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A Framework for Texture Analysis
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James Michael Coggins

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A FRAMEWORK FOR TEXTURE ANALYSIS BASED ON SPATIAL FILTERING
BY

James Michael Coggins

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Computer Science

I982

ABSTRACT
A FRAMEWORK FOR TEXTURE ANALYSIS BASED ON SPATIAL FILTERING
By

James Michael Coggins

A texture analysis method motivated by a theory of human visual
information processing and based on spatial filtering is defined and
evaluated for classification and segmentation of textured images.

The problem of texture analysis is viewed as an attempt to
duplicate the texture analysis performance of human vision. This
performance is considered to be a consequence of certain information
reductions (filtering) performed in early stages of vision which are
modelled by a sequence of filters defined in" the spatial frequency
domain. The implementation of the model results in a sequence of
spatial domain filtered images which contain limited spectral
information from the original image.

Features which are interpreted as measurements of average local
energy are defined and evaluated in texture classification experiments.
The energy features are found to outperform power spectral features;
this is attributed to the use of phase information in the filtered
images. This contrasts with previous studies in which phase was
assumed to be unimportant for texture analysis. The channel filtering
features are found to be insensitive to global, constant gray level
changes, making some preprocessing operations unnecessary. Procedures
are demonstrated for determining that two images portray the same

I texture at different magnifications or orientations.

A method for computing a texture feature vector for a neighborhood
about each pixel in the image is defined and demonstrated in texture
segmentation experiments. An image is segmented by identifying
clusters in the feature space and labelling each pixel by the cluster
in which its feature vector lies. A cluster validity statistic is used
to determine an appropriate number of clusters. The results indicate
that the channel filtering feature space is an appropriate

representation of image texture for segmentation.

TABLE OF CONTENTS

List of Tables .................................................. v
List of Figures ................ ..... ............ . ..... . ...... viii
Acknowledgements . ................. ...... ..... .... .......... ..... x
l lntroduction
1.] Computational Vision ...... .... ............. ...... ......... l
1.2 Texture ............................... .......... . ....... .. 2
l.3 Guidance from Studies of Human Vision .............. ....... 3
l.h Spatial Filtering ............... ......... .. .......... ..... 5
l.5 Organization of This Dissertation ......................... 6
2 Toward a Definition of "Texture" V
2.l Introduction .................... ........ .................. 8
2.2 Studies of Human Texture Perception .............. ......... 9
2.3 Properties of Texture and of Texture Perception .......... l2
2.h Comments on the Catalog of Texture Definitions ... ...... ... l5
2.5 Summary .................................................. l6
3 Models and Methods in Texture Analysis
3.l Introduction ............................................. 17
3.2 Local Analysis Methods ............................. ..... . 17
3.3 Global Analysis Methods .................................. 2i
3.h Intermediate Analysis Methods ............................ 26
3.5 Image Modelling Methods .................................. 29

3.6 Summary .................................................. 3i

h A Texture Analysis Method Based on a Theory of Human Vision
h01|ntr°ducti°n 000...... ..... ......OIOOOOOOO0.0.0.0000...... 33

h.2 A Critical Re-evaluation of Texture Analysis Methodology . 33

h.3 Spatial Frequency Channels ....................... ........ 35
h.h Constraints on Possible Texture Features ............. .... Ah
h.5 Properties of Channel-Filtered Images . .................. . L7
h.6 Definition of Texture Features ............ ......... ...... A8
h.7 How Will the Texture Features Be Used? .... ........ ....... 5i

h.8 Summary .................................................. 52

5.l Introduction ............................................. 53
5.2 Evaluations of the Features on Natural Images ............ 55
5.2.] Experiment l: Natural Images, 6hx6h Subimages ........ 58
5.2.2 Experiment 2: Natural Images, 32x32 Subimages ........ 62
5.2.3 Experiment 3: Natural Images, l6xl6 Subimages ........ 6h
5.2.h Summary ........... . ........ ......... ....... .......... 65

5.3 The Effect of Histogram Equalization ..................... 65

5.3.1 Experiment h: Histogram Equalized Images, 6hx6h Subimages.

5.3.2 Experiment 5: Histogram Equalized Images, 32x32 Subimages.

5.3.3 Summary .............................................. 75
5.h Experiment 6: Uniform Gray Level Changes ................. 76
5.5 Experiment 7: Magnification Changes ...................... 79
5.6 Experiment 8: Orientation Changes ....... ............... .. 82
5.7 Experiment 9: Phase Spectrum Changes .. ........... . ..... .. 86
5.8 Second-Order Statistics and Channel Filtering ............ 92

5.8.] Experiment 10: Application of the Co-occurrence Method,95

5.8.2 Experiment ll: Application of Channel Filtering ..... lOl

Evaluation of Channel Filtering Features for Texture Classification

69
72

5.8.3 Summary ......... ......... ... ...... ..................

5.9 Computational Simplifications ...... ........ . ......... ...

5.9.i Experiment 12: Using Fewer Channels ... ....... .......

5.9.2 Experiment 13:

5.10 Summary .....

Ideal Bandpass Channels ..............

IO3
10b
l0“
IOS

107

6 Evaluation of Channel Filtering Features for Texture Segmentation

6.l Segmentation .......

6.2
6.3
6.h
6.5
6.6
6.7
6.8
6.9

7 Summary and Conclusions

00.000.000.000...0.0.00.0... ..... 0...

Computing Texture Features for Segmentation . ....... .....
Segmentation Using Feature Images ............. ..... .....
Evaluating the Segmentations ............................
Segmentation Experiment I: Dot Textures .................

Segmentation Experiment 2: Gaussian White Noise .........

Segmentation Experiment 3: Natural Image Composite ......

Segmentation Experiment h: SCRE Image ...................

Summary .......

7.1 Summary . ............................... . ................

7.2 Conclusions ........................... .. .............. ..

7.2.l Classification ...

7.2.2 Segmentation . ..... ......

7.

2.3 General ..

7.3 Advantages of the Channel Filtering Method ..............

7.h Disadvantages of the Channel Filtering Method ...........

7.5 Suggestions for Further Research ......... ............ ...

Appendix A:
Appendix B:

List of References .......

A Catalog of Texture Definitions ..................

Definition of Channel Filters .....................

l09
llO
II3
IIS
116
123
12h
I36
136

M3
m.
IAI.
1A6
IA]
IAB
11.9
150
152
l56
158

List of Tables

Table 1: Classification of Eight Natural Image Classes
Using 6hx6h Subimages ......... . ....................... 59

Table 2: Classification of Eight Natural Image Classes
Using 32x32 Subimages ..... ... ....... ...... ............ 63

Table 3: Classification of Four Natural Image Classes
Using l6xl6 Subimages ............ ....... ... ........... 65

Table h: Classification of Eight Histogram-Equalized
Natural Image Classes Using 6hx6h Subimages ........... 70

Table 5: Classification of TILE, ROCK, SAND. PAPE and
TILQ, ROCQ, SANQ, PAPQ Using 6Ax6h Subimages ........ .. 71

Table 6: Classification of CORK, GRAS, WOOD, SCRE and
CORQ, GRAQ. WOOQ, SCRQ Using 6hx6h Subimages ........ .. 72

Table 7

Classification of Eight Histogram-Equalized
Image Classes Using 32x32 Subimages ...... ... ..... ..... 73

Table 8: Classification of TILE, ROCK, SAND. PAPE and
TILQ, ROCQ, SANQ, PAPQ Using 32x32 Subimages .......... 7h

Table 9: Classification of CORK, GRAS, WOOD, SCRE and
CORQ, GRAQ, HOOQ. SCRQ Using 32x32 Subimages ......... . 75

Table 10: Classification Results Showing the Effect of
Average Gray Level Changes .............. ...... ........ 78

Table 11: Size Change Experiment Using 6 Spatial
Frequency Channels ..................... ............... 80

Table l2: Size Change Experiment Using 5 Spatial
Frequency Channels 0.00.00.00.00.000000000000000.000.0. 82

Table I3: Orientation Experiment Using No Channel Shifting ...... 85

Table lh: Orientation Experiment Using Circular
Channe' Shifting ......OOOOOOOOOOOO0.00.....000000.0... 86

Table 15: Classification Results on Four Phase-Modified
Gaussian White Noise Classes .......................... 90

\l

Table 16: Classification Results Illustrating the Effect
of Phase Spectrum Changes on Gaussian White Noise Images 9]

Table 17: Phase Modification Experiment with Indiscriminable
Classes Merged OI000......0............OOOOIOOOOOOO0... 92

Table 18: Black-Black Displacement Vectors in Four-Dot
Micropatterns 00......OOOOOOOOCOOOOOOOOOOOOOO. ...... 0.0 96

Table 19: Computation of Expected Number of Black-Black
Co-occurrences in 256x256 Four-Dot Images .... ......... 98

Table 20: Classification of Four-dot Textures Using
Co-occurrence Matrices ................. ...... ........ 100

Table 21: Classification of Four-dot Textures by
Channel Fi‘tering ......OOOOOOOOOOOOO...... 00000000 0.010]

Table 22: Classification of Four-dot Textures Using
Six Spatial Frequency Channels ................. ...... 102

Table 23: Classification of Four-dot Textures Using
Four Orientation Channels ............................ 103

Table 2h: Classification Results on Natural Images Using
Eight Channels ......OOOOOOOOOOOOOOOO000...... ..... 0.0106

Table 25: Classification Results on Natural Images Using
Ideal Bandpass Channels ...................... ..... ... 107

Table 26: Evaluation of Clustering on Dots Image Using
8x8 Averaging Windows ................................ 122

Table 27: Evaluation of Clustering on Dots Image Using
16x16 Averaging Windows .......... .................... 123

Table 28: Evaluation of Clustering on Gaussian White Noise
Image Using 8x8 Averaging Windows ............. ..... .. 131

Table 29: Evaluation of Clustering on Gaussian White Noise
Image Using l6xl6 Averaging Windows .................. 132

Table 30: Evaluation of Clustering on Composite Natural
Image Using 8x8 Averaging Windows .................... 13h

Table 31: Evaluation of Clustering on Composite Natural
Image Using l6xl6 Averaging Windows .................. 135

Table 32: Evaluation of Clustering on SCRE Image Using
8x8 Averaging Windows ................................ 1&0

vi

Table 33: Evaluation of Clustering on SCRE Image Using
l6xl6 Averaging Windows ........... ..... .............. 1&1

vii

Figure
Figure
Figure
Figure
Figure

Figure

Figure
Figure

Figure

Figure
Figure
Figure
Figure
Figure

Figure

Figure
Figure

Figure

Figure

LIST OF FIGURES

' Sinusoidal Gratings ............................. ..... . 2h

Diagram of the Spatial Filtering Procedure ........ .... 38

: A Spatial Frequency Channel Filter ........ .......... .. 39

A: An Orientation Channel Filter ......................... #0

10:
ll:
12:
13:
1h:

15:

16:

17:
18:

An Example of Channel Filtering ....................... £2

Indiscriminable Textures which Could Be Discriminated
Based on the Edge Structure of the Micropatterns ...... A5

Texture Feature Definitions ... ....... ................. 50

. Natural Image Classes ................................. 56

° Mean Values of Feature 1 in Each Channel for

the Eight Natural Image Classes .......... ............. 61
Histogram-Equalized Natural Images ............ ..... ... 67
Gaussian White Noise Images ....... ....... ............. 77
Bar Images for Orientation Experiment ......... ........ 8h
Phase Spectrum Modification Procedure ................. 88
Effect of Phase Modification on GWNI ..... ..... ........ 89

Four-Dot Micropatterns and Corresponding
Image Classes .........OOOOOOOOOOOOOOOO......OOOOOOOOOO 93

Diagram of the Segmentation Procedure ................ 111
Dots Image for Segmentation Experiment 1 ............. 117

Segmented Images for Dots Using 8x8 Averaging
Windows .........O...........................OOOOOOOOO1‘9

Segmented Images for Dots Using l6xl6 Averaging
Windows ......OOOOOOOOOOOOOOOOOOOOOOO0.000000000000000 ‘20

viii

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

20: Gaussian White Noise Image for Segmentation

Experiment 2 ....................... . ..... . ........... 125
21: Segmented Images for Gaussian White Noise

Using 8x8 Averaging Windows .... ..... .... ............. 126
22: Segmented Images for Gaussian White Noise

Using l6xl6 Averaging Windows ........................ 127
23: Natural Image Composite for Segmentation

Experiment 3 ..... .................. . ............ ..... 128
2A: Segmented Images for Natural Image Composite

Using 8x8 Averaging Windows ..... .. ...... .. ........... 129
25: Segmented Images for Natural Image Composite

Using 16x16 Averaging Windows ....... . .............. .. 130
26: SCRE Image for Segmentation Experiment A ..... ........ I37
27: Segmented Images for SCRE Using 8x8 Averaging

Windows ........................ .. .. ..... .. . ........ 138
28: Segmented Images for SCRE Using 16x16 Averaging

Windows ....... O... ..... ..OOOOOOOOOOOOOOOOOOOOO ....... 139

ACKNOWLEDGEMENTS

I would like to thank Dr. AniI K. Jain for his guidance,
patience, and persistence in his role as advisor, critic, editor, and
taskmaster. His careful editing has contributed greatly to the quality
of this document and his critical scrutiny of my work has kept me out
of a lot of trouble. I am also grateful to Major Arthur Ginsburg,
whose filtering model of human vision forms the foundation on which my
work is built. In addition to teaching me about the spatial filtering
model, psychOphysics. and scientific writing, Maj. Ginsburg also
served on my doctoral committee. I would also like to thank the other
members of the committee, Dr. Richard Dubes, Dr. Carl Page, and Dr.
James Zacks for their contributions throughout my research.

Several persons have provided software tools without which some
aspects of my work would have been nearly impossible. These include
Larry Johnson, George Cross. Ken Dimoff, Steve Smith, Neal Wyse. and
Gautam Biswas.

I would also like to thank Dr. Harry Hedges for his support, and
Ardeshir Goshtasby, John Piippo, Steve Smith, and Steve Fullenkamp for

their various contributions.

Chapter 1

Introduction

1.1 Computational Vision

Computer applications involving visual input include problems in
aerial image interpretation [Darling and Joseph. 1968: Kettig and
Landgrebe, 1976: Landgrebe, 1981], biomedical image analysis [Bacus,
1976; Pressman, 1976; Hall et al, 1977; Landeweerd and Gelsema, 1977:
Mui et a1, 1977; Jain et a1, 1980: Trussel, 1981], industrial processes
[Perkins, 1978; Tennenbaum et al, 1978; Agin, 1980], and robotics and
scene analysis [Duda and Hart, 1973: Marr and Nishihara, 1978; Barrow
and Tennenbaum, 1981; Stevens, 1980: Aggarwal et a1, 1981]. Hardware
for acquiring, storing, and displaying images is available, and current
computers are capable of performing some image analysis tasks in
real-time. The development of algorithms for processing images has
proven to be a slow and difficult task [Gurari and Wechsler. 1982].
Image analysis methods have been developed in the fields of pattern
recognition [Duda and Hart, 1973; Fu, 197A, 1977: Pavlidis, 1977],
image processing [Pratt, 1978: Rosenfeld and Kak, 1981] and artificial
intelligence [Winston, 1977; Nilsson, 1980]. The inquiries in these
three fields involving approaches to automatic image analysis,

interpretation. and understanding are sometimes referred to

collectively as “computational vision” [Brady, 1982: Barrow and
Tennenbaum, 1981].

In order to cape with the variety and complexity of activities
associated with vision, several subproblems within computational vision
have been identified including image enhancement, edge detection,
segmentation, image registration, and texture analysis. These
subproblems have been attacked separately and have tended to evolve
into subfields themselves. This has the advantage that many different
techniques with different characteristics are available as tools for
use in applications. The separation of the subproblems has the
disadvantage that similarities in the solutions to different problems
may be overlooked and that diverse solutions to the subproblems of
vision complicate the construction of unified computational vision

systems.

1.2 Texture

Human observers are capable of some image segmentation and
discrimination tasks under conditions (such as brief exposure to a test
image) which prevent detailed scrutiny of the image. This ability is
referred to as “effortless” or "pre-attentive” visual discrimination.
When an image does not portray any particular object or form, only
certain aspects of the overall pattern of gray level changes in the
image is effortlessly perceived. "Texture" sometimes refers to the
pattern of gray level variations produced by some image generation
procedure. However, different procedures may yield images which are

not effortlessly discriminable to human observers. In this thesis, two

images which do not portray particular objects or forms will be
considered to have the same "texture" if they are not effortlessly
discriminable to human observers.

Texture is recognized as being fundamental to the perception of
regions and surfaces in images [Brady, 1982: Stevens, 1980]. Textural
information can potentially be used by automatic vision systems in
region identification, image segmentation and classification tasks.
Texture analysis is a major component in discussions of general
computer vision systems [Sklansky, 1978: Wechsler, 1980: Barrow and
Tennenbaum, 1981: Brady, 1982].

The potential importance of texture for automatic vision systems
has inspired many attempts to develop algorithms for texture analysis.
Unfortunately, the characterization of texture in terms of human
performance does not suggest a simple measurement on images which can
duplicate human texture perception. This lack of precise guidance has
led to a proliferation of ad hoc texture analysis methods based on
diverse mathematical, statistical and heuristic measurements on images.
Most texture analysis methods duplicate human performance reasonably
well for some image classes, but they fail to duplicate human

performance in more general problems.

