found to occasionally differ among bands for the same subplot, although
no patterns could be identified.

In the course of investigating the cause of unbounded variogram ranges and their
apparent dependence on wavelength, imagery portions corresponding to subplots were
examined for the presence of trend in pixel DNS. The procedure, sometimes known as
trend surface analysis (Bailey and Gatrell, 1995, p. 168) and described in Appendix 2,
regards pixel DNS as the product of a linear association between a function of image row
and column indices known as the trend or first-order autocorrelation and a model of
second-rder, or local, autocorrelation. In this study, the second order autocorrelation
embedded as a component of the imagery DNS was assumed to represent the spatial
pattern of reflectance formed by tree crowns. Imagery processing for the removal of
potential trend would enable quantification of reflectance autocorrelation independent of
non-tree-crown related influences. Post-trend-processed empirical variogram ranges were
always bounded and of a magnitude within the range of dominant/co-dominant tree
crown diameters present in the subplots (Appendix 2, Figure 8.2). At the same time,
trend removal eliminated differences in range magnitude among bands (Appendix 2,
Figure 8.3). Subsequent variogram analyses were performed strictly on imagery
processed for trend using only the NIR band.

Variogram range computation of post-trend-processed imagery was automated by
fitting a cubic spline (Hastie and Tibshirani, 1990) to the estimates of semivariance. The
spline operated as a semivariance smoothing function, capable of eliminating sporadic
non-monotonic fluctuations of semivariance estimates considered to be artifacts of a

relatively small numbers of pixel pairs separated by Short lag distances. The range was

106

tnfleeaio
OVereStt
tenterc
designg
illdn at
Dmitri
plXEl i:
r613 65:
10 21 l
”Sits
fined
decre;
Spline

ln1)3

onem

subsequently calculated as the lag distance for which the slope of the corresponding
spline segment was smaller than 5%. Reducing the length of lag increments to 1/3rd of the
pixel size allowed for a more precise range calculation. Range values rounded to the
closest integer were used as the proper window sizes for LMF imagery processing.

The appropriate window size for each subplot pixel was derived by modifying the
standard slope break approach used by Wulder et al. (2000) to include a set of heuristic
rules. Initial investigations had revealed that slope breaks computed as the first upward
inflection point in DN value along a transect (the standard approach) were consistently
overestimating crown, and hence window, Size by extending slope break distances to the
center of small canopy openings usually positioned in shadow. In the modified approach
designed to correct for such bias, the processed pixel was placed in the middle, rather
than at the origin, of a 30-pixel directional transect and a local regression (Cleveland and
Devlin, 1988) was fitted to the DNS of the transect pixels. Placement of the processed
pixel in the middle of the transect would eliminate transect-end-related biases in local
regression predictions. The length of the diagonal transects (SW-NE and NW-SE) was set
to 21 pixels to account for larger pixel spacing in those directions. The use of a local
regression along each transect, in essence a UN smoothing function similar to the spline
fitted on semivariance estimates mentioned previously, aimed at providing a monotonic
decrease in DN from crown apex to crown periphery. It Should be noted that fitting a
spline instead of using local regression would be inappropriate due to the large variability
in DNS of adjacent pixels along the transects.

The slope break value sbpi, for a transect centered at the processed pixel and

oriented towards each of the 8 cardinal directions was computed as

107

SbDir =

Where 1' (
local-reg

and D”

SlOpe bl

Sb : im

“here '1

 

 

 

f (1'5,_I > 13,.) and(13i+] > 13,) (3.3a)
Vi 6 [15,30] |
. . (D. > D. > 13. ), and (3.3b) Dir e {N, E, s, W}
“1111(1) t—l 1 1+1
SbDir = for 01' ~ 5 and
which (—.é——‘—1)>2( .." —l),and (3.3c) Vielllilll
Di DI.+1 Dir 6 (NE, SE,
~ ~ sw, NW}
D — D . ‘
~ ~ TR(max) TR(mm)
\ Di > [DTR(min) 2 ] 63‘”

where i denotes the distance in pixel increments from the origin of the transect, 5'. the

local-regression-fitted DN value for a pixel at distance i from the origin of the transect,

and DTR . and 5 the minimum and maximum 5. of all pixels in the transect. The
(min) T R(max) l

slope break value for the processed pixel was subsequently computed as
sb = int(é—Zszir ), VDir e {N, NE, E, SE, 8, SW, w, NW} (3.4)

where int() represents a function that rounds a real value to the closest integer.

The set of heuristic rules embedded in equations (3.3b) and (3.3c) shorten szir in
the presence of an abrupt reduction in the slope of the local, directional reflectance
gradient ofien found to occur at the periphery of canopy openings. Equation (3.3d)
dismisses sbpir value shortening involving any of the brighter half of pixels on the
transect. Equation (3.3a) represents the standard form of the Slope break approach.
Processed pixels with DN values smaller than the DNS of all of their 8 neighbors (i.e.
local reflectance minima) were automatically assigned a 0 Slope break and were excluded
from window development. For all other pixels, the minimum size window was rescaled
to 3 x 3. Window size computations were performed using scripts developed in the C

programming language and optimized for computational efficiency. Empirical variogram

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computation for each of the pixels in a subplot using custom developed scripts, was
found to outperform, in terms of computation efficiency, commercially available software

by a 1:10 margin.

3.4.5. Tree Apex Identification via LMF Imagery Processing

In the standard implementation of LMF, a pixel is characterized as a tree apex if
and only if it carries the maximum reflectance value or DN for the window centered on it
(Franklin et al., 1996; Wulder et al., 2000; Treitz, 2001). This implicitly assumes that the
tree apex is located at the center of the crown and that the rate of reduction in reflectance
or DNS from the tree apex to the crown periphery is isotropic (directionally independent).
Those assumptions may be valid in coniferous species with conically shaped crowns, but
they are potentially unrealistic for other coniferous and most deciduous species. Because
the standard LMF approach considers as tree apex a pixel at the center of the window, it
operates only with windows of side length equal to an odd number of pixels
(henceforward referred to as ‘odd-sized’). They require that the variogram range or slope
break average computed at the previous analysis stage be rounded to the closest odd
number, thereby introducing window sizes smaller or larger than the magnitude of the
local imagery autocorrelation gradient. Preliminary investigations in several subplots
showed large tree omission rates where tree identification was performed using the
standard LMF approach, particularly in the presence of deciduous cover types.

To resolve the limitations mentioned above and to improve tree identification
rates, a new approach is proposed here in which the window corresponding to each
processed pixel ‘votes’ as tree apex the pixel having the highest DN within the window,

regardless of where within the window the ‘voted’ pixel is located. When the appropriate

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window is ‘even-sized’, it cannot be centered on the processed pixel because it has four
central pixels instead of one. In such circumstances, the processed pixel is assigned to
each of the four central pixels in the even-sized window and the voting process proceeds
as before except that only a quarter vote is cast for each of the four window instances.
Pixels with one half or more votes are labeled tree apex candidates. Candidate pixels are

finally labeled tree apexes if their DN is larger that the DNS of all 8-neighboring pixels.

3.4.6. Computation of Canopy Structure Parameters

Identified tree apexes, variogram ranges, and directional slope breaks associated
with the apexes were used to provide estimates of stem density, mean crown diameter,
and canopy closure under the assumption that there existed a unique, one-to-one
correspondence between identified tree apexes and stems. All estimates of the canopy
structure parameter values were computed at the plot level to minimize estimate
dependence on subplot boundary effects. Estimate aggregation at the plot level was
encouraged by the fact that field observations revealed no apparent differences in forest
canopy structure within the plots.

Stem density estimates were computed as the fraction of the total number of tree
apexes identified (i) via the variogram range method and (ii) via the slope break approach
employed in image LMF image processing within each subplot to the total plot area.
Three mean plot crown diameter estimates were computed. The first estimate was
obtained by (i) initially delineating circular crowns of diameter equal to the variogram
range for each pixel identified as a tree apex via variogram LMF image processing, (ii)
splitting the circular crown overlaps (if any) between adjacent trees, (iii) calculating the

‘diameter’ of the resulting non-overlapping crown shapes, and (iv) finally computing the

110

geometric mean of all ‘diameters’ in a plot. The second mean plot crown diameter
estimate was obtained by (i) using pixels identified as tree apexes via slope break LMF
image processing, (ii) delineating the corresponding tree crown using directional slope
break length values sz,-, for each tree apex pixel, (iii) splitting potential crown overlaps,
(iv) calculating the ‘diameter’ of resulting crown shapes, and (v) computing the
geometric mean of all ‘diameters’ in a plot. The third mean plot crown diameter estimate
was computed as the geometric mean of the variogram ranges derived for each subplot
using all subplot pixels and thus it did not involve tree apex identification and crown
delineation efforts. It should be noted that mean crown diameter estimates were in
reference to the crown portion visible from above and not to the true horizontal extent of
a crown. The methodology for computing a ‘diameter’ estimate for a crown shape is
presented in detail in Appendix 1. The use of the geometric mean instead of the
arithmetic mean aimed at reducing the influence of outliers in the distribution of crown
diameter estimates on computed plot mean diameter values.

Canopy closure estimates were obtained by computing the ratio of the plot area
occupied by crowns delineated for the derivation of the first two plot mean crown
diameter estimates mentioned above. The portion of tree crowns with identified apexes
outside the plot boundary was also considered in the computation of canopy closure
estimates.

Computed stem density, mean crown diameter, and canopy closure estimates were
compared to those obtained by field measurements. The methodologies for converting
field measurements to canopy structure parameter values are discussed in Appendix 1.

Predicted canopy closure parameter values were regressed against observed parameters

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values. Regression parameter values were examined for statistical significance.
Differences in the slope and mean of linear regression models pertaining to different

methodologies used in canopy structure parameter derivation were also evaluated.

3.4.7. Cover Type Classification of Tree Apexes

In the presence of a pre-defined forest cover type scheme (Aspen, Northern
Hardwoods, Oak, Red Pine Plantations, and Natural Pine), a supervised classification
approach was selected. Among the many available options within the domain of
supervised classification, the maximum likelihood (ML) option was selected because it
would enable an evaluation of the statistical significance of classification results for
signature development alternatives, while facilitating comparison of classification results
obtained using only pixels corresponding to tree apexes and those obtained using all
subplot pixels (Chapter 2).

All pixels identified as tree apexes and having their centers within the subplot
boundary were used for signature development and classification performance evaluation.
Pixel membership to a subplot was determined via spatial overlays of image frames with
vector subplot boundaries in image coordinates. The subplot was selected as the
classification unit. A cross-validation approach (Lachenbruch and Mickey, 1968) was
undertaken for signature development involving two geographic extents: i) site -specific,
and ii) global. A subplot Q2 (belonging to plot Q) in Site I for example, was classified via
three sets of spectral signatures developed: 1) using all pixels in the remaining subplots at
site I except those in the related subplots (Q1, Q3, and Q4) and all the subplots in site II,
2) using the pixels in the remaining (unrelated) subplots of site I only, and 3) using all

pixels in site II subplots but no pixels from site I subplots. Subplots in site II were

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classified in a similar fashion for a total of five classification products. Absent this cross-
validation approach, it would be difficult to ensure that the potentially low spectral
variability within a plot compared to the variability among plots of the same cover type
would not inflate classification accuracy estimates. Subplot classification was applied to
both raw DNS and to a dataset that had been corrected for between-band misregistration
and normalized for BRDF/brightness variability, for a total of 10 classification scenarios.

Classification results were processed with majority filters that assigned a single
class (cover type) to each subplot. Classification accuracy estimates were derived from
confusion matrices and associated indicators (percent of subplots correctly classified and
kappa coefficients) (Congalton, 1991) computed after the application of the majority
filters. Differences in the classification performance were evaluated using parametric
statistical tests. Details on the tests and the computation of confusion matrices and
accuracy indicators are provided in Appendix 1. The power of each classification result
was evaluated by imposing five different ML probability thresholds (none, 0.1, 0.25,
0.50, 0.75) that pixel class-conditional probabilities had to exceed prior to their allocation
to a class. Pixels with all class conditional probabilities below the imposed threshold

remained unclassified.

3.5. Results

3.5.1. Local Maximum Filtering Methods

For the few (16/142 or 11%) subplots in which first-order DN autocorrelation was
observed, subplot trend surface processing practically eliminated differences in computed
variogram ranges among bands (Appendix 2, Figure B.3). All 16 trend occurrences were

either in aspen or red pine plantation subplots characterized by high (> 80%) canopy

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closure values. For the remaining 126 subplots, the difference of variogram ranges
computed before and after trend surface processing for a given band was always equal to
or less than 1/3rd of a pixel. Between bands, the mean difference of computed variogram
ranges before and after processing was larger (0.39 pixels, standard deviation 0.09), but
no pattern in the distribution of the difference magnitude could be identified.

Variogram ranges and mean, omnidirectional slope break estimates computed for
a large number of subplot transects showed the former to vary substantially less than the
latter (Figure 3.1). For 23 subplots (6 in northern hardwoods, 11 in aspen, and 6 in red
pine plantations), the span of variogram ranges was smaller than 2/3'ds of a pixel. For all
subplots, the mean variogram range of subplot pixels exceeded corresponding mean slope
break lengths. Often though, the variogram range for a particular pixel would be shorter
than its slope break equivalent, particularly for pixels positioned at or near the center of
the sunlit portion of a large crown. Conversion of mean slope break and variogram range
estimates computed for subplot pixels into corresponding window sizes for LMF imagery
processing resulted in Similar conversion RMSE estimates (0.102 and 0.113 pixels,
respectively). The fact that variogram range estimates were computed in 1/3”d of a pixel
increments, while mean slope break estimates were unrestrained real numbers appeared
to influence computed window sizes only minimally.

A comparison of variogram ranges computed using the automated method
introduced in this study with variogram ranges determined manually via visual inspection
for more than 50 circular imagery regions with a diameter of 30 pixels randomly
distributed across cover types, canopy closure, and stem density conditions revealed that

the automation process performed very well for most regions yielding an RMSE of 0.062

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pixels. The method’s performance was occasionally suboptimal for circular regions
located within aspen and to a lesser extent red pine plantations and northern hardwood
stands characterized by a smooth canopy surface, very high canopy closure values, and
small variability in crown sizes. In such conditions, the empirical variograms exhibited a
substantial semivariance fluctuation at the sill level potentially allowing for range
overestimation. It should be noted that manual derivation of ranges via visual inspection
of empirical variograms repeated at different times and in random region sequence
produced a range variability twice as large as the one obtained from imagery regions
characterized by rough canopy surfaces.

Local regressions fitted to subplot pixel DNS altered the value of the original DNS
only slightly, generally maintaining the form of the DN profile along the transect (Figure
3.2). In the typical example shown in Figure 3.2, a zero-length directional slope break
would be assigned and no window would be generated for the pixel at transect position
15 (middle of transect) regardless of whether the original or the local-regression-fit DNs
were to be used, given that, in both cases, the preceding and following pixels along the
transect had larger DNS. For a pixel at transect position 23, the directional slope break
sbpi, would be 4 pixels when the heuristic rules described in equations 3.3a to 3.3d were
applied but 5 pixels in their absence. The pixels at transect positions 6 to 8 and 27 to 30
correspond to shadowed canopy openings. As such, szir truncation from 5 pixels to 4
would contribute to a window size reflecting that better matches the size of the tree
crown at that location. Slope break lengths computed for transects parallel to the solar
plane and extending through canopy openings were sometimes shorter for pixels situated

on sunward crown portions than those for crown portions facing away from the sun. Such

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instances occurred sporadically in northern hardwoods and oak subplots but rarely in the

other cover types.

3.5.2. Stem Density

Strong linear relationships were found between predicted and observed plot stem
densities (Figure 3.3) for both variogram and slope break methods. Slope break-derived
density predictions, denoted as triangles in Figure 3.3, approximated observed densities
(1 :1 line) better than variogram-derived predictions (denoted as squares in Figure 3.3).
Densities below approximately 350 stems/ha were generally slightly overestimated while
those larger were increasingly underestimated. Discrepancies between predicted and
observed stem densities increased at high and low density levels. Linear regression of
predicted on observed stem densities using plots in all cover types (pooled regression)
exhibited very high R2 coefficients (Table 3.1). The pooled regression of slope break-
derived density had a higher (0.864) and significantly different (at or=0.01) slope that
(0.741) of the pooled regression for variogram-derived density. Regression means were
also significant at or=0.01. Both pooled regressions had slopes significantly different than
the slope of the 1:1 at 0:00]. High R2 coefficients (>0.947) were also present when
individual cover types were considered, with the exception of the aspen plot stem
densities computed using variogram ranges (Table 3.1). Regression slopes for individual
cover types were higher for slope break-derived than for variogram-derived densities
except for oak, but slope differences were not significant at or=0.05 except for natural
pine plots. Cover type-specific regression means, however, were significant between
methods at or=0.05 or or=0.01 except for natural pine plots. Regression residual plots did

not suggest the presence of any patterns or heteroskedasticity. Compared to observed

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density, variogram-derived stem density exhibited root mean square errors (RMSE)
approximately two times larger than those of the slope break-derived stem densities
(Table 3.2). When expressed as percent of the cover type mean observed values,
variogram-derived density errors ranged from a minimum of 6.1% for natural pine to a
maximum of 12.5% for aspen; slope break-derived density errors ranged from a

minimum of 3.6% for natural pine to a maximum of 7.4% for red pine plantations.

3.5.3. Tree apexes

Figure 3.4 is a typical example of tree apexes identified in a high density and
crown closure aspen subplot. It is evident from the figure that in this aspen subplot there
were no discrepancies in the position of pixels identified as tree apexes by the two
methods, excluding cases with apex omission or commission errors. Positional
discrepancies of correctly identified apexes were also rare in the remaining cover types.
Where present, they involved two or fewer apexes per subplot and had a magnitude of a
single pixel. For the subplot shown in Figure 3.4, the stem density obtained using field
observations was 549 trees per hectare. Imagery LMF processing using variogram ranges
correctly identified 22 apexes, missed 4, and had 2 false positives (commission errors),
resulting in a predicted stem density of 507 trees per hectare and a prediction error of 8%
(Figure 3.4a). Processing using slope breaks correctly identified 24 apexes, missed 2, and
committed 1, resulting in a predicted stem density of 528 trees per hectare and a
prediction error of 4% (Figure 3.4b).

It is evident from an examination of the NIR band image depicted in Figure 3.4
that the image portion with row indices approximately 20 to 40 contains larger tree

crowns and would therefore yield larger variogram ranges than the remaining part of the

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image. Influenced by the adjacent larger crowns, variogram ranges computed for subplot
pixels in rows 15 to 20 would likely overestimate the appropriate window size used in
apex identification, and increase the probability of omission errors for that image portion,
particularly in the presence of high stem density. Because slope break lengths are
calculated using a spatially limited (local) scope, they are independent of the crown sizes
of trees not in the immediate vicinity of the processed pixels, and would therefore be less
susceptible to apex omission errors. The tree apex at location [23,20], correctly identified
using the slope break method, but missed when using the variogram method,
demonstrates how differences between the two methods to adapt to local reflectance

conditions influences the error rates of stem density predictions.

3.5.4. Canopy Closure

Plots of predicted vs. observed plot canopy closure showed strong linear
relationships, but there was little evidence to support the superiority of either variograms
or slope breaks (Figure 3.5). Variogram-derived canopy closure predictions appeared to
envelope the 1:1 line in Figure 3.5 for the entire range of observed canopy closure values.
Slope break-derived predictions behaved similarly at lower canopy closure conditions but
appeared to slightly underestimate canopy closure at higher values. The pooled regression
of variogram-derived prediction of observed canopy closure values yielded an R2=0.941,
while the pooled regression of Slope break-derived canopy closure values produced an
R2=0.930. However, the two pooled regressions had significantly different slopes at
or=0.01. All individual cover type R2 values exceeded 0.800 for both methods
(Table 3.3), but exhibited substantial regression slope variability both across derivation

methods and cover types. Differences in regression slope between methods were

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significant at 0:00] or OL=0.05 for all cover types except oak. The RMSE of canopy-
closure predictions were comparable for both derivation methods, with the exception of
aspen for which slope break-derived prediction error was less than one third of

variogram-derived prediction error for plot canopy closure (Table 3.4).

3.5.5. Crown Diameter

Plot mean crown diameter predictions derived using variogram ranges were found
to overestimate diameter for smaller crowns and underestimate it for larger ones, while
slope break predictions appeared to be unbiased except perhaps for crowns with mean
diameters exceeding 7m (Figure 3.6). Linear models provided an adequate representation
of the relationship between parameter derivation methods when simultaneously
considering all cover types. Similar observations were made for plot crown diameters
predicted via variogram ranges estimated with subplot scope (alternative variogram
method) rather than the pixel-specific scope, the latter being the standard method used for
predicting plot stem density and canopy closure. The former method overestimated the
size of small crowns and exhibited heteroskedastic behavior with increasing crown size
(Figure 3.7). Pooled regressions of variogram-, alternative variogram-, and slope break-
derived predictions of observed mean crown diameter values had R2 coefficients of
0.942, 0.921, and 0.990, respectively, and significantly different regression slopes at
or=0.01, except for the slope break — variogram regression pair (Table 3.5). Variability in
cover type-specific regression slopes across crown diameter prediction methods was
significant only for the oak plots. The RMSE of plot mean crown diameter predictions

were comparable in magnitude for both the variogram and alternative variogram

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parameter value derivation methods, but substantially larger than the prediction errors

computed via the slope break method (Table 3.6).

3.5.6. Crown Delineation

Figure 3.8 portrays the delineation of crowns using either variogram ranges or
directional slope break lengths for an oak subplot. Because variogram ranges and slope
breaks performed identically in tree apex identification for this particular subplot, they
rendered it a good demonstration case of the performance of slope breaks and variogram
ranges for crown delineation, which in this research is a precursor to predicting canopy
closure and mean crown diameter. Positional discrepancies between identified tree
apexes and observed tree stems are apparent in both methods. The solar azimuth angle at
the time of image acquisition for this oak subplot was 172° (measured from north). The

angular components of the displacement vectors between actual stems and identified

apexes were restricted to the 1350 to 1800 range. As such, it is likely that the pixels
identified as tree apexes actually represent the middle of the sunlit portion of the crowns
rather than the stem location. Such discrepancies occurred at, but were not limited to,
coordinate locations [4, -7], [-6, -2], and [4, 2.5]. Non-conformal crown morphology,
however, (i) often placed identified tree apexes elsewhere, as is evident in coordinate
locations [-4, l] and [-5.5, 7]; (ii) caused more than one apex to be identified for one
observed stem, as in locations [0, 4] and [2,5]; or (iii) resulted in stem omission, as in
location [8.5, 3]. Positional discrepancies between stem and identified tree apexes were
smaller for coniferous than for deciduous cover types.