1.3 Guidance from Studies of Human Vision

Since a texture analysis algorithm is supposed to duplicate the
performance of human vision, it seems reasonable to look to vision
science for guidance in developing such algorithms. Computational

methods need not emulate the human visual system, but knowledge of the

limitations and strategies present in human vision could guide the
development of useful algorithms.

Some texture analysis algorithms have been guided by results of
psychophysical experiments designed to find an upper bound on the
complexity of texture perception. The nature of texture is described
by specifying a statistical property which indiscriminable textured
images appear to have in common. This type of description is intended
to constrain the nature of texture by a criterion which is independent
of human performance, but the generality or minimality of such a
criterion is difficult to establish. Such results have guided many
texture analysis studies, but bounds on the complexity of
indistinguishable stimuli do not necessarily suggest a particular
algorithm which will reproduce human performance.

While algorithms for computational vision need not emulate human
vision at the neural level, knowledge of the overall strategies used by
the visual system for analyzing images could provide more definite
guidance for developing algorithms. We will use one such theory in
this dissertation to motivate the development of a new approach to
texture analysis.

This theory characterizes early stages of the human visual system
as being composed of quasi-independent mechanisms,called channels,
which decompose an image into certain bands of spatial frequency and
orientation [Ginsburg, 1971]. This decomposition is modelled by a
spatial filtering operation using filters defined in the spatial
frequency domain [Ginsburg, 1978, 1980b]. The result of the
decomposition is a sequence of filtered images in the spatial domain

which contain limited spectral information from the original image.

The channel filtering theory is not simply a generalization of
human visual behavior; it is an attempt to describe the information
content and possible processing strategies in early human vision. The
theory implies that many aspects of visual perception are consequences
of the information reduction (filtering) performed by the perceptual
system [Ginsburg, 1978, 1980b]. Thus, in order to characterize texture
perception, it may be most effective to determine first how the human
visual system filters the information in an image. The particular
decomposition of an image performed in early stages of vision can

explain why certain stimuli are discriminable and others are confused.

l.h Spatial Filtering

The channel filtering theory asserts that the early processing of
an image by the human visual system is effectively modelled by a
spatial filtering operation. Spatial filtering is a technique which
has been useful in several areas of computational vision. Two
equivalent implementations of spatial filtering exist; one involves
convolution in the spatial domain, and the other involves
multiplication in the spatial frequency domain. The use of spatial
filtering as a computational tool for image analysis is attractive
because of its well-known mathematical basis, because of the
availability of efficient algorithms for performing the Fourier
transform, and because of the existence of intuitively satisfying
interpretations for the Fourier transform and for spatial filtering.

Some uses for spatial filtering in computational vision are

two-dimensional extensions of well-known one-dimensional operations

[Papoulis, 1962]. Low-pass filtering has been used to remove noise
from an image [Rosenfeld and Kak, 1981]. High-pass filtering has been
applied to edge detection, and in fact, a certain filtering approach
has been shown to be an "optimal" edge detection method [Shanmugam et
al, 1979]. Band-pass filtering has been applied to form and edge
detection [Ginsburg, 1976, 1978, 1979a, 1980a, 1980b: Crowley and
Parker, 1978: Marr et a1, 1979; Marr and Hildreth, 1980]. Spatial
filtering was also used in an implementation of a theory of stereo
vision which involved Operations similar to those required in image
registration [Marr and Poggio, 1979]. Several approaches to texture
analysis, such as those based on edge detection or template matching
can be implemented using spatial filtering operations [Laws, 1980].

In this study, a computational vision system will be defined by
specifying its filtering properties in the spatial frequency domain.
The filter characteristics to be used are adopted from studies of human
vision, but this study will not attempt to determine in detail the
correspondence between human vision and the computational vision
system. Methods for texture classification and segmentation based on

the computational vision system will then be defined and evaluated.

1.5 Organization of This Dissertation

This dissertation will begin by reviewing the results of previous
research in texture analysis. Chapter 2 reviews attempts to define or
at least to delimit the nature of "texture". This review includes
results from vision science and principles derived from human intuition

and experience with texture perception. In Chapter 3, texture analysis

algorithms proposed in the literature will be reviewed. Chapter A will
present a new texture analysis method based on spatial filtering.
Chapters 5 and 6 present the results of experiments which evaluate the
proposed method for classifying and segmenting textured images. The
conclusions of this study will be summarized and further research will

be suggested in Chapter 7.

Chapter 2

Toward a Definition of “Texture”

2.1 Introduction

In order to use textural information, the computer vision system
requires an operational definition of "texture". In the absence of a
sufficiently precise general definition, the operational definition of
texture is implicitly supplied in the features computed from an image.
This feature space then constitutes a model of "texture”.

How can an operational definition for texture be constructed? A
reasonable first step is to observe the texture analysis performance of
the human visual system [Haralick et al, 1973; Barrow and Tennenbaum,
1981]. Texture is a common and important aspect of human visual
perception. Everyday experiences with texture analysis and recognition
tasks provide an extensive background of intuition regarding the nature
of “texture". One common manifestation of this intuition is in the
adjectives we use to describe textures. For computational texture
analysis, however, the nature of texture must be precisely quantified.
Texture analysis has sometimes been approached as the problem of
quantifying our intuition and our vocabulary about texture.

Some early attempts to construct automatic texture analysis

procedures referenced certain results from vision science which

appeared to limit the complexity of human texture perception. Textured
areas which did not differ in certain simple statistical measurements
were found to be indiscriminable to human observers. These
psychophysical results provided a useful upper bound on the complexity
of texture in human vision but little guidance concerning what
approaches should be effective for computational purposes. Section 2.2
reviews these influential findings and recent extensions and
modifications to them.

Several intuitive properties of texture and of texture perception
were identified, and image analysis techniques were proposed which
seemed to measure aspects of an image which were relevant to those
properties. These results provide some valid insights into the nature
of texture, though they actually tell more about how textures are
perceived than about what texture is or how to compute texture. A
summary of these results is presented in Section 2.3.

The intuitive insights into the nature of texture have not
produced. a characterization from which simple computational procedures
can be developed. Researchers attempting to present new texture
analysis techniques have found it awkward and difficult to describe the
properties of images which their techniques are supposed to measure.
Section 2.A will discuss the Catalog of Texture Definitions in Appendix

A.

2.2 Studies of Human Texture Perception

Experiments by Julesz [Julesz, 1962, 1965, 1975; Julesz et al,

1973] have influenced the development of texture analysis methodology.

10

In these experiments, human observers are presented an image composed
of subimages which are generated by different rules. The subject's
task is to find the different subimages. The composite image is
displayed to the observer for very brief periods (100 ms) in order to
prevent the observer from scrutinizing the image to find the different
areas. Since the test images typically contained many repetitions of
some micropattern and since the segmentation was to be performed
without scrutinizing the image, the subimages were considered to have
different ”textures" and the experiments were interpreted as tests of
pre-attentive human texture analysis ability. The tests would
demonstrate the complexity of the processing performed in the visual
system before detailed analysis involving cognition or memory could
begin.

Notice that in such experiments, including [Julesz, 1962, 1965,
1975: Julesz et a1, 1973: Pratt et al, 1978; Richards and Polit, 197A],
“texture" is treated as an intrinsic property of an image determined by
the image generation procedure. Pre-attentive human vision is then
tested, and can succeed or fail in the texture discrimination task.
The results of these tests were examined to find some properties of the
generated images which could predict whether the human visual system
could preattentively discriminate different subimages.

One generalization of the results of these preattentive
discrimination experiments became known as the "Julesz Conjecture".
This conjecture asserted that image areas which do not differ in their
second-order gray level joint probability distributions cannot be
preattentively discriminated by human observers. The conjecture was

seen to imply that computational methods no more complex than the

ll

computation of second-order gray level distributions should be
sufficient to rival human performance in texture discrimination tasks.
Texture analysis researchers used this conjecture as a justification
for limiting the complexity of their techniques to fairly simple
computations.

Unfortunately, the Julesz Conjecture was wrong. Later studies
[Caelli and Julesz, 1978a, 1978b: Julez et a1, 1978; Julesz, 1981:
Gagalowicz, 1981] have produced many examples of images which have
identical second- and even higher-order gray level joint probability
distributions but which are visually discriminable.

Revisions to the original Julesz Conjecture have been attempted.
One recent attempt [Julesz, 1981] involves the assumption of special
geometrical structures called "textons" which, allegedly, are detected
in early stages of vision. The textons involve local geometrical
structures and include "corner”, "closure”, and "connectivity".
Detection of these special features is assumed to enable discrimination
of textures which have identical second-order distributions.

Another recent paper [Gagalowicz, 1981] modifies the original
conjecture by suggesting that the actual co-occurrence matrices (an
estimate of the second-order gray level distribution; see Section 3.2)
derived from Ithe given image should be used to characterize textural
properties rather than the underlying probability distribution. The
argument is that two discriminable texture fields can be produced from
the same probability distribution if the generating process is not
ergodic [Papoulis, 1965]. In such a case, the random differences
between the images due to the non-ergodicity of the generating

procedure can be a textural discriminating factor.

12

In spite of the problems which have been discovered with texture
characterization based on second-order distributions, methods based on
the Julesz Conjecture are still used in texture analysis applications.
One study [Pratt et al, 1978] attempts to characterize the cases when
the conjecture fails and when the conjecture works. They conclude that
the Julesz conjecture is a reasonable approximation to human

performance in many texture discrimination problems.

2.3 Properties of Texture and of Texture Perception

Introspective observation of human texture perception has provided
some insight into the nature of texture. These observations do not
constitute a definition of texture: instead, they serve to guide and
constrain the development of computational texture analysis methods.

The use of constraints in the absence of precise definitions is a
basic approach in artificial intelligence (AI) research. As
computational vision problems (such as texture analysis) have been
found to resist attempts to define fundamental terms, the AI approach
of finding and exploiting constraints has been adopted [Zucker, 1981].

The intuitive guidance for texture analysis methods can be
summarized in four principles (cf. [Beck, 1980]).

1. Texture is a property of areas: the texture of a point is
undefined. Thus, operations on a random sampling of pixels would not
be an appropriate texture analysis procedure since texture does not
exist in context-free intensities. Texture is a global property of a
region, but the region under consideration can be a fairly small

subimage of a larger scene. Analysis of textures over small areas

13

occurs when one attempts to find a boundary between two textured areas
[Haralick, 1975; Thompson, 1977].

2. Texture involves the spatial distribution of gray levels
throughout a region. This spatial property could be characterized by
statistical features computed over regions or by maintaining position
(or relative position) information throughout processing. A
one-dimensional gray level histogram is not, by itself, an appropriate
texture analysis tool because it captures no spatial information.
Two-dimensional histograms, or co-occurrence matrices (Section 3.2),
are more reasonable texture analysis tools because a spatial parameter
is incorporated in the histogram computation.

The minimum size of an image which adequately characterizes a
texture depends on several factors including the apparent size of
”objects" in the image, the resolution of the image acquisition system,
and the size of the ”operators” used in the texture analysis procedure.
The perception of texture depends on the assumption of a frame of
reference [Haralick, 1979] governing the sizes of gray level changes
'which are to be considered significant and the spatial scale which is
to be Operated upon. Since texture information can be found at many
different scales, recent papers have advocated multi-level or
hierarchical descriptions of regions for texture analysis [McCormick
and Jayaramamurthy, 1975: Crowley and Parker, 1978; Ehrich and Foith,
1978: Tomita, 1981; Zucker and Kant, 1981]. Alternatively, the
frame(s) of reference can be adopted from human performance [Ginsburg
and Coggins, 1981].

3. Texture is perceived in image regions which contain many

equally significant gray level changes. This implies that the gray

1A

levels in a "textured” region have low redundancy and high information
content [Resnikoff, 1981]. A textured region can be created by
inserting large numbers of "objects” such as edges, regions of constant
gray level, or micropatterns [Hall et al, 1977]. Alternatively,
texture can be created by removing all "enumerable objects" [Richards
and Polit, 197A]. In either case, a "texture" is perceived when
significant individual forms are not present.

A. Textural properties of regions are invariant through moderate
changes in overall brightness, orientation, and size (as in
magnification/shrinkage). While these changes are observable, an
original texture and a modified version of the same texture are
recognizable as being samples of the same texture. (Some interesting
points about textural invariance are made in [Modestino et al, 1981;
Ginsburg and Coggins, 1981].)

Another potential source of guidance is in the perceived qualities
of texture. Textural qualities are typically expressed by adjectives
such as coarse, streaked, sharp, irregular, fine, cellular, rippled,
directional, etc. One texture study [Tamura et a1, 1978] investigated
rank correlations between human evaluations of natural textures and
statistical features designed specifically to quantify textural
adjectives. Six perceptual dimensions of texture were specified, as
follows: coarseness (coarse vs. fine), contrast (high contrast vs.
low contrast), directionality (directional vs. non-directional),
line-likeness (line-like vs. blob-like), regularity (regular vs.
irregular) and roughness (rough vs. smooth). In psychophysical
experiments, subjects evaluated 16 natural textures from [Brodatz,

1966] along the six dimensions. Correlations among these six features

15

indicated that the features were not independent. In fact, the
features cluster into two groups [Ginsburg and Coggins, 1981]. One
group (coarseness, contrast, and roughness) appears to be affected by
the apparent size of the texture while the other group (directionality,
line-likeness, and regularity) appears to be affected by directional
dependencies in the image. The clustering of the subjective features
suggests that more general or fundamental descriptions of textured
images may exist. Statistical features designed to duplicate the human
evaluations of image textures along the six intuitive dimensions

yielded poor results.

2.A Comments on the Catalog of Texture Definitions

Appendix A contains a collection of attempts by texture analysis
reSearchers to define “texture". It should be noted that many papers
dealing with methods for quantifying visual texture do not even attempt
to define the concept of “texture". The selections in the appendix are
typical of the definitions which do appear.

Usually, attempts to define “texture” are either constructed
specifically for a particular texture analysis approach [Appendix A,
items 1, 3, A], or they are so general that they are of little
practical value [item 2]. Some “definitions” simply characterize
“texture” by certain aspects of the human perception of textures [items
A-6].

Texture can be characterized as a global property [items 5, 7], a
local property [item 2], a random phenomenon [item 3], a non-random

phenomenon [item 9]. a property of a region which remains when all

16

”objects” are removed [item 6], a property of a region when many
"objects" are present [item 5], a property determined by structural
arrangements of objects [items 1, A, 5, 9], a property determined by
statistical distributions [items 3, 7].

Unfortunately, these attempts to define texture have not suggested

simple computational texture measurements [item 10].

2.5 Summary

Texture is a commonly perceived quality of regions and surfaces,
but no precise, general definition of texture exists. Texture analysis
research has been guided by some results concerning the complexity of
texture analysis in human vision and by intuitive properties of
texture. These results serve to constrain the nature of texture, but
not to define texture or to suggest what computational approaches might
be appropriate for texture analysis. An attempt to directly quantify
the textural qualities perceived by human observers yielded poor
results. Due to the lack of more precise guidance, awkward and even
contradictory “operational definitions” of texture have appeared in the

literature.

Chapter 3

Models and Methods in Texture Analysis

3.1 Introduction

The process of analysis or measurement of texture is inseparable
from the process of creating an operational definition of texture. The
features computed from an image and the decision procedures applied to
the features constitute a working definition of ”texture". Existing
reviews of texture analysis methods [Hawkins, 1969: Rosenfeld and Troy,
197A; Sklansky, 1978: Haralick, 1979: Wechsler, 1980] concentrate on
the mathematical or computational techniques on which the methods are
based. This review will organize the methods according to the nature

of the operational definition of “texture" implied by the methods.

3.2 Local Analysis Methods

The unifying aspect of texture analysis methods reviewed in this
section is a dependence on small groups of neighboring pixels. This
local information may then be averaged or accumulated over a region for
use in characterizing the texture of the region.

This approach is typical of many "statistical” texture analysis

procedures. Among these are the gray level run length method

17

18

[Galloway, 1975], the gray level difference method [Weszka et al, 1976]
and the gray level co-occurrence method [Haralick et al, 1973]. All
three methods involve counting the occurrences of a simple local
property over the entire region. In each case, the local property is
easy to identify and each instance of the property involves only a few
pixels. Since the local property depends on the gray levels of the
pixels, accumulations are stored in a matrix whose size depends on the
number of gray levels available in the quantization procedure.
Statistics are then computed from the matrix for use as texture
features.

In the gray level run length method, the local property is the
number of linearly adjacent pixels with a specific gray level. The
matrix Rd(i,j) gives the number of runs of length j of pixels with gray
level i in direction d. Four such matrices can be computed, for d-O,
A5, 90, and 135 degrees.

In the gray level difference method, the local property is the
absolute difference between the gray levels of pixels at a specified
displacement d-(dx,dy) from each other. The matrix Gd(i) gives the
number of times that a gray level difference of i occurs between pixels
at displacement d from each other.

In the gray level co-occurrence method, the local property
consists of the gray levels of two pixels with a given displacement
d-(dx,dy). The matrix Hd(i,j) gives the number of occurrences of a
pixel with gray level i at displacement d from a pixel with gray level
j.

The displacement vectors for the difference and co-occurrence

methods could be any vectors which can occur within the image. In

19

practice, however, fairly small vectors (|d|<10) are used. Since the
co-occurrence matrix is sensitive to gray level changes over a certain
distance, the use of small displacement vectors involves an assumption
that texture exists in the gray level distributions in local areas of
an image.

In the co-occurrence method especially, the matrices for several
displacement vectors can be added together to remove certain
orientation dependencies. For example, Haralick uses a definition
which involves the sum of the co-occurrence matrices for vectors
i(dx,dy) and (-dx,-dy) [Haralick, 1979]. This particular definition
results in a symmetric co-occurrence matrix.

In comparative evaluation studies [Weszka et al, 1976; Conners and
Harlow, 1980a] involving these texture analysis methods, the
co-occurrence method was found to be superior, with the gray level
difference method a close second. These comparative studies have
influenced the frequent use of the co-occurrence method in
applications.

Some of the problems associated with local analysis methods are as
follows:

(1) The choice of the displacement vectors is critical.

(2) The visual significance of the features computed from .the
matrices is sometimes difficult if not impossible to understand. This
difficulty has led to attempts to capture textural adjectives directly
in statistical features [Tamura et al, 1978: Conners, 1979].

(3) The local analysis methods are sensitive to ”noise" due to
their dependence on actual gray level values. In addition, the gray

scale resolution determines the size of the accumulation matrices

20

independent of the image size, making comparison of textural properties
of images digitized under different circumstances difficult.

(A) Local analysis methods are insensitive to global aspects of
the image such as brightness gradients and directional tendencies.

Another type of local analysis method attempts to characterize the
pattern of gray levels encountered in one-dimensional scans of the
image. This scan can be analyzed as a one-dimensional function using
time series techniques [McCormick and Jayaramamurthy, 197A: Deguchi and
Morishita, 1978] or heuristic analysis of extrema in the function
[Ehrich and Foith, 1978: Mitchell et al. 1977: Mitchell and Carlton,
1978]. In the time series analysis method, autoregression coefficients
are the texture features. This method has been used for synthesis of
certain types of streaked textures, but its applicability to less
directional or less regular textures is questionable [Haralick, 1979].
Heuristic analysis of the one-dimensional scan involves identifying
gray level extrema and associated properties such as the height and
width of the peaks and the distance to the next higher peak. The
texture features computed from such methods include the average height
(contrast) of peaks and the density of peaks of a particular height.

The density of edges in a local region can also be used as a
texture feature [Rosenfeld and Thurston, 1971: Rosenfeld et al, 1972:
Rosenfeld and Troy, 197A]. A simple local edge operator such as the
gradient can be used to identify edge pixels. The gradient computation
can be adjusted to be a function of distance to obtain a hierarchical
characterization of edge densities in the image.

Edge detection can be expressed as a spatial filtering operation

by defining a set of templates in the spatial domain and convolving

21

them with the image. One such template is the Sobel operator [Pratt,
1978]. Laws [1980] uses several templates (including Sobel operators
and gradients) to detect edges at different orientations and with

different contrasts.

3.3 Global Analysis Methods

Global tendencies in an image such as the average sizes of objects
or areas or directional preferences are difficult to capture using
local analysis methods. Since such global information seems to be
related to texture (in particular, to coarseness and directionality),
methods which describe global properties of the image could be useful
in texture analysis.

Global size and directional tendency information can be derived
from the autocorrelation function [Hayes et al, 197A]. LetiI(x,y) be
the image function which gives the gray level at position (x,y) for 0
<= x,y <8 N-l and is 0 otherwise. The values of'I(x,y) are integers
with 0 <- IKx,y) <= G-l. The (normalized) autocorrelation function
R(dx,dy) is the product of the image function with a shifted [by

d-(dx,dY)] copy of itself. That is,

 

 

 

 

N-l N-l
I \
R (dx,dy)= ---- [ > > I(X.y) *I(x+dX.Y+dY) J
R0 / /
x-O y=0

where R0 is a normalizing factor. The maximum value of R(dx,dy) occurs
at R(0,0). If the image contains large areas of constant gray level,
the autocorrelation function will decrease slowly with distance from

(0,0); if the image contains mostly small areas of constant gray level

22

(the texture is "busy") then the autocorrelation function will drop off
sharply. If the image is periodic, the autocorrelation function will
rise and fall with the same period as the pattern in the image.

The value of R(dx,dy) is related to the co-occurrence matrix

Hd(gl,gZ) where d-(dx,dy) as follows:

 

 

I \ \
R(dx,dy)= ---- [ > > gl*gZ*Hd(gl,gZ) ]
R0 / /
9180 92-0

 

 

Thus, the autocorrelation function can be derived from the entire
ensemble of N**2 co-occurrence matrices of the image, but the converse
is not true. For a given displacement, the co-occurrence matrix
provides a more detailed characterization of the spatial distribution
of gray levels than the autocorrelation at the same displacement.

The Fourier transform has been used more frequently than the
autocorrelation function as a texture analysis tool [Lendaris and
Stanley, 1970; Bajcsy, 1973: Bajcsy and Lieberman, 1976: Weszka et al,
1976: Conners and Harlow, 1980a; D'Astous and Jernigan, 1981; Eklundh,
1979]. The two-dimensional Discrete Fourier Transform (DFT) of an NxN

image I(x,y) is defined as follows:

 

 

 

 

N-l N-l
\ \
F (u,v)= > > I(x,y) exp[-j2h’(ux+vy)] .
/ / /¢
x=0 y-O

The Fast Fourier Transform algorithm can be used to compute the
two-dimensional DFT [Johnson and Jain, 1981]. The Fourier spectrum can

also be expressed in magnitude-phase form as

23

F(u,v) = M(u,v) exp[jP(u,v)]

An intuitively appealing interpretation of the Fourier transform is
based on the representation of an image as a weighted sum of sinusoidal
gratings (Figure 1) [Rosenfeld and Kak, 1981; Duda and Hart, 1973].
The parameters u and v determine the frequencies of the horizontal and
vertical sine waves in the gratings. The amplitude of the sine waves
(the contrast of the grating) is given by M(u,v), and their phase is
given by P(u,v).

We note that the autocorrelation function and the power spectrum
(M(u,v)z) are a Fourier transform pair. Thus, by the argument given
earlier, the ensemble of N2. possible co-occurrence matrices also
determines the magnitude spectrum [Julesz and Caelli, 1979].

As spatial frequency (distance from. (0,0) increases, the
wavelength of a cycle decreases. Thus, high spatial frequency is
associated with small areas and low spatial frequency is associated
with large areas in the image. This association means that a coarse
texture - one composed of large areas of constant gray level - will
have strong low spatial frequency components and a fine texture will
have strong high spatial frequency components.

Because of the associations between size and spatial frequency,
several texture features have been defined on the power spectrum. The
phase spectrum has been largely ignored because of associations between
phase and position. Since textures can be identified regardless of the
position of particular components in the visual field or the position
of a (sufficiently large) window in a uniformly textured plane, phase

information has been assumed to be unimportant for texture analysis but

. .21 It'll-11.. infill III. 1|

24

 

 

 

I

(c)

 

 

 

 

 

 

Figure 1: Sinusoidal Gratings.

(a) 3 cycles per image horizontal (b) 8 cycles per image horizontal

(c) Combination of five spatial frequencies with arbitrarily

selected amplitudes. This is an example of a "one-dimensional texture".
(d) 8 cycles per image horizontal and 8 cycles per image vertical

25

useful for pattern recognition [Richards and Polit, 197A (Appendix A,
item 6): Bajcsy and Lieberman, 1976]. Some recent studies have
attempted to reexamine the potential of phase information for texture
analysis, but the results have not been encouraging [Eklundh, 1979;
Julesz and Caelli, 1979: Zucker and Cavanaugh, 1980: D'Astous and
Jernigan, 1981]. It will be argued later that the apparent failure of
phase information in texture analysis is due to its improper use.

Two types of features are computed from the power spectrum:
spatial frequency energy and orientation energy [Weszka et al, 1976:
Haralick, 1979]. Spatial frequency energy features have the form

(using polar coordinates)

7.11 (kl-Ar
‘2.
F :.-. 3 F (rcoselrsine) 0L" ((9
K 0 r1
These features give the total energy in a limited band of spatial

frequencies. Orientation energy features have the form (again in polar

coordinates)
r 0K+A9

00‘ I 3 Fz(rc0593rsine) gigolr‘
0

9K

These features give the total energy in limited orientation bands,
which indicate directional tendencies in the image.

These global analysis methods have several disadvantages.

(1) The shapes and widths of the spatial frequency and orientation
bands are free parameters which are arbitrarily specified.

(2) Differences in illumination, contrast, or gray level
resolution cause significant changes in the power spectrum. This

problem can be alleviated by preprocessing techniques such as histogram

26

equalization, but this can cause a loss of gray level resolution and
image fidelity [Haralick, 1979] and can dramatically change the
appearance of the image.

(3) Computation of the Fourier transform or autocorrelation
function over irregularly shaped regions (as are commonly encountered)
involves some difficulty [Wechsler, 1980].

(A) Every entry in F(u,v) is determined by all of the image
function. It is not possible to extract spatially-limited information
from F(u,v) by any method short of an inverse Fourier transform. This
implies that the spatial frequency domain features cannot be used for
texture segmentation without recomputation of the Fourier transform for
each subimage to be analyzed [Bajcsy, 1973; Bajcsy and Lieberman,

1976].

3.A Intermediate Analysis Methods

Several texture analysis methods are based on the relationships
among particular types of objects ("primitives”) in an image. These
methods typically involve definition of primitives, extraction of
primitives from -a textured image, and characterization of the texture
by formal language or heuristic methods.

In the formal languages approach, textures are considered to be
language classes for which separate grammars can be inferred. Texture
analysis is seen to consist of extracting the primitives and then
parsing the image according to the texture grammars. Unfortunately,

both of these operations are nontrivial, even in simple test cases.

27

Alternatively, the primitives can be analyzed by heuristic
methods, often involving statistical measurements of the structure of
the primitives. For example, ”generalized co-occurrence matrices"
[Davis et a1, 1979; Haralick, 1979] can capture some aspects of the
spatial distribution of primitives. A generalized co-occurrence matrix
gives the number of times different primitives occur in the image at a
particular displacement. The same features used for the gray level
co-occurrence method can be computed from generalized co-occurrence
matrices.

An orderly review of intermediate analysis methods is obtained by
examining them in order of increasing complexity of the primitives.

One method based on formal language techniques uses 9x9 pixel
windows as the primitive [Lu and Fu, 1978a, 1978b]. The texture is
characterized by a stochastic tree grammar which specifies the
assignment of gray levels to the windows. Error-correcting parsing
methods are used to eliminate noise, and functions to compute the
”distance". between languages are used to measure differences between
texture classes.

Another simple primitive is an area of constant or nearly constant
gray level [Tsuji and Tomita, 1973; Tomita and Yachida, 1973; Tomita,
et a1, 1973]. Features such as size, gray level, curvature and
directionality are computed to characterize the regions. Textures are
identified by multiple modes in the histograms of feature values.
Labelling each region by the mode in which it appears provides a first
approximation to the textured regions. Generalized co-occurrences or

split-and-merge techniques can then be used to refine the segmentation.

28

One obvious disadvantage of this approach is that its complexity
increases rapidly with the fineness of the texture and with the gray
scale resolution due to the large number of primitive areas which must
be evaluated.

An edge can also be used as a primitive. One recent texture
analysis method attempts to characterize repetitive patterns of edge
pixels in an image [Vilnrotter et a1, 1981] using an "edge repetition
array" constructed from horizontal and vertical scans of the image.
The array is then analyzed to find repetitive edge structures. In
another approach, texture is characterized by computing generalized
co-occurrences of edge pixels [Rosenfeld, 1979]. A spatial frequency
domain form extraction method [Crowley and Parker, 1978] which
identifies edges whose contrast exceeds a threshold is also suggested
for texture analysis.

A more complex type of primitive involves geometric shapes such as
lines, curves, angles, open polygons, and closed polygons. These
primitives are difficult to use, but in some cases complex geometrical
texture patterns can be synthesized from simple grammars and fairly
complex primitives [Carlucci, 1972: Siromoney et al, 1972].

A theoretical scheme for an intermediate-level structural analysis
of texture is presented in [Zucker, 1976]. In this theory, an observed
texture is considered a transformation of an "ideal texture" which is
typically a polygonal tesselation of the plane. The ideal texture
governs the placement of primitives, and transformation rules determine
the relationships between primitives (such as superposition, adjacency,
etc.). This theory is an idealized characterization of "structural"

texture analysis, but there seem to have been no practical spinoffs of

29

the theory.
Other intermediate-level analysis methods have been suggested
based on combinations of statistical and structural methods [Tomita,

1981: Conners and Harlow, 1980b].

3.5 Image Modelling Methods

This class of methods for characterizing texture assumes that the
textured image is a realization of some stochastic process which is
governed by a few parameters. Texture analysis is viewed as a
parameter estimation problem: given an image I(x,y), estimate the
parameters of the assumed random process so that the probability of
obtaining I(x,y) is maximized. The estimates of the parameters serve
as texture features for classification problems. The estimates can
also be used to synthesize other images with similar (in the sense of
the model) texture.

One type of image synthesis model is based on stochastic
tesselations of the plane [Schachter et al, 1978a: Ahuja and Rosenfeld,
1981]. These random mosaic models produce polygonal regions in the
image plane. Conceptually, the models produce a textured image either
by generating random lines through the image or by generating random
points and growing regions around them. In [Modestino et al, 1981],
gray scale random textured images are generated which are reminiscent
of the random mosaic images. This model allows control of gray level
correlations between adjacent regions as well as control of the
polygonal generation process. A log-likelihood texture analysis and

segmentation procedure based on the synthesis method is presented and

30

demonstrated on compound images composed of subimages generated by the
model. The segmentation results are good. Further experiments reveal
some difficulties in generalizing the method to discriminate natural
textures.

A different, very flexible image generation model is developed in
[Pratt et al, 1978; Gagalowicz, 1978; Pratt et al, 1981]. In this
model, an image is considered to be the output of a homogeneous spatial
operator responding to noise input. The noise input supplies the
randomness in the texture and the spatial operator supplies local
structure. Characterization of a texture then requires specification
of a noise distribution and a spatial operator.

Several statistical models for image generation and image
modelling are reviewed in [Kashyap, 1980; Garber and Sawchuk, 1981;
Chellappa and Kashyap, 1981a, 1981b].

One class of well-known texture models is based on the Markov
random field [Rosenblatt and Slepian, 1962: Besag, 197A: Hassner and
Sklansky, 1978; Cross and Jain, 1981; Chellappa and Kashyap, 1981a,
1981b; Garber and Sawchuk, 1981; Schmitt and Massaloux, 1981].
One-dimensional Markov random field models have been used to synthesize
images for psychophysical experiments [Julesz 1962, 1965] and for
theoretical comparisons of texture analysis methods [Conners and
Harlow, 19803]. In one recent study [Cross and Jain, 1981], parameters
of a Markov process were fitted to natural textures from [Brodatz,
1966]. The parameters were then used in the model to generate random
images. The results are typical of the fundamental problem with
model-based approaches to characterizing textures: while some

successful model-based parameterizations can be found, and the model

31

can be used to randomly generate some images which appear similar to a
prototype, in general, natural images are not bound to conform to the
restrictions of a particular model. This fundamental problem severely
limits the potential for model-based approaches in general texture

analysis problems.

3.6 Summary

A critical review of texture analysis methods has been presented.
The large number and the variety of texture analysis methods is caused
in part by the lack of a general definition of texture and by the
difficulties encountered when existing methods have been applied to
general texture analysis problems. Many methods have been developed on
an ad hoc basis guided by intuition.

The few comparative evaluations which exist conclude that the
co-occurrence method is the best statistical approach to texture. The
co-occurrence matrix is widely used in applications and as a basis for
more sophisticated techniques including generalized co-occurrences,
visually interpretable texture features, and combined
statistical-structural approaches to texture.

Features from the Fourier transform of the image have been
suggested, but their performance has been poor. The comparative
studies conclude that the statistical features provide better results
than power spectral features, and attempts to develop texture features
from the phase spectrum have been unsuccessful.

The performance of existing texture analysis methods depends on

the data. Acceptable performance can be obtained for some specific

32

problems, but the approaches lack generality. Many approaches have
disadvantages such as insensitivity to some aspects of texture or

susceptibility to irrelevant gray level variations (”noise").

Chapter A

A Texture Analysis Method Based on a Theory of Human Vision

A.l Introduction

In this chapter, the channel filtering theory of early human
vision will be used to motivate a new approach to texture analysis.
First, however, we pause to explain why and how this theory of human
vision will be used to guide the development of a texture analysis
method. Then, the channel filtering theory and its potential
significance for computational vision will be briefly presented. A
feature space for texture analysis will then be developed and its

plausibility will be examined.
A.2 A Critical Re-evaluation of Texture Analysis Methodology

Computational vision methods are not evaluated for use in
applications based on whether the methods accurately emulate the
mechanisms (or sometimes even the performance) of human vision.
Methods are sometimes evaluated by correlations with human performance,
but correlation does not imply equivalence or causality. High
correlations with human performance might be obtained using processes

very different from those present in human vision. But if correlation

33

3A

with human performance is desirable, it seems reasonable to base the
computational techniques on whatever is known about human vision.
Insights into human vision can serve to motivate computational texture
analysis procedures.

How should information concerning human vision be used to guide
computational vision research? Ideally, we would know the overall
strategies used in human vision to analyze an image. We could then
implement a vision system which might well rival human performance on
many visual tasks. But the computer vision system would not
necessarily emulate the human visual system at the neural level. The
operation of low-level components of a complex system may give no
useful information about the overall strategies used in the system.
(This is discussed at length by Hofstadter [1979].) Once the overall
strategies in vision are identified, their implementation can be
tailored to whatever devices or constraints are relevant.