Variability in the spatial distribution of crown sizes appeared to influence canopy

closure predictions when crowns were delineated with the variogram range method.

120

Larger crown sizes at the western half of the oak subplot shown in Figure 3.8, resulted in
variogram ranges approximating the diameter of those crowns well. Crowns delineated
for apexes at locations [-10, 1] and [-8, 7] in Figure 3.8a were in close agreement to
observed crown boundaries. Variogram range-based delineation of smaller crowns
adjacent to larger ones (location [6, -1] and [-2, -8]) caused substantial overestimation of
crown extent for the former. Crown overestimation is represented in purple in Figure
3.8a. Smaller crown sizes east and south of the subplot resulted in variogram ranges
shorter that the crown diameters present in the east half of the subplot, thus causing
substantial crown underestimation, represented in yellow in Figure 3.8a. At the subplot
level, however, crown underestimation for a few trees was nearly compensated by crown
overestimation for others resulting in prediction error of only 2%. Crown delineation via
slope breaks for this oak subplot appeared to be superior to the delineation produced
using variogram ranges in the sense that the absolute crown under- and overestimation
was more confined and showed no patterns in its spatial distribution (Figure 3.8b). Slope
break delineation sometimes tended to overestimate crown extent towards canopy
openings (location [2, -3], [-7, -4], [-10, -3], [-1, 9], etc.), resulting in an overall

prediction error of 4%.

3.5.7. Cover Type Classification of Tree Apexes

Classification results obtained with signatures generated from pixels identified as
tree apexes using variogram ranges, were practically identical to those obtained using
slope breaks. Associated confusion matrices developed for each of the five geographic
extents of signature development were found to have a maximum of4/136 or 3/72

(pending on signature geographic extent) of subplots assigned to different cover type

121

classes between the two methods. Given these similarities, only slope break-related
results are presented here.

Classification accuracy estimates and kappa coefficients derived from confusion
matrices constructed using original DNS ranged among classification scenarios from
70.3% to 72.2% and 0.628 to 0.652 respectively (Table 3.7a-e). Use of brightness-
norrnalized imagery resulted in classification accuracy and kappa coefficient estimates
ranging from 84.4% to 87.5% and 0.804 to 0.844 (Table 3.7f-j). Brightness normalization
improved classification accuracy among classification scenarios by an average of 14.6%
with coefficient of variation 0.060; brightness normalization improved kappa coefficients
by 0.182 (coefficient of variation 0.057). In all classification scenarios, results were
significant at 01:00] (Table 3.7a-j). Pair-wise comparisons of classification outcomes
based on the computation of standardized differences of respective kappa coefficients
showed no statistical significance at or=0.10 among classification scenarios using original
DNS and among classification scenarios operating on brightness normalized imagery. All
pair-wise comparisons involving a classification scenario using original DNS and a
scenario operating on brightness normalized imagery were significant at (1:001 or

=0.05 (Table 3.8).

In classification scenarios based on signature development from and testing on all
subplots using original DNS, about one fourth of the total number of deciduous subplots
(21/80) was assigned to a wrong deciduous class, but within the deciduous cover type
group. About one fifth of the coniferous subplots (12/56) was assigned a wrong
coniferous class but within the coniferous cover type group. Five subplots were assigned

to the wrong cover type group'(Table 3.7a). Brightness normalization reduced the numbe

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of subplots assigned to the wrong class and correct group to 12 for deciduous and 5 for
coniferous classes and eliminated all instances of subplots assigned to the wrong cover
type group (3.70. Classification error rates between cover type classes and cover type
groups are shown in Table 3.9.

Brightness normalization dramatically improved class-conditional kappa
coefficients for all classification scenarios (Table 3.10) and averaged 0.175 for aspen,
0.129 for northern hardwoods, and 0.164 for oak. The improvement was higher and less
variable across scenarios for red pine plantations and natural pine, averaging 0.194 and
0.255 respectively. Class-conditional kappa improvement was practically uniform across
classification scenarios and ranged from 0.17 5 to 0.196, but it was at least twice as
variable for scenarios involving signature development and testing in the same site than
scenarios involving signature development in one site and testing in the other.

The effect of frame brightness normalization on the structure of classification
Signatures can be assessed by examining the percentage of classified pixels for different
maximum likelihood thresholds (Figure 3.9). For thresholds up to 0.25, there was little
difference in the percentage of classified pixels before and after brightness normalization.
A threshold of 0.50 classified approximately 50% of tree apex pixels in the original DN
imagery and about 20% more for the set normalized for brightness. Even at high
percentages, a substantial percentage (~ 25) of original DN, and approximately half of
brightness-normalized pixels were still classified. Differences in the percent of classified
pixels for different classification scenarios did not exceed 10% even for high maximum
likelihood probability thresholds. It Should be noted that the reference to classification

results using DNS in Figure 3.9 implicitly assumed that LMF processing using original

123

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DNS identified the same pixels as tree apexes as those identified with the normalized
imagery set. Although preliminary investigation had indicated that such an outcome
would have been likely, LMF imagery processing using original DNS was not conducted
for all subplots. The substantial amount of pixels that remained classified even for high
(0.75) maximum likelihood probability thresholds indicated that constraining signature
development to include only pixels identified as tree apexes results in signatures far more
compact and, hence, likely more separable that those obtained using all subplot pixels.
Using tree apex pixels instead of all pixels produced statistically significant increases
(Table 3.11) in classification accuracies from approximately 45% to 70% for
classification based on original DNS and from approximately 50% to 85% when

brightness normalization was employed.

3.6. Discussion

Prediction of canopy structure parameters in this chapter was based on analysis of
crown surface morphology. Identified tree apexes were used as a surrogate for stem
density predictions while canopy closure and mean crown diameter were derived directly
from the imagery. It should not therefore come as a surprise that stem density predictions
yielded larger RMSE than canopy closure and crown diameter predictions (Table 3.2, 3.4,
and 3.6), particularly when employing slope breaks for parameter value estimation,
despite the fact that the latter two were based on the former.

Oak and northern hardwood subplots in this study contained large, mature trees
with crowns of complex morphology and often two or more reflectance maxima, and
several canopy openings, sometimes of similar size and uniform distribution within the

subplots and sometimes of variable size and distribution. Further, stand structure

124

complexities were introduced by shorter co-dominant tree apexes positioned at the edge
of larger adjacent crowns with which they formed composite crowns, whose tree-specific
components were sometimes difficult to discern even with field inspection. In the
presence of large-crown trees and uniform crown and canopy opening size distribution,
the slope break-based and variogram-based methods performed equivalently in stem ..
density prediction. By contrast, the presence of crown size variability or variable-sized
canopy openings resulted in better accuracy for slope-break derived predictions of stem
density, thereby corroborating that slope breaks are capable of adjusting well to local
stand structure conditions. The minimal variability in canopy-opening and crown-size
precluded a reliable assessment of canopy structure conditions on stem density
predictions for the remaining three cover types.

Commission errors due to multiple tree maxima and corresponding tree apexes
identified using variogram ranges in the presence of large northern hardwoods and oak
trees produced mean crown diameter underestimation proportional to crown size, but
appeared to only minimally affect the accuracy of canopy closure predictions. Note that it
requires only 1 out of 10 trees with average crown diameter of 10m to be mistakenly
identified as two separate stems in a subplot for an 8% reduction in subplot mean crown
diameter value to occur. As a result, crown diameter predictions in large tree crown
stands were more susceptible to errors of commission than of omission.

Stem density was underestimated for most of the natural pine and all of the red
pine plantation and aspen subplots largely because the presence of small crows increased
omission error rates. Errors of omission would often occur where most of the sun-facing

crown portion of a co-dominant tree was in the shadow cast by adjacent dominant trees

125

(resulting in a lower brightness tree apex for that tree). Errors of omission occurred more
frequently where pixels correctly identified as tree apexes were separated by distances
smaller than half the variogram range or the slope break length calculated for those apex
pixels. The second source of tree omission error could be potentially eliminated in such
conditions by removing the LMF processing rule that necessitates all pixels identified as
tree apexes to have DN larger that those of their 8 neighbors. Elimination of this LMF
rule, however, would cause deterioration of stem density predictions obtained in stands of
trees with larger crown sizes. LMF rule implementation conditional upon variogram
range or slope break magnitude should be considered as a stem-density-prediction
alternative worthy of investigation.

Stands exhibiting small crown size and high canopy closure were found to exhibit
low tone or DN variability in digital imagery. Precise range estimation for variograms
computed in those circumstances was challenging, even when performed manually, in
part because of non-monotonic semivariance variability between consecutive lag
distances and in part because semivariance often tended to increase slowly with lag
distance and plateau (reach a sill) at distances larger than the diameter crowns present.
Because such semivariance behavior persisted even after imagery processing for first-
order autocorrelation removal, it was assumed that in smooth-canopy-surface stands,
individual tree crowns may not necessarily be the main structural canopy element, and
that perhaps parametric quantification of DN autocorrelation is susceptible to existing
lower fractal dimensions of reflectance. Imagery spatial resolution was sufficiently fine to
eliminate concerns of smooth canopy surface appearance originating from reflectance

aggregation issues. LMF window Size overestimation due to imprecise variogram

126

computation was considered the primary reason for larger stem density prediction RMSE
than the one obtained with LMF window sizes conditioned upon slope break lengths.

A special case of variogram range-based stem density overestimation could arise
in stands with systematic and anisotropic tree arrangements such as in red pine
plantations where past thinning operations were performed along the rows. In such
plantation stands, if sufficient time (>10 years) had elapsed between the thinning
operation and the imagery acquisition, the trees will utilize the extra growing space and
the variability in canopy reflectance along the rows will be reduced. In such conditions,
the computed variogram range length could exceed the planting space between rows by
50% or more (particularly for rows oriented in the East-West direction) potentially
causing tree omission errors. Such canopy structure conditions would also promote an
overestimation of canopy closure and crown diameter, because the space actually
occupied by the omitted trees would typically be assigned to adjacent trees along the
rows during the crown delineation process, thus inflating crown diameter (i.e. a canopy
opening would rarely be predicted). Systematic tree arrangements can also introduce a
bias in the slope break-enabled crown delineation related to image resolution. This is
especially the case where tree-spacing length is slightly less or more than 0.5 pixels the
nearest pixel length multiple. For example, a 12ft (=3.66m) spacing would likely produce
4-m slope break lengths and cause crown size and canopy closure overestimation. Such
bias is expected to cancel out among trees in natural stands.

The imposition of the heuristic rules on the slope break computations were
undertaken to avoid substantial overestimation of LMF window sizes, and its negative

impact on canopy closure and mean crown diameter predictions. Without the heuristics,

127

canopy openings between trees would occur only as sliver polygons between adjoined
crowns or because of crown representation fidelity issues due to the limited number of
directions analyzed around each identified tree apex. The implication of these limitations
on the values of the canopy structure parameters would likely be negligible in high
canopy closure stands, but substantial in the presence of canopy openings. The critical
issue here is how to identify the appropriate value for the coefficient at the right side
component of equation 3.3c, whose role is to inhibit directional slope break extension
into canopy openings. The value used was the product of experimentation and, as shown
in Figure 3.8b, did a good job in delineating crowns, while observing canopy openings, in
all northern hardwoods, oak, and natural pine stands where openings were present.
Coefficient values would likely need to be modified in the presence of large solar zenith
angles, diffuse illumination, reduced foliage vigor and density, or finer imagery
resolution. Coefficient adjustment for pixel size would be required in response to finer
reflectance sampling, and the resulting finer reflectance value change utilized in equation
3.3c.

Applying the procedures presented in this chapter might not be advisable to derive
stand-structure parameters for stands with medium or low canopy closure or where stand
conditions permit direct illumination of the forest floor or background vegetation. In such
conditions, grass, exposed sandy soil, or shrubs could easily be misidentified as tree
apexes during LMF processing, and the variogram ranges would mistakenly represent the
mean diameter of the canopy openings rather than the size of crowns. Note that the 60%
minimum canopy closure threshold imposed as a prerequisite for plot installation

precluded any occurrences of sunlit background in the plots. Although openings did exist

128

and were sometimes of sizes equivalent to those occupied by the dominant trees, the
height of adjacent trees would place them in shadow. Preliminary imagery processing
using band rationing could potentially reduce the effect of non-vegetated, sunlit stand
backgrounds on the predicted canopy parameter values.

The pooled and individual cover type regression models of predicted vs. observed
canopy structure parameter values for each cover type, presented in Tables 3.1, 3.3, and
3.6, are only intended to provide a preliminary understanding of the relationship between
parameters and cover types. The small number of plots installed in each cover type and
the often compressed range of observed values for the canopy structure parameters within
each cover type suggest that the regression model parameter value might change if a
larger number of plots in varying stand structure conditions were available in each cover
type.

The classification results (Table 3.2, 3.4, and 3.6) indicate that the slope break-
enabled stem density and mean crown diameter predictions are superior, not only to those
obtained using variogram ranges, but also to those obtained during stand data cruising by
experienced foresters in the Midwest region (Roger Meck and Larry Pedersen, MDNR
analysts, personal communication). For canopy closure predictions, both methods exceed
the accuracy typically obtained by stand cruising. Those observations suggest that
automated imagery processing using the techniques of this chapter has a potential to
become the standard approach for acquiring forest stand structure information, at least for
stand conditions that approximate those in the plots used in this study. This potential is
tempered by significant computational costs. Using 2003 vintage equipment, it would

require several hours (~5) for the processing of one hectare of forest land using 0.9m

129

imagery. An exception to this is predicting mean crown diameter using the alternate
variogram method, which is at least two orders of magnitude faster than the analytical
variogram and slope break methods.

The classification results corroborate that brightness variability among imagery
frames increases class covariance values in feature space and thus reduces class
separability. In addition, the smaller variability in kappa coeffrecients or accuracy
estimates obtained for different classification scenarios using tree apex pixels compared
to those obtained using all pixels indicate that the brightest pixels in a crown manifest the
cover type-specific reflectance characteristics better and with greater stability. Brightness
normalization costs are warranted by the significant improvement in overall and class-
specific classification accuracy. The fact that discrepancies in the number of pixels
identified by each of the LMF processing methods hardly affected classification
outcomes suggests that alternative, and likely computationally less costly, classification
procedures based on bright pixel detection might be capable of delivering comparable
classification products. Tree apex-based classification, however, offers the additional
advantage of allowing for estimation of species composition within cover types. The
presence of species with substantially different reflectance characteristics in the same
cover type, for example white pine/aspen, often present in the Midwest region, could
render the processing of classification results with majority filters inappropriate and
cause a significant reduction in classification accuracy. In such cases, class-assignment
of plots or forest stands could alternatively be based on heuristic rules. Reflectance

variability only between big tooth and quaking aspen and absent among the species

130

present in each of the remaining cover types, at least when only tree apex pixels were

considered, has precluded the development and evaluation of such alternatives.

3.7. Conclusion

The two methods of quantifying DN autocorrelation that were used in this study,
the parametric variogram analysis and the non-parametricset of simple heuristic rules,
have revealed the promising potential of hi gh-spatial-resolution digital imagery as a
source of reliable forest canopy structure information. The other known investigations
that have attempted stem density predictions, primarily in coniferous forests, found
prediction error rates that have rendered them and the methodologies employed of little
utility for inventory or management purposes. In this study, the field acquisition of a
detailed and positionally precise set of observations on stand structure distributed among
five deciduous and coniferous cover types in northern Michigan, has provided a better
understanding of the relationships between canopy characteristics and the reflectance
regimes embedded in digital imagery. Methods were developed or modified that are
capable of producing reliable predictions not only of forest stand density but also of
canopy closure and mean crown diameter.

The methods that were developed support automation and entail parsimonious
parameterization: 1) determination of the minimum slope between successive cubic
spline segments fit to empirical variograms to determine the variogram’s range; and 2)
derivation of a coefficient used to hinder directional slope break extensions into canopy
openings. Proper values for each parameter can be identified by visual inspections of
empirical variograms generated over an area of interest and by examining pixel DN

profiles traversing canopy openings. Because only stands with high canopy closure were

131

used to refine these methods and evaluate the results, the application of these techniques
to medium or low canopy closure condition should be undertaken with caution.

The brightest crown pixels, identified automatically by the methods presented in
this chapter, appear to be dominated by Spectral information specific to the cover type
they belong. Maximum likelihood classification of cover types based on those pixels is
capable of delivering a high classification accuracy (> 85%) that remarkably improves
(35% in this study) the accuracy obtained by traditional classification approaches that
operate on all pixels in a forested area. Experimentation with scenarios that involved
signature development and classification testing over varying geographic extents revealed
that this classification performance was robust, thereby allowing optimism for regional
applicability. Although computational loads currently restrict operational implementation
of the methods presented, it is expected that continuous improvements in computational
power would ultimately render the approaches investigated here useful for forest

inventory and management purposes.

132

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138

Tables

Table 3.1. Parameter values of linear regression models obtained by fitting plot stem
density values predicted via application of two image LMF processing techniques on
field measurements of stem density.

 

 

 

 

 

LMF using Variogram LMF using Slope Regr 688101?
Ranges Breaks parameter deviates
between techmques
Cover #of .5 E E" .5
Type plots 0 .2 § 2 0 93. 0 .93.
R2 3 g 48, 2% R2 3 g ,3 3:9 Slope Mean
"’ 8 E 8 m 8 m 8
o u u 0
ASP 7 0.744 0.773‘ 59.3 0.935 0.802“ 76.4 0.030 -34.14”
NH 7 0.947 0.844“ 63.7‘ 0.994 0.815“ 53.1“ -0029 18.71“
Oak 6 0.994 0.905“ 50.8“ 0.981 0.822“ 57.9‘ -0.083 14.67‘
RPP 7 0.994 0.770” 69.3“ 0.990 0.822“ 65.7‘ 0.052 -2771”
NP 7 0.997 0.826” 71.1“ 0.996 0.906” 34.4‘ 0.091‘ -8.14
All 34 0.986 0.741” 91.8“ 0.996 0.864“ 44.7“ 0.117“ -694‘

 

 

 

 

 

 

Significant at or = 0.05
Significant at or = 0.01

Table 3.2. Root Mean Square Errors (RMSE) or discrepancies, between stem density
values predicted via LMF image processing and corresponding field measurements. Stem
density is expressed in trees per hectare. Values in parentheses represent percent absolute
error from observed cover type mean of stem density.

 

 

 

 

L RMSE Values (stems/ha)
over Type # of plots . .
LMF usrng LMF usrng Slope
Variogram Ranges Breaks

ASP 7 71.84 (12.5) 37.39 (6.5)
NH 7 24.00 (8.5) 10.78 (3.8)
Oak 6 26.97 (10.2) 18.45 (7.0)
RPP 7 72.07 (1 1.9) 44.53 (7.4)
NP 7 30.22 (6.1) 17.67 (3.6)
All 34 50.67 (1 1.3) 29.06 (6.5)

 

 

 

 

 

 

139

Table 3.3. Parameter values of linear regression models obtained by fitting plot canopy

closure values predicted via tree apex identification using image LMF processing

techniques and crown delineation algorithms on field measurements of canopy closure.

 

 

 

 

 

 

 

 

 

. . . Regression parameter
LMF us1ng Vanogram LMF us1ng Slope deviates between
Ranges Breaks .
techmques
Cover #of ... ... .. ...
Type plots 0 .§ §§ 0 .§ .1, f2
R2 3‘ g g 5% R2 53% 3.5% Slope Mean
m 8 g 8 V’ 8 m 8
U U U 0
ASP 7 0.896 0 503" 49.8" 0.918 0.951” 4.2 0.448' 3.50”
NH 7 0.802 1.010“ -2.7 0.864 0.527” 40.9“ -0.483‘ .031
Oak 6 0.927 0.734" 17.5 0.981 0.81 1" 17.0’ 0.077 -522”
RPP 7 0.989 1.161“ -1 1.1 0.969 0.861“ 8.5 -0300" 4.90”
NP 7 0.953 1.098” -6.6 0.951 0.727“ 23.2‘ -0.371' -0.49
All 34 0.941 1.098” -7.7” 0.930 0.817“ 15.3” -0281“ 0.64

 

Significant at a = 0.05
. Significant at on = 0.01

Table 3.4. Root Mean Square Errors (RMSE) between plot canopy closure predictions
obtained using LMF image processing for tree apex identification and crown delineation
algorithms and corresponding field measurements. Canopy closure is expressed in

percent of plot area. Values in parentheses represent percent absolute error from observed
cover type mean of canopy closure.

 

 

 

 

 

 

 

 

 

RMSE Values (stems/ha)

Cover Type # of plots , . .
LMF usmg Vanogram LMF us1ng slope
Ranges breaks

ASP 7 3.51 (3.7) 0.99 (1.1)
NH 7 2.97 (3.3) 2.86 (3.2)
Oak 6 2.72 (3.7) 3.09 (4.2)
RPP 7 3.05 (3.7) 3.70 (4.5)
NP 7 2.62 (2.1) 3.28 (2.6)
All 34 3.00 (3.6) 2.93 (3.5)

 

 

140

Table 3.5. Parameter values of linear regression models obtained by fitting mean
crown diameter value estimates obtained via variogram and image morphology analysis

to corresponding diameter estimates derived from field observations. Image crown

delineation was based on LMF processing techniques and associated crown delineation

 

 

 

 

 

 

 

 

 

 

 

 

 

algorithms.
LMF using Variogram LMF using Slope Using mean variogram
Ranges Breaks range of subplots
Cover # of E ‘5. E E E- E E
T ltS Q)... 0'" 0.... Q... 0.... ..—
YP" 9° R2 88 88 R2 88 88 R2 .88 88
‘0 8 g 8 m 8 m 8 m 8 m 8
L) U U U U 0
ASP 7 0.706 0.952‘ 0.65 0.868 1.213“ -O.87 0.426 0.928 0.73
NH 7 0.870 0.750“ 1.25 0.962 0.843" 0.94 0.653 0.808‘ 1.01
Oak 6 0.913 0.823" 0.75 0.976 0.875” 0.68 0.964 1.272“ -1.59
RPP 7 0.545 0.976‘ 0.40 0.649 0.930‘ 0.31 0.840 1.237" -0.71
NP 7 0.935 0.758" 1.20 0.974 0.974“ 0.21 0.919 0.837“ 0.85
All 34 0.942 0.700“ 1.58“ 0.990 0.921“ 0.42‘ 0.921 0.847“ 0.91”
Regression Parameter Deviates between
LMF using Variogram LMF us1ng Vanog LMF using Slope Breaks and]
. Ranges and the Mean .
Cover Type Ranges and LMF us1ng . the Mean Vanogram Range
Vanogram Range among
Slope Breaks among Subplots
Subplots
Slope Mean Slope Mean Slope Mean
ASP 0.261 0.32” -0023 0.03 0.285 0.29“
NH 0.092 0.28” 0.057 -0. 13 0.035 -0.15
Oak 0.052 -0.24‘ 0.449’ -041‘ -0398‘ 0.17
RPP -0.046 0.28“ 0.261 0.03 -0307 0.25“
NP 0.216 0.00 0.079 -001 0.137 0.01
All 0.222” 0.02 0.148“ -009 0.074 0.1 1‘

 

 

 

 

 

Significant at a = 0.05
Significant at a = 0.01

141

 

Table
predic
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Table 3.6. Root Mean Square Error (RMSE) between plot mean crown diameter
predictions obtained i) via crown delineation based on image LMF processing using
variogram ranges, ii) via crown delineation based on image LMF processing using
directional Slope breaks, and iii) as the mean variogram range among subplots, and mean
crown diameter estimates derived from field observations. Values in parentheses
represent percent absolute error from observed cover type mean of mean crown diameter.