In some approaches to computational vision, a technique which
appears to reproduce or explain human performance is developed, then
neural mechanisms are postulated which correspond to some aspects of
the computational methods [Julesz et al, 1973; Julesz, 1981; Marr et
al, 1979; Marr and Hildreth, 1980: Marr, 1980; Hildreth, 1980]. The
use of vision science to construct post hoc justifications for existing
methods is not effective since the value of a proposed technique for
computational vision is determined by correlations between observed and
desired performance. Correspondences between a proposed computational
method and hypothesized mechanisms of human vision are ultimately

irrelevant.

35

In this study, the opposite approach is used. Information from
vision science will be used to guide the development of a new method
for texture analysis, not to bolster or to validate an existing method.
A theory which attempts to describe the possible processing strategies
in early human vision will be used to guide the development of the.

computational procedure.

A.3 Spatial Frequency Channels

In the late 1960's, researchers found that the threshold
visibility of sinusoidal gratings (Figure 1) depends on the spatial
frequency of the gratings [Campbell and Robson, I968; Pantle and
Sekuler, 1968; Blakemore and Campbell, 1969; Campbell and Maffei,
1970]. The potential power of Fourier analysis as a tool for studying
human vision was noted immediately [Campbell and Robson, 1968].
Attempts were made to determine how well spatial frequency domain
analysis of visual stimuli correlated with actual human performance.
One key issue involved whether the visual system combines spatial
frequency information linearly, and thus whether visual analysis of
complex objects could be expressed easily in terms of the spatial
frequencies in the complex stimuli. Another important issue was
whether the analysis of a stimulus by the visual system involves
several independent mechanisms (called channels) which analyze
different aspects of the stimulus. It was hypothesized that the
channels might have a convenient spatial frequency domain
representation. This hypothesis sparked additional activity in which

neurological and psychophysical experiments were interpreted as

36

providing evidence for or against various single-channel or
multi-channel models of early stages of human visual processing. For
reviews of this activity, see [Graham, 1981; Ginsburg, 1978].

These results were unified and extended in [Ginsburg, 1978,
1980b]. An implementation of the multi-channel theory was used to
illustrate the action of spatial frequency domain filters on various
images containing complex forms, visual illusions, multistable images,
and certain visual textures. In addition, the contrast sensitivity of
abnormal visual systems was found to have unique properties in the
spatial frequency domain. The channels in the visual system are
modelled by filters defined in the spatial frequency domain, but a
critical feature of this particular channel analysis is the assumption
that phase information is an essential part of the internal
representation of visual stimuli. Thus, the decomposition of an image
is modelled by a sequence of spatial domain filtered images [Ginsburg,
1971].

These studies did not develop algorithms for automatic image
analysis, but other papers [e.g. Ginsburg, 1973, 1979a] suggested that
filtering in spatial frequency channels might be useful for machine
pattern recognition, including texture analysis.

The assumption of a channel decomposition of an image suggests two
computational implementations [Hall, 1972; Nathan, 1970: Ginsburg,
1979b]. In one, a series of point spread functions, or templates, is
convolved with the image to obtain a series of distorted (filtered)
versions of the original image. Alternatively, the convolution can be
performed in the spatial frequency domain by applying an inverse

Fourier transform to the product of the filter transfer function (the

37

Fourier transform of the point spread function) and the Fourier
transform of the image. This process is illustrated in Figure 2. The
resulting sequence of filtered images is exactly the same as those
produced by spatial convolution. The choice of the method is largely a
matter of convenience and computational efficiency. For this study,
the spatial frequency domain method will be used due to the
availability of fast algorithms for the discrete Fourier transform
[Johnson and Jain, 1981] and due to the intuitive value of defining the
filters in the spatial frequency domain [Ginsburg and Coggins, 1981:
Graham, 1981].

The next issue is to decide the shapes, sizes, locations, and
number of the channels. The filtering properties of the human visual
system are not precisely known, but psychophysical and neurological
data can be used to guide the selection of the filter parameters. This
study will use filters whose parameters are within the constraints
specified in [Ginsburg, 1978]. The transfer functions for spatial
frequency channels are defined by a Gaussian function (on a log scale):
their center frequencies are one octave apart and their width is
between 1 and 2 octaves. The number of spatial frequency channels used
depends on the size of the image (see Appendix B for details). Figure
3 shows two representations of a spatial frequency channel filter in
the spatial frequency domain (u-v plane). The height of the surface
above the u-v plane (Figure 3a) and the intensity of the gray levels
(Figure 3b) represent the filter amplitudes, |F(u,v)|, which are
between 0 and 1. Four orientation channels are implemented with center
orientations directed horizontally, vertically, and along the two

diagonals (see Appendix B for details). Figure A shows two

38

 

 

 

 

 

 

 

 

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Figure 2: Diagram of the Spatial Filtering Procedure.
This procedure is repeated once for each channel.

                 

  

 

(a)
(b)

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40

 
   
      

(a) A transect plot portraying the amplitude of the real part of
the filter transfer function in the spatial frequency domain.

zero-frequency component is in the center of the region.

Figure A: An Orientation Channel Filter-

The

(b) An image representation of the same filter transfer function.

Al

representations of an orientation filter in the u-v plane.

Other channel filtering models for human vision have been
developed [Sachs et al, 1971; Richards and Polit, 197A: Mostafari and
Sakrison, 1976; Wilson and Bergen, 1979]. We note also that some
arguments against a Fourier model of vision have appeared [Julesz and
Caelli, 1979; Ochs, 1979: Zucker and Cavanaugh, 1980].

The sequence of filtered images obtained from a 128x128 sample of
a ceiling tile image [Brodatz, 1966] are shown in Figure 5. Each
channel responds to gray level changes over different sized regions or
at different orientations. Energy from large objects is displayed in
low spatial frequency channels; energy from small objects is displayed
in high spatial frequency channels. Orientation channels respond to
gray level changes with a directional preference. Since the phase
information from the original image is retained in the filtered images,
the spatial distribution of the spectral energy in each channel is
apparent in the positions of gray level variations in the filtered
images. The use of phase information captures in the filtered images
the gray level spatial distribution information which is essential to
texture.

The specification of the channels completes the definition of the
initial information processing stage of a computational vision system.
The output of this stage is a series of channel-filtered images, each
of which contains limited spectral information from the original image.
The next task is to exploit the channel decomposition, reducing the
series of filtered images down to a set of texture features which can
be used to duplicate some texture analysis capabilities of human

vision.

42

 

 

 

 

 

 

 

 

(b)

 

 

 

 

 

 

 

(c) (d)

 

 

 

 

(E)

Figure 5: An Example of Channel Filtering.

(3) Original 128x128 TILE image. (b)-(l) filtered images with

center frequencies (in cycles per image) and orientations (in degrees)
as follows: (b) 0 degrees (c) 45 degrees (d) 90 degrees

(e) 135 degrees (f) 1 c/i (g) 2 c/i (h) A c/i (i) 8 c/i

(j) 16 c/i (k) 32 c/i (l) 64 c/i

A3

 

 

 

 

 

 

 

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AA

A.A Constraints on Possible Texture Features

Pragmatic requirements constrain the nature of the features we are
willing to compute from the filtered images. The features must be very
simple since we now have a whole series of images to analyze rather
than a single image on which more extensive analysis can be performed.
We would like to find some evidence from vision science to suggest that
simple features which duplicate human performance could exist.

Several observations suggest that texture is a consequence of
crude information reduction in vision which simple computational
methods should be sufficient to capture. First, textures can be
analyzed and discriminated by the human visual system quickly and
effortlessly, but only very simple, crude mechanisms have been found in
the early stages of mammalian visual systems [Hubel, I963; Ginsburg,
1978; Graham, 1981]. Second, texture is perceived most clearly in an
image area which has many intensity changes and thus small areas of
constant intensity [Crowley and Parker, 1978; Resnikoff, 1981].
Individual edges and their placement are not critical for identifying
textures. In fact, very different generation procedures can yield
images which are not preattentively discriminable. ”Texture" appears,
then, to be the result of a crude information reduction which occurs in
an image area with no distinctive individual features.

This crude information reduction is evident in several
indiscriminable textures presented by Julesz (Figure 6). In these
images, a simple check of the edge structure of the micropatterns would

immediately yield discrimination of the different regions, yet these

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Figure 6: Indiscriminable Textures which Could Be Discriminated
Based on the Edge Structure of the Micropatterns.
(Each image contains two micropatterns which are reflections

of each other.

From Julesz, 1973.)

A6

are among the most difficult patterns to visually discriminate, even
given the nature of the difference between the micropatterns. Simple
pixel-level operations could be constructed to discriminate the image
fields in Figure 6, but the criteria for the discrimination would no
longer be "texture". The ability to discriminate micropatterns does
not necessarily imply that textures composed of the micropatterns are
easy to discriminate [Beck, 1980; Ginsburg, 1978].

Further evidence for the simplicity of human texture perception
comes from psychophysical experiments involving "one-dimensional
textures" (Figure 1c). In these images, the gray levels in each column
are constant and the gray levels along each row are determined by a
weighted sum of sinusoidal functions. Psychophysical experiments show
that arbitrary one-dimensional textures can be matched with images
containing only a few (A) selected spatial frequencies [Richards and
Polit, 197A]. Another study shows that human similarity judgements
between one-dimensional textures are predicted better by the outputs of
four spatial frequency channels than by the actual spatial frequencies
present in the textures [Harvey and Gervais, 1981].

An observation made in passing by Julesz et a1 [1973:Figure 6]
provides further evidence that texture is a consequence of simple
operations on images. Two patterns generated by a geometrical method
involving repetitions .of four-dot micropatterns were presented in an
image. The generation method insures that the two patterns have
identical "second-order statistics", and it was observed that the
patterns are not effortlessly discriminable to human observers. Julesz
then presented a "blurred“ version of the image in which the patterns

were found to be discriminable. In addition, it was noted that the

A7

blurred patterns have different second-order statistics. The
significance of this observation is that "blurring" is an alternative
characterization of certain spatial filtering operations. Blurring can
enable discrimination using simpler measurements than were required on
the original image.

Thus, there is evidence that simple operations on channel-filtered

images could be effective for texture analysis.

A.5 Properties of Channel-Filtered Images

In addition to the evidence for the simplicity of ”texture"
presented in the last section, we can obtain guidance in constructing
texture features from certain properties of the channel-filtered images
which are consequences of the filter definitions and of the spatial
filtering operation. Four properties which have proven useful from
preliminary studies are as follows:

1. The mean gray level of the channel-filtered images can be
fixed in advance. In the implementation used in this study, the mean
gray level of the filtered images is made equal to the mean gray level
of the original image by setting the value of the zero-frequency
component of the filters to 1, thereby passing the zero-frequency
component (average gray level) of the original image unchanged. This
property makes possible meaningful displays and comparisons of the
channel filtered images. Keeping the average gray level of the
filtered images the same simplifies the construction of features which

are invariant over global, constant gray level changes.

A8

2. The gray level frequency histograms of the filtered images
tend to be symmetrical about the mean gray level due to the symmetrical
response of the filters to objects in the original image. Asymmetry in
the gray level histograms is caused by the interaction of the responses
of spatially close objects.

3. The magnitude of the deviation of the gray level of a pixel in
a filtered image from the mean gray level is directly related to the
spectral energy contained in a neighborhood of that pixel in the
original image. Since phase information is retained in the filtered
images, the spatial distribution of the spectral energy passed by the
filter is reflected in the gray level distribution in the filtered
image. Thus, the spectral energy in different spectral bands arising
from small spatial areas can be measured from the sequence of filtered
images without recomputing a Fourier transform for each local area of
interest.

A. The differences between the channel-filtered images lies in
their sensitivities to gray level variations in the original image over
regions of different sizes and orientations. The channel
decomposition, then, allows separate measurements of local energy over

spatial domain neighborhoods of different sizes and orientations.

A.6 Definition of Texture Features

Property 3 above implies that the gray levels in each filtered
image can be interpreted as representing the spectral energy arising
from local areas of the original image. This interpretation motivates

the selection of features for use in texture analysis experiments in

‘19

this thesis. The features will measure the average local spectral
energy in an image by computing the spread of the gray level frequency
histogram of the filtered images.

A number of features can be defined to measure the spread of the
histograms. We have used eight such features in classification
experiments (Figure 7). The first feature is the average absolute
deviation from the mean gray level. Features 2-A are functions of the
second through fourth moments of the gray level histogram. Feature 2
is actually the standard deviation of the gray levels. We note that
the third moment is not strictly a measure of spread, but it is
included for completeness. Functions of the moments are used rather
than the actual values of the moments because of computational
difficulties encountered in preliminary experiments caused by the large
magnitudes of the third and fourth moments. Features 5-8 are heuristic
spread measurements which assume that the histogram is symmetric.
Property 2 from the previous section states that this assumption is
generally reasonable, but can fail in specific cases. The threshold
values of .25, .50, .75, and 1.0 used in the feature definitions are
arbitrarily selected.

Similar features are investigated by Laws [1980], though the
filters in that study are defined as small spatial domain templates.

The sequence of filters satisfies the requirement that texture be
measured at several different scales. Each gray level in the filtered
images is determined by a neighborhood in the original image, so the
filtered images are consistent with the spatial property of texture.
Statistics of the gray level histograms of filtered images are easy to

compute, so they satisfy the pragmatic requirement that channel

 

 

 

 

 

 

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F6k = d such that Sk(d) = .50*N2
F7k = d such that Sk(d) 3 .75*N2
_ 2
F8k d such that Sk(d) - N

Figure 7: Texture Feature Definitions.
fk(g) denotes the frequency of gray level g (osgsc) in the

filtered image for channel k. C denotes the mean gray level.
Image size is NxN pixels.

51

filtering features be simple. Moreover, the features have reasonable
visual interpretations in terms of spectral energy, size, and
orientation. In addition, these features can be computed for any
subimage without repeating the channel filtering Operation; this

property will be important for texture segmentation (Chapter 6).

A.7 How Will the Texture Features Be Used?

An image will be represented by a feature vector consisting of the
values of one of the texture features computed over each filtered
image. The feature vector will map the image into a point in the
feature space: this point will represent the image's texture. The
distance between points in the feature space will be used as a measure
of the textural difference between images.

In most approaches to texture analysis, a number of features are
defined and then they are applied in various combinations to classify
texture samples [e.g. Weszka et al, 1976: Faugeras and Pratt, 1980;
Haralick and Shanmugam, 1973]. This approach is more likely to
produce, at some point, ”good" classification results than using each
feature in isolation. But combining various features whose properties
are not well understood leads to problems in interpreting results. In
this study, the features will be used separately, expecting that the
results for all of them (except perhaps Feature 3) will be similar.
Selection of the "best" feature from these will have to be based on
computational considerations and compatibility with solutions to other
image analysis problems such as form extraction, image registration, or

edge detection.

52

A.8 Summary

Existing texture analysis methods use little guidance from
properties of human visual perception. A theory concerning the early
information processing in human vision was used to motivate the
development of a new feature space for texture analysis. The theory
asserts that an image is decomposed by the human visual system into
channels which are modelled by spatial filtering operations. Since
phase is retained in the channel-filtered images, the spectral energy
caused by gray level variations in local spatial areas can be measured
from the channel-filtered images. Features which measure this local

energy were defined for use in texture analysis studies.

Chapter 5

Evaluation of Channel Filtering Features for Texture Classification

5.1 Introduction

This chapter will present the results of several experiments
designed to evaluate the channel filtering features, to compare their
performance against some other texture features proposed in the
literature, and to illustrate properties of the feature space which may
be useful in applications.

The experiments in this chapter are texture classification
problems using a supervised learning paradigm. Sets of test images are
labelled according to an external criterion which, for these
experiments, is a visual evaluation of the image texture. The sets of
images are then analyzed by the channel filtering method, resulting in
a feature vector for each image. These feature vectors are then input
to a classification algorithm, and the estimated error rate is used to
evaluate the class separations in the feature space.

Most of the experiments in this chapter use 25 samples of each
image class. The samples are extracted as subimages from a large
(256x256 pixels) image which represents a single texture class.
Nonoverlapping subimages are extracted as far as possible, then the

sampling origin is shifted by half the subimage size to complete the

53

5A

set if necessary. The number of samples is fairly small, but since the
large images are homogeneous, with no complications such as shadows,
receding surfaces, or magnification, this number of samples from
throughout the image should adequately characterize the image texture.
However, in interpreting the estimated error rates, we must keep in
mind that the estimates are based on a small number of samples.

In all of the experiments in this chapter, different texture
features are used in separate classification problems. The feature
vector for each image consists of the values of one of the texture
features F1...F8 defined in Figure 7 computed over all of the
channel-filtered images. The dimensionality of that vector depends on
the size of the images being analyzed: for 6Ax6A images, eleven
channels (four orientation, seven spatial frequency) are used: for
32x32 images, ten channels (four orientation, six spatial frequency)
are used.

For the experiments in this chapter, a Nearest Neighbor Classifier
will be used. The decision rule is to classify an unlabelled point
into the class of its nearest labelled neighbor in the feature space,
where the distances are determined by the Euclidean distance metric.
This decision rule results in piecewise linear decision boundaries.
The error rate of the classifier will be estimated using the
Leave-One-Out rule, which is often used when sample sizes are small.
In this method, each point in turn is treated as a test sample with all
other points as training samples. The results will be presented as a
confusion matrix for each feature. The (i,j)th entry of the matrix

gives the number of times a sample from class i was classified as class

j.