 

 

 

 

 

 

 

 

RMSE Values (%)
Cover # of _
Type PIOtS [QMF us1ng LMF using Slope Mean Variogram
anogram Breaks Range among Subplo
Ranges
ASP 7 0.43 (9.5) 0.33 (7.3) 0.42 (9.2)
NH 7 0.41 (6.4) 0.15 (2.3) 0.41 (6.3)
Oak 6 0.39 (6.3) 0.15 (2.4) 0.25 (4.1)
RPP 7 0.32 (7.7) 0.08 (2.0) 0.28 (6.8)
NP 7 0.18 (3.9) 0.12 (2.6) 0.18 (3.8)
All 34 0.36 (6.9) 0.13 (2.5) 0.32 (6.3)

 

 

 

142

Table 3.7a. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using Spectral Signatures
developed from pixels identified as representing apexes of individual trees (slope break
method) for subplots in sites I and II and original pixel DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

143

Observed
ASP Oak RPP NP Row Total
Aspen (ASP) l9 3 0 28
3 Northern Hardwoods (NH) 3 0 0 28
'8 Oak 17 0 1 23
8 Red Pine Plantation (RPP) 0 22 7 29
Natural Pine (NP) 1 5 20 28
Column Total 28 24 28 28 136
Accuracy (%) Errors (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 67.86 67.86 32.14 32. 14 0.00 100.00
NH 71.43 71.43 28.57 28.57 0.10 97.86
Oak 70.83 73.91 29.17 25.00 0.25 85.93
RPP 78.57 75.86 21.43 25.00 0.50 47.54
NP 71.43 71.43 28.57 28.57 0.75 26.68
Class Conditional Kappa
ASP 0.5952 Overall Accuracy (%) 0.7206
NH 0.6402 Kappa Coefficient 0.6503
Oak 0.6832 s2k 0.0015
RPP 0.6960 zk 16.5563‘
NP 0.6402 . Significant at a = 0.01

 

 

Table 3.7b. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters Obtained by using Spectral Signatures

developed from subplot pixels identified as representing apexes of individual trees (slope
break method) in Site I for subplots in Site I and original DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 12 2 1 0 0 15
E Northern Hardwoods (NH) 9 2 O 14
"'3‘ Oak 1 9 O l 11
8 Red Pine Plantation (RPP) 0 0 12 5 17
Natural Pine (NP) 0 0 4 10 15
Column Total 16 12 12 16 16 72
Accuracy (%) Errors (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 75.00 80.00 25.00 18.75 0.00 100.0
NH 75.00 64.29 25.00 41.67 0.10 97.8
Oak 75.00 81.82 25.00 16.67 0.25 85.9
RPP 75.00 70.59 25.00 31.25 0.50 51.1
NP 62.50 66.67 37.50 31.25 0.75 29.3
Class Conditional Kappa
ASP 0.7429 Overall Accuracy (%) 0.7222
NH 0.5714 Kappa Coefficient 0.6515
Oak 0.7818 82k 0.0029
RPP 0.6218 2.. 12.0627‘
NP 0.5714 ’ Significant at a = 0.01

144

 

 

Table 3.7c. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using Spectral Signatures
developed from subplot pixels identified as representing apexes of individual trees (Slope
break method) in Site II for subplots in site I and original DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 11 2 2 0 0 15
3 Northern Hardwoods (NH) 4 8 1 0 0 13
E Oak 0 2 9 l 12
'8 Red Pine Plantation (RPP) 0 0 0 12 4 16
Natural Pine (NP) 1 0 0 4 11 16
Column Total 16 12 12 16 16 72
Accuracy (%) Errors (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 68.75 73.33 31.25 25.00 0.00 100.00
NH 66.67 61.54 33.33 41.67 0.10 97.58
Oak 75.00 75.00 25.00 25.00 0.25 84.75
RPP 75.00 75.00 25.00 25.00 0.50 43.54
NP 68.75 68.75 31.25 31.25 0.75 20.03
Class Conditional Kappa
ASP 0.6571 Overall Accuracy (%) 0.7083
NH 0.5385 Kappa Coefficient 0.6341
Oak 0.7000 s2k 0.0030
RPP 0.6786 2.. 1 1.5934‘
NP 0.5982 ‘ Significant at a = 0.01

145

 

 

 

(‘lassificd

 

 

 

 

 

 

 

Table 3.7d. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral Signatures
developed from subplot pixels identified as representing apexes of individual trees (slope
break method) in Site II for subplots in Site II and original DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 9 3 2 0 0 14
E Northern Hardwoods (NH) 0 10 1 O 0 11
'5» Oak 0 9 0 0 12
5 Red Pine Plantation (RPP) O 0 0 9 3 12
Natural Pine (NP) 3 O 3 9 15
Column Total 12 16 12 12 12 64
Accuracy (%) Errors (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 75.00 64.29 25.00 41.67 0.00 100.00
NH 62.50 90.91 37.50 6.25 0.10 97.75
Oak 75.00 75.00 25.00 25.00 0.25 83.37
RPP 75.00 75.00 25.00 25.00 0.50 49.80
NP 75.00 60.00 25.00 50.00 0.75 24.46
Class Conditional Kappa
ASP 0.5604 Overall Accuracy (%) 0.7188
NH 0.8788 Kappa Coefficient 0.6492
Oak 0.6923 82k 0.0033
RPP 0.6923 2k 1 1.3649‘
NP 0.5077 ’ Significant at a = 0.01

 

 

146

Table 3.7e. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral Signatures
developed from subplot pixels identified as representing apexes of individual trees (Slope
break method) in Site I for subplots in Site II and original DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

147

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 9 4 1 O 0 14
3 Northern Hardwoods (NH) 1 10 3 O 0 14
'3‘ Oak 1 8 0 0 11
5 Red Pine Plantation (RPP) 0 0 9 3 12
Natural Pine (NP) 1 0 3 9 l3
Column Total 12 16 12 12 12 64
Accuracy (%) EITOYS (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 75.00 64.29 25.00 41.67 0.00 100.00
NH 62.50 71.43 37.50 25.00 0.10 97.91
Oak 66.67 72.73 33.33 25.00 0.25 85.02
RPP 75.00 75.00 25.00 25.00 0.50 42.06
NP 75.00 69.23 25.00 33.33 0.75 21.04
Class Conditional Kappa
ASP 0.5604 Overall Accuracy (%) 0.7031
NH 0.6190 Kappa Coefficient 0.6284
Oak 0.6643 0.0034
RPP 0.6923 10.7614‘
NP 0.6213 ‘ Significant at a = 0.01

 

 

Table 3.7f. Cross—validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral Signatures

developed from pixels identified as representing apexes of individual trees (slope break
method) for subplots in Sites I and II and brightness-normalized pixel DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

148

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 23 2 2 0 0 27
E Northern Hardwoods (NH) 4 25 2 O 0 31
'3} Oak 20 0 0 22
'5' Red Pine Plantation (RPP) O 0 25 2 27
Natural Pine (NP) 0 0 3 26 29
Column Total 28 28 24 28 28 136
Accuracy (%) Errors (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 82.14 85.19 17.86 14.29 0.00 100.00
NH 89.29 80.65 10.71 21.43 0.10 98.27
Oak 83.33 90.91 16.67 8.33 0.25 90.21
RPP 89.29 92.59 10.71 7.14 0.50 68.91
NP 92.86 89.66 7.14 10.71 0.75 53.00
Class Conditional Kappa
ASP 0.8134 Overall Accuracy (%) 0.8750
NH 0.7563 Kappa Coefficient 0.8435
Oak 0.8896 s2k 0.0008
RPP 0.9067 2.. 29.1529‘
NP 0.8697 . Significant at a = 0.01

 

 

 

Table 3.7g. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using Spectral Signatures developed
from subplot pixels identified as representing apexes of individual trees (slope break
method) in site I for subplots in Site I and brightness-normalized pixel DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 13 1 1 0 0 15
E Northern Hardwoods (NH) 2 10 l 0 0 13
'c'g’ Oak 1 1 10 0 0 12
5 Red Pine Plantation (RPP) 0 0 O 14 1 15
Natural Pine (NP) 0 0 0 2 15 17
Column Total 16 12 12 16 16 72
Accuracy (%) Errors (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 81.25 86.67 18.75 12.50 0.00 100.00
NH 83.33 76.92 16.67 25.00 0.10 98.28
Oak 83.33 83.33 16.67 16.67 0.25 90.73
RPP 87.50 93.33 12.50 6.25 0.50 68.96
NP 93.75 88.24 6.25 12.50 0.75 50.39
Class Conditional Kappa
ASP 0.8134 Overall Accuracy (%) 0.8611
NH 0.7563 Kappa Coefficient 0.8258
Oak 0.8896 82k 0.0017
RPP 0.9067 2.. 19.9145’
NP 0.8697 ’ Significant at a = 0.01

 

 

 

149

 

Table 3.7h. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures developed
from subplot pixels identified as representing apexes of individual trees (slope break
method) in site II for subplots in site I and brightness-normalized pixel DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

150

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) l4 1 l 0 0 16
3 Northern Hardwoods (NH) 2 10 1 0 0 13
"'3‘ Oak 0 10 0 1 l
5 Red Pine Plantation (RPP) 0 0 O 13 2 15
Natural Pine (NP) 0 3 14 17
Column Total 16 12 12 16 16 72
Accuracy (%) EITOFS (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 87.50 87.50 12.50 12.50 0.00 100.0
NH 83.33 76.92 16.67 25.00 0.10 98.2
Oak 83.33 90.91 16.67 8.33 0.25 89.0
RPP 81.25 86.67 18.75 12.50 0.50 61.6
NP 87.50 82.35 12.50 18.75 0.75 46.8
Class Conditional Kappa
ASP 0.8393 Overall Accuracy (%) 0.8472
NH 0.7231 Kappa Coefficient 0.8081
Oak 0.8909 8% 0.0019
RPP 0.8286 Zn 18.6765.
NP 0.7731 ‘ Significant at a = 0.01

 

 

Table 3.7i. Cross-validation—based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using spectral signatures
developed from subplot pixels identified as representing apexes of individual trees (slope
break method) in site II for subplots in site II and brightness-normalized pixel DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 11 1 1 0 0 13
3;; Northern Hardwoods (NH) 0 14 2 0 0 16
E Oak 0 9 0 0 10
is): Red Pine Plantation (RPP) 0 0 11 l 12
Natural Pine (NP) 1 0 1 11 13
Column Total 12 16 12 12 12 64
Accuracy (%) Errors (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 91.67 84.62 8.33 16.67 0.00 100.00
NH 87.50 87.50 12.50 12.50 0.10 98.44
Oak 75.00 90.00 25.00 8.33 0.25 89.85
RPP 91.67 91.67 8.33 8.33 0.50 66.80
NP 91.67 84.62 8.33 16.67 0.75 54.76
Class Conditional Kappa
ASP 0.8107 Overall Accuracy (%) 0.8750
NH 0.8333 Kappa Coefficient 0.8431
Oak 0.8769 s2. 0.0018
RPP 0.8974 zk 19.9988‘
NP 0.8107 ‘ Significant at ct = 0.01

 

 

151

Table 3.7j. Cross-validation-based Maximum Likelihood classification results and
associated accuracy assessment parameters obtained by using Spectral Signatures
developed from subplot pixels identified as representing apexes of individual trees (slope
break method) in site I for subplots in Site II and brightness-normalized pixel DNS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

152

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 10 2 1 0 0 13
E Northern Hardwoods (NH) 1 l3 1 0 15
E Oak 10 0 12
6 Red Pine Plantation (RPP) 11 2 13
Natural Pine (NP) 1 10 ll
Column Total 12 16 12 12 12 64
Accuracy (%) Errors (%) ML Probability Classified
Producer’s Consumer’s Commission Omission Threshold Pixels (%)
ASP 83.33 76.92 16.67 25.00 0.00 100.00
NH 81.25 86.67 18.75 12.50 0.10 98.37
Oak 83.33 83.33 16.67 16.67 0.25 88.25
RPP 91.67 84.62 8.33 16.67 0.50 64.72
NP 83.33 90.91 16.67 8.33 0.75 44.85
Class Conditional Kappa
ASP 0.7160 Overall Accuracy (%) 0.8438
NH 0.8222 Kappa Coefficient 0.8042
Oak 0.7949 s2. 0.0021
RPP 0.8107 zk 17.3489’
NP 0.8881 ‘ Significant at at = 0.01

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Table 3.9. Classification error rates of subplots conditional upon cover types group
(deciduous or coniferous) produced with maximum-likelihood based cross validation for
all plots in the Study area before and after brightness normalization using subplot pixels
identified as tree crown apexes. Apex identification was performed using slope break-
based imagery LMF processing.

 

 

 

 

 

 

 

 

 

 

 

 

As en Northern Oak Red Pine Natural
p Hardwoods Plantation Pine
. . Deciduous 7 (25%) 8 (29%) 6(25%) 1 (4%) 8 (4%)
Onglnal DNS
Coniferous 2 (7%) 0 (0%) l (4%) 5 (18%) 8 (25%)
Brightness Deciduous 5(18%) 3(11%) 4(17%) 0 (0%) 9 (0%)
normalization Coniferous 0 (0%) 0 (0%) 0 (0%) 3 (11%) 7 (7%)

 

154

 

Table 3.10. Change in class-conditional Kappa coefficients computed before and after
brightness normalization using tree apex Signatures.

 

Cover Original Brightness

 

 

 

 

 

 

Type DNS Corrected AKapp a
ASP 0.5952 0.8134 0.2182
NH 0.6402 0.7563 0.1 161
All subplots using Signatures from Site I and 11 Oak 0.6832 0.8896 0,2064
RPP 0.6960 0.9067 0.2107
NP 0.6402 0.8697 0.2295
ASP 0.7429 0.8134 0.0705
NH 0.5714 0.7563 0.1849
Site I subplots using Site I Signatures Oak 0.7818 03896 01078
RPP 0.6218 0.9067 0.2849
NP 0.5714 0.8697 0.2983
ASP 0.5604 0.8107 0.2503
NH 0.8788 0.8333 -0.0455
Site II subplots using site II signatures Oak 0.6923 0.8769 0.1846
RPP 0.6923 0.8974 0.2051
NP 0.5077 0.8107 0.3030
ASP 0.6571 0.8393 0.1822
NH 0.5385 0.7231 0.1846
Site I subplots using Site II Signatures 03k 07000 03909 0.1909
RPP 0.6786 0.8286 0.1500
NP 0.5982 0.7731 0.1749
ASP 0.5604 0.7160 0.1556
NH 0.6190 0.8222 0.2032
Site 11 subplots using Site I Signatures Oak 06643 07949 0.1306
RPP 0.6923 0.8107 0.1184
NP 0.6213 0.8881 0.2668
ASP 0.1754
NH 0.1287
Average across all five classification scenarios Oak 0.1641
RPP 0.1938
NP 0.2545

 

155

Table 3.11. Z-scores of subplot classification result comparison for combinations of
cross-validation-based classification scenarios, computed as standardized differences of
respective kappa coefficients. Associated p-values are in parentheses. Scores in bold
indicate significance at 01:0.01. Classification scenarios entailed signature development
using 1) all pixels in a subplot, and 2) pixels corresponding to subplot tree apexes
identified via slope break-based imagery LMF processing.

 

 

 

 

 

 

 

 

 

All pixels, All p1xels, Tree alpex
Original DNS Brightness .p 1xe 8’
normalrzatron Original DNS
All pixels
. ’ 0.7511
Bnghineis (0.4576)
normahzatron
Tree apex pixels, 5.5137 4.7196
Original DNS (0.0000) (0.0000)
Treggpi’t‘nggels’ 9.9054 9.0144 4.0285
g . . (0.0000) (0.0000) (0.0001)
normalrzatron

 

156

Figures

 

 

     

 

 

 

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8
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8 ar-
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N- .
+ Variogram Range
* Variogram Window Size
+ Mean Slope-Break Length
0 "' Slope Break Window Size
0 5 10 15 20 25 30
Cell Position along Transect

 

 

 

Figure 3.1. NIR band variogram ranges and mean slope-break lengths (circles) and
corresponding window sizes (squares) computed along a transect dissecting a northern
hardwoods subplot. Lines serve visualization purposes only.

157

 

 

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8
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I
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Cell Position along Transact

 

 

 

Figure 3.2. Original NIR band Digital Numbers (DN), DN-fit via local regression, and
pixel identified as Slope-break-length truncation locations, along a 30-pixel transect in a
Natural Pine subplot.

158

 

 

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0 Northern Hardwoods
8‘ Oak
Red Pine
Natural Pine
l Computed with Variogram Ranges
8- ‘ Computed with Slope Breaks
N — 1:1 Line
fl 1 l l l r
200 300 400 500 600 700

Observed Stem Density (trees/ha)

 

 

 

Figure 3.3. Observed vs. predicted stem density at the plot level for five forest cover
types. Stem density estimates were Obtained from tree apexes identified on NIR-band
imagery via local maximum filtering (LMF) with window sizes conditioned upon (a)
computed variogram ranges, and (b) mean Slope break estimates. Plot cover types are
color-coded while the LMF techniques employed are symbol-Shape-coded.

159

 

 

 

 

 

 

 

 

 

 

 

Figure 3.4. NIR band of an aspen subplot and tree apex locations identified by using
local maxiruum filtering with window sizes conditioned upon (a) computed variogram
ranges, and (b) mean slope break estimates.

160

 

 

    

 

 

 

 

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Natural Pine
l Computed with Variogram Ranges
‘ Computed with Slope Breaks
- 1:1 Line
0.
(O
I l l I l
60 70 80 90 100
Observed Canopy Closure (%)

 

 

Figure 3.5. Observed vs. predicted canopy closure for plots in five forest cover types.
Canopy closure estimates were obtained from crown delineation based on crown apexes
identified on NIR-band imagery by using local maximum filtering (LMF) with window
sizes conditioned upon (a) computed variogram ranges, and (b) mean slope break
estimates. Cover types are color-coded while employed LMF techniques are symbol-
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Natural Pine

v.

I Computed with Variogram Ranges
A Computed with Slope Breaks

- 1:1 Line

 

 

 

-
q

r
4 5 6 7

 

Observed Mean Crown Diameter (m)

 

Figure 3.6. Observed vs. predicted mean crown diameter for plots situated in five forest
cover types. Mean crown diameter estimates were obtained from crown delineation based
on crown apexes identified on NIR-band imagery by using local maximum filtering
(LMF) with window sizes conditioned upon (a) computed variogram ranges, and (b)
mean slope break estimates. Cover types are color-coded while employed LMF
techniques are symbol-shape-coded.

162

 

 

 

    

 

 

 

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Northern Hardwoods
Oak
Red Pine
Natural Pine

‘H - 1:1Line
I I T I
4 5 6 7

Observed Mean Crown Diameter (m)

 

 

 

Figure 3.7 . Observed vs. predicted mean crown diameter for plots situated in five forest
cover types. Mean crown diameter estimates were calculated as the mean range of
variograms computed using the NIR band Digital Numbers for every subplot in a plot.
Cover types are color-coded.

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Classified Pixels (%)

~ 0 Post Brightness Normalization
l Original DNs

— All subplots, signatures from both Sites
— Subplots in Site I, signatures from Site I
— Subplots in Site I, signatures from Site II
— Subplots in Site II, signatures from Site II
—' Subplots in Site II, signatures from Site I

 

 

 

0.0 0.2 0.4 0.6
Maximum Likelihood Probability Threshold

 

 

Figure 3.9. Percentage of classified pixels for various probability thresholds imposed on
cross-validation-based maximum likelihood classification scenarios of cover types prior
to and after imagery brightness normalization. Development of classification signatures
was based on pixels identified as tree crown apexes via slope break-based imagery LMF
processing. Lines serve visualization purposes only.

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CHAPTER 4

AN INVESTIGATION OF THE UTILITY OF SECOND ORDER TEXTURE FEATURES
FOR FOREST COVER TYPE CLASSIFICATION USING HIGH-SPATIAL-

RESOLUTION AIRBORNE DIGITAL IMAGERY

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Abstract

Image texture seldom has been used in forestry optical remote sensing applications, in
part because of the complexity associated with its quantification and in part due to the
absence of examples that substantiate its usefulness. In this chapter, a procedure based
on image intensity co-occurrence is presented that provides with a quantitative
evaluation of second order image texture features that carry discriminatory potential for
forest cover type classification purposes. Procedure development and evaluation is based
on two independent data sets and five common forest cover types present in the Midwest
region. Analysis results indicate that classification accuracies exceeding 60% can be
achieved by using only image texture information. In its current level of development,
procedure applicability may be limited because of substantial computational cost,
absence of computer software that could facilitate its automation, and the complexity of

methodologies integral to feature selection process.