55

The performance of the channel filtering features will be compared
to the performance of another feature, the total power spectral energy
(PSE) in the sequence of filtered spectra. This feature has been used
with ideal band-pass channels in previous studies (Section 3.3). This
feature uses no phase information, by definition, but it uses the same
power spectral information as the channel filtering features. The
effect of using phase information in the channel filtering features
will be determined by comparing the error rates of PSE and channel
filtering features.

The experiments will first establish the performance of the
proposed texture features on classification of natural images whose
sizes are 6Ax6A, 32x32, and l6xl6 pixels. Then the effect of histogram
equalization on the natural images will be evaluated. The sensitivity
of the features to changes in the average gray level, magnification,
and orientation of the textured images will be evaluated.
Computational simplifications of the channel filtering procedure using
fewer channels and using channels with an ideal band-pass
characteristic will also be evaluated. The features will also be
applied to a particular set of images to compare their performance to

that of the co-occurrence method.

5.2 Evaluations of the Features on Natural Images

In this sequence of experiments, eight images from [Brodatz, 1966]
will be used to provide an initial test of the proposed texture
analysis method. The data for these experiments consists of subimages

of eight 256x256 images illustrated in Figure 8. The images (and their

56

 

Figure 8: Natural Image Classes.
(3) TILE (b) ROCK (c) SAND (d) PAPE
(e) CORK (f) GRAS (g) WOOD (h) SCRE

57

 

Figure 8: (cont'd)

58

abbreviations) are as follows: ceiling tile (TILE), beach .pebbles
(ROCK), beach sand (SAND), handmade paper (PAPE), pressed cork (CORK),
grass lawn (GRAS), wood grain (W000), and straw screening (SCRE).
These images were selected to provide a variety of textural properties
and a range of difficulty in discrimination. The images were digitized
using a Spatial Data Systems Eyecom image processing system. No
preprocessing was applied to the digitized images for the experiments

in this section.

5.2.1 Experiment 1: Natural Images, 6Ax6A subimages

In the first experiment, 25 samples of size 6Ax6A were extracted
from the 256x256 images. Sixteen of the samples were nonoverlapping,
and nine more were extracted by shifting the sampling origin by
(32,32). The 256x256 images are visually discriminable. The feature
space will now be tested on smaller images which could, in principle,
provide a more difficult discrimination problem since a smaller texture
sample is available for analysis. Each of the 200 samples were
filtered and the eight features in Figure 7 were computed on all of the
filtered images.

The classification results for all of the features are given in
Table 1. The PSE feature provides 69% correct classification while all
of the channel filtering features (except feature 3) provide better
than 90% correct classification. Feature 3 is the only channel
filtering feature which does not measure the spread of the gray level
frequency histogram of the filtered images and therefore cannot be

easily interpreted as a local energy measure. Feature 3 yields 79.52

59

Table 1: Classification of Eight Natural Image Classes
Using 6Ax6A Subimages.

PSE TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE l9 2 3 1 O 0 O O
ROCK 3 l8 1 0 1 0 1 1
SAND A 0 1A 2 O l A O
PAPE O 0 l 22 l 1 O 0 69%
CORK 0 O O O 15 10 O 0 accuracy
GRAS 0 O O l 9 l3 2 0
W000 2 O 5 O O A 1A 0
SCRE O 0 0 0 0 2 O 23
F1 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 22 2 l 0 O O O O
ROCK 1 2A 0 O O O O 0
SAND 0 0 25 O O O O O
PAPE O 0 0 25 O 0 0 O 982
CORK 0 O O 0 25 0 0 0 accuracy
GRAS 0 0 0 0 O 25 0 0
W000 0 O O 0 0 O 25 0
SCRE O 0 0 O O O 0 25
F2 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 22 2 l 0 O O 0 O
ROCK 0 25 0 O O 0 0 O
SAND 0 0 23 O 0 2 0 0
PAPE O 0 0 25 0 O O 0 97.5%
CORK 0 0 O 0 25 0 0 0 accuracy
GRAS O O 0 O O 25 0 0
W000 0 0 O 0 0 0 25 O
SCRE O O O O 0 O 0 25
F3 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 25 0 O 0 0 0 0 0
ROCK 2 16 0 O 1 5 1 0
SAND 0 0 16 2 l O 3 3
PAPE 0 O 0 25 O 0 O 0 79.52
CORK O 0 l O 17 A 1 2 accuracy
GRAS 0 O 0 2 11 12 O 0
W000 O O l 0 0 O 23 l
SCRE O O O O O 0 O 25
FA TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 23 1 l O 0 0 0 O
ROCK 0 25 O O 0 0 O O
SAND O O 23 0 O 2 0 0
PAPE O O O 25 O 0 0 O 98%
CORK O O O 0 25 0 0 0 accuracy
GRAS 0 O 0 0 0 25 0 0
W000 O O O O 0 0 25 O
SCRE O 0 O O O O O 25

60

Table l (cont'd)

F5 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 21 1 l O O 2 O O
ROCK 5 20 0 0 0 0 O 0
SAND 1 0 22 0 O 2 O 0
PAPE O 0 O 25 0 O O O 92%
CORK O O O 0 2A 1 O 0 accuracy
GRAS O O 1 0 0 2A 0 O
WOOD O O O 1 O l 23 O
SCRE O 0 0 0 O O 0 25
F6 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 22 l 1 0 0 l O O
ROCK 3 22 0 0 0 0 0 O
SAND O 0 2A 0 O 1 0 O
PAPE O O 0 25 O O 0 O 96.5%
CORK O 0 O 0 25 0 O 0 accuracy
GRAS O 0 O 0 O 25 O 0
W000 0 O O 0 0 O 25 O
SCRE 0 O O 0 0 0 0 25
F7 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 23 1 1 0 0 0 0 O
ROCK 1 2A 0 0 0 O O O
SAND 0 O 25 O 0 0 O 0
PAPE O 0 0 25 0 0 0 0 98.5%
CORK O 0 0 0 25 O O 0 accuracy
GRAS O O O 0 O 25 O 0
W000 O O O 0 O O 25 O
SCRE 0 O O O O O 0 25
F8 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 22 0 l O O 2 O 0
ROCK 0 25 O O 0 0 0 O
SAND O 0 l9 0 2 A 0 O
PAPE O O O 25 O O O O 912
CORK 0 O 2 2 21 0 0 0 accuracy
GRAS 0 O 5 O O 20 O 0
W000 0 O O 0 O 0 25 0
SCRE O O 0 0 O O 0 25

correct classification in this experiment.

Some insight into the structure of the patterns in the feature
space can be obtained by plotting the average, over the 25 subimages,

of the feature value in each channel. Figure 9 shows the plot for

6,1:

 

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Figure 9: Mean Values of Feature 1 in Each Channel for the Eight
Natural Image Classes

 

61.1:

 

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Channel number

Figure 9: Mean Values of Feature 1 in Each Channel for the Eight
Natural Image Classes

62

feature 1 for the eight natural image classes. The plot of the mean
feature values in each channel has unique properties for each image
class. For example, ROCK is the only class with high feature values in
low frequency channels due to the presence of large objects in the ROCK
image. SCRE has a unique pattern in orientation channels: the
horizontal channel (number 1) has a high value and the other
orientation channels have low values. This reflects the horizontal
directional tendency and the regularity of SCRE. In addition, SCRE has
low feature values in spatial frequency channels except for the channel
centered at 32 cycles per image which captures the periodicity 'of the
bars in the screen. For other texture classes, the description of the
mean feature value plot might not be as easy or convenient. These
examples show how the values of the channel filtering features can be
interpreted as visible image properties.

In the remaining experiments, the results of only the PSE feature
and feature 1 will be reported. The channel filtering features (except
feature 3) were found in preliminary experiments to have similar
performance. Feature 1 is selected for reporting because its behavior
was typical of the channel filtering features, because it is a simple
feature to compute, and because the feature has its own intuitive

interpretation.

5.2.2 Experiment 2: Natural Images, 32x32 subimages

The second experiment involves 32x32 samples of the same eight
256x256 images. The same procedures as in the first experiment were

used except that six spatial frequency channels (rather than seven)

63

Table 2: Classification of Eight Natural Image Classes
Using 32x32 Subimages.

PSE TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 19 0 5 1 0 0 0 O
ROCK A 11 1 O O l 6 2
SAND 2 O 19 3 O O 1 O
PAPE l 0 O 23 0 0 O O 68%
CORK O 0 O 0 21 2 0 2 accuracy
GRAS 0 O O O A 12 8 1
W000 0 O A 0 1 11 9 0
SCRE O 0 0 0 0 A 0 21
F1 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 20 l 2 0 O 2 0 0
ROCK O 22 O O O 0 3 0
SAND 1 0 22 O O 2 0 O
PAPE 0 O O 25 0 0 0 O 91%
CORK 0 O 0 0 25 O O 0 accuracy
GRAS 0 0 6 O O 19 0 0
W000 0 l 0 O 0 0 2A 0
SCRE O 0 O 0 0 0 O 25

were computed. The decreased size of the subimages means that no
information beyond the Nyquist frequency of 16 cycles per image width
is available, so the highest-frequency channel from the previous
experiment (center frequency 6A cycles per image width) is not usable.
The classification results for the PSE feature and feature 1 are
given in Table 2. The PSE feature provides 692 correct classification,
which is almost the same as for the 6Ax6A subimages, but the errors
occur between different classes. In spite of the reduction in the size
of the subimages from those used in the previous experiment, the
results show that there is only slight degradation in the performance
of the channel filtering features; feature 1 provides 91% correct
classification. About half of the errors occur between the GRAS and
SAND classes. These results imply that the 32x32 subimages contain
enough textural information to enable good classification results on

the eight natural image classes. This result increases our confidence

6A

in the adequacy of the 6Ax6A subimage size for characterizing the

textural properties of the natural images.

5.2.3 Experiment 3: Natural Images, l6xl6 subimages

In this experiment, 50 samples of size 16x16 are extracted from
four of the natural images (TILE, ROCK, SAND, PAPE). For subimages of
this size, only five spatial frequency channels are useful. Because of
this limitation and the small size of the subimages, the number of
samples per class was doubled for this experiment.

The classification results for the PSE feature and feature 1 are
given in Table 3. In this experiment, the PSE feature achieved 83%
correct classification with errors distributed mostly among TILE, ROCK,
and SAND. The improved performance of the PSE feature using these
small subimages may be due to the larger variance in the average gray
levels of small subimages. The increased variance can result in the
(accidental) formation of clusters from the same image class which
enhance the classification accuracy using the nearest-neighbor
classifier. The sensitivity of the PSE feature to changes in the
average gray level of an image will be demonstrated in Experiment 6.
Channel filtering feature 1 yields 68% correct classification with more
than half of the errors occurring between TILE and SAND. In fact, the
TILE and SAND classes are practically indistinguishable. The results
indicate that l6xl6 subimages do not capture enough of these texture
patterns to enable accurate nearest-neighbor classification using the

channel filtering features.

65

Table 3: Classification of Four Natural Image Classes
Using 16x16 Subimages.

PSE TILE ROCK SAND PAPE
TILE 39 2 9 0
ROCK 7 Al 2 o 832

SAND 3 1 Al 5 accuracy
PAPE l 0 A A5

Fl TILE ROCK SAND PAPE
TILE 20 7 22 1
ROCK 8 38 A O 682

SAND l6 1 32 1 accuracy
PAPE 1 O 3 A6

5.2.A Summary

This sequence of experiments has served as a test of the channel
filtering features on a variety of natural textures which were not
preprocessed. Images of different sizes were extracted from large
images which are visually interpreted as having different textures.
The results show that a nearest-neighbor classifier using channel
filtering features is able to identify the image classes with 90% or
greater accuracy when the subimages are as small as 32x32. An attempt
to extend this to 16x16 subimages failed when classes TILE and SAND
proved indistinguishable to channel filtering features and error rates

between other pairs of classes were also higher.

5.3 The Effect of Histogram Equalization

One common preprocessing technique applied in existing texture
analysis studies is histogram equalization [Haralick et a1, 1973]. The

technique is used in texture studies to standardize the average gray

66

level and contrast of the images, though the method has also been used
for contrast enhancement. For some images, histogram equalization can
dramatically change the image's appearance while for other' images,
histogram equalization has little or no effect. The procedure takes an
image with G gray levels and an arbitrary gray level frequency
histogram and produces an image with G' gray levels (G'<G) and a
flattened gray level histogram [Rosenfeld and Kak, 1981].

This series of experiments will determine the effect of histogram
equalization on the texture of an image as measured by the channel
filtering features. The image classes for this experiment will consist
of the eight natural image classes from the previous experiments and
equalized versions of those images which will be coded TILQ, ROCQ,
SANQ, PAPQ, CORQ, GRAQ, W000, and SCRQ (Figure 10). The equalized
images are of size 256x256 with 128 gray levels (instead of 256 gray
levels in the original images). The histogram equalization procedure
is applied to the entire 256x256 image, not on each sample subimage.
This serves to limit the effect of histogram equalization on the
subimages since without this constraint the procedure could produce
widely varying effects on different subimages of the same image class.

Of special importance is the fact that the 256x256 ROCQ image is
almost identical to the 256x256 ROCK image. In experiments in which
both image classes are used, we will require ROCK and ROCQ to be
evaluated as the same texture class, and we will ignore
misclassifications between them in computing error rates, leaving a
seven-class discrimination problem.

The experiments to be reported evaluate the performance of the

feature space on classification problems involving the equalized images

68

 

(cont'd)

Figure 10

69

alone and combined with the original image classes for subimage sizes

6Ax6A and 32x32.

5.3.1 Experiment A: Histogram Equalized Images, 6Ax6A subimages

From the eight histogram-equalized images, 25 samples of size
6Ax6A are extracted, each of the 200 samples is filtered and features
are computed from the filtered images. Using the nearest-neighbor
classifier and estimating the error rate using the leave-one-out rule,
the results shown in Table A are obtained. The PSE feature gives 63%
correct classification. Feature 1 achieves 962 correct classification
with all but one of the errors occurring between GRAQ and SANQ. This
result indicates that 6Ax6A subimages are adequate to provide good

discrimination of the histogram-equalized textures.

70

Table A: Classification of Eight Histogram Equalized
Natural Image Classes Using 6Ax6A Subimages.

PSE TILQ ROCQ SANQ PAPQ CORQ GRAQ wooo SCRQ
TILQ 12 1 9 O O 3 O 0
ROCQ 3 16 I o o I A o
SANQ 2 O 12 O 1 9 1 O
PAPQ o o I 23 I o o o 63%
CORQ 0 O 3 1 l6 5 0 0 accuracy
GRAQ 1 O 10 O 6 7 1 O
wooq o A I o o A 16 o
SCRQ 1 O O O O O 0 2A
F1 TILQ ROCQ SANQ PAPQ CORQ GRAQ wooq SCRQ
TILQ 25 O O 0 O O O O
ROCQ 0 2A 0 o o o I o
SANQ 0 O 21 O O A O O
PAPQ O O O 25 O O O O 96*
CORQ O O O 0 25 0 O 0 accuracy
GRAQ O O 3 O O 22 O 0
wooq o o o o o o 25 o
SCRQ 0 O O O 0 0 O 25

Another important question is whether the equalized images are

perceived by the channel filtering features to be different from the

71

Table 5: Classification of TILE, ROCK, SAND. PAPE and
TILQ, ROCQ, SANQ, PAPQ Using 6hx6h Subimages.
(percent accuracy reflects merging of ROCK and ROCQ)

PSE TILE ROCK SAND PAPE TILQ ROCQ SANQ PAPQ
TILE l9 2 3 l O O O O
ROCK 3 8 l O 0 l3 0 O
SAND 5 0 l7 3 O O O 0
PAPE O O 2 22 l O O O 75.5%
TILQ 2 O O 1 lb 0 8 0 accuracy
ROCQ 3 lo I 0 2 9 O O
SANQ O O O h 5 0 I5 l
PAPQ 0 O O O O O 1 2h
Fl TILE ROCK SAND PAPE TILQ ROCQ SANQ PAPQ
TILE 22 l l O O l O O
ROCK O 2 O O O 23 O O
SAND O O 25 O O O 0 O
PAPE O O O 25 O O O O 98.52
TILQ O O O O 25 0 O 0 accuracy
ROCQ 0 2i 0 O O b O O
SANQ O O 0 O O O 25 O
PAPQ O O O O O O O 25

original images. Table 5 shows the results obtained by taking 6hx6h
subimages of TILE. ROCK, SAND, PAPE and their equalized versions.
Ignoring misclassifications between classes ROCK and ROCQ as explained
earlier, we find that the PSE feature yields 75.5% correct
classification, and feature 1 yields 98.5% correct classification.
Table 6 shows the results obtained by taking 6hx6h subimages of CORK,
GRAS, WOOD. and SCRE and their equalized counterparts. The PSE feature
gives 68.5% classification accuracy while the channel filtering feature
l yields lOOX correct classifications. This result shows that except
for the ROCK-ROCQ, histogram equalized images are perceived by the
channel filtering features as having different textures from the

original classes.

72

Table 6: Classification of CORK, GRAS, HOOD, SCRE and
CORQ, GRAQ, WOOQ, SCRQ Using 6Ax6A Subimages.