4.1. Introduction

One of the better-known weaknesses of traditional remote sensing image
classifications approaches, including those discussed in Chapters 2 and 3, is their sole
reliance on the spectral response pattern at individual pixel locations (Chen, 1999). Many
other types of information could become available for classification purposes if the
methods for extracting that information from the imagery were not so fragmented and
poorly developed (Franklin et al., 2000). One of the promising alternatives to pixel-based
classification has been to consider classification of image data in a spatial context

(Khazenie and Crawford, 1990). The latter translates into either using information on the

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spatial variation of imagery tones independently or incorporating such information into
an existing, spectrally-based classification process. The premise in the second case is that
a pixel’s assignment to a class when viewed in isolation may change when viewed in
some context (Haralick and 100, 1986). Imagery derivatives that contain such contextual
information and describe spatial relationships between image entities are usually known
as textural features. Spectral and textural features are interdependent because, as pointed
out by Haralick et a1. (1973), .. texture and tone have an inextricable relationship to one
another . . .”.

An operational definition of image texture is challenging. It is generally regarded
as a quantification of the spatial variation in image tone values. A more precise definition
is complicated by the perceptual character of texture (Hay et al., 1996). Although
investigations in the field of machine vision have revealed that the use of texture
originates in the powerful, innate ability of humans to recognize textural differences, the
complex neural and psychological processes by which this is accomplished have, so far,
evaded detailed scientific explanation (Shapiro and Stockman, 2001).

Tone and texture are always present in an image, although one property can
dominate the other at times, depending on the smoothness or roughness of the objects
present, and on the image resolution relative to the surface roughness of each objects. If
tonal variation inside a limited spatial extent is relative small, spectral information will
dominate. Conversely, if tonal variation is large and presents meaningful structures, then
texture will be dominant (Haralick et al., 1973). In H-resolution imagery (Strahler et al.,
1986) depicting forested landscapes, the presence of pixels with smaller size than the

image footprint of a single tree crown, together with the complex horizontal and vertical

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structure of stand canopies, usually generate substantial tonal variability. In such cases,
the analysis of texture might be well suited to detecting and quantifying canopy structure
and cover-type variation across the landscape. One activity that routinely utilizes texture
information is the interpretation of aerial photographs, which allows experienced
operators to identify changes in the spatial distribution of forest vegetation (Hay and
Niemann, 1994). With the increased availability of H-resolution digital imagery from
airborne (Anger, 1999) and satellite platforms (Barnsley, 1999), it is expected that digital
texture will become an important information source for many other forestry purposes
(Green, 2000).

Insight into how texture might be analyzed digitally has focused on the structural
and statistical properties of textures (Haralick, 1986). Those (outlined briefly in the next
section) include first-order imagery statistics (e.g., standard deviation and variance),
second-order statistics, frequency domain of Fourier power spectrum, spatial
autocorrelation function (e.g., semivariance), and structural image features. In addition to
their value for classification applications (Lark, 1996; Ryherd and Woodcock, 1997),
structural and statistical texture properties of digital imagery have been used in forestry
as stand-pattern predictors (Coops and Culvenor, 2000), and for the qualitative
assessment of forest stand structure, age, density, and leaf area index (Cohen and Spies,
1992; Wulder et al., 1996, St-Onge and Cavayas, 1997; Franklin et al., 2001). A common
characteristic among the aforementioned texture-based forestry applications is that they
were developed using features defined a-priori. Because (as demonstrated below) most
texture measures include a substantial number of associated features, those best suited for

a particular investigation objective need to be identified using a systematic approach.

169

Unless there exists theoretical proof or experimental evidence that a particular feature, or
set of features, is optimal for a particular application, limiting one’s analysis to a
selection of features found to perform well in other applications, or for that matter to
those supported by a particular software package, will only fortuitously augment the
chances for exploiting the full potential texture has to offer for that application (Conners
and Harlow, 1980).

The objective of this chapter is to evaluate the utility of second-order texture
features derived from spatial co-occurrence matrices for forest cover type classification
of digital, high resolution imagery. More than 20 features were evaluated using
established feature selection strategies. Feature selection and classification accuracy
assessment was based on field observations within five forest cover types common in the

Midwest region.

4.2. Digital imagery texture measures

The main texture recognition measures can be categorized into four groups. The
first approach defines texture features that are derived from the Fourier power spectrum
of the image via frequency domain filtering. Because different textures demonstrate
different frequency patterns, it is reasonable to postulate that texture features are related
to the distribution of spatial frequency components. The second approach is based on
statistics that measure local properties that are thought to be related to texture, such as the
mean or standard deviation of pixels values within a neighborhood. The third, and by far
the most common, approach used in forest remote sensing applications, is the use of the
joint gray level probability density (Haralick et al., 1973). The final approach is based on

modeling the image using assumptions (e. g. that the image being processed possesses

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fractal properties (Mandelbrot, 1982; Agterberg and Cheng, 1999)) or can be modeled

using multiplicative, autoregressive random fields (Frankot and Chellapa, 1987).

4.2.1. Co-occurrence-based texture measures

The widely used co-occurrence methods attempt to characterize the second-order
properties of an image. Co-occurrence can be regarded as the relative frequency, or joint
probability, of image properties, occurring under predefined constraints. Pixel intensities,
usually expressed in Digital Numbers (DNS), intensity variance, or intensity gradient are
the image properties commonly used. These can be measured under such constraints as
pixel spacing, both in magnitude and orientation, or other higher-order neighborhood
definitions, for example windowing. Co-occurrence is typically represented in the form
of a matrix. Gray Level Co-occurrence Matrices (GLCM) (Haralick, 1973) represent the
probability of co-occurrence of image pixels intensities i and j, under the spatial
constraint of d pixels separation between the pixels. Other forms of co-occurrence
measures included the Gray Level Run Length Matrix (Galloway, 1975), the Statistical
Feature Matrix (Wu and Chen, 1992), the Neighboring Gray Level Dependence Matrix
(Sun and Wee, 1983), and the Generalized Co-occurrence Matrix (Davis et al., 1979).

The GLCM of an Ng gray-level (i.e., single band) image on a domain DCZ2
models the image as a 2D function I : D —> G, where G={l, ..., Ng}. The GLCM element
P(i,/' | d,6) is an estimate of the second-order joint probability density function of gray-
level pairs within the image. Each matrix element is an estimate of the probability that
two image pixels, separated by a displacement vector of magnitude d and orientation

angle 6, have intensities i and j, where i and j e G and

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#{k,leD|I(k)=i, 1(1):]; ||k-I||, z(k—z)=0}

(4.1)
#{m,n EDI ||m-n ||=d, A(m-n)=6}

 

P(i,j|d,t9)=

where # is read as ‘number of (pixels)’, .4 is read as ‘angle between two pixel centers’,
H M denotes displacement vector magnitude or Euclidean distance between two pixel
centers, and k, l, m, and n are valid image pixel locations. Because of the discrete nature

of digital image intensities, P is, in fact, a discrete density rather than a continuous one.

Therefore, for any given d and (9,

ZPO'J) | dfl) =1 (4.2)
I"!
and
Vi,jeG, 0.<.P(i,j|d,6)$l (4.3)

As an example, Figure 4. la shows a gray-scale (or level) image with a range of
intensities from 1 to 4 and, for simplicity, the pixel-pair counts (the numerator of
equation (4.1)), rather than probability estimates. The upper left entry in the GLCM
computed for d=1 and (9:00 (Figure 4.1d), has a value of 2, which represents the number
of times a pixel with intensity equal to 1 has an immediate neighbor to the right with
intensity also equal to 1. Note that angular displacements are measured in a Cartesian, not
geographic, coordinate system and that the distance measures are usually expressed in
pixel increments in image row and column indices rather than true geometric quantities.

In the later case and for adjacent pixels with angular displacement of 450 or 135°, d=1 is

used although the true distance separating them is actually J5 . This often necessitates
proper scaling of the true distance between pixels to integer values, particularly when the

length of the displacement vector is determined by spatial investigations (e. g., variogram

172

analysis). A comparison of Figures 4.1e and 4.1 g shows that different 6 ’s can produce
markedly different GLCMS. Note also that GLCMS can be computed for multiple angles
or ranges of angles (Figure 4.1h, 4.1i) and that simultaneous consideration of opposite
angles (6 and 6+7r) does not, in general, produce the same matrix, i.e.

P(i, j | d, 6) at P(j,i | d, 6). In the latter case, isometric matrices (Figure 4.1i) are often
formed by averaging the matrices calculated for opposite angles.

In addition to pixel displacement parameters d and 6 , co-occurrence texture
analysis procedures require the user to specify the level of requantization the original
imagery has to undergo (3-bit, 4-bit, other), and, in the presence of multispectral imagery,
the band(s) whose texture is to be evaluated. Most contemporary sensors offer 8-bit or
higher radiometric (data) resolution, which is prohibitively fine for GLCM computations.
Indeed, if an original imagery resolution of 8-bit (Ng=28=256) were to be used, the
resulting GLCMS would contain Ng2 (=65,536) elements. A radiometric resolution of 16-
bit would necessitate a matrix with approximately 4.3"‘109 elements. In addition to
considerations related to computation load, such large matrix dimensionalities would
seriously compromise the ability to derive meaningful and class-discriminatory texture
features due to the large number of empty, or zero-value, matrix elements present
(Conners and Harlow, 1980). Image requantization to a lower data resolution, sometimes
known as image (radiometric) compression, can be performed either linearly or by using
histogram equalization (Conners and Harlow, 1978). Other available techniques are less

attractive because they require user intervention.

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4.2.2. Gray Level Co-occurrence Matrix features

Information is extracted from GLCMS via secondary feature functions.
Approximately 20 such features appear in the literature (Table 4.1) (Haralick et al., 1973;
Conners et al., 1984). These can be grouped into four main types: 1) measures of an
image’s statistical properties; 2) measures of an image’s visual characteristics; 3)
measures based on information theory; and 4) measures of information based on
correlation. Many of these secondary features are derived by weighting each of the co-
occurrence matrix element values, and then summing these weighted values to form the
feature value. The weighting applied to each element is based on a feature weighting
function, so by varying this function, different texture information can be extracted from
the matrix. Table 4.1 lists the weighting functions as coefficients of matrix element
values P(ij) in the equations used to compute matrix features. Matrix element weighting
functions fall into two main categories: 1) Weighting based on the element’s value, and
2) weighting based on the spatial position of the element. A graphical representation of
feature-specific weighting functions is provided in Figure 4.2.

Because matrix features are secondary image derivatives, their interpretation is
occasionally somewhat less than intuitive. The value of feature inertia, often referred to
as contrast, for example, increases with the frequency of adjacent bright and dark pixels
and decreases when image intensity is strongly autocorrelated. Weighting is reversed in
the Inverse Distance Moment feature weighting scheme which produces higher values for
images that contain gradual DN changes. Feature energy, sometimes known as angular
second moment, will be larger 11 non-zero matrix elements are concentrated in one or a

few portions of the GLCM with a relatively large proportion of the total matrix being

174

either zero or near zero. The presence of patches of uniform intensity in the image would,
therefore, produce larger energy values while images with a ‘salt and pepper’ appearance
yield low energy values. These latter images, however, would be rich in entropy. It
should be noted that texture feature values are strongly dependent on the relationship
between pixel and object sizes. An image depicting a corn field just prior to harvesting,
for example, would likely be of high entropy if acquired with 0.3m resolution, but of low

entropy if acquired with 1.0m spatial resolution.

4.2.3. Image classification using GLCM features

It is evident from the discussion above that imagery classification using co-
occurrence-based approaches tends to generate large amounts of intermediate texture
information products. The analyst can often be confronted with as many as 50 pixel
displacement vectors (d, a used in GLCM construction, 5 or more spectral bands, 6 or
more image band requantization and compression procedures, and more than 20 possible
features extracted from each co-occurrence matrix. Exploring all these analysis choices
would produce more than 10,000 variables, which would, most likely, overwhelm even
the most sophisticated classifier. In addition, such an expansive set of choices would
require a very large and expensive data set for classifier training. The term ‘classifier’
here is used to denote a rule, or set of rules, which assigns (or allocates) each unknown
pixles to one and only one by using information from one or more attributes (features).

Visual analysis of texture displays has been used to understand the way in which
class texture represents differences in the imagery (Franklin and Peddle, 1990) and thus
to reduce the number of processed texture variables. Obviously, this approach is of

limited utility in the presence of a large number of texture displays. The number of

175

GLCMS assumed to be capable of producing texture features useful for class
discrimination can potentially be reduced via 1) investigations based on information
theory; adoption of multi- rather than single-angular pixel displacement vectors (Sun and
Wee, 1983), or 3) feature selection statistics to identify the optimal texture features for a
particular classification application.

GLCM ranking in terms of information content can be used to select the
displacement vector that has the potential of maximizing the discriminatory power of the
derived texture features (i.e. texture features with similar values for objects of the same
class membership, but with different values for objects of alternate classes). In that
regard, each co-occurrence matrix can be treated as a contingency table formulated by
two variables A and B, containing a and b classes respectively. If variables A and B are
interpreted as pixel intensities at either end of the displacement vector (d, 6), and the
classes into which they fall as the N . gray levels, then the correspondence between a
GLCM and a contingency table becomes clear. Texture information conveyed by co-
occurrence matrices, is related to the strength of the statement that can be made about
intensity level i given observations about intensity level j (and vice versa). If image
texture is highly structured and the co-occurrence matrix is capable of capturing that
structure, then observations i should bias the probability of observing various j intensity
levels. If, on the other hand, structure is not captured, then observations about i will not
influence the probabilities of j, and i and j should be considered independent. Hence, the
amount of image structure, or texture, conveyed by a co-occurrence matrix depends on

the choice of i and j, and therefore is a function of (d, 6).

176

A quantitative measure of this structure can be obtained by hypothesizing that the
variables i and j in a co-occurrence matrix are independent, and then using a chi-square
goodness-of-fit test to determine the degree to which this hypothesis can be rejected by

the image pixel intensities. In the presence of texture in an image, the statistic

 

re.

2 N N (xij—IJN)2

Z =:: ’r.c. (4'4)
i j I%

calculated for each GLCM computed from that image would follow a chi-square

distribution with (Ng-l)2 degrees of freedom, provided that the sum of matrix element
values N is sufficiently large (Zucker and Terzopoulos, 1980). In equation (4.4), x
represents the pre-normalized (numerator of equation (4.1)) matrix element values and r
and c represent matrix row and column sums, respectively.

In images of forested landscapes, it is possible, although rare, that one or more
gray levels is absent, especially for images with a small number of pixels, resulting in
matrices with one or more columns and rows composed exclusively of zero-value
elements. For such images, an adjustment of degrees of freedom for the ,1; statistic is
necessary, so that p-values associated with the image intensity independence test
mentioned above can be compared. Details on how such adjustment may be performed
are provided by Zucker and Terzopoulos (1980). More ofien, different displacement
vectors would result in a varying number of zero-value matrix elements. In the examples
of Figure 4.1d-g, although no zero-valued columns or rows exist, 8 or 9 elements do have
a zero value. In such circumstances, the influence of these elements on the ability to

identify structure via co-occurrence computations can be accounted for by a f-statistic

177

normalization known as Cramer’s V coefficient (Cramer, 1946). An illustration is
provided in Figure 4.3a, which depicts a IOOXIOO, 4-bit image with a regular (geometric)
texture, exhibiting a repeated 10x10 pixel pattern, sometimes known as a ‘texton’. For

this image, 20 GLCMS were computed using incremental pixel displacement distances

and, for simplicity, O0 angular displacement. Cramer’s V coefficients computed for these
20 matrices have an absolute maximum at d = 10 and local maxima at d = {5, 15, 20}
(Figure 4.3b), which indicates that the matrix information content quantified via the
statistic in equation (4.4) is capable of detecting texton sizes and therefore can be useful
in identifying the proper pixel displacement vector for co-occurrence-based
investigations of texture.

Even when there is confidence that the proper displacement vector was used in
co-occurrence matrix construction, the large number of features than can be extracted
from the matrix for use in the classification process can compromise the classification
accuracy achieved, were all features to be used by the classifier, unless a very large data
set is available for classifier training (Silverrnan, 1986). This is known as the Hughes
phenomenon (Hughes, 1968; Shahshahani and Landgrebe, 1994) or sometimes also
referred to as the ‘curse of [feature] dimensionality’ (Bellman, 1961). The Hughes
phenomenon can be shown by a simple example: Let X denote a two-dimensional,
normally distributed vector and let the two-dimensional measurement vector x, where x =
[x 1, 29] represent 100 realizations of random variable X. The histogram of the first variate
x; = [Xu, , xmoof, representing the extraction of one feature, is shown in Figure 4.4a.
Note that the expected frequency for each of the 10 histogram bins is on the average 10

(=100/ 10), and that the histogram shape is an adequate approximation of the true

178

underlying distribution from which the realizations were extracted. The second variate x;
= [Xu, , xz,]00]T, represents the extraction of a second feature. It is now necessary to
estimate the new two-dimensional histogram containing 100 bins, with only the original
number of (now 2-D) data points. The second histogram, shown in Figure 4.4b, contains
many empty bins and all other bins have very low counts. On average, there is only

100/ 100 = 1 measure per bin. Therefore, the more features extracted, the more inaccurate
the estimate of the underlying multivariate distribution becomes.

For classification purposes, where an unknown texture is to be allocated to one of
several classes, it is important to accurately estimate the underlying class-conditioned
feature distributions. While it would be desirable to extract only a minimal number of
‘useful’ secondary features (i.e. those whose class-conditional distributions exhibit
statistical differences between classes), it is usually not known a priori which features
will be useful. It is common practice to use all of the secondary features and subsequently
reduce the resulting high-dimensional feature space using discriminant analysis and
feature selection techniques. Such practice allows a more accurate estimation of the true
distribution of features for each class based on the limited training data available.
Reducing feature set dimensionality usually involves removing those features that
provide little or no extra information to distinguish between texture classes either because
they are correlated to other features or because their discriminatory power is very low.
However, an increase in the number of features that need to be evaluated as candidates to
participate in a classifier, results in an exponential increase in the number of possible
feature combinations to be evaluated in the process. In the presence of 20 features, the

number of possible combinations exceeds 1 million! Even if the optimal feature subset

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dimensionality for classifier development is known a priori, say 4, there would still be
4,845 [= 20!/((20!-4!)4!] feature combinations to be evaluated.

While the performance of a classifier is best evaluated by computing its
classification error rates (McLahlan, 1976; Habbema and Herrnans, 1977), computational
considerations necessitate alternative strategies. One such alternative is to use class-
separability measures to estimate classification error rates. These measures attempt to
assign a figure-of-merit to a feature, based on how ‘dissimilar’ the class-conditioned
distributions of the feature are. One measure of dissimilarity is the amount of overlap
between the class-conditioned distributions, with less overlap meaning more
dissimilarity. Other measures quantify the separation between the distributions,
normalized by the variance of each distribution. The second category of measures operate
on the assumption that the greater the distance between class-conditional density
functions, the less is the overlap among the density functions in feature space, and the
smaller the probability of classification error becomes. Many probabilistic distance
measures have been defined in the literature including the Mahalanobis (1936),
Bhattasharyya (1943), Chemoff (1952), and Matusita (1956). Their use allows searching
for an optimal subset of features from a pool of possible candidate features that are
believed to maximize the discriminatory power of the feature set. Various strategies have
been suggested for restricting the search to a smaller number of ‘good’ feature subsets.
The three most popular are ‘forward selection’, ‘backward elimination’, and ‘stepwise
selection’. Details on their structure and implementation can be found in Kittler (1986).
Although these procedures reduce the computation load significantly and provide viable

feature selection schemes, they may not identify the globally optimum subset that would

180

be ‘uncovered’ by an ‘all-subsets’ search. Detection of the global optimum subset is
guaranteed, albeit computationally costly to implement, by a procedure known as the
branch-and-bound algorithm (Yu and Yuan, 1993).

The identification of the optimal feature subset is followed by the development of
the classifier, which is used to assign previously unseen objects or observations to a class
using the selected features. Most classifiers, including the popular linear and quadratic
discriminant functions, are parametric mathematical rules with Bayesian structure. As
such, they assume that the class-conditioned feature data are multi-variate normal.
Quadratic discriminant functions are more sensitive than linear functions to departures
from multi-variate Gaussian distributions in high-dimensional feature spaces
(Lachenbruch, 1975; Seber, 1984). However, it is known that quadratic discriminant
functions are robust against minor departures from normality (McLachlan, 1992). Also,
because they are capable of exploring inequalities in the class-conditioned covariance
matrices (linear functions assume equal covariance matrices among classes), they can
improve the definition of decision boundaries compared to linear discriminant functions,
thus leading to the possibility of lower classification error. Figure 4.5 presents an
illustration of decision boundaries obtained by linear and quadratic discriminant functions

fit in a two-class data set using two features.

4.3. Methods

4.3.1. Study Site Characteristics and Imagery Description
The study area comprises two sites, the one in the south-central part of Grand
Traverse County (Site I) and the other in the northern part of Wexford County (Site 11),

Michigan (Figure 2.1). Note that figures in this dissertation oflen contain color. The sites

181

are separated by about 10km in the northwest-southeast direction and extend over 8,805
and 12,626 hectares of land, respectively. More than half (5 6%) of the study area is
owned and managed by the Michigan Department of Natural Resource. Most of the study
area consists of forests and wetlands (82%), while agricultural use, mainly row crops,
represents 8%. Other land use classes include orchards (4%) and residential areas (4%).
Residential development is concentrated in the northwestern part of site I. Geomorphic
features include moraines and outwash. The average slope, calculated by using the finite
differences algorithm on a 10m, l:24,000 USGS Digital Elevation Model available for
the area is 3.5% and 2.7% for sites I and II respectively. Relief is more prominent along
the Manistee River, which crosses site II from northeast to southwest.

The study area is characterized by pronounced spatial heterogeneity of forest
cover types. The majority of the forest cover types extant in the northern Lower
Peninsula of Michigan are present in the forested part of the study sites. These include: 1.
Aspen, consisting of Big Tooth (Populus grandidentata) and Quaking (Populus
tremuloides) aspen; 2. Northern hardwoods, consisting primarily of Sugar Maple (Acer
saccharum), Red Maple (Acer rubrum), American Beech (Fagus americana), Black
Cherry (Prunus serotina), Basswood (T ilia americana) and White Ash (F raxinus
americana); 3. Oak, consisting of White (Quercus alba) and Red (Quercus rubra) oak; 4.
Natural Pine, mainly White Pine (Pinus strobus); 5. Pine plantations consisting primarily
of Red Pine (Pinus resinosa); and 6. Cedar swamps dominated by Northern White Cedar
(T huja occidentalis). The main forest management objectives of the MDNR include

timber production, enhancement of wildlife habitat, recreation, preservation of aspen, and

182

riparian best management practices. Several private land owners offer a network of tracts
used seasonally for horseback riding and snowmobiling.