PSE CORK GRAS WOOD SCRE CORQ GRAQ WOOQ SCRQ
CORK l3 9 O O 3 O O O
GRAS 8 12 3 O O 2 O O
WOOD O h l9 0 O l l O
SCRE 0 2 0 23 0 0 O O 68.52
CORQ 2 O O 0 l7 6 O 0 accuracy
GRAQ h 2 o o 7 II I o
HOOQ O 2 6 O 0 2 l5 0
SCRQ o o o o o o o 25
Fl CORK GRAS WOOD SCRE CORQ GRAQ NOOQ SCRQ
CORK 25 O O O O O O O
GRAS O 25 O O O O O O
HOOD O O 25 O O O O O
SCRE O O 0 25 O O O O 1002
CORQ O O O O 25 O O 0 accuracy
GRAQ O O O O O 25 O O
HOOQ O O 0 O O O 25 O
SCRQ O 0 O O O 0 O 25

5.3.2 Experiment 5: Histogram Equalized Images. 32x32 subimages

The experiments of the previous section were repeated using 32x32
subimages. In the experiment using all eight histogram equalized image
classes (Table 7), the PSE feature yields 6&2 correct classification.
Feature l yields 80% correct classification, but 2h of the ho
misclassifications occur between SANQ and GRAQ, indicating that those
classes are indistinguishable to this feature. Using 32x32 subimages
from the original textures, only 6 misclassifications occurred between
SAND and GRAS. This result indicates that the histogram equalization
procedure confuses the differences which exist between the SAND and
GRAS images, so that the histogram equalized versions cannot be

discriminated by the channel filtering procedure using 32x32 subimages.

73

Table 7: Classification of Eight Histogram-Equalized
Image Classes Using 32x32 Subimages.

PSE TILQ ROCQ SANQ PAPQ CORQ GRAQ NOOQ SCRQ
TILQ lb 0 O O 5 O O
ROCQ 2 13 l O O 2 5 2
SANQ h 0 IL I l 5 O O
PAPQ O O l 23 l O O 0 6&2
CORQ O O 2 h 17 2 O 0 accuracy
GRAQ 2 3 8 l l 9 l O
WOOQ O h l O 0 h I6 0
SCRQ l l O O O l O 22
Fl TILQ ROCQ SANQ PAPQ CORQ GRAQ HOOQ SCRQ
TILQ 2] O l O O 3 O O
ROCQ O 20 O O 0 O 5 O
SANQ l 0 I2 0 0 l2 0 O
PAPQ O O O 25 O O O O 802
CORQ O O 0 O 25 O 0 0 accuracy
GRAQ 2 0 I2 0 0 ll 0 O
WOOQ O h 0 O 0 0 2l 0
SCRQ O O O O O O O 25

The classification results between the original and equalized

versions of the image classes yielded results similar to those obtained

7h

Table 8: Classification of TILE, ROCK, SAND, PAPE and
TILQ, ROCQ, SANQ, PAPQ Using 32x32 Subimages.
(percent accuracy reflects merging of ROCK and ROCQ)

PSE TILE ROCK SAND PAPE TILQ ROCQ SANQ PAPQ
TILE 19 O 5 l O O O O
ROCK 2 6 O O I l6 0 O
SAND 2 O 20 3 0 O O O
PAPE l O l 23 O O O O 80.5%
TILQ 0 O 0 O 15 0 l0 0 accuracy
ROCQ 2 l2 l O 2 8 O O
SANQ O O l O A 0 I9 I
PAPQ O 0 O O O O 2 23

Fl TILE ROCK SAND PAPE TILQ ROCQ SANQ PAPQ
TILE 2l 0 3 O l O O 0
ROCK O 3 O O O 22 O O
SAND 2 O 23 O O 0 O O
PAPE O O O 25 0 O 0 O 952
TILQ l O O O 22 O 2 0 accuracy
ROCQ 0 2l 0 O O A O O
SANQ O O O O l 0 2h 0
PAPQ O O 0 O O O O 25

in the 6Ax6A experiment reported earlier. In the experiment using

TILE, ROCK, SAND. PAPE and their equalized versions, and ignoring
misclassifications between ROCK and ROCQ (Table 8) the PSE feature
yields 80.52 correct classification and feature 1 yields 95% correct
classification. Table 9 gives the results of the experiment using
32x32 samples from CORK, GRAS, WOOD, SCRE and their equalized
counterparts. The PSE feature yields 69% correct classification
results. Feature I yields 97% correct classification results with all
misclassifications occurring between WOOD and NOOQ. Using 6Ax6A
subimages, no misclassifications occurred between WOOD and WOOQ.
suggesting that the channel filtering features have some difficulty

discriminating these classes.

75

Table 9: Classification of CORK, GRAS, WOOD, SCRE and
CORQ, GRAQ, WOOQ, SCRQ Using 32x32 Subimages.

PSE CORK GRAS WOOD SCRE CORQ GRAQ NOOQ SCRQ
CORK 20 2 O 2 O l O O
GRAS A ll 0 l 0 l O O
WOOD 1 l0 ll 0 O l 2 0
SCRE O A 0 2i 0 O 0 O 69%
CORQ 3 2 l 0 IO 1 O 0 accuracy
GRAQ 3 7 2 l l lo I O
HOOQ O O 5 O O A l6 0
SCRQ O O O I O l O 23
Fl CORK GRAS HOOD SCRE CORQ GRAQ WOOQ SCRQ
CORK 25 O O O O O O 0
GRAS O 25 O O O O 0 O
WOOD O O 22 0 O O 3 O
SCRE O O 0 25 O O O O 97%
CORQ O O O O 25 O 0 0 accuracy
GRAQ O O O O 0 25 O O
WOOQ O O 3 O 0 O 22 O
SCRQ O O O 0 O O O 25

5.3.3 Summary

This section has presented experiments which evaluate the ability
of the channel filtering features to discriminate histogram-equalized
images from each other and from the corresponding unequalized images.
The results show that histogram-equalized images are perceived by the
channel filtering features to have different textures from the original
images. In addition, histogram equalization was found to confuse some
discriminable (unequalized) image classes. These observations imply
that histogram equalization should be used with caution as a
preprocessing procedure when channel filtering features are used for
texture analysis.

The performance of the PSE feature continues to be poor relative

to the channel filtering features.

76

5.A Experiment 6: Uniform Gray Level Changes

The conclusion of the previous section suggests that histogram
equalization should not be used to preprocess images for the channel
fiiltering features. Without preprocessing, however, irrelevant gray
level variations can interfere with texture analysis unless the
features are insensitive to such variations. Since the channel
filtering features are defined relative to the average gray level of
the image, we might expect them to be insensitive to changes in the
average gray level. This experiment will test this hypothesis.

The data to be used for the following experiment consists of four
artificial image classes in which the gray level at each pixel is an
independent random variable from a Gaussian distribution. The means
and variances are selected to enable the effects of changes in the mean
and changes in the variance to be determined. The image classes are
illustrated and the generation parameters are given in Figure II. The
parameter values used insure that three standard deviations about the
mean gray level are within the allowed gray level range of O to 255.
Gray levels generated outside that range were rejected.

Twenty-five subimages of size 6Ax6A for each class were used in
this experiment. The results for the PSE feature and channel filtering
feature I are given in Table ID. The PSE feature discriminates all
four classes perfectly, indicating that the PSE feature is sensitive to
both the variance and the average gray level of the images. This
implies that the PSE feature is not a good texture measurement since

average gray level changes should not affect the image texture unless

 

 

 

 

 

 

 

 

Figure 11: Gaussian White Noise Images
(a) GWNl: mean 160, sd 30 (b) GWNZ: mean 160, sd 10
(c) GWN3: mean 96, sd 30 (d) GWNA: mean 96, sd 10

78

Table l0: Classification Results Showing the Effect of
Average Gray Level Changes.

PSE GWNl GHNZ GWN3 GWNA
GWNI 25 O O O
GNNZ O 25 O O
GWN3 O O 25 O
GNNA O O O 25
Fl GWNl GWNZ GWN3 GWNA
GWNI l7 0 8 O
GWNZ O 9 0 l6
GWN3 lO 0 l5 0
GNNA 0 lO 0 IS
the change is so severe that the gray level distribution is modified by
limitations of the image acquisition system. In the evaluations by the
channel filtering features, the classes which have different means but
identical variances are confused. Feature l misclassifies an: of the
subimages, and all of the misclassifications are between classes with
different means and identical variances. Classes with different
variances are discriminated with 100% accuracy by the channel filtering
features.

This experiment has demonstrated that the channel filtering
features are insensitive to moderate variations in the average gray
levels of the regions being analyzed. The features were found to be
sensitive to differences in the gray level variance as might be
expected since the variance determines the spectral energy, which is
measured by the channel filtering features. Changes in the mean affect
only the zero-frequency component and are eliminated by computing the
features relative to the mean gray level of the filtered images. This
result also verifies that the discrimination performance observed in

earlier experiments using images which were not preprocessed were not

due to average gray level differences between the image classes. The

79

PSE feature was found to be sensitive to both the mean and the variance
of the gray level distribution. This enabled the PSE feature to
discriminate all four Gaussian white noise classes when properties of
human texture perception indicate that certain classes should be

confused.

5.5 Experiment 7: Magnification Changes

This experiment will attempt to determine whether and how changes
in the apparent size (magnification) of a textured image can be
identified by the channel filtering method. The objective is to take a
textured image and a magnified version of the same image and determine
from the channel filtering features that the two images are from the
same texture class.

The data for this experiment are taken from the TILE, ROCK, SAND
and PAPE image classes used previously. Twenty-five subimages of size
32x32 from each class will be compared with twenty-five subimages of
size 6Ax6A generated by expanding each pixel from the 32x32 subimages
into a 2x2 pixel block. This means that the 6Ax6A images are 2X
magnifications of the 32x32 subimages. The magnified image classes
will be abbreviated TI2X, ROZX, SA2X, and PAZX.N

The difference between images which is of interest in this
experiment is not simply a change in image size. For example, a 6Ax6A
image and another 6Ax6A image which portrays a magnified 32x32 area
provide different coverage of the texture pattern, so the variance of
the features may differ for the two classes. This difference could

enable the nearest-neighbor classifier to discriminate the classes even

80

Table II: Size Change Experiment Using 6 Spatial Frequency Channels.

PSE TILE ROCK SAND PAPE TIZX ROZX SAZX PAZX
TILE 18 O A 3 0 O 0 O
ROCK 3 22 O O O O 0 O
SAND 2 O 20 3 O O O O
PAPE l 0 2 22 O O O O
T|2X O O O 0 13 O A 3
ROZX O l 0 0 3 21 0 0
SAZX 0 O O O 2 0 20 3
PAZX O O O O 1 O 3 21

F1 TILE ROCK SAND PAPE TIZX ROZX SA2X PAZX
TILE l6 0 8 O l O O O
ROCK 0 11 O O O lA 0 O
SAND 5 O 20 O O O O 0
PAPE O O 0 25 0 O O O
TIZX l 0 0 0 l7 0 7 O
ROZX 0 1A 0 O O 11 O O
SAZX O 0 0 0 5 0 20 O
PAZX O O O O 0 0 0 25

though they portray the same texture. Thus, we will require the
classes to provide equivalent coverage of the texture pattern. This
restriction makes the fundamental frequency of an object in the
textured image appear in the same channel at both magnification levels.
In the spatial frequency domain. the effect of this magnification is to
add a high frequency channel which contains noise caused by the 2x2
pattern of the magnified pixels.

Another critical factor is the number of spatial frequency
channels to use in the classifier. Orientation channels cannot be
used; since they contain information from all spatial frequencies, they
can provide discriminating information between image classes which
portray the same texture. Clearly, the number of channnels to use for
this problem must be less than or equal to the number of channels
available from the smaller subimage size, in this case six. Table II

shows that using six spatial frequency channels, all of the image

8l

classes are discriminable. This discrimination is based on the spatial
frequency information available in the sixth channel. Channel 6 has a
center frequency of 32 cycles per image, which is beyond the Nyquist
frequency for 32x32 images. Thus, only a fraction of the spatial
frequency information for channel 6 is present in the image. For 6Ax6A
images, the center frequency of channel 6 is the Nyquist frequency, so
more spatial frequency information is available in the channel.

The results after eliminating channel 6 from consideration,
leaving five spatial frequency channels for the classifier, are shown
in Table l2. The PSE feature provides overall classification accuracy
of BIZ. Using channel filtering features, the image classes which
portray the same texture are completely confused in spite of the
difference in magnification. Merging theimage classes which portray
the same textures yields a four class discrimination problem with 50

samples per class. In this four-class problem, feature I achieves

82

Table l2: Size Change Experiment Using 5 Spatial Frequencerhannels.
(percent accuracy reflects merging of classes
which portray the same texture)

PSE TILE ROCK SAND PAPE TIZX ROZX SAZX PAZX
TILE l8 0 6 l O O O O
ROCK 3 22 O 0 O O O 0
SAND 2 O 20 3 0 0 O O
PAPE l 0 3 2l 0 O O O 81%
TIZX 0 0 0 0 l8 0 6 1 accuracy
ROZX O l O O 3 2] O 0
SAZX O O O O 2 0 20 3
PAZX O 0 O O I O 3 2l
Fl TILE ROCK SAND PAPE TIZX ROZX SA2X PAZX
TILE 2 O 2 O 20 O l O
ROCK O O O O O 25 O O
SAND 2 O 2 0 O O 21 O
PAPE O O O 10 O O O 15 95.5%
TI2X 22 0 O 0 2 O l 0 accuracy
ROZX O 25 0 O O O O O
SAZX 2 0 20 O l 0 2 O
PAZX O O O 16 O O O 9

95.52 classification accuracy.

This experiment has demonstrated the ability of the channel
filtering features to identify textures through magnification changes.
Certain restrictions were imposed for processing images to test whether
the images might portray the same texture at different magnifications.
These restrictions were justified by the interpretations of the spatial
frequency filters. Further research may provide insights which will
relax these restrictions and enable simpler, more natural procedures

for identifying texture through magnification changes.

5.6 Experiment 8: Orientation Changes

This experiment will test whether the channel filtering method can
determine when two images portray the same texture at different

orientations. The method to be used involves determining the minimum

83

distance between patterns using any cyclical shift of the feature
values from orientation channels. This minimum distance gives the best
fit of one texture to another through the orientations tested.

The data for this experiment consists of four 256x256 images
containing regular bar patterns at horizontal (ZOOO), vertical (2090)
and diagonal (ZOA5 and Zl35) orientations (Figure l2). The bars are
about 6 pixels wide. The results of nearest-neighbor classification on
25 samples per class using only the four orientation channels and
without any shifting are shown in Table I3. The classes are perfectly
discriminated by both the PSE feature and feature Fl. Using the
minimum distance between patterns produced by a circular shift of the
orientation features, the results in Table IA are obtained. This table
shows that the circular shift enables both features to confuse the
diagonal bar patterns and to confuse the horizontal/vertical bar
patterns. The features are still able to separate the diagonal bar
patterns from the horizontal/vertical bar patterns. The results
indicate that the diagonal bar patterns are somehow different from the
horizontal and vertical patterns. This may be attributed to the

slightly different bar width caused by the rectangular quantization

8A

 

”WI!!!

l

Illlll

Figure 12: Bar Images for Orientation Experiment
(3) 0-degree bar pattern (b) AS-degree bar pattern
(c) 90-degree bar pattern (d) l35-degree bar pattern

    
 

 
 

       

85
Table I3: Orientation Experiment Using No Channel Shifting.

PSE zooo zons 2090 2135
2000 25 0 O 0
ZOA5 0 25 0 0
2090 0 0 25 0
Zl35 0 O 0 25
Fl Z000 ZOA5 2090 Zl35
2000 25 0 0 0
ZOA5 0 25 0 0
2090 0 0 25 0
Zl35 0 0 0 25
grid and to the different bar lengths in the diagonal orientations due
to the square image shape.

In this experiment, the PSE feature provides the same results as
the channel filtering features. This is because the power spectral
energy of all the subimages is concentrated in a single orientation
channel which is different for each class. Since the differences
between these image classes is apparent in the power spectrum, the PSE
feature is able to duplicate the performance of the channel filtering
features.

This experiment shows that a circular treatment of orientation

channels can easily detect orientation differences of 90 degrees, but

that due to the square shape of the images and the quantization grid,

86

Table IA: Orientation Experiment Using Circular Channel Shifting.

PSE 2000 ZOA5 2090 2135
2000 0 0 l8 7
ZOA5 O O O 25
2090 0 O 18 7
Z135 0 0 0 25

F1 2000 ZOA5 2090 2135
2000 O 0 l8 7
ZOA5 O 0 O 25
2090 O 0 l8 7
2135 0 O 0 25

A5 degree orientation differences are more difficult to detect. The
perceived difference between diagonal and horizontal/vertical channels
might be overcome by computing features only within a circular

subimage.

5.7 Experiment 9: Phase Spectrum Changes

In this experiment, the phase spectra of the Gaussian white noise
subimages (Section 5.A) will be modified to determine the effect of
such changes on the textural evaluations by the PSE feature and the
channel filtering features. Only the phase spectra will be modified:
the modified images will have the same power spectra as the Gaussian
white noise images.

Determining the nature of the modifications which could be made
was a difficult task. Since each entry in the phase spectrum affects
the entire image, even slight perturbations can have drastic effects
[Oppenheim and Lim, I98I]. The most troublesome constraint in
generating the images for this experiment was that the phase-modified
images had to remain in the gray scale 0 to 255. Otherwise, the

phase-modified images would have to be scaled, and scaling changes the

37

power spectrum of the image.