The imagery data set used in this study was acquired on August 11, 1999, using
the Digital Airborne Imaging System (DAIS [Space Imaging, 1999]). It contains four
bands, three in the visible and one near infrared that were acquired by frame (digital
array) cameras equipped with appropriate band-specific filters in a 2x2 arrangement.
Appendix 1 contains detailed information on the technical specifications of the system
(Table A. 1), flight line orientation, and the spatial arrangement of frames in each study

site (Figure A.1).

4.3.2. Field Measurements

Two sets of field measurements were obtained. In the first set a total of 34 plots,
16 in site I and 18 in site II, were installed in the study area stratified across the major
forest cover types present with the exception of cedar swamps that were excluded due to
accessibility issues. Plots were allocated on level land, within homogeneous stands, and
away from cover type ecotone zones. Stand homogeneity was evaluated with field
inspections. A minimum 60% canopy closure threshold was imposed by the MDNR as a
selection criterion. All plots were situated within the inner quarter area of the associated
image frame, resulting in plot-center view angles less than 10°. Field measurements were
obtained in the summer of 2,000, exactly a year after the acquisition of imagery,
following the FIA/F HM field protocols (Appendix 1, Figure A.2). Subsequent to their
allocation, plot and subplot centers and subplot boundaries were precisely georefenced to

image coordinate systems using field survey techniques. All spatial data were organized

183

as geographic information system (GIS) layers translated into the image coordinate
system. Details on the methodologies employed are available in Chapter 2.

The second set of field observations was independent of the first and contained
cover type and canopy closure data obtained by visual inspections for a total of 112
point-locations (60 in site I and 52 in site II), with no more than one location in a given
forest stand, and no locations in stands with a plot from set one. Twenty two locations
were in Aspen, 26 in Northern Hardwoods, 19 in Oak, 24 in Red Pine Plantations, and 21
in Natural Pine. As in the first set, all point locations were situated away from cover type
ecotone zones and in homogeneous stands with canopy closure exceeding 60%.
Locations were georeferenced using differential Global Positioning System technology.
Their geographic coordinates were translated to image coordinates via manual image
frame georeferencing using leaf-on and leaf-off, 1:12,000 scale Digital Ortho
Quadrangles (DOQs) available for the study area (Michigan Department of Natural

Resources, 2001) and nearest neighbor pixel interpolation.

4.3.3. Image Pre—processing
Image frame regions composed of pixels whose center was within a subplot’s
boundary were extracted from the frame and compressed to 4-bit data resolution using

equation (4.5),

, DN (x, y) — DNmin
V(x,y), I (x,y) = floor{ DN _ DN —15.999} +1 (4.5)

 

where the coordinate pair (x, y) is a valid image region pixel, I ‘(x, y) is the requantised
(or compressed) value of the DN of the pixel at (x,y), and the function floor() reduces a

real-valued quantity to the largest integer lower than the function’s argument. The

184

addition of 1 results in a requantised intensity range of I ’(x, y) e {1,...,l6 } and allows

intensity level ‘0’ to indicate background pixels not to be processed. Linear
requantisation was also used to compress circular, 30-pixel-diameter image regions
centered on each of the 112 locations mentioned. Note that during image requantisation,
any brightness discrepancies among frames or frame regions known to affect spectrally-
based image analyses (Chapters 2 and 3) are eliminated, provided that any brightness
variability originates from linear changes in sensor sensitivity or gain during image
acquisition. Comparison of requantized imagery region histograms prior to and after
correcting for brightness variations among frames revealed no differences.

A popular alternative to linear quantization, known as histogram equalization, was
not considered here, because it produces a flat histogram. Maintaining histogram shape
(guaranteed when using linear requantization), is important, because it ensures that the
second-order probability statistics that are used subsequently in this study, and which are

constrained by first-order probabilities, are not modified.

4.3.4. Band selection, co-occurrence matrix development, and texture
feature selection

The large number of possible combinations of pixel displacement vectors than can
be used in the construction of co-occurrence matrices and of the features that can
subsequently be computed from these matrices, increases further in the presence of
multispectal imagery. This necessitates an early evaluation of the potential each of the
three factors (number of bands, texture features, and displacement vectors) possesses in
supporting cover type classification endeavors. In this research, such an evaluation was

performed using imagery texture information at the l 12 locations with known forest

185

cover type. The same information was subsequently used for training a classifier
operating on the derived texture features. The accuracy of the resulting classification
procedure was estimated using information from the 134 subplots installed in the study
area.

Early investigations, including visual and quantitative (Cramer’s V) texture
evaluations, revealed that the spectral collinearity known to exist among bands in the
visible portion of the spectrum is also evident in the GLCMS computed from them. Paired
T-tests of texture feature values obtained from matrices generated using various
displacement vectors showed no significant differences among visible bands. Texture
feature value differences between the visible bands and the NIR band were significant at
or=0.05 for approximately 1/3rd of the features tested. On this basis two of the visible
bands (blue and red) were eliminated from further consideration.

Based on findings from experimentation with various single-direction
displacement vectors, it was decided to proceed with multiple direction vectors of the
form (d, {135+7r, 0, 45, 90}) shown in Figure 4.1h. Although there are obvious
differences in the structure of GLCMS computed using the same d, but different 6for
small images or frame portions (Figure 4.1), these differences practically disappear in
images depicting forested landscapes containing more than 300-350 pixels and they were
found to persist among different d’s. Matrix information content was evaluated by

computing corresponding Cramer’s V coefficients for all 6 6 [1,10]. Texture feature

evaluation was restricted to matrices that maximized information content.
A series of Hawkins (1981) tests performed using various combinations of texture

features derived from the matrices that exhibited the highest information content showed

186

that, in general, the distribution function for each of these combinations could be
considered multivariate normal. As a result, no feature value transformations towards
normality were attempted. The optimal feature subset for cover type classification based
on imagery co-occurrence derivatives was identified using the branch-and—bound
algorithm by Yu and Yuan (1993). The algorithm was implemented using the
Bhattacharyya metric to quantify distance between class-conditional densities. This
metric was selected because of its ability to provide robust estimates when the feature
distribution is Gaussian, or near-Gaussian, form. The metric is of non—parametric form

and is computed as (Bhattacharyya, 1943)

 

D8 = -log [fix la)l )...(p(x lwc )dx (4.6)

where x = [x1, ..., xNU] represents a set of NU candidate feature vectors, p(x|a)g) is the
class-conditional probability density of x for class ax, and c is the number of classes

present. When the class-conditional distributions of the features are known and of

Gaussian form, equation (6) can be expressed for two classes as

1
1 T l 1] 1'2-(2|+22)l
D =_ — 2: +2 ‘ - +—o 4-7
B 404, #2)[, 2104, #2) 2 g lelllzzl ( )

 

where ,u,- and 2,- are the mean vector and covariance matrix of x for class i, and IZI
represents the determinant of 2. In the presence of more than two classes (5 in this
research), the metric value is estimated as the average of all pair-wise combinations.
Following identification of the optimal feature space, the classification rule based on a
quadratic discriminant function was developed. The decision boundaries imposed onto

the feature space generated 5 multidimentional regions. Using the texture feature set

187

identified in the previous step, each of the 134 subplots was then assigned to the cover

type class k that maximized the quantity

 

—-1—xT(2_'-2"')x+( Tz“- T2:“)x—V (48
2 k I ”k k ”I l )
where
V-ll lzkl 1 Tr." T2“ 49
—3n '2' +—2-(flk kflk—fll (”1) (')
l

and 1 denotes any of the remaining c-l classes. Note that equation (8) assumed that
misclassification cost and prior probabilities were equal among classes. Classification
accuracy estimates were derived from confusion matrices and associated indicators
(percent of subplots correctly classified and kappa coefficients) (Congalton, 1991). Image
compression, GLCM computations, feature extraction and optimal subset identification,
and classifier training and testing were all implemented using scripts developed in C
programming language, interfaced with Splus (Mathsofi, 2000) and Matlab (MathWorks,

1999) sofiware in a Unix operating system.

4.4. Results and Discussion

As demonstrated already in Figure 4.3, co-occurrence matrices are capable of
identifying the size of textons or patterns in digital images characterized by a regular
texton arrangement. Assuming that the crowns of dominant and co-dominant trees in
forested landscapes could be perceived as scene textons, it could be expected that co-
occurrence matrices would capture scene texture characteristics and yield higher
information content estimates when computed for pixel displacement vectors

approximating in magnitude the size of tree crowns present. Contrary to expectations

188

though, analysis results indicated that, in imagery covering forested land, as the
magnitude of pixel displacement distance increases, the information content of the
resulting GLCMS, as quantified by Cramer’s V statistic, decreases sharply for d > 1
(Figure 4.6), and fluctuates very little thereafter, even in stands where tree arrangement is
regular (e. g. red pine plantations). Matrix elements with higher values were generally
concentrated along the main matrix diagonal for d = l, but formed a roughly circular
cluster for larger distances. Figure 4.6 shows that d = 1 produces GLCMS with four times
the information content of those produced with d > 1.

This somewhat unexpected finding prompted an investigation that involved
construction of artificial surfaces in which either 1) a texton of set size was repeated
randomly at varying spacing or 2) a texton of variable size was repeated at a set distance.
Both cases produced GLCMs with information content patterns similar to those in Figure
4.6. As a result, it was concluded that the absence of strict regularity in tree-crown
arrangement in forest stands causes a reduction in the ability of GLCMS produced using
d .>_ 2 to capture textural differences pertinent to stand structure conditions and cover type
affiliation. Note that this result should not be perceived as contradicting earlier research
findings (e.g., Franklin et al., 2000) which concluded that quantified imagery reflectance
autocorrelation is useful in texture-based investigations. Those studies focused on the
mean value and variance of image intensity which are first-order imagery properties
while co-occurrence features explored here are second-order image properties.

The ability of multispectral, optical imagery to contribute in co-occurrence-based
forest cover type classification endeavors can be seriously affected by the analysts’

choices in the imagery requantisation process. When linear compression is employed

189

during imagery pre-processing, the presence of exposed soil in canopy openings or other
spectrally bright targets within the forest stand, and the skewed-to-the-right intensity
histograms they produce for the visible bands, confine vegetation related pixel intensity
values i and j along the upper left 1/16‘h (i, j S 4) of co-occurrence matrices computed for
those stands. Under such circumstances, there is practically no variability in the structure
of the matrices and texture features derived regardless of the cover type. Masking of non-
vegetative scene components via Normalized Difference Vegetation Index (N DVI) or
other band ratioing techniques prior to linear compression should be considered a
necessary step in stands with medium or low canopy closure conditions or where
presence of illuminated non-vegetation objects is suspected. Because the symmetry of
NIR band intensity histogram is affected very little by reflectance regimes in and around
canopy openings, co-occurrence matrices computed for that band are free from
systematic bias in the distribution of intensity values present in them, thus rendering band
pre-processing with NDVI filters redundant.

By observing the typical GLCMs computed for each cover type using pixel
displacement distance d = l and multidirectional angular displacement (Figure 4.7), it
appears that co—occurrence matrices can indeed be useful cover type discriminators, at
least for the five types investigated. Visual matrix structure comparisons indicated that
there might be some confusion between oak and red pine plantations, although the former
exhibited a stronger intensity value concentration along the matrix diagonal. Northern
hardwoods and natural pine stands showed higher probabilities for certain combinations
of high (>12) intensity values, but for the latter cover type the percentage of darker tones

was higher. This is probably due to the more extensive shadowing between adjacent

190

crowns. Aspen showed a concentration of matrix element values around mean intensity
levels, characteristic of smooth canopies. However, the assessment of matrix structure
separability among cover types must be substantiated in a quantitative form, such as the
one offered by matrix-extracted feature values.

The brand-and-bound algorithm identified 4 features (energy, entropy, inertia, and
homogeneity), all pertaining to the NIR band, as comprising the feature subset that
provided the highest discrimination of cover type. When forced to identify only two
features, the algorithm selected energy and inertia. When it was set to identify the three
best features, it selected energy, inertia, and entropy. However, both of those smaller sets
yielded a higher value for the mean Bhattacharyya metric, indicating that they are sub-
optimal to the 4-feature set. Enforced feature set expansion resulted in the selection of
shade and then second diagonal moment, both for the NIR band. It required a feature
dimensionality of 8 for a green band feature to be included (as last) in the set. When NIR
energy, entropy, inertia, and homogeneity were excluded, green energy was included as
the 3rd feature, in a 3-dimensional feature set, behind NIR shade and NIR second diagonal
moment. It is evident, therefore, that texture features computed using visible band
imagery are inferior, in terms of cover type discriminatory power, compared to features
computed using the NIR band. An important consideration here is that it might be
inappropriate to label the discriminatory power of a feature as higher than that of another
feature simply because it is present in a 5-feature optimal subset while the other feature is
not. This is especially true when other features generated with the same type of value
weighting mechanism are already included in the optimal subset. This is because co-

occurrence matrix features are not orthogonal, and therefore feature correlation can

191

influence the membership of an optimal feature subset. In addition, relative to the number
of features and classes considered, the small sample size may promote feature selection
instability. The 112 observations used for feature selection are probably not a large
sample, especially when 5 classes and 42 features (21 each for the NIR and green bands)
participated in processes. However, the selection results obtained using many smaller
feature sets indicated that the algorithm would have identified the same four optimal
features even if a much large number of observations were available.

Two-dimensional representations of feature space depicting texture feature values
and cover type class affiliation for each of the 112 observed locations (Figure 4.8)
showed good seperability between most of the class pairs, when the appropriate feature
pair combination was selected. The energy-inertia space for example, allowed
discrimination between natural pine and red pine plantations, while the inertia-
homogeneity space separated oak from most other classes. Oak and NH were better
separated in entropy-inertia space, however, and a distinction between coniferous and
deciduous cover types was better achieved using the energy-homogeneity space (Figure
4.8). Although impossible to visualize, class separability can be extended to four
dimensional feature space. The only cover type that the identified features failed to
discriminate effectively was aspen, which showed substantial and consistent overlap with
all other cover types and particularly with oak in all two—dimensional feature space
combinations. For the entropy-inertia space, aspen was present in all class regions
identified by the quadratic discriminant function-based classifier (Figure 4.8). This
finding is somewhat surprising considering that visual depictions of aspen co-occurrence

matrices had revealed patterns in intensity arrangement that differed from those observed

192

for the other cover types. Apparently, the texture features derived from the matrices were
not very effective in quantifying those differences. A possible explanation is that the
absence of orthogonallity between texture features affects their discriminatory power for
cover types whose GLCM exhibits a concentration of pixel intensity values at or around
their center. This limitation can be potentially overcome by comparing class GLCMS
directly for classification purposes, that is without using the extracted features.
Preliminary investigations in that direction have yielded promising results.

The feature value arrangement shown in Figure 4.8 justified the use of the
quadratic instead of the linear discriminant function, because it became apparent that
class probability density functions, assumed by the linear function to be equal among
classes, were markedly different. However, the use of the quadratic function sometimes
generated ‘strange-looking’ feature space regions with instances of discontinuity. In the
entropy-inertia space for example (Figure 4.8), the oak region had two disconnected
components, one centered on coordinate location (inertia, entropy) = [8.5, 2.05] and the
other around [5.0, 2.15]. In the entropy-homogeneity space, the oak region practically
split the aspen region. In all two-dimensional feature space combinations (Figure 4.8), the
means of aspen and oak were in close proximity. Aspen exhibited much higher feature
value variability. The oak feature regions were approximately centered on the position
occupied by the means, while the feature regions for aspen were ‘pushed’ away from the
means.

Observations made in regard to class separability using the training data set were
found to hold for classification rule testing using the 132 subplot data. The overall

classification accuracy achieved was 65% with a kappa coefficient of 0.56, significant at

193

or=0.01(Table 4.2). Only small discrepancies were observed between producer’s and
consumer’s accuracies obtained for northern hardwoods, red pine plantations, and natural
pine, but they varied substantially for aspen and oak. Only 2 out of 12 subplots were
erroneously assigned to aspen (83% consumer’s accuracy), but 18 aspen subplots were
misclassified to other cover types (36% producer’s accuracy). Consumer’s accuracy was
lowest for oak (50%), with 16 erroneously committed subplots. This classifier behavior
was attributed to the positioning of oak feature values in the center of the four-
dimensional feature space, where the tails of the northern hardwoods, red pine plantation
and natural pine density distribution functions met. Small departures in oak feature values
from the class mean resulted in class members being assigned to those other classes. The
aspen feature space portion, being ‘pushed’ away from the feature space center, only
minimally overlapped with the other classes, thus resulting in high consumer’s accuracy.
Substantial confusion rates were also observed between red pine plantations and natural
pine, with 7 subplots of the former misclassified as the latter. It should be noted that these
7 subplots belonged to just 2 plots, a pattern also observed between northern hardwoods
and aspen. Such a concentration of misclassification instances to particular plots
indicated their smaller variability in texture, as opposed to spectral (Chapter 3),
characteristics within these plots. The overall classification accuracy obtained via linear
discriminant function-based classification yielded a kappa coefficient equal to 0.49, thus
indicating that the flexibility of quadratic decision boundaries to adapt to class-
conditioned feature densities rendered them superior to their linear counterparts.

A comparison between texture classification results to those obtained using

spectrally-based methods is shown in Table 4.3. Texture-based classification was

194

statistically superior at or=0.01 to spectral classification methods that used all pixels

(Chapter 2). It was not statistically different at or=0.10 to spectral classification that used
only pixels identified as tree apexes on original DN imagery, and it was found to be
inferior at or=0.01 to classification methods that used only pixels identified as tree apexes
on imagery corrected for brightness variations. Texture-based classification errors
involving a particular cover type were found to be spatially correlated and often included
all subplots in a plot, while errors of spectral classification were generally spatially
random. It is likely that a hierarchical classification approach operating on both textural
and spectral data might be capable of substantially increased classification accuracy
compared to either classification method used independently. The ability of co-
occurrence-based texture features to enhance cover type discrimination might be limited
for stands characterized by smooth canopy surface.

Because image texture features operate in a spatial domain, their derivation
necessitates images on which homogeneous textural regions are delineated. Such regions
can often be obtained by overlaying imagery with digital versions of existing stand maps.
In practice though, stand boundaries sometimes represent management units rather than
homogeneous stands, or they encompass variable structural and texrural stand attributes,
especially for uneven aged stands, or they are outdated. In the absence of reliable stand
boundary information, texturally homogeneous regions can be identified with visual
imagery inspection. Investigations in the study area revealed that 300-350 contiguous
pixels of approximately 0.9m (.2. 3ft) that were representative of the textural stand
structure suffice for a robust estimate of the stand texture features. As always, the analyst

should exercise caution and avoid regions in which vegetation ecotones are suspected.

195

The accuracy of forest cover type classification via co-occurrence analysis of
pixel intensity using imagery from the satellite platforms currently available may fall
short of the accuracy obtained using multispectral airborne imagery, primarily because
satellite platforms offer H-resolution imagery only for panchromatic bands. As indicated
by the findings in this research, GLCMS computed using visible bands vary very little,
thus compromising the ability of co-occurrence analysis to discriminate cover types
effectively. Observations of forested landscapes in northern Michigan using 0.82m
panchromatic IKONOS imagery has, however, demonstrated clearly identifiable texture
differences among cover types, suggesting that alternative texture quantification
techniques may be better suited to cover type classification efforts.

GLCM computations are efficient even for multidirectional pixel displacements.
Currently available computer processors limit the time required to compute the matrix of
a 20-hectare forest stand image with 1m pixels to a few ( < 10) seconds, while texture
feature extraction is practically instantaneous. Texture-feature-based classifier training
and testing is also expeditious. Optimal texture feature set identification, however, is a
computationally intensive process, even for optimized search algorithms. Implementation
of analytical texture-based approaches for forest classification is further complicated by
the absence of software packages supporting the series of steps required by the process.
Under such circumstances, information on features that possess discriminatory power for
texture-based investigations, or at least on an approximate optimal feature space
dimensionality, is important for operational methodology implementation.

Findings of the analysis presented in this chapter can provide a basis for the

initiation of texture-based cover type classification efforts. In the presence of mature,

196

high canopy closure stands, a single pixel displacement vector length and an angular

range of 1800 (half a circle) are likely among the best choices for GLCM construction.
NIR bands available in multispectral imagery should be given priority over visible bands.
Results suggest that the optimal co-occurrence matrix feature subset would usually
include at least one feature produced with element value weighting and one feature with
positional weighting, and that the energy, entropy, inertia, and homogeneity features are
likely to be optimal subset members.

It is important to remember that the formulation of this analysis strategy was
based on incremental optimization. In that regard, the displacement vector used for
GLCM construction was selected on the basis of matrix information content, and feature
selection was based only on GLCMS that maximized information content and used a
single distance metric among class-conditioned feature densities. Although those
decisions are warranted by the need to reduce analysis extent to manageable levels, it is
possible that the results obtained only constitute a local maximum in the domain of
classification accuracy, and that other combinations of intermediate analysis choices
could offer an improvement. On-going efforts aiming at procedure automation would
allow a more detailed investigation on the ability of image texture to support stand-level

forest cover type and structure classification.

4.5. Conclusion

Investigations on the utility of image texture for forest classification purposes
have been sporadic and likely not well understood by the forestry community primarily
due to the complexity associated with the quantification of texture. Classification

accuracies obtained in those investigations have generally been too low to be useful and

197

were found to exhibit significant variability among geographic regions and stand
structures.

This research explored one dimension of image texture depicting forested
landscapes based on pixel intensity co-occurrence. Instead of relying on a priori selected
sets of texture features derived from co-occurrence matrices, which is the usual practice,
this study investigated all alternatives present in a sequence of steps used to compute
feature values. The results indicated that understanding the influence that intermediate
analysis choices have on the value of computed texture features can yield substantial
improvements in the resulting classification accuracy. In addition, because co—occurrence
texture features are derived using band-specific information, they are independent of
distortions generated by band registration problems and brightness variability among
frames (defects often present in H-resolution imagery). Potential limitations in using co-
occurrence-based features for image classification occur 1) in the presence of stands with
smooth canopies; 2) from the need for pro-existing, positionally accurate stand
delineations; and 3) from the complexity associated with the procedures used to identify
the optimal co-occurrcnce feature subset.

Outcomes of this research also indicate that texture-based classification is capable
of detecting stand cover type differences missed by spectrally-based classification, given
that the two techniques result is different spatial distributions of misclassifications.
Identifying the causal factors that result in those misclassification differences should
allow composite classification strategies that could substantially improve classification

accuracies achieved by each technique independently.

198

To date, texture information in forestry applications of optical remote sensing
applications has been regarded as only complimentary to that obtained via spectral
analysis. The low appreciation fbr texture-based analyses might be due to the limited
utility that texture-based past studies had revealed for forestry applications using coarse
resolution imagery. Findings in this research indicated that the texture information
content of digital, H-resolution imagery has the potential for significant contributions in

support of forestry applications.

199

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Tables

Table 4.1. Commonly-used Gray Level Co-occurrence Matrix features.

 

 

 

Features Equations

Energy: F l = Zr}! P(i, j)2

Entropy: F2 = - ZU- P(i,j)logP(i,j)
Homogeneity: F3 = ZIJ [1/(1 + (i ‘ Dz ”P(i, I)
Inertia: F4 = X.,-(1' -1’)2P(i.j)
Correlation: F5 = - X.,-[0'-#,)(f‘#y)/\/<F;]P(i’f)
Shade: F6 = z,,,(i+j—p, —y,)3P(i,j)
Prominence: F7 = 21:310."- j ' H, " .Uy )4 P(i, I)
Variance: F8 = 2131'“ ‘ #x)2P(i,j)

Sum Average F9 2:28 iPx+y(i)

Sum Entropy: F10 = - 23:28 iPx W (i) log Px U (i)
Sum Variance: F11 = - 2,2338 (i - F9)2Px+y(i)
Difference Average: F12 = Z:%-lil’1r_y(i)

Difference Entropy: F13 == Z:%—l - Px__y(i)long_y(i)
Difference Variance: F14 = 2:134 (i - I712)2 Px_y(i)
Information Measure: F15 = [F 2 - HXYl]/max(HX, HY)
Coefficient of Variation: F16 = 0(P(i, j ))/ ,u(P(i, j ))

Peak Transition Probability: F17 = max(P(i, i»

Diagonal Variance: F18 = 02(1)“, j))

Diagonal Moment: F19 = 2131‘ J(0.5 | i — j | P(i, j))
Second Diagonal Moment: F20 = 2131(0'5“ ‘ j l P(i,/J)
Triangular Symmetry: F21 = Zwl P(i, I) " P(j,i) l

 

r, = 2.12,. 1100'. j)

0x = Zi(i‘/lx)ZZJ-P(l,j)
110') = 2,130.1)
Px+y(k)=zi,j|i+j=kp(i’j)

u, = Z, 12:100. 1)

a, = 2,0 — #922,100.»
13(1) = 2P0,»

P,_,(k) = Z,,,,._,.. P(zuj)

HX and HY are the entropies of Px(i) and Py( j) respectively
HXY 1 = *2, jP(i, j) 10g(P, (013(1))

 

204

Table 4.2. Forest cover type classification results and associated accuracy assessment
parameters obtained by using a quadratic discriminant function-based classifier operating
on four imagery texture feature (energy, entropy, inertia, and homogeneity) derived from
Gray Level Co-occurrence matrices and trained with independent data (112 observations).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observed
ASP NH Oak RPP NP Row Total
Aspen (ASP) 10 l l 0 0 12
“,3 Northern Hardwoods (NH) 6 22 3 0 29
E Oak 6 5 l6 3 2 34
'8 Red Pine Plantation (RPP) 2 0 1 21 7 31
Natural Pine (NP) 4 0 3 4 19 30
Column Total 28 28 24 28 28 136
Accuracy (%) Errors (%)
Producer’s Consumer’s Commission Omission
ASP 35.71 83.33 64.29 7.14
NH 78.57 70.97 21.43 32.14
Oak 66.67 50.00 33.33 66.67
RPP 75.00 67.74 25.00 35.71
NP 67.86 63.33 32. 14 39.29
Class Conditional Kappa
ASP 0.7901 Overall Accuracy (%) 0.6471
NH 0.6344 Kappa Coefficient 0.5594
Oak 0.3929 52.. 0.0017
RPP 0.5938 2.. 13.6023‘
NP 0.5383 " Significant at or = 0.01

 

 

Table 4.3. Statistical comparison of texture-based forest cover type classification
accuracy estimates with results obtained by using various spectrally-based, maximum
likelihood classification schemes. Z-statistics correspond to standardized differences of
corresponding kappa coefficient values.

 

 

 

 

 

 

Texture Classification
A(k.,.,-k,p,.c) Z-statistic (p-value)
8 Tree Apexes, Original DNs -0.0909 -l.6069 0.1081
g 3 Tree Apexes, Brightness Correction -0.2841 -5.6820 0.0000
53- ‘g All Pixels, Original DNS 0.2306 3.8433 0.0001
U All Pixels, Brightness correction 0.1843 3.0717 0.0021

 

 

 

205

 

 

 

 

 

 

 

 

 

Figures

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

d=1, d 1,
0:0 19-45
I j
1 2 3 4 1 2 3 4
3 3 3 3 1 2 2 1 o 1 1 1 3 0
33444 20400 .20220
33444 30052130014
(3) 4 0 0 0 4 4 0 0 0 2
(d) (e)
d 1, d=1,
a 90 9:135
Graylevelj j j
1 2 3 4 1 2 3 4 1 2 3 4
-_- 1(1,1)(1,2)(1,3)(1.4) l 3 0 2 0 1 2 O 0 O
E 2 (2.1)(2.2)(2.3)(2.4) 2 0 3 3 0 _ 2 1 2 3 0
E; 3 (3.0(3.2)<3.3)(3.4) 3 0 0 3 3 l 3 0 0 3 2
O 4 (4.1)(4.2)(4.3)(4.4) 4 0 0 0 3 4 0 0 1 2
(b) (0 (g)
d=1’ (1:1, 4 90
90% 6e {135+n, 0, 45, 90} g: $131313; 956+“;
45°+1t 135°+1t . .
J J
0 1 2 3 4 1 2 3 4
0+“ 00 18460 116460
2 0 11 5 0 , 2 4 22 8 0
135° 90° 45° 3 0 3 1310 ' 3 6 8 2612
400210 4001220
(11) (i)

206

Figure 4.1. (a) A hypothetical 2-bit (4 gray levels) 5x5 image with, (b) Corresponding
general (pre-normalized) GLCM form with gray levels 1-4. (c) Between-pixel angles
used in the computation of GLCM, (d)-(i), GLCM structure for distance of 1 pixel and
choices of angular displacements.

 

 

 

 

WG-1)

WG-1)

 

Entropy weighting
WU. i) = -10g P(i, i)

 

 

°<

 

 

1- T v v i
0 0 O 2 0.4 0.6 0 8

P(i,j)

Energy weighting
WU. i) = P(i, i)

 

 

 

 

v 1 i r i
0.0 0 2 0 4 0 6 0.0

PM)

IDM Weighting
W(i.j)=1/(1+(i-j)2)

Inertia Weighting
W0.» = (.- —j)2

12 16

1 1 1 1

 

 

 

 

 

 

  

 

 

 

Correlation Weighting
W031) = (i - 1“fo - fly)/ 0,0

1 1 1

 

    

 

 

 

Shade Weighting
W0.» = (Hi—ix, —p,)3

y

Variance Weighting
W0.» = (i — 102
4

8
1 41

 

 

  

 

 

Prominence Weighting

Wii.j)=(i+j—u,—iiy)‘

8 12 16

1 1 1

 

 

 

 

 

 

 

 

Figure 4.2. Pictorial representation of two classes of GLCM weighting functions:
Weighting dependent on matrix element value (entropy and energy features), and

 

 

 

 

weighting dependent on an element’s spatial position (remaining features). Darker shades
indicate larger element weighting.

207

 

 

 

 

 

 

 

 

 

 

Q -i
w. _
o
I
> «2-
.2 ° I
D
E
8 8 -
I
,I I"
N -.-\ /\ I. I..~. /\ /
o- - I.. .,l 1 l,-
O. _
o
I f I I r
i i i . i i 0 5 10 15 2o
0 2° 4° 5° 3° 100 Distance (in pixels)
(a)

(b)

Figure 4.3. 4-bit image exhibiting geometric (regular) texture, and Crarner’s V statistic
calculated from image GLCMS as a function of displacement distance d. Angular pixel
displacement ( 6) used was 0°).

 

 

 

   

 

 

 

 

 

 

 

 

O
20‘ #
’8 ,-°
8 5
15‘
’3 r z .7:
IE «1
g ,1
e 41
a“. 10- "g
o
a
W
54
'5
....
0. , rsz 2 ,,
-3 -2 -l 0 l 2 3 4
Feature]
(a)

(b)

Figure 4.4. Pictorial representation of the Hughes phenomenon showing the decrease in
expected feature class probability as data dimensionality increases from l-D (a) to 2-D
(b). 100 realizations were drawn for each feature class from Gaussian [~N(1,0)],
independently and identically distributed data.

 

 

208

 

 

 

 

 

 

 

 

 

 

 

 

 

l 41_ I J I I l I
4-1 i- 4-
21 >- 2—4
N
N o
9 5
.5. 0‘ r .. O-i
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IL
.21 1- '2-1
-4« - .4-
I I
r r r r I r r r l I I
-4 2 O 2 4 6 «4 2 0 2 4 6
Featuret Featuret

 

 

Figure 4.5. Decision boundaries for a two-class data set produced by a linear (a) and
quadratic (b) discriminant function developed using two object features. Object class is
color-coded.

209

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.96

Cramer's V
or

fi-flfifi’.\._.

 

 

 

 

1 1 1 1 7

 

 

 

4 6 a
Distance (in pixels)

 

 

 

Figure 4.6. NIR-band Normalized Gray Level Co-occurrence Matrices of an aspen
subplot produced 6={ 135+n, 0, 45, 90} and various pixel displacement distances d, and
values of corresponding Cramer’s V statistic.

210

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ASP NH

 

Oak RPP

 

 

NP

 

 

 

 

 

 

 

 

 

Figure 4.7. NIR-band Normalized Gray Level Co-occurrence Matrices produced for
five subplot, each situated in one of the forest cover types present in the study area, using
d=1 and 6= {135+7r, 0, 45, 90}.

211

 

 

 

0.016 "

0.014 "

0.012 -

Energy

0.010 ‘

 

 

 

 

 

0.”

 

 

 

0.016 -

0.014 4

0.012 -1

Energy

0.010 -

 

 

 

 

 

0.”

 

 

 

 

 

 

 

 

 

 

 

0.25 0.3) 0.3 0.40 0.45 0.50

 

I Aspen

. Northern Hardwoods
A Oak

9 Red Pine

7 Natural I’inc
—Decision Boundary

 

 

 

Figure 4.8. Forest cover type classification rules developed via quadratic discriminant
functions for texture feature pairs derived from NIR-band Gray Level Co-occurrence

Matrices calculated using [d = 1, 6 = {135+7r, 0, 45, 90}] pixel displacement vectors.

212

CHAPTER 5

SUMMARY

213

5.1. A Critique of Analysis Methods

It is evident from the presentations in the previous chapters that the analysis of
digital, airborne, high-resolution, imagery is an effort intensive process. This is because
of the small footprint of such imagery, the frequent occurrence of geometric and
radiometric imagery imperfections, and the absence of software packages that provide a
complete suite of analytic capabilities needed. If the still substantial cost associated with
imagery acquisition is also considered, it should not come as a surprise that examples of
forestry applications using this type of remotely sensed data are rare. As shown in this
dissertation, however, digital hi gh-resolution imagery is a technology that can provide
forest canopy attribute information with the accuracy required for forest management
decision-making at the operational level. At the same time, this technology is compatible
with classic uses of imagery in forestry, including cover type classification, and the
potential was demonstrated to extend classification endeavors to the individual tree level.

It could be argued that the band registration problems present in the imagery were
an isolated case originating from an unstable camera mounting and that, as imagery
vendors accumulate experience, such problems will diminish. Unfortunately, this
statement is probably only half-true. Personal communications with digital array camera
manufacturers and users of digital airborne imagery revealed that band registration
problems, although usually less pronounced than those found in the imagery used in this
research, persist even after diligent camera mounting on the body of the aircraft. This is,
in part, because the array detectors are aligned on a surface that is only approximately
planar and, in part, because the orientation of the focal plane in relation to the body of the

camera differs even among cameras of the same make and sequential serial numbers.

214

Precise alignment is possible, albeit very costly, for detector arrays mounted permanently
on the same device, but practically unattainable for digital arrays belonging to individual
cameras, such as those used for acquiring multispectral imagery from airborne platforms.
Therefore, the need for misregistration detection and correction procedures, such as those
developed in this study, would likely become a standard imagery pre-processing step.
Brightness variations among image frames should also be expected in airborne
digital imagery for the foreseeable future. As mentioned in Chapter 1, cameras currently
used for the acquisition of airborne imagery adjust the sensor’s gain factor for each
frame. Researchers investigating the sudden oak death problem in California acquired
imagery using the Advanced Digital Airborne Spectrometer (ADAR) system, which has
technical characteristics virtually identical to those of the DAIS system. They discovered
that the gain factor quantification was accurate, but not precise. By employing targets of
known reflectance in the study area, they found that their brightness-corrected imagery
contained a near-infrared Digital Number (DN) RMSE of 6 for 8-bit NIR imagery. This
corresponds to more than 2% of the theoretical DN range. Assuming that the gain factor
quantification error is comparable between the two systems, the mean brightness
variability among DAIS frames could exceed 1,500 DNs even after an adjustment based
on spectral gain factors. Evidently, frame spectral brightness normalization would still be
required even if the spectral gain factors were to be available. The methodology
presented in Chapter 2 could be used to provide such normalization. It was shown to
reduce the mean, among-frame brightness variability to 0.2% of the theoretical DN range.
The methodology to correct the Bidirectional Reflectance Distribution Function

(BRDF) effect used in this study was developed in accordance with the imagery

215

acquisition protocol and the cover type distribution present in the study area. Visual
comparisons of frame brightness prior to and after normalization suggested that the
methodology performed well and quantitative evaluation of post-correction brightness
variability along frame paths supported that assessment. It may, however, be difficult to
extend this BRDF correction methodology to other imagery sets featuring a particular
cover type, or cover type group. Fitting of a kemel-based BRDF model to the imagery
data was implemented successfully (given that model coefficient convergence was
achieved) for deciduous forests in the study area. There is no assurance that BRDF model
parameter convergence could be achieved for other cover type groups or where the
number of frames available is relatively small (<20). In addition to a non-linear increase
in computational costs, a large number of frames would help model parameter
convergence, but at the same time would decrease the probability of cover type presence
in all overlapping areas between frames.

Reduction in computational cost and the less strict requirements for large number
of frames and uniform spatial distribution of cover types can be achieved by substituting
the brute-force BRDF effect normalization technique used in this study with techniques
for which parameter estimation is analytical rather exhaustive-search-based. Mikkola and
Pellikka (2002) describe such an analytical technique. The drawbacks of the analytical
approaches are that they still require prior spatially explicit information of cover type
distribution and also a minimum 66% overlap between adjacent frames along and
between flight lines. Such high frame endlap rates are possible in the acquisition of aerial
photographs, but not for digital array scanners. At least currently, the time required for

information transfer from each detector to the on-board information storage system

216

precludes such a cycling rate. It was calculated that the maximum endlap rate that the
DAIS camera system could sustain along the flight line 2,000m above ground altitude is
about 40%. Obviously there are no technical restrictions for the amount of sidelap
between flight lines. The 20% frame endlap rate present in the data set did not allow
consideration of alternative BRDF effect normalization approaches.

A comparison of spectral classification accuracy results using all pixels in a stand
or other image region (Chapter 2) to those obtained using only pixels identified as tree
apexes (Chapter 3) leaves little doubt that the cost associated with tree apex identification
is justified. It could be argued that substantial cost savings could be achieved by
substituting pixels identified as tree apexes with those belonging to an upper, say 95“,
spectral brightness percentile, which could be easily identified via spectral histogram
computations. Those alternatives have been examined for several brightness percentiles
and the results showed a reduction in classification accuracy in excess of 7% and
sometimes as much as 15%. Classification accuracy discrepancies between the two
alternatives should be expected to be even larger in mixed stands, and particularly in
stands characterized by spectral brightness variability among dominant species. Using
histogram information to identify tree apexes that are subsequently used for estimating
canopy structure parameters was found to produce very poor results. This was because of
excessive errors of omission due to bright pixel clustering around the apex of a single tree
and the lower crown brightness of co-dominant trees that were partially in shadow.

The feature selection approach presented in Chapter 4 allowed a reduction in
texture feature space dimensionality reduction from 42 to 4. This bypassed the Hughes

phenomenon restrictions, and sustained a texture-based cover type classification accuracy

217

of about 65%. Obviously, feature selection can be used to serve objectives other than
categorical classifications. Experimentation with co-occurrence feature subset
optimization in support of stand classification based on canopy closure indicated that the
two-dimensional space defined by the energy and variance features could provide very
accurate canopy closure discrimination (< 10% error) in a 3-class formulation. There
were no natural clusters in the distribution of canopy closure values for the 134 subplots
used in the classification testing process. This indicates that image texture could be a
useful discriminator for the continuous variables associated with canopy structure, at least
for certain parameter value ranges. Hypotheses regarding of the utility of texture features
for cover type discrimination could only be evaluated on a trial basis, given that cover
type is a qualitative variable.

The need for computational efficiency has been mentioned more than once in this
dissertation. Although efforts were made to optimize the scripts, there are still
opportunities for improvement, particularly with the canopy parameter estimation via
slope breaks. Those opportunities reside where C scripts “call” functions of supportive
software packages, which are in turn executed via a software-package-specific language
interpreter. One such example is the local regression fitted on the DNs of transects
analyzed during the computation of window size in support of local maximum filtering.
The magnitude of computational gain possible can be realized by considering that the
processing via slope breaks of a one-hectare stand requires approximately 50,000 calls to
the local regression function. The entire computation overhead cost associated with
function interpretation external to the C scripts can be eliminated by including the

function in the compiled C script. Experimentation with central processing units

218

operating at 3.0GHz showed that if all computations were to be performed via a stand-
alone C script and by using the slope breaks approach, derivation of canopy attributes for
an entire, average-sized (~1500 Ha) forest compartment could be completed in less than
36 hours.

In all previous chapters and the discussion presented above there is a frequent
allusion to the link between spatially explicit cover type information and image-analysis
information products. Identification of spectrally homogeneous image frame regions,
such as those belonging to the same cover type, is important for the BRDF/brightness
normalization efforts shown in Chapter 2 and they are a prerequisite for texture and
canopy structure parameter estimation using DN autocorrelation presented in Chapters 3
and 4. Identification of such regions, or image segmentation as it is better known
(Edwards, 1995), has been pursued. The current stage of image segmentation
development, along with its implications on classification and canopy parameter

estimation, is outlined below.

5.2. The Role of Image Segmentation

The purpose of image segmentation in forestry remote sensing is to partition
forested land in regions of uniform reflectance patterns thought to correlate with spatial
variables of interest. Image segmentation is usually accomplished via identification of
boundaries or edges obtained using a series of filters or operators. Many of these
operators, including those proposed by Prewitt (1970) and Roberts (1965) and the more
sophisticated Laplacian of Gaussian and Canny operators, were used to segment a few
image frames in the study area. Details on the theoretical foundation of such operators

and how they can be computed are available in Pitas (1993). The results obtained by

219

these preliminary investigations were very poor with the number of identified boundaries
rivaling the number of trees present. Apparently, those operators perceive the spatial
variability of tones in high spatial resolution imagery as noise, even when imagery
smoothing is performed prior to applying the operator. Poor segmentation quality results
were also obtained by using the lattice-wobbling algorithm (Fortin and Drapeau, 1995).
It appears that the segmentation of high-spatial resolution imagery of forested
landscapes should be redefined as the quest for imagery regions that are homogeneous in
their tonal heterogeneity rather than comprising uniform tones, which implicitly
introduces the concept of image texture in the image segmentation process. Very often,
the regions on either side of a boundary that is easily identifiable by visual inspection
have practically identical average tonal values over some area element comprising many
pixels, but different arrangement of tones. This condition does not allow the gradient
change seeking operators mention above to detect the boundary. So far, the best (visually
assessed) image segmentation results over the study area have been obtained by
modifying a technique introduced by Pekkarinen and Sarvi (2002), that combines region
growing and tonal gradient seeking algorithms. Its merits include flexibility in band, or
band combination, usage, the ability to restrict the size of delineated regions to be above
a user-specified areal threshold, (i.e. the minimum mapping unit), and computational
efficiency. This technique succeeded in consistently identifying boundaries among
adjacent red pine plantations of different age, or thinning prescriptions and among
adjacent stands characterized by differences in canopy closure and stem densities. It
appeared to perform less than optimally in the presence of wide transition zones

(ecotones) among cover types or canopy structure conditions.

220

In the absence of reliable, spatially explicit information delineating forest stands,
image segmentation should be regarded as the first step in imagery analysis of forested
areas. Until the boundary detection fidelity of segmentation methodologies improves
sufficiently to allow automation, the identified forest regions would likely need to be
examined manually and boundaries added where the segmentation process failed.
Following this tessellation of forests into regions, tree apex identification could be
obtained with the techniques of Chapter 3, and used for region assignment to a cover
type, with an ensuing, independent allocation to a cover type using textural information.
It is assumed that field observations or other forms of ancillary information, including
manual forest cover type assessment from the imagery set, would have been used for
prior development of spectral and textural signatures. Canopy structure parameter
values, in addition to serving as an independent information product, could be used to
assist in the development of cover type classification rules. If, for example, canopy
structure analysis of an image region were to yield a mean crown diameter of 7m, while
textural and spectral imagery derivatives suggested an allocation to the aspen cover type,
the crown diameter information could be used to modify the cover type region
assignment to the second texturally and spectrally most probable class (e. g. northern
hardwoods), given that a 7m crown diameter value for aspen would be rather improbable
in the study area. Using a regression tree approach could identify the exact form of such a
hybrid classification rule. Details on the development and the merits of decision-tree-
based classification can be found in Friedl et al. (1999) and Hansen et al. (2000). A
preliminary investigation involving such a regression-tree-based classification rule has

yielded a cover type classification accuracy of approximately 93%.