The method which was finally found satisfactory was to change the
phase angles of entries near the zero-frequency component in the
Fourier transform as illustrated in Figure I3. Due to the small number
of entries changed and the low energy associated with those entries,
the effect on the space domain image is minimal. The entries which are
changed affect spatial frequency channels centered at l, 2, A, and 8
cycles per image. The orientation channels are also slightly affected.

Figure lA shows the result of the changes in GWNI (mean I60,
standard deviation 30) which yield a new phase-modified image labelled
PHMI. The figure also shows the original and modified filtered images
for two spatial frequency channels. The effect of the phase
modification is to increase the regularity of the filtered images,
resulting in lightened or darkened patches at the center of each side
and a barely visible diamond shape in the PHMI image. Since only the
lowest spatial frequency channels are affected by the modifications,
the changes apparent in the PHMI image are large in size. Due to the
low energy in the affected spectral region, however, the contrast of

the changes is small.

88

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Figure 13: Phase Spectrum Modification Procedure.
Phase spectrum entries around the zero-frequency component
(marked with an X) were replaced with the values shown above.

89

 

 

(E)

Figure 14: Effect of Phase Modifications on GWNl.

(a) GWNl. (b) PHMl. (c) Filtered image of GWNl using the spatial
frequency channel centered at A cyles per image (c/i).

(d) Filtered image of PHMl using 4 c/i filter.

(e) Filtered image of GWNl using 8 c/i filter.

(f) Filtered image of PHMl using 16 c/i filter.

90
Table l5: Classification Results on Four Phase-Modified
Gaussian White Noise Classes.
PSE PHHI PHMZ PHM3 PHMA
PHMI 25 0 0 0
PHMZ 0 25 0 0
PHM3 0 0 25 0
PHMA 0 0 0 25
FI PHMI PHMZ PHM3 PHMA
PHMI I8 0 7 0
PHMZ O 9 0 l6
PHM3 9 0 I6 0
PHMA 0 IA 0 II

In the classification experiment, the phase modification was
performed separately on each of the 25 samples of the Gaussian white
noise images. The classification results are given in Table IS. The
PSE feature obtains perfect discrimination of the four classes.
Channel filtering feature I does not discriminate image classes which
came from Gaussian white noise images with identical means. This is an
additional demonstration of the invariance of the channel filtering
representation of texture to changes in average gray level. This
result will be used to allow us to merge pairs of the phase modified
classes in the next experiment.

The effect of the phase modification on the texture features will
be demonstrated by using Vthe Gaussian white noise classes and the
phase-modified Gaussian white noise classes together in a
classification experiment. The results of this experiment are shown in
Table I6. The PSE feature confuses each Gaussian white noise class
with its phase-modified version. This can be attributed to the fact
that the PSE feature does not use phase, thus the differences which

exist between the image classes are ignored. The results from channel

filtering feature I are more clearly illustrated in Table I7, where the

91

Table I6: Classification Results Illustrating the Effect of
Phase Specturum Changes on Gaussian White Noise Images.

PSE GWNI GWNZ GWN3 GWNA PHMI PHHZ PHM3 PHMA
GWNI O O O O 25 O O 0
GWNZ O 3 O O 0 22 O O
GWN3 0 O O O O O 25 0
GWNA 0 O O 0 O O O 25
PHMl 25 0 0 O 0 0 O O
PHMZ 0 22 O O O 3 O O
PHM3 0 O 25 0 0 0 O O
PHMA 0 O 0 23 O 0 0 2

Fl GWNl GWNZ GWN3 GWNA PHMI PHMZ PHM3 PHHA
GWNI 15 O 7 0 3 O 0 O
GWNZ O A O 8 0 11 O 2
GWN3 9 0 l3 0 O O 3 0
GWNA 0 5 O 9 O 3 0 8
PHMl 3 O O 0 l6 0 6 O
PHMZ O 10 0 l 0 A O 10
PHM3 0 O 3 0 8 0 1A 0
PHMA O 3 O 5 O 8 O 9

image classes which have been found indiscriminable to feature I in
previous experiments are merged. Taking these identities into account
leaves a four-class discrimination problem with 50 samples per class.
In this four-class problem, feature I separates the classes with
different variances. In addition, the phase-modified class with
standard deviation 30 is separated from the unmodified class with
standard deviation 30.

This experiment has illustrated the effects of a small phase

spectrum change on textural evaluations using the channel filtering

92

Table 17: Phase Modification Experiment with
Indiscriminable Classes Merged.

FI GWNI PHMI GWN2 PHMZ
GWN3 PHM3 GWNA PHMA
GWNI,3 AA 6 0 0
PHMI,3 6 AA 0 0
GWN2,A 0 0 26 2A
PHM2,A 0 0 I9 31
method. The PSE feature is completely insensitive to phase changes, by
definition. This was borne out in the results of this experiment.
However, the phase modified images were discriminated from the original
image classes by the channel filtering feature for the classes with
standard deviation 30. Due to the lower energy in the images with

standard deviation I0, the effect of the phase change in the image is

decreased. The smaller effect is not detectable using feature Fl.

5.8 Second-Order Statistics and Channel Filtering

In this section, the results of experiments designed to compare
the performance of the co-occurrence and channel filtering methods will
be presented. Four image classes will be generated using a procedure
based on the four-disk method of [Caelli and Julesz, I978a, I978b].
Pairs of 9x9 micropatterns are generated by a geometrical method such
that two images constructed of randomly rotated copies of the
micropatterns will have identical second-order gray level
distributions. In this experiment, however, the micropatterns will not
be rotated through random angles: instead, rotations through random
multiples of 90 degrees will be used. This results in images with
slightly different second-order statistics and thus slightly different

power spectra. The micropatterns to be used and the corresponding

93

 

 

 

 

 

 

 

 

 

 

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Figure 15: Four-Dot MicrOpatterns and CorreSponding Image Classes.
(The squares in the micrOpattern diagrams correSpond to black
pixels. The labels correspond to the usage in Table 18.)

(a) MicrOpattern 1A (b) Micropattern 13 (c) Part of image JUlA
(d) Part of image JUlB (e) MicrOpattern 2A (f) MicrOpattern 2B
(g) Part of image JUZA (h) Part of image JUZB

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95

image classes are illustrated in Figure I5. The image classes are

visually discriminable.

5.8.I Experiment I0: Application of the Co-occurrence Method

The definition of the co-occurrence matrix [Haralick, I979]
involves the selection of a displacement vector. Since there exist
N2 possible displacement vectors for an NxN image, some guidance in
selecting the displacement vector is required. The choice of the
displacement vector is critical. The displacement vectors to be used
in this experiment will be chosen by a (suboptimal) strategy which
takes advantage of known differences between the micropatterns.

The black pixels in the micropatterns in Figure I5 are numbered to
demonstrate the similarities between micropatterns of each pair. The
placement of onIyI one dot (labelled O and 0') differs in the
micropatterns of each pair. This implies that there exists a

black-black co-occurrence which involves a different displacement

96

Table I8: Black-Black Displacement Vectors in Four-Dot Micropatterns.
(arrows indicate vectors which discriminate the micropatterns)

Micropattern IA Micropattern IB
Points Displacement Points Displacement
0-1 (-2, A) 0'-I (-2, 0)
0-2 ( 2. 0) o'-2 ( 2,-A)
0-3 ( I, 2) <********> o'-2 ( I,-2)
l-2 ' ( A,-A) I-2 ( A,-A)
1-3 (39-2) 1-3 ( 39-2)
2-3 (-l,-2) 2-3 (-I.-2)
Micropattern 2A Micropattern 28
Po'nts Displacement Points Displacement
0"] ('19 3) 0"] (T‘s-1)
0-2 ( I, I) 0'-2 ( l,-3)
0-3 ( 2, 2) <***A****> o'-3 ( 2,-2)
1‘2 ( 2.-2) 1'2 ( 2.'2)
1-3 ( 3.-l) l-3 ( 3.-l)
2'3 l I. l) 2'3 ( l. 1)

vector in the two micropatterns. This displacement vector will be used
to discriminate the image classes. (Note: due to symmetry in the
co-occurrence matrix definition, vectors (dx,dy) and (-dx,-dy) are
considered to be identical.) Table I8 shows the displacement vectors
between all pairs of black pixels in each micropattern. This
information can be used to select an appropriate displacement vector to
distinguish the micropatterns. For example, the (I,I) displacement
vector can be used to discriminate the micropattern pairs.
Micropatterns 2A and 28 contain black-black co-occurrences at
displacement (I,I) but micropatterns IA and IB do not. Similarly, the
(l,2) vector can discriminate the micropatterns of the first pair, and
the (2,2) vector can discriminate the micropatterns of the second pair.
These three displacement vectors, selected specifically to capture the
differences between micropatterns, will be used to compute

co-occurrence matrices for the textures.

97

For these displacement vectors, there are no interactions between
different copies of the micropatterns for black-black co-occurrences.
Thus, we can compute the expected number of black-black co-occurrences
in the image from rotations of individual micropatterns as shown in
Table I9. The number of micropatterns occurring in the 256x256 image
is known (78A), so we can estimate the number of micropatterns
occurring at each of the four allowed orientations (I96). By counting
the number of black-black co-occurrences in each micropattern at each

orientation, we can then compute for each displacement vector the

98

Table I9: Computation of Expected Number of Black-Black
Co-occurrences in 256x256 Four-dot Images.

Number of black-black Expected no. black-black
co-occurrences at each orientation co-occurrences in image

DISPLACEMENT
(l,I)-(-I,-I) Rotation angle

0 90 I80 270 total
Micropattern ----------------

IA 0 0 0 0 0 0*196 . 0
IB 0 0 0 0 0 0*195 a 0
2A 2 0 2 0 A AA196 . 73g
28 2 0 2 O A A*]96 . 78A
DISPLACEMENT
(1.2)‘('1.-2) Rotation angle
0 90 180 270 total
Micropattern ----------------
IA l 0 I 0 2 2*]95 . 392
I8 0 0 0 0 o 0*]96 . 0
2A 0 0 0 0 0 0*195 . 0
28 0 0 0 0 0 0*196 . 0
DISPLACEMENT
(2.2)'('2.'2) Rotation angle
0 90 180 270 total
MicrOpattern ----------------
IA 0 0 0 0 0 0*196 . 0
IB 0 0 0 0 O 0*196 . 0
2A I I I I A AAIQB 3 735
28 0 2 0 2 A AA]96 . 73g

expected number of black-black co-occurrences in the entire image.

The result of this computation shows that the expected number of
black-black co-occurrences at displacement (l,2) is different for the
first pair of images (Figure l5a). Thus, the number of black-black
co-occurrences at displacement (l,2) should be able to discriminate
image classes IA and ID. The other vectors do not provide
discriminating information between IA and IB. In the second image pair
(Figure I5b), the expected numbers of black-black co-occurrences are

equal for all three displacement vectors. Even the (2,2) displacement

99

vector, which could discriminate the micropatterns, cannot discriminate
images 2A and 28. The vectors which differ in the second pair of
micropatterns have the same length, but their orientations are 90
degrees apart. Since the micropatterns are rotated by random multiples
of 90 degrees, the difference between the micropatterns is confused in
the images. These results use only black-black co-occurrences to help
select reasonable displacement vectors for use in the co-occurrence
method. The three vectors will now be used to compute co-occurrence
matrices for use in classification problems.

The performance of the co-occurrence matrix method will now be
demonstrated on 25 6Ax6A subimages from each class. Since the images
are binary, the co-occurrence matrices are of size 2x2, and since the
definition of the co-occurrence matrix tobe implemented [Haralick,
I979] imposes symmetry on the matrix, the co-occurrence matrix involves
three different values: the numbers of black-black, black-white, and
white-white co-occurrences in the image. These numbers are used as
features. The nearest-neighbor classification results are given in
Table 20. The (I,I) displacement vector discriminates the two pairs
but does not discriminate between textures in the same pair. The (l,2)
vector can identify texture IA, but the other classes are confused.
The (2.2) vector discriminates between the pairs, but the
discrimination within each pair is poor: the (2,2) vector was
originally intended to discriminate the second image pair. However,
since the black-black co-occurrences are known not to contribute to the
discrimination of these classes. the discrimination which does occur
can be attributed to white-black and white-white co-occurrences. The

results using all three co-occurrence matrices combined are also shown.

100

Table 20: Classification of Four-dot Textures
Using Co-occurrence Matrices.

(I,I) JUIA JUIB JU2A JUZB
JUIA 2 23 o o
JUIB 2 23 o o
JUZA o o I 2A
JU28 o o 9 I6

(1.2) JUIA JUIB JU2A JUZB
JUIA 25 o o o
JUIB o I A 20
JUZA o 2 A I9
JU28 o 2 o 23

(l.3) JUIA JUIB JUZA JU28
JUIA I 2A 0 o
JUIB 7 I8 0 o
JU2A o 0 I8 7
JU28 o o 9 I6

ALL JUIA JUIB JU2A JU28

JUIA 25 0 0 0
JUIB 0 25 0 0
JUZA 0 0 I3 I2
JUZB 0 0 7 I8
This result uses nine features: the three values in each of the three

co-occurrence matrices. The images of the first pair are identified,

but the second pair is not well separated.

l0I
Table 2l: Classification of Four-dot Textures
by Channel Filtering.

PSE JUIA JUIB JU2A JU28
JUIA II IA 0 O
JUI8 I7 8 O 0
JU2A 0 0 I7 8
JU28 0 0 9 l6

Fl JUIA JUIB JU2A JU28
JUIA 25 0 0 O
JUIB 0 25 0 0

JU2A O O 25 O
JU28 0 O O 25

5.8.2 Experiment II: Application of Channel Filtering

The channel filtering approach was applied to the same samples of
the four four-disk textures. The classification results are shown in
Table 2l. The PSE feature discriminates the different pairs, but
cannot discriminate the textures within each pair. Feature I achieves
I002 correct classification on all four classes. In this experiment,
it is of some interest to determine whether the discrimination of the
texture classes is due to the action of orientation channels, spatial
frequency channels, or both. Since these images are composed of dots,
it might seem that no orientation or size selectivity exists between
the image classes. Table 22 gives the classification results using
only the six spatial frequency channels, and Table 23 gives the results
using only the four orientation channels. The results show that both
orientation and spatial frequency information contribute to the
discrimination of the classes. These contributions can be understood
by considering the interpretation of spatial filtering as a moving

average operation. Each gray level in a filtered image is the result

102

Table 22: Classification of Four-dot Textures Using
Six Spatial Frequency Channels.

PSE JUIA JUIB JU2A JU28
JUIA I2 I3 0 0
JUIB I3 I2 0 0
JUZA 0 0 2l A
JU28 0 O 7 I8
Fl JUIA JUIB JUZA JU28
JUIA 2A I 0 0
JUIB 0 25 0 0
JU2A 0 0 2A l
JU28 0 0 I 2A
of an averaging operation over an area of the original image defined by
the filter point spread function. The result of this averaging can be
expressed for these particular images as a consequence of the local dot
density. Variations in the dot density in local areas of different
sizes and orientations provides the discriminating information between
the image classes. Since the number of dots in a local area determines
the average gray level of the area (which is a component of the power

spectrum), this interpretation is consistent with the characterization

of the channel filtering features as “average local energy" measures.

I0 3

Table 23: Classification of Four-dot Textures Using
Four Orientation Channels.

PSE JUIA JUIB JUZA JU28
JUIA 13 12 O O
JUIB I3 12 O O
JU2A O O 18 7
JU28 0 O 9 16

F1 JUIA JUIB JUZA JU28
JUIA 25 0 O O
JUIB 3 22 0 0

JU2A O O 25 O
JU28 O O O 25

5.8.3 Summary

This series of experiments compared the performance of the
co-occurrence method to the channel fitering method for discriminating
a particular set of textured images. A procedure for selecting
displacement vectors for co-occurrence matrices was applied. The
displacements were chosen to detect known differences in the
micropattern structures. For one image pair, the combined
co-occurrence results were satisfactory: for the other, the
co-occurrence matrices performed poorly. The method for selecting the
displacement vectors was not optimal or exhaustive, but the results
demonstrate that the selection of displacement vectors is critical and
that the performance of a particular displacement vector cannot be
reliably predicted from its performance on micropatterns. In these
experiments, only certain black-black co-occurrences could be
investigated in detail. Some results indicated that the white-white
and black-white co-occurrences might also contribute to class

discriminations. The problem of selecting suitable displacement

10A

vectors is a major disadvantage to the use of the co-occurrence method.

Channel filtering feature Fl yielded I002 classification results.
Both spatial frequency and orientation channels were found to
contribute to this result. The performance of the PSE feature
indicates that the different image pairs have significantly different
power spectra, but the power spectra of the images within each pair are
not discriminable. These observations imply that the performance of
feature Fl is not due to power spectral differences; it is the use of

phase information which enables discrimination of all of the classes.

5.9 Computational Simplifications

In this section, two computational simplifications of the channel
filtering approach will be tested to determine if such simplifications

cause any significant degradation in classification performance.

5.9.I Experiment l2: Using Fewer Channels

One possible simplification is to use fewer channels. Since
texture is perceived in regions containing small areas of constant gray
level, the low-frequency channels, which respond to gray level
variations over large areas, might be eliminated without degrading
performance. In addition, the highest spatial frequency channel does
not capture any spectral information which is not available in other
channels.