221

5.3. Evaluation of Analysis Results

Analysis findings indicated that extracting the information content of digital
airborne imagery for forestry applications requires analysis methods specifically tuned to
its characteristics. The ability to assign cover type affiliation to individual crowns, and
thus determine species mixture and distribution for individual forest stands, cannot be
paralleled by the coarser resolution imagery typically used today. However, technical
problems associated with digital airborne imagery, including brightness variability among
acquired imagery frames, and the, sometimes substantial, geometric distortions,
potentially limit the opportunities for direct utilization of such technology for
classification purposes. The series of techniques presented in Chapter 2 proved that the
technical imperfections of such imagery could be corrected, in which case combinations
of spectral (Chapter 3) and textural (Chapter 4) signatures could provide classification
accuracies suitable for operational imagery utilization. Unfortunately, those
developments are practically attainable only in the presence of experienced analysts and
at considerable computational costs.

An area in which digital airborne imagery could become of unprecedented utility
for forest inventory and management purposes is the retrieval of canopy structure
parameters. As shown in Chapter 3, the presence of detailed field information allowed for
a better understanding of the interaction between forest canopies and incident solar
radiation as manifested in digital imagery, and supported the development of techniques
capable of translating such knowledge into quantitative canopy parameter estimates. The
sometimes impressively accurate canopy structure parameter estimation via image

analysis, coupled with its independence from frame brightness and BRDF effects and

222

minimal requirements for user input, emphasize the importance of these findings, at least
for high canopy closure stands. Although the computational cost associated with
parameter estimation is currently substantial, continuous improvements in processing

power and script optimization is expected to reduce the cost to manageable levels.

5.4. Evaluation of Field Data Collection Methods

It was mentioned in Chapter 3 that the availability of spatially precise data is an
invaluable resource for methodology refinement that could determine the success or
failure of the investigation. Because, at the same time, a field data collection campaign
that involves survey-grade measurements is a very expensive endeavor, it is important to
assure that the data collected meets the anticipated standards. Some of the lessons learned
are outlined below for the benefit of the reader contemplating similar field data collection
efforts.

Distance measurements obtained by electronic range devices are very reliable
when taken using a line of sight free from any obstructions. However, measurements
acquired under canopy may be prone to systematic biases, especially in the presence of
dense understory vegetation. Up to 5% distance errors could be expected where portions
of tree stems, branches, or leaves are contained in a 0.5m-radius virtual cylinder centered
on the line of sight. Selection of sampling sites, and identification of reference objects
used in plot georeferencing should be scheduled, if possible, after the acquisition of
imagery for four reasons, presented here in decreasing order of importance: 1) On-site
measurement accuracy evaluation is possible. 2) The availability of imagery allows plot
allocation conditional upon frame boundaries. It might be desirable to avoid frame edges

so that, for example, BRDF effects could be minimized. 3) Identification of suitable

223

reference objects used for plot referencing in image frame coordinates is much easier on
digital or hard copies of the imagery and allows for an evaluation of contrast between a
candidate reference object and the image background. 4) High-resolution imagery is an
excellent navigation tool.

Dense forest canopies and a paucity of objects that can be used as positional
reference often necessitate lengthy transects with many vertices for plot boundary
determination in image coordinates. Regardless of how careful the instrument operator is,
angular and distance measurement errors are bound to happen and can be corrected
relatively easily when the personnel and equipment are still in the field. Unfortunately, it
requires only one measurement error to convert the plot center from a point to a polygon
of substantial size and thus deprive the analysts from the opportunity to use the plot
information in a spatially explicit manner. The importance of the ability to verify
measurement accuracy in the field is appreciated when expensive plot data becomes
useless because it cannot be placed accurately on the image frame (M. Wulder, personal
communication, 2000).

The use of the Forest Inventory and Analysis (F IA) field data collection protocol
undoubtedly enhances the potential for a wider application of these study findings, but it
also reduced plot allocation flexibility especially where stand homogeneity is a
prerequisite for plot installation and in forests exhibiting intense fragmentation. In
addition, the use of the FIA protocol often necessitates installation of a larger number of

transect vertices, particularly in dense stands and inclined terrain.

224

5.5. Further Research Opportunities

Slope break computations were implemented using a set of heuristic rules whose
mathematical description was presented in equations 33b-d in Chapter 3. It was stated
that the appropriate value for the coefficient at the right side of equation 3.3c could be
identified by examining the DNS of imagery transects for each of the cover types present.
Such a requirement for user input could be relaxed by modifying Equation 3.3c to include
an upper slope break length limit. It was observed that DN reduction along a transect
connecting a pixel identified as a tree apex and a local DN minimum (corresponding to a
canopy opening in shadow) is very often sigmoidal. The pixel along the transect at which
the first decrease in the DN reduction rate occurs could be used to identify the proper
upper slope break length limit aforementioned. Tentative implementation of a modified
heuristic rule revealed that the proposed slope break length limits are cover type specific.
Comparisons between heuristic-rule-estimated slope break lengths and field observations
of crown extents showed that the former are unbiased and of similar variability to the one
obtained by the current version of heuristic rule implementation.

Canopy closure estimates obtained in Chapter 3 treated tree crowns as opaque
objects. Hence, these canopy closure estimates are likely exaggerated in comparison to
the traditional definition of canopy closure (i.e. the percent of the sky sphere that can be
observed from the ground). A link between the two canopy closure definitions can
potentially be obtained by comparing the canopy closure estimates obtained in this study
to canopy closure estimates obtained by digital hemispherical canopy photographs
acquired at 4, equally-spaced points in each of the 134 subplots. Preliminary

investigations have shown that the relationship between opaque and “transparent” canopy

225

closure definitions is cover type specific and of moderate strength. Estimate
transformation, however, was found to improve estimate correlation.

It was shown in Chapter 4 that apparent differences in co-occurrence matrix
structure sometimes remained elusive when matrix structure was quantified via
computation of secondary features. Such observations raised skepticism as to whether the
use of secondary features is the most powerful alternative for texture quantification and
lead to the development of a matrix discrimination technique. The latter attempts to
identify those matrix elements that contain maximum discrimination potential. The idea
is particularly attractive given that it does not require feature extraction and thus is not

sensitive to feature dimensionality problems.

5.6. Conclusion

To date, distributed forest attribute information is obtained via either stand
cruising or aerial photo interpretation. Budget constraints, reductions in the number of
experienced photointerpreters available, and the need for digital integration of
information all necessitate solutions that can provide forest attribute information from
digital means. High-resolution, digital. airborne imagery appears to be the most
promising technology capable of delivering forest information products that meet current
needs and expectations. The work compiled in this dissertation asserts the potential of
airborne digital imagery to serve cover type classification purposes and the extraction of
information related to forest canopy structure under high stand density conditions.
Additional investigations would be needed to determine how, and if, the same technology
can be used to deliver the same types of information in different stand density conditions

or in other biotic regions.

226

Literature Cited

Canny, J .F. 1986. A computational approach to edge detection, IEEE Tran. Pattern Anal.
Mach. Intel., 82679-689.

Edwards, G. 1995. Methods for assessing local map accuracy in thematic classifications
derived from remotely sensed imagery, Proc. 1 7’” International Cartographic Conf,
Barcelona, Spain, p. 1521-1530.

Fortin, M.-J., and P. Drapeau. 1995. Delineation of ecological boundaries: comparison of
approaches and significance tests, Oikos, 72:323-332.

Friedl, M.A., C.E. Brodley, and AH. Strahler. 1999. Maximizing land cover
classification accuracies produced by decision trees at continental to global scales,
IEEE, Trans. Geosci. Rem. Sensing, 37:969-977.

Hansen, M.C., R.S. Defries, J .R.G. Townsend, and R. Sohlberg. 2000. Global land cover
classification at 1km resolution using a classification tree approach, Int. J. Rem.
Sensing, 21:1331-1364.

Mikkola, J, and P. Pellikka. 2002. Normalization of bi-directional effects in aerial CIR
photographs to improve classification accuracy of boreal and subarctic vegetation for
pollen-landscape calibration. Int. J. Rem. Sensing, 23:4719—4742.

Pekkarinen, A., and V. Sarvi, V. 2002. Detection of clearcuttings with help of high-
altitude panchromatic aerial photographs and image segmentation, Proc. Operational

Tools in Forestry using Remote Sensing Techniques, Forest SAT Symposium,
Edinburgh, Scotland (CDROM).

Pitas, I. 1993. Parallel Algorithms for Digital Image Processing, Computer Vision, and
Neural Networks, John Wiley, New York.

Prewitt, J. 1970. Object enhancement and extraction. In Picture Processing and
Psychopictorics, B. Lipkin and A. Rosenfeld [Eds], Academic Press, New York.

Roberts, LG. 1965. Machine perception of three dimensional solid, Optical and Electro-
optical Information Processing, J.T. Tippell (Ed), MIT Press, Massachusetts.

227

APPENDIX 1

228

A.1. Crown delineation

Let [V1 V2 Vn]T an n-element vector of distance and azimuth offsets from tree
stems in the subplot coordinate system. Each vector element represents field
measurements of vertices on the crown periphery as the latter is defined when viewed
from above. Hence, the term ‘crown’ in this application corresponds to the projected-to-
the-ground portion of tree foliage that is unobstructed by the foliage of adjacent trees
when viewed from directly above. For simplicity in the example presented here it is
assumed that the stem is dimensionless (a point), it is positioned at the origin of the
coordinate system, and the first vector element belongs on the Y-axis (Figure A.5). Note
that figures in this dissertation, including the Appendices often contain color. The
objective is to link the planar representation of vector elements (points A to D in Figure
A.5), by using a closed convex spline. The spline is assumed to depict the periphery of
the crown. It should pass through all the field-measured points (exact representation) and,
preferably, maintain a derivative everywhere along its length (absence of discontinuities).
The last criterion provides the spline with an aesthetically appealing, smooth form
characteristic of objects in natural settings. The objective is stochastic in nature since
there is an infinite number of splines that meet the convexity, point exactness, and
continuity criteria.

One possible spline realization is produced as a linear combination of circular arcs
and projected are components. The algorithm that generates the crown realization rotates
each vector element V, until the azimuth of its rotated version coincides with the azimuth
of the next-in-sequence vector element Vii]. Vi rotation around the origin (tree stem)

draws a circular arc segment, which in the illustrative example of Figure A5 is

229

represented by a dashed line. Generally, sequential vectors have different lengths
(|V,|¢|V,+i|), so the arc segment produced by rotation of V1 would miss the vertex of VH1.
In such cases, the difference |V,|-|V,+1|, measured along Val, is bridged by shifting the
projection of the arc segment on the X axis proportionally to the (|V,|-|Vi+1|)/|V,| ratio.
Arc shifting along the X-axis ensures that sequential arc segments, represented with solid,
colored lines in Figure A.5, would form a closed convex spline. Because the derivative is
meaningfirl everywhere on a circle or forms of circle translation, every spline derived
with this algorithm is free of discontinuities.

Spline coordinates for each quadrant can be calculated using the following

 

 

 

formulae:
sy =(:)‘[(Ry(i+l) 41”.)? —x2 , (A.1)
VX E [in’Rx(i+l) _ in:
(R . —R .)-(R . —R .)
2 x(t+l) x1 y(t+l) yr
5 =(i) (R . —R .) + X’ (A-Z)
x [J y(t+l) y, (Ry(i+l)—Ryi)

where Rx,- and Rm. 1) are the vertex coordinates of elements V,- and Val on the X-axis, and
Ry,- and Ry(i+ 1) are the vertex coordinates of V, and V1.1 on the Y-axis. Note that the signs
of S, and Sy are quadrant specific, with Sy taking positive values in quadrants l and 4 and
negative values in quadrants 2 and 3. S, takes positive values in quadrants 1 and 2 and
negative values in quadrants 3 and 4.

Crown representation fidelity is a function of crown shape, number of offset
measurements, and the number of spline vertices calculated. Trees in even-aged
coniferous stands have crown projections to the ground that approximate circles. Four to
five offset measurements would, in general, suffice for delineating regularly shaped

crowns. In uneven aged deciduous stands, tree competition for light and nutrients,

230

management practices, and disturbances, among other factors, often result in
polymorphic, irregular crowns. In such circumstances, adequate crown delineation may
require more than 15 crown-offset measurements. Spline segment vertices were
calculated for 3cm increments along the X and Y axes.

The spline-based crown delineation approach outlined above, produces small
overlapping regions between adjacent trees. In GIS terminology these small regions are
known as “sliver polygons” and need to be eliminated prior to GIS-based analysis
operations. Maintaining sliver polygons would, for example, result in a positive bias of
average subplot crown diameter estimates. A sliver polygon between two adjacent
touching crowns could be eliminated by merging it with the largest adjacent crown, or
with the crown of the taller tree. Or it could be dissected using a line perpendicular to the
line that joins the stems of the two trees, with each of the two new polygons produced by
the dissection subsequently merged to the corresponding crown. The proper sliver
polygon elimination approach was selected in each case after consulting field notes with
information on the vertical arrangement and the relative crown height between adjacent
trees. Crown polygons were organized as ArcInfo GIS vector layers in subplot coordinate

system.

A.2. Crown centroid calculation

All GIS software packages automatically calculate the area of polygons in vector
layers. Centroid calculation is usually offered as an option. However, most packages,
including ArcInfo, calculate a pseudo rather than the true centoid. The pseudo-centroid is
calculated as the center of the bounding rectangle around a polygon. Note that coordinate

system rotation would affect the location of pseudo-centroids. Depending on polygon

231

shape, there might be a significant discrepancy between the true and the pseudo centroid.

The area A of a polygon and coordinates (Cx, Cy) of its true centroid can be calculated as:

:%Z[(X1Y 1+1 Xi+lYi)]’ (A3)
C. 7,2101 +X...><X.-Y- -X...Y.-.1, (4.4)
Cy 6AZ[(Y+Y1+1)(X1Y1+I —X1'+1Y1')]’ (A°5)

Compared to crown centroids, tree stems are more frequently located close to the
visible crown periphery, or even outside of it, particularly in uneven aged deciduous
stands (Figure A.3). Although it is theoretically possible for either the true or pseudo
centroids to lay outside the crown, in practice this is very rarely the case, especially for
true centroids, because visible-from-above crown portions tend to have convex
peripheries (Figure A.6). Increasingly irregular crowns exhibit larger discrepancies
between their true and pseudo centroids (Figure A.6). Therefore, true crown centroids are

a reasonable choice when there is a need for point representations of crowns.

A.3. Crown diameter calculation

Crown diameter is perhaps an awkward term because of its implicit reference to a
circular tree crown shape is often unrealistic. However, it is frequently used as input in
green biomass, wood volume, crown closure, and wildlife habitat models. A crown
diameter estimate can be calculated efficiently as the diameter of a circle of the same
area. An alternative estimate can be obtained by measuring the within-crown length of

linear segments that pass through the crown’s centroid. The second approach is

232

potentially superior to the first because it accounts for crown shape. Diameter estimate
bias can be introduced when only a small number of linear segments is employed.
Experimentation with many crown shapes and sizes revealed that for regularly shaped,
nearly circular crowns the linear-line-segment-derived estimate is equivalent to the
diameter of a circle occupying the same area with the crown, provided that an adequate
number of line segments has been utilized (Figure A.7). For significantly non-circular
crown shapes, the circle-area-based estimates are consistently larger that those calculated

with the line segment approach (Figure A.7).

A.4. Bidirectional Reflectance Distribution Function Model

The linear, kernel-driven, three-parameter model developed by Roujean et al.
(1992) is a semi-empirical approach designed to correct BRDF effects for heterogeneous
surfaces. The model considers the surface reflectance of an object to be the synergistic
effect of two processes: a diffuse reflection component that accounts for the geometrical
structure of opaque reflectors located at the surface of the object and a scattering
contribution from the volume of the object. The model in a generic form can be expressed

as

p = apgeom + (I — a)pvol (A6)

where p is the object’s spectral reflectance, and a is an empirical coefficient that
characterizes the relative weight of the geometric and volume components pgeOm and pm,

respectively. The model can be explicitly written as

p16S,HV,(p)= 110 + 1]];(195,av,¢)+ 112/2 (656,10) (A7)

233

where 6, is the solar zenith angle, 6,. is the view zenith angle, and (p is the relative
azimuth angle. k0 is the bi-directional reflectance for 6,: 6,.=0, k, is the weight for the
geometric scattering function f, and k2 is the weight for volume scattering kernel function
f2. The physical meaning of the angular parameters 6,, 6,, and ¢ is shown in Figure A.4.

Coefficients k0, k,, and k; are determined empirically. Functions f, and f2 are defined as

 

 

 

1 . tan6 +tan6 +G

f(6 ,6 ,(p)=—-[(7r—(o)cosgo+srn(o]tan6 tan6 — S " (A8)
I s v 271' s v 71'
4 1 7t 1
6,6 , =-—— —- cos +sin —— A.9

f2( 5 V (a) 3n cos6s +cos6v [[2 g] 4‘ 6] 3 ( )
where 5 is derived from
cosé‘ = cos 65 cos 6v + sin 65 sin 6) cosgo (A.10)
and G from
G=\/tan2 6s+tan2 6v-2tan6s tan6vcosrp (A.11)

Typical BRDF correction implementation entails multiplying pixel values with

the ,oo(6sO ,6v0 ,(po ) / p165 ,6v,(o) ratio, also known as the BRDF coefficient, where
p0(6s ,6) ,(p0) is pixel reflectance for standard viewing and illumination geometry and
0 0

p163 ,6v,(o) for actual geometry. Table A.3 shows the geometry parameter values for

standard and actual BRDF corrections used in this study.
The empirical component of the model, is demonstrated by the fact that model
intercept and function weighting coefficients are surface or, for the purposes of this

study, cover type dependent. In practice, their values are determined by using radiometric

234

measurements of cover type reflectance either in situ, in lab settings (Loechel et al., 1997,
Deering et al., 1999, Weiss et al., 1999), or alternatively by examining correlations
between DNs and scattering angles of reference sample areas on overlapping images
(Mikkola and Pellikka, 2002). In the absence of known coefficient values appropriate for
the biome present in the study area, coefficient values were determined via the
optimization exercise outlined in Chapter 2. In the interest of limiting the number of
coefficient value combinations needed to be evaluated, a set of values found to perform
well in a warm temperate forest were used for the initiation of the optimization process
(Table A.2). Given that the imagery set was acquired with a nadir looking sensor and a
maximum view angle of 12.360 (Table A.3) over gentle terrain, combinations of k0, k,,
and k; values that yielded correction coefficients outside the 0.7-1.3 range were rejected

as invalid.

A.5. Maximum likelihood classification

Maximum likelihood (ML) is a supervised classification method. The probability
of a pixel belonging to each of a predefined set of classes is calculated, and the pixel is
assigned to the class for which the probability is highest. ML is based on the Bayesian

probability formula:
P(q,r) = 1’(r | q)P(q) = P(q l r)l’(r) (A-12)

where q and r are generally called ‘events’. P(q,r) is the probability of coexistence of
events q and r, P(q) and P(r) are the prior probabilities (of occurrence) of events q and r,
and P(q | r) is the conditional probability of event q given (the presence of) event r.

P(r | q) is defined in the same manner. In remote sensing applications, an event is

235

equivalent to a pixel for which a size k vector is defined (k represents the pixel’s spectral
dimension or the number of bands present). If q,- is the vector of k spectral values (DN,
radiance or reflectance) for the ith pixel and rj is information class j then (A.12) can be

rewritten as:

P(q, Irj)P(rj)
P(q,)

 

P(r, 14,.) = (A.13)

It is commonly assumed that P(q) is unifome distributed, and therefore its function in
(A. 1 3) is to standardize the fraction on the equation’s right hand side. Hence, (A.13) can

be rewritten as:

Pixel i can thus be allocated to class Ithat maximizes P(wkl x,-) in (A.14). The

classification criterion is then expressed as:

Wk = max[P(qi Irj)P(rj )] ij (A.15)

Equation (A. 1 5) offers the maximum a posteriori solution, which maximizes the product
of conditional probability and prior probability. In most remote sensing classification
applications, the prior probability P(r) is also set to be uniformly distributed primarily
because often there is no information on class distribution in the area of interest, which

further reduces (A. l 5) to:

P(r, 14,.) cc P(q, lrj) (A.16)

Allocating pixel i to class rthat maximizes (A. 1 6) provides the maximum likelihood

solution.

236

Normally, the conditional probability P(q,- | rj) is assumed to follow a Gaussian

distribution. P(q,- | rj) can then be expressed as:

l

P(q.|r.)=
' ’ 27tk|Cj|

exit—$0,. -# ,)Tc;‘(q,. —u ,1 (AM)

where C]- is the covariance matrix of class rj with dimension k, p,- is the mean vector of

class rj, and | - | denotes the determinant.

In practical applications, equation (A. 1 7) can be reduced to the following

expression by taking the natural logarithm:
1 P 1 )—:111(2 >11“ lC i—1( - )TC‘k - ) (A18)
Ill (q, rj]—2 n 7T 2 n j zq,‘ ”j j ql ”j '

which is computationally advantageous to (A. 1 7) because it avoids the exponential term.
Because the term kln(2 it) is the same for all classes, it can be regarded as a constant and
be eliminated from equation (A. l 8) without affecting the ranking of

the ln[P(ql. |rj.)] values. Equation (A. 1 8) is finally multiplied by —2 to give:

—1niP(q,. 15.)] =1 C, i+<q,. —1z,)TC;‘<q,. —1i,.) (A.19)

Obviously, maximizing equation (A. 1 7) is equivalent to minimizing equation
(A. l 9). It should be noted that the second term in the right hand side of equation (A.19) is
the Mahalanobis distance, and therefore the geometrical shape of the cloud of points in k-
dimensional spectral space formed by a set of pixels belonging to a given class can be
described by an ellipsoid. The shape of the ellipsoid depends on the covariance among

the features in the spectral space. In the presence of only two bands (two dimensional

237

spectral space), the maximum likelihood firnction delineates ellipsoidal, equally-probable
contours, which can be regarded as decision boundaries. A careful examination of
equation (A.19) reveals that an inadequate number of pixels in a class and/or a large
number of bands involved can produce considerable biases in the computation of the
class statistics, including the mean vector and covariance matrix, which is ultimately
translated into biases in the classification results. Hence, there is a need for an accurate
estimate of class statistics if maximum likelihood classification is to perform in a
satisfactory way (Landgrebe, 1998). Accurate estimates of such statistics, sometimes
known as distribution moments, representative of a class can be computed when pixel

membership in the class spectral signature is adequate.

A.6. Cross-validation and classification accuracy assessment

An important part of every classification is the assessment of its accuracy. The
term ‘accuracy’ denotes the level of agreement between class labels assigned by the
image processing method and class allocations based on ground data. Often, ground data
do not necessarily represent reality, due to observation and recording errors, or because
of the time elapsed between observations and the acquisition of imagery. If a separate set
of ground observations is not available, accuracy can be evaluated relative to the data set
used to train the classifier, but the degree of accuracy will be overstated. In these
circumstances, the use of cross—validations is preferable. In cross validation, ground
observations are subdivided into n subsets of approximately equal size. The majority (n-
l) of these subsets are used for training the classifier. The remaining nth subset is used for

classification error estimation. Each of the n subsets is used in turn for testing, with the

238

remaining (n-I) subsets being used for training. Once this cycle of training and testing is
completed, the error estimates are combined (Schaffer, 1993).

The most common measures of classification accuracy assessment in remote
sensing are based on the computation of the confusion or contingency matrix, a v x v
square matrix, where v is the number of classes. The matrix shows the relationship
between the class labels assigned by the classifier and the class labels assigned by ground
observations. The diagonal elements represent correctly classified entries while off-
diagonal elements correspond to classification errors. An index of overall classification
accuracy can be obtained by dividing the sum of the diagonal entries of the confusion
matrix by the total number of samples. Overall accuracy estimates can be misleading,
however, as they do not provide any class-specific accuracy estimate nor do they account
for the relative proportion of samples tested. Accuracy estimates for individual classes
are embedded in the concepts of producer’s accuracy and user’s accuracy. For each
information class i in a confusion matrix, the producer’s accuracy is calculated by
dividing the entry (i,i) by the sum of column I (the total number of class i pixels in the
ground data), while the user’s accuracy is obtained by dividing the entry (i,i) by the sum
of row i (the total number of class i pixels labeled by the classifier). Thus the producer’s
accuracy indicates the proportion of samples in the testing data set that are correctly
recognized by the classifier. The user’s accuracy measures the proportion of samples
identified by the classifier as belonging to class i that agree with the testing data. It is
evident that all these indices utilize only a small portion of the information in the
confusion matrix. A multivariate index, known as the kappa coefficient (Cohen, 1960),

that largely overcomes the limitation of the indices mentioned previously, is favored by

239

many analysts. The kappa coefficient quantifies the probability of chance agreement of
class labels assigned by the classifier and those present in the testing data set. It should be
noted that a number of authors (e. g. Foody, 2000) argue that the kappa coefficient
overestimates chance agreement and underestimates accuracy and they suggest

alternative formulations. In any case, the standard kappa coefficient is defined as:

 

k: i=1 i=l (A.20)

where k (k-hat) is the estimated kappa coefficient, v is the number of rows and columns
in the matrix, x,-,- is the matrix element at row and column 1, + represents row and column

summation over the index, and N is the total number of samples in the testing data set.
An important property of this index is that its ratio to the square root of its

variance follows a Gaussian distribution, provided that the number of samples in the

confusion matrix is sufficiently large. Hence, the ratio k/ (rim can be used for

parametric comparison of kappas obtained by using different classifiers, and variable
testing sample sizes. The large sample variance of kappa (Rosenfield and Fitzpatrick-

Lins, 1986; Hudson and Ramm, 1987) is computed as:

2 2
__1_ 191(1-19')+2(1—a,)(219,612-a,+(1—19') (194-4192

 

 

o . — : (A.21)
[k1 N (1.192)2 (1-62)3 (1-62)4
where
V x..
91:27:71, (A22)

240

V x. x.
6 :2 1+ +1, (A23)

V x..(x. x .)
193 = Zl—'—Ni2—+—, and (A.24)
1:
V V
04:22:31; 1'(xi]:/-3x+i)2 (A25)

The test of significance between two independent kappas is formulated as

(Rosenfield and Fitzpatrick-Lins, 1986):
Z = l 2

6 . + 6 .
if [k1] [k2]

where Z is the standard normal deviate. A Z score larger than 1.645, 1.960, or 2.576

 

(A.26)

would indicate significant differences between the two kappas at the 90, 95, and 99

percent probability level, respectively.

241

Literature Cited

Cohen, J. 1960. A coefficient of agreement for nominal scales, Educational and
Psychological Measurement, 20:37-46.

Deering, D.W., T.F. Eck, and B. Banerjee. 1999. Characterization of the reflectance

anisotropy of three boreal forest canopies in spring-summer. Rem. Sensing Environ.,
67:205-229.

Foody, G.M., 2000. Accuracy of thematic maps derived by remote sensing, In Proc. of
the Accuracy 2000 Conference, G.B.M. Heuvelink, and M.J.P.M. Lemmens [Eds],
Delft University Press, Amsterdam, pp217-224.

Hudson, W.D., and CW. Ram. 1987. Correct formulation of the kappa coefficient of
agreement, Photogramm. Eng. Rem. Sensing, 53:421-422.

Landgrebe, D. 1998. Information extraction principles and methods of multispectral and
hyperspectral image data. In Information Processing for Remote Sensing, CH. Chen
[Ed], World Scientific Publishing, River Edge, New Jersey.

Loechel, S.E., C.L. Walthall, E. Brown de Coulston, J. Chen, B.M. Markham, and J.
Miller. 1997. Variability of boreal forest reflectances as measured from a helicopter
platform. J. Geophys. Res., 1022495-503.

Mikkola, J, and P. Pellikka. 2002. Normalization of bi-directional effects in aerial CIR
photographs to improve classification accuracy of boreal and subarctic vegetation for
pollen-landscape calibration. Int. J. Rem. Sensing, 23:4719—4742.

Rosenfield, G.H., and K. Fitzpatrick-Lins. 1986. A coefficient of agreement as a measure
of thematic classification accuracy, Photogramm. Eng. Rem. Sensing, 52:223-227.

Roujean, J.L., M. Leroy, and P.Y. Deschamps. 1992. A bi-directional reflectance model
on earth’s surface for the correction of remote sensing data, J. Geophys. Res., 97:455-
468.

Schaffer, C. 1993. Selecting a classification method by cross validation. Mach. Learning,
13: 135-143.

Weiss, M., F. Baret, M. Leroy, A. Bégué, O. Hautecoeur, and R. Santer. 1999.
Hemispherical reflectance and albedo estimate from accumulation of across-track
sun-syncronous data, J. Geophys. Res., 104:122-132.

242

Tables

Table A.1. DAIS technical specifications

 

Camera
Manufacturer/model
Array size
Pixel size

Spectral resolution

DALSA CA—D7-1024T digital frame camera
1024 x 1024 pixels

12 x 12 micrometers (100% fill factor)

16 bits per pixel

 

 

Lenses
Nominal focal length 28mm
Aperture range F2.8 to F16
Angular field of view 24.6 degrees
Interference filters
Filter bandpasses Blue 450-530nm
Green 520-6 lOnm
Red 640-720nm
Near Infrared 770-880nm

 

Camera mount
Model
Roll/Pitch compensation range
Yaw compensation

Degree of stabilization

Zeiss T-AS Gyro Stabilizer
i5 degrees

:t6.5 degrees
1:10 to 1:30

 

Camera control unit

Maximum frame capture rate

Storage capacity

1 frame every 3.5 seconds

Sufficient for 8 hours continuous imaging at
maximum frame capture rate

 

Sensor orientation
Position

Attitude

Post-processed kinematic GPS

0.: 0.3m

0y: 0.3m

oz: 0.3m

Applanix POS/AV 510 post-processed with GPS
0,0”: 20 arcsecs

opimhz 20 arcsecs

oyaw: 60 arcsecs

 

243

Table A.2. Coefficient values used in the Roujean et al. (1992) BRDF model for

deciduous forest and those derived with the brightness normalization process.

 

 

 

Coefficient
Initial Optimized
k0 k, k; k0 k, k;
Blue 0.030 0.000 0.087 0.153 0.1 15 0.036
'2 Green 0.030 0.000 0.087 0.183 0.147 0.052
t3 Red 0.030 0.000 0.087 0.147 0.099 0.058
NIR 0.400 0.040 0.295 0.281 0.058 0.301

 

Table A.3. Standard and actual BRDF viewing and illumination geometry parameter
values used in brightness normalization.

 

 

Standard Actual

Geometry Geometry
Solar zenith angle' 19, 35° Site 11: 31.190 — 38.94°, Site 1: 28.46° — 29.120 2
Solar azimuth angle' a. 180° Site 11: 127.090 — 154.58°, Site 1: 169.120 — 195.48° 2
View zenith angle 6v 0° 0° — 12.36° 3
View azimuth angle (pv NA’ 0° — 360° 3
Relative view angle (0° NA" 0° -— 360° 3

 

I Computed using software available at http://www.susdesign.com/sunangle/, maintained by C.
Gronbeck, Sustainable By Design, Seattle, Washington.

2 Overlapping frame region specific, calculated for the region’s center.
Pixel specific.

4 Nadir looking sensor.

5 ¢= es- cov-

244

Figures

 

 

Flight
Directionl

   

n
mm
ooc
1e
H...“
D

Site II

    

(13:15 EDT)

(11:44 EDT)
End

5..
m
S

22.311114

  

 

IE—IEE—iim-ihi—h."

 

10 Kilometers

7.5

 

 

Acquisition date: August 11, 1999.

 

 

Figure A.1. Spatial arrangement of DAIS image frames for Sites I and II.

245

 

 

 

 

 

 

FIA/FHM Plot Structure
’ "' ~ \
/ ~ A
Standard subplot \ Subplot 2
Expanded subplot l " N
1
X/A I
’ I
\
\ /
‘ _
8
_ 18
’ x
I \
I
I \
l \
Subplot 4 ‘ ’1 Subplot 3
\ \
’ \ x I
I . ‘ _ .— 1 l
l ‘1 Subplotl l ‘
| 7.32m 14— j ‘
I
\ l \
\ \
I /
\ \ _ ’ I \ ~ - .— ’
+1 12.00111 11—

 

 

 

Figure A.2. Plot design according to the FIA/FHM protocol.

246

 

 

5m

 

 

 

 

 

Total crown area: 261.2m2
P ' "-.. J ' ‘ tree stem Subplot area: 314.
Non-dominant tree stem Canopy closure: 83.14%
Subplot center

Crown of tree with stem within the subplot area
Crown portion of tree with stem outside the subplot area
Subplot perimeter

IUD..-

 

 

 

Figure A.3. Vertical tree crown projection map for a northern hardwood subplot (243).
Crowns correspond to the portion of tree foliage visible from above. Dots represent tree
stems and are of size proportional to stem DBH.

247

 

Sensor

 

 

 

 

 

 

 

95 = solar zenith angle
(1)5 = solar azimuth angle
9v = View zenith angle
¢v = View azimuth angle
(11 = relative view angle

 

 

 

Figure A.4. Illustration of target viewing and illumination geometry, and associated
angular parameters used in BRDF models. The figure, drawn in perspective, preserves
angles but not distances.

248

 

 

V1 (0,4)

>' V4 (-2,0) V2 (5.0)
Stem (0,0)

 

 

V3 (0,-3)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure A.5. Spline-based tree crown delineation using four, projected-to-the-ground
offsets of crown periphery. Offsets are expressed as vectors V1 to V4. Dashed lines in the
bottom part denote circular arc segments for each of the four quadrants defined by pairs
of clockwise adjacent vectors. Solid line spline segments S6,, 8,) represent the derived
horizontal extent of the crown and are produced by circular are shifting along the X-axis,
proportional to the (R,.-R,,)/Rx ratio. RX 2 |V,| and Ry = |Vi+1|.

249

 

 

 

 

. Crown pseudo centroid True/Pseudo Centroid Discrepancy

. Crown true centroid Mean: . . 0.12m

:1 Tree crowns within the subplot area Standard Devratron: 0-07111

— Subplot perimeter Maximum: 0.28m
Mrnrmum: 0.03m

 

 

 

 

 

Figure A.6. Vertical tree crown projection map for a northern hardwood subplot (24B).
Crowns correspond to the portion of tree foliage visible from above. Dots represent true

and pseudo crown centroids.

250

 

 

 

 

 

D = 1.123!!! D = 2.653m
st.dev(D) = 0.313m st.dev(D) = 0.278111
Dc = 1.179m Dc = 2.677111

 

 

 

 

 

 

 

 

 

Figure A.7. Calculation of crown diameter D as the mean length of lines revolving at 10°
increments around the crown’s centroid. Dc denotes the diameter of a circle occupying
the same area with the crown.

251

APPENDIX 2

252

B.1. Effects of Brightness/BRDF Normalization on Semivariogram

Range Computation.

Let Z(xij) be the digital numbers (DNS) of pixels in the 51 rows by 51 columns
image depicted in Figure B. 1 a and corresponding to a portion of a coniferous forest stand
in the near infrared band, where i and j represent image row and column indices
respectively. An omnidirectional empirical variogram (Figure B.1b) computed for the
image carries a range of approximately 5 distance (pixel width) units. Note that figures in
this dissertation, including the Appendices often contain color. A linear translation
[(Z(x,-J)*1.5)-5000] of the image (Figure B.1c), similar to the one performed during
brightness normalization has no effect on the form of the empirical variogram or its
range, but it does alter the variogram’s sill (Figure B.1d). Such variogram behavior is
expected since addition or subtraction of a DN amount from all pixels does not affect the
square difference of DNS in pixel pairs separated by distance h (Chapter 3, Equation 3.2).
At the same time multiplication of DNS with a constant is a monotonic operation that
preserves the relative ordering of square difference sums for different lag increments.
When however, the original DNS are processed with a non-monotonic or anisotropic
function, such as the one depicted as a surface in Figure B.1f, the square difference of
DNS for pixel pairs separated by distance h and situated at or close to surface locations
with high autocorrelation gradient will be smaller than the square differences of DNS for
pixel pairs separated by the same distance h, but situated at surface locations
characterized by weaker a anisotropy gradient, thus altering the variogram form and
hence its range and sill. Because H-resolution images of forested landscapes contain

intrinsic autocorrelation gradients, the effects of image DN processing with non-

253

monotonic, anisotropic operators on the image variogram would be detectable only when
the autocorrelation gradient introduced by those operators would be weaker than the
intrinsic autocorrelation gradient. Kernel-based BRDF models such as that by Roujean et
al., (1992) involve image processing with functions that exhibit strong autocorrelation
and bi-directional distribution factors (BRFS) usually within the 0.7 to 1.3 range.
Therefore, under most circumstances, BRDF correction operations would only
minimally, if at all, affect computed variogram parameters. In the example of Figure B. l ,
the image processing function represented as a surface, is bounded within the range
aforementioned and, as expected, it does not modify the range of the corresponding

variogram although it appears to influence its form, at least for the larger lag distances.

B.2. Trend Surface Analysis

Let Z be a single band image with Z(s) representing the value (DN, radiance,
reflectance, etc.) of an image pixel at location s with spatial coordinates (s;,s,-), where i
and j represent image row and column indices. Z, as any other image, can be modeled as
a spatially continuous random surface of large-scale variations around a mean value. The
model involves the fitting of polynomial functions of the spatial coordinates S(Si,Sj) of
each pixel, to corresponding image pixel values. The multiple regression model
employed, known as ordinary least squares regression, may be written as
Z(s) = xT(s),8 + e(s) (B.1)
where Z(s) is the image value at location s, xT(s),6 represents the trend or mean value of
the surface at s, and 15(5) is a zero-mean random variable representing fluctuations from

the trend. The (p x 1) vector of x(s) consists of p functions of the spatial coordinates (Si,Sj)

254

of point s. For a linear trend model x(s) = (l , Si, s,-)T, for a quadratic model x(s) = (1, s,-, s,-,
52,-, s2}, sis”) T, and accordingly for higher-order models. ,6 is a (p x 1) vector of parameters

to be estimated when the model iS fitted to the pixel values. Ordinary least squares

estimates ,6 as

19 = (X TX )"I X TZ (13.2)
where Z is the vector of pixel values and X is an (n x ,0) matrix with row vectors xT(s,-j),

i = 1, , n, and j = 1, , m, with n and m representing the number of image rows and
columns respectively.

In imagery of forested landscapes, xT(s),6 can be thought of as the broad-scale DN
variation due to, for example, topographic effects, vegetation ecotones, etc., and a(s) as
the local DN variation due to the structural characteristics of forest canopy. In variogram
analysis of forest stands depicted in hi gh-Spatial-resolution digital imagery and aiming at
identifying the proper window size for subsequent local maximum filter (LMF) imagery
processing (Chapter 3), the presence of a non-zero xT(s)/3 imagery component would
introduce systematic biases in computed variogram ranges (Figure 3.2) (Cressie, 1991),
thus necessitating its elimination. The latter could be accomplished by estimating the
value of vector ,6 elements in equation (8.1) so that s(s) could be isolated from Z(s).
Variogram analysis could then proceed using the 6(8) image component only.

Unfortunately, equation (B.1) assumes that 5(s) is independent among locations
and has constant variance; thus in its equation (8.1) form s(s) cannot be thought of as

representing the structural characteristics of forest canopy. One way to avoid the

implausibility of the assumption in the basic form of the trend surface regression model is

255

to relax the assumption of 6(s) independence by the use of the generalized least squares
approach. The model then becomes

Z(s) = xT(s)fl + U(s) (13.3)
where U(s) is again a zero-mean random variable representing fluctuation from the trend
exhibiting a covariance function C(). In this formulation, the previous least squares
estimates for ,6 is replaced by its generalized least squares equivalent

[5? = (XTc"X)“ XTC'lZ (34)
where C is an (mm x mam) matrix of covariances between all possible U(Sij) pairs in the
image. Generalized least squares provide a way of including both first- and second-order
variation in the model while assuring that parameter estimates allow for spatial
dependence. The only remaining difficulty is that the covariance matrix C is unknown. In

practice, the model described by equation (B. 1) is fit to the pixel values initially using

ordinary least squares regression. Regression residuals are used to estimate a variogram
model )7(), giving rise to an equivalent covariogram model C () . The latter allows the
construction of an estimated covariance matrix C between pixel locations. Subsequently,
the model described by equation (B3) is fit to the pixel values using generalized least

squares with the estimated covariance matrix C. This process adjusts both the model
parameter estimates and the standard errors of the ordinary least squares regression for
second-order autocorrelation. If necessary, the process can be iterative until estimates of

,6 and C() are obtained. The validity of the final model depends upon 1) the choice of an

appropriate form of trend surface, and 2) the choice of an appropriate variogram model.

The decomposition of the image into first- and second-order components in the

256

methodology described above is, to some extent, arbitrary. In reality, the two components
are confounded; certain types of second-order variation can lead to trend-like effects
making it impossible to objectively distinguish between the two components. Additional
obstacles for the application of the generalized least squares approach appear when
process automation is contemplated, primarily because appropriate covariogram model
specification necessitates analyst intervention.

In this study, the effect of trend on variogram range was investigated. Variogram
ranges were computed (i) using the original DNS, (ii) after DN processing with ordinary
least squares, and (iii) after DN processing with five-iteration, generalized least squares.
More than two hundred 50-pixel-wide, circular imagery regions with centers within a
subplot, and equally distributed among cover types were analyzed in the process. The
range of empirical variograms was determined automatically as the shorter lag distance
for which the slope of line segments connecting vertices of a Spline (Hastie and
Tibshirani, 1990) fitted to the empirical variogram was lower than 5%. The lag increment
was set to one third of a pixel.

Fitting of the spline to the empirical variogram was a step necessary towards
process automation. Attempts to determine the range of empirical variograms as the lag
distance for which the corresponding semivariance estimate declines for the first time
(Franklin et al., 1996) proved inappropriate because they were susceptible to sporadic
semivariance underestimation for Short lags. Such a circumstance can be observed at the
post-trend-processed semivariance estimates in Figure B.2 between lag = 2.66 and

lag = 3.00. Using the spline in that case allowed restoring the automatically computed

257

range from 3.00 distance units (pixels) to 5.00, which coincides with the range
determined with visual inspection of the variogram.

Analysis revealed that the instances of unbounded variograms calculated using the
original DNS, were eliminated when either ordinary or generalized lease squares trend
removal was used. In 83% of the total number of imagery regions processed, both
regression models produced identical variogram ranges and in 13% the difference of
computed range was 1 lag increment (i.e. 1/3rd of a pixel). For 4% of the regions, the use
of ordinary and generalized least squares regression on region DNS produced variogram

3’°s of a

ranges that differed in magnitude between 2 and 5 lag increments (2/3rds and 5/
pixel respectively). However, no patterns in the Spatial distribution of regions for which
discrepancies in the range of DN variograms calculated after processing with ordinary
and least squares regression could be established. Thus was decided to use ordinary least
squares regression for the first-order DN autocorrelation removal. Variogram ranges

computed automatically on the trend-processed imagery were used to determine

appropriate window sizes for subsequent LMF imagery processing.

258

Literature Cited

Cressie, N. 1991. Statistics for Spatial Data. John Wiley, Chichester, UK.

Franklin, S.E., M. Wulder, and M. Lavigne. 1996. Automated derivation of geographic
windows for use in remote sensing digital analysis. Comp. Geosci., 222665-673.

Hastie, T.J., and R.J. Tibshirani. 1990. Generalized Additive Models. Chapman and Hall,
London, UK.

Roujean, J.L., M. Leroy, and P.Y. Deschamps. 1992. A bi-directional reflectance model
on earth’s surface for the correction of remote sensing data, J. Geophys. Res., 97:455-
468.

259

Figures

 

 

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(e)

 

Figure 13.1. (a,b) Portrayal of original digital numbers Z(XU) for row i and column j
indices of the NIR band for a coniferous stand and corresponding omnidirectional
empirical variogram.(c, b) Portrayal of digital numbers after image linear translation and
corresponding empirical variogram. (e, f, g). Portrayal of digital numbers after processing
original imagery with surface D(x,J) approximating an imaginary anisotropic kernel
Similar to those typically embedded within BRDF normalization models, and
corresponding empirical variogram.

260

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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by using the DNS of pixels within the subplot prior to and after processing for removal of
first order autocorrelation. Circle in orange superimposed on the image denotes the
subplot boundary. Lines in the variogram plot denote a spline fit on the estimates of
semivariance.

261

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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depicting a Red Pine subplot.

262