In this experiment, the two lowest spatial frequency channels and
the highest spatial frequency channel will be eliminated. The 6Ax6A

images will be filtered by four orientation channels and four spatial

105

frequency channels (center frequencies A, 8, I6, and 32 cycles per
image). The results of using these eight channels on the eight natural
image classes are given in Table 2A. The 65.52 correct performance of
the PSE feature is slightly worse than its performance using all ll
channels. Feature l provides 982 correct classification, the same as
with all of the channels present.

Using only eight spatial frequency channels does not appear to
degrade the performance of the channel filtering features. The minimum
number of channels required for texture discrimination depends on the

particular set of textures.

5.9.2 Experiment l3: Ideal Band-Pass Channels

The filtering operation using Gaussian filters requires that the

filter amplitudes and the image spectrum be multiplied. If the filter

l06

Table 2A: Classification Results on Natural Images
Using Eight Channels.

PSE TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE I7 2 A I 0 0 I 0
ROCK 3 IS I 0 2 0 0 A
SAND A 0 l2 2 0 0 7 0
PAPE 0 0 2 22 I 0 0 0 65.52
CORK 0 0 0 0 I6 9 O 0 accuracy
GRAS 0 l I 0 8 l2 2 I
WOOD 2 0 5 I 0 A I3 0
SCRE 0 0 0 0 0 I 0 2A

Fl TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 22 I 2 0 0 0 0 0
ROCK 0 25 0 0 0 0 0 0
SAND l 0 2A 0 0 0 0 0
PAPE 0 0 0 25 0 0 0 0 982
CORK 0 0 0 O 25 0 0 0 accuracy
GRAS 0 0 0 0 0 25 0 0
W000 0 0 0 0 0 0 25 0
SCRE 0 0 0 0 0 0 0 25

amplitudes were all either zero or one, the multiplications could be
avoided. In this experiment, channels with an ideal band-pass

characteristic will be applied to the natural image classes.

The spatial frequency channels to be used are the same as those
defined for power spectral energy features in [Weszka et al, I976].
The channels pass all spatial frequencies in nonoverlapping bands whose
lower and upper bounds, in cycles per image, are as follows: [2,A],
[A.8], [8,I6] and [I6,32]. The orientation channels to be used pass
all spectral information within A5 degrees of horizontal, vertical, and
both diagonal orientations. The use of ideal band-pass filters causes
additional ripples in the filter responses due to the abrupt filter
cutoffs in the spatial frequency domain. The response is still
symmetrical about the mean gray level, however. In [Marr and Hildreth,
I979] these ripples were found to interfere with edge and form

detection in filtered images. Table 25 shows that the ideal band-pass

107

Table 25: Classification Results on Natural Images
Using Ideal Bandpass Channels.

PSE TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 21 1 3 0 O O 0 O
ROCK A 20 O O O O 0 1
SAND A O 19 0 0 O 2 O
PAPE O 0 2 22 O 1 O O 772
CORK 0 0 0 0 l9 6 0 0 accuracy
GRAS 0 0 2 0 9 1A 0 0
WOOD 1 0 6 0 1 2 15 O
SCRE O 0 O O O 1 0 2A
F1 TILE ROCK SAND PAPE CORK GRAS WOOD SCRE
TILE 23 1 1 0 O 0 O O
ROCK 1 2A 0 O O O O O
SAND 1 0 2A 0 O O 0 0
PAPE O 0 O 25 0 O 0 O 983
CORK 0 0 0 0 25 0 0 0 accuracy
GRAS O O O O 0 25 0 0
W000 0 O 0 0 0 0 25 O
SCRE O O 0 O 0 O 0 25

filters do not seem to degrade texture analysis performance: feature I
provides 982 correct classification results. The PSE feature achieves
772 correct results, which is better than the 692 performance recorded
using Gaussian channels. The PSE feature gave similar performance in

another study using ideal band-pass filters. [Weszka et al, I976].

5.IO Summary

This chapter has presented the results of experiments designed to
demonstrate properties of the channel filtering feature space. The
performance of the method on natural and artificial image classes, on
images which differ in average gray level, magnification, orientation,
and phase spectra was examined. Some computational simplifications of
the channel filtering method were also presented and found not to

seriously degrade the performance of the features. Throughout the

108

experiments, the power spectral energy in each channel was used as a
feature to demonstrate the effect of using phase information in the
channel filtering features. The channel filtering features provide
superior performance. A comparison of the channel filtering method
with the co-occurrence method on one set of images demonstrated that,
even when the displacement vectors for the co-occurrence matrix are
chosen specifically to capture differences between the micropatterns in
a textured image, the channel filtering method outperforms the

co-occurrence matrix method.

Chapter 6

Evaluation of Channel Filtering Features for Texture Segmentation

6.l Segmentation

The previous chapter evaluated the channel filtering features in
texture classification problems. In more realistic situations, the
images being analyzed contain an unknown number of textured regions
which must be identified, thus segmenting the image. This texture
segmentation problem is different from a general image segmentation
problem in which the objective is to identify objects in a scene.

Segmenting an image into textured regions is more difficult than
classifying textured images in three ways. First, the number of
classes is specified in advance in classification problems whereas in
segmentation problems the number of classes is unknown. This requires
a segmentation algorithm to include some means for determining the
actual (or at least an appropriate) number of classes from the data.
Second, the objects being classified in classification problems are
subimages. In segmentation problems, the objects to be classified are
individual pixels. The number of classifications required in
segmentation is very large. For example, segmenting a 128xI28 image
requires each of the l6,38A pixels to be classified. This large number

of classifications will require some simplifications in the methods to

109

110

be used. Third, in classification experiments the subimages being
classified are known to contain a single texture, but in segmentation
experiments, the neighborhoods of some pixels will involve more than
one texture.

The segmentation procedure in this chapter will require a
determination of the texture in a neigborhood about each pixel. A
channel filtering feature will be used for this purpose. A feature
vector will be computed for each pixel in the image. The number of
texture classes present will be determined from the feature vectors,
and all of the pixels in the image will be classified. Figure I6 shows

a block diagram of the segmentation procedure.

6.2 Computing Texture Features for Segmentation

Ideally, a “resolution-preserving textural transform” [Haralick,
I975] would be applied to the image which would replace the gray levels
by texture feature values computed over some neighborhood about each
pixel. Such an ideal is often not practically attainable, but a
reasonable solution exists using the channel filtering approach. By
applying two operations to the filtered images, the gray level at each
pixel of the filtered images can be replaced by a new gray level which
is related to the value of channel filtering feature I. In the first
step, we replace each gray level as follows:

Ik' (x.y)- 2* |E-Ik(x,y)|
where Ik(.,.) is the kth filtered image and G is the mean gray level
of the filtered images. This step produces an image. Ik'(.,.), in

which the gray levels are related to the absolute deviation from the

 

 

 

 

111

IMAGE

1 Channel filtering

 

 

 

 

FILTERED IMAGES

1 Ik'(x,y) = 2*Ilk(x,y)4al

 

 

Fifi] Ik'(.,.) IMAGES

1 Averaging procedure

 

 

 

 

ll

Minimum-
Distance
Classifier

I

3.1,

 

 

 

FEATURE IMAGES

  
 
 

Extraction of 64
representative pixels

 

.....

 

 

 

SEGMENTED IMAGE

 

I

 

 

PATTERN
MATRIX

CLUSTER
CENTERS

Figure 16: Diagram of the Segmentation Procedure.

112

mean gray level. Simply taking the absolute deviation would result in
an image with about half the original number of gray levels. Since
gray levels are integer values, the absolute deviation is scaled to
increase the precision of the averaging step which occurs next. In the
experiments, 872 was added to the pixel values to enhance the
visibility of the Ik'(.,.) image.

The second step involves computing a moving average over the
'Ik'(.,.) images. In the definition of channel filtering feature I,
the absolute deviation from the mean is averaged over the entire
subimage. For segmentation experiments, the averaging is performed
over small neighborhoods about each pixel. Therefore, we wish to
replace each pixel in Ik'(.,.) with the average gray level in a
neighborhood about the pixel. This can be accomplished either by a
convolution in the spatial domain or by a filtering operation in the
spatial frequency domain. The window which defines the neighborhood
must be large enough to capture an adequate texture sample, but not so
large that transitions between different textures are blurred over a
large area. The result of the averaging is a I'feature image" in which
the gray level at each pixel is a measure of the texture present at the
corresponding location of the original image.

The experiments in this chapter will use 8x8 and l6xl6 square
windows in computing the feature images. In these experiments, the
spatial domain averaging method is used.

The feature images defined here correspond to the ”texture energy
planes“ of Laws [1980]. In that study, the filters were defined as
spatial domain templates which were convolved with the original image.

The filtered images had an average gray level of zero, resulting in a

113

slightly different computational procedure for producing the feature
images. The present study differs from Laws [I980] in the use of
spatial frequency domain filters rather than spatial domain templates,
in the decomposition of the image by isolating bands of spatial
frequency and orientation rather than by detection of "edges", "spots",
and "rings", and in the use of results from vision science to guide the
development of the computational methods.

Note that the computation of the feature images does not require
each neighborhood to be filtered separately. This contrasts with some
earlier approaches to texture segmentation in which the entire
computational procedure is repeated for each neighborhood considered

[Haralick, I975; Bajcsy, 1973; Bajcsy and Lieberman, 1976].

6.3 Segmentation Using Feature Images

The feature images provide an evaluation of the texture in small
neighborhoods about each pixel in the image. Corresponding to each
pixel is a feature vector in which the number of features equals the
number of channels used. The texture segmentation problem has now been
transformed into the feature space. The next problem is to assess the
structure of the patterns in the feature space. This assessment will
be made by applying a clustering algorithm [Anderberg, 1973: Everitt,
197A]. Previous uses of clustering in segmentation problems are
discussed in [Mitchell and Carlton, I978: Schachter et al, I978b:
Rosenfeld, l98l; Coleman, I979: Davis and Mitiche, I982]

The clustering algorithm to be used, called CLUSTER [Dubes and

Jain, I976], is a partitional clustering procedure which attempts to

11A

mimimize a squared-error criterion. CLUSTER was selected because the
clusters it produces are not limited to hierarchical relationships and
because this algorithm does not require user-specified parameters.
CLUSTER provides partitionings of the data with the number of clusters
going from 2 to a user-specified bound (8 in this study). Each
partitioning of the data corresponds to a segmentation of the given
image. It will be necessary to evaluate these clusterings to determine
which ones are appropriate representations of the data, and several
statistics are provided by CLUSTER for this purpose.

Clustering algorithms are computationally very demanding. Most of
them are designed to cluster only a few hundred points. To segment a
128x128 image using clustering alone would require the algorithm to
process l6,38A points. To reduce computational requirements, only 6A
pixels spaced l6 rows and I6 columns apart will be clustered. This
simplification assumes that the textured regions to be segmented will
not be irregularly shaped or very small in area. Additionally, only
eight channels, the four orientation channels and spatial frequency
channels 3-6 (center frequencies A, 8, l6, and 32 cycles per image)
will be used. These eight channels were found in section 5.9.I to
provide good classification results. This provides a sample of 6A
points in 8 dimensions for clustering. The cluster centers will be
used to define a minimum-distance classifier to classify the remaining
pixels. The classification results will be displayed as a segmented
image in which gray levels denote the cluster labels assigned to each
pixel.

Note that the segmentation is completely determined by the

structure of the points in the feature space according to the

115

clustering algorithm. This differs from interpretation~guided
segmentation [Barrow and Tennenbaum, I981] where semantic information

is used to guide the segmentation process.

6.A Evaluating the Segmentations

The number of segments obtained in an image depends on the
clustering algorithm. A problem facing users of any clustering
algorithm is the question of cluster validity [Dubes and Jain, I979].
Since any clustering algorithm will produce clusters regardless of the
distribution of points in the feature space, the user must determine
whether the partitioning obtained is a consequence of structure in the
points or an artifact of the clustering algorithm. A related problem
is to determine the actual number of clusters present in the data.

CLUSTER provides several statistics which can be used to
qualitatively assess the validity of a clustering. One statistic,
which measures the spread of a cluster in the feature space is the
average within-cluster distance which is defined for cluster k as
follows:

Mk) 0
\ \ 2
CLAVGD(I<)= l: l/N(k) 2" > > [X(i.j)-C(k..l)] :]

/ /
I-I j=l

1/2

 

 

 

 

where N(k) is the number of points in cluster k, C(k,.) is the cluster
center for cluster k, D is the dimensionality of the feature space, and
X(i,j) is the value of the jth feature for the ith pattern.

A measure of the “validity" of cluster k which takes into account

the compactness and the isolation of the cluster is defined as

II6

 

 

D
mIn \ 2
l > [C(k’j)-c(‘!j)]
U” /
S(k) = j=1
CLAVGD(k)

Large values of S(k) indicate compact, well-isolated clusters. This
statistic will be used to determine the acceptability of a clustering.
An acceptable clustering is one in which the value of S(k) for all
clusters exceeds a threshold. We have empirically determined a
threshold of 1.70 for S(k) by tuning the threshold in preliminary
experiments to yield approximately the number of clusters perceived by
preattentive human vision. This particular value is only an
approximation: we found a threshold of ‘2.0 to reject too many
reasonable clustering solutions and a threshold of 1.5 to accept too
many clusterings.

The threshold value requires that for each cluster the minimum
distance to another cluster center be at least 1.70 times the average
within-cluster distance. The clusterings which are accepted by this
criterion will be ranked by the value of the average of S(k) over all
clusters weighted by the number of points in the clusters. Clusterings

with higher average S(k) values will be preferred.

6.5 Segmentation Experiment I: Dot Textures

The data for this experiment consists of a 128xl28 binary image
illustrated in Figure I7. The left half of the image is a regular dot

pattern in which the dots are separated by 3 pixels from their

117

 

Figure 17: Dots Image for Segmentation Experiment 1.

118

horizontal and vertical neighbors. The right half of the image is a
random dot pattern in which the probability that each pixel is black is
independent of the other pixels and is approximately equal to l/9.
(The exact probability is the number of dots in the regular texture
divided by half the number of pixels in the image, which results in
identical average gray values for both textures). This image was
segmented using 8x8 and l6xl6 windows in the averaging step for
computing the feature images.

The segmented images produced using 8x8 windows are shown in
Figure 18, and the segmented images produced using l6xl6 windows are
shown in Figure 19. The figures show only the segmentations for 2, 3,
A, and 5 clusters because the gray levels used for labelling each
segment become too difficult to see when more classes are present.
Note that the actual gray levels in the segmented images have no
significance other than to distinguish the regions.

The two-cluster segmentations for both window sizes accurately
distinguish the regions of different texture: over 982 of the pixels
are correctly labelled. The 8x8 segmentation contains a few small
areas in the random texture which are classified with the regular
texture. These misclassifications do not appear in the l6xl6
segmentation because the probability that a region of random dots will
resemble a regular texture is lower for larger regions. The
segmentation results corresponding to more than two clusters break up
the random texture into irregularly shaped regions. The regular
texture is not subdivided. None of the segmented regions lie across

the boundary between the textures.

119

 

Figure 18: Segmented Images for Dots Using 8x8

Averaging Windows.
(b) 3-cluster solution
(d) 5-c1uster solution

(a) 2-c1uster solution

(c) A-cluster solution

120

 

Figure 19: Segmented Images for Dots Using 16x16

Averaging Windows. (a) 2-c1uster solution
(b) 3-cluster solution (c) A-cluster solution
(d) 5-cluster solution

121

We now need to determine which of the segmentations are reasonable
using the validity test defined earlier. The number of points in each
cluster, the value of S(k) for each cluster, and the weighted average
values of S(k) are shown in Table 26 for the 8x8-averaged feature

images and in Table 27 for the 16x16-averaged feature images. In both

122

Table 26: Evaluation of Clustering on Dots Image
Using 8x8 Averaging Windows.
(* indicates accepted clustering solutions)

k N(k) S(k) k N(k) S(k)
2 CLUSTERS 7 CLUSTERS
l 32 6.93 l 32 5.75
2 32 2.31 2 3 2.19
AVG A.62 A 3 3 1.19
A 9 I.3A
3 CLUSTERS 5 9 1.13
I 32 6.17 6 5 1.31
2 l9 I.AI 7 3 1.53
3 l3 I.2A AVG 3.55
AVG 3.76
8 CLUSTERS
A CLUSTERS I 32 5.75
I 32 6.08 2 3 1.98
2 20 I.A8 3 3 1.19
3 8 I.I5 A 9 I.AI
A A 2.20 5 3 I.66
AVG 3.78 6 5 1.31
7 3 1.53
5 CLUSTERS 8 6 1.29
I 32 6.08 AVG 3.59
2 13 1.05
3 8 I.IA
A A 2.I6
5 7 0.975
AVG 3.6A
6 CLUSTERS
I 32 5.75
2 7 I.53
3 3 1.19
A II 1.2A
5 6 1.07
6 5 I.A7
AVG 3.53

cases, only the two-cluster solution is accepted. The tables also show
that the S(k) value for cluster I, which corresponds to the regular
texture, is always very high. Since the cluster of points from the
regular texture is always compact and well-isolated, the regular

texture is never subdivided in the segmented images.

123

Table 27: Evaluation of Clustering on Dots Image
Using l6xl6 Averaging Windows.
(* indicates accepted clustering solutions)

k N (k) S (k) k N (k) S (k)
2 CLUSTERS 7 CLUSTERS
1 32 9.39 1 32 8.06
2 32 3-79 2 7 1.39
AVG 6.59 * 3 8 1.58
A 5 1.8A
3 CLUSTERS 5 2 1.77
1 32 8.86 6 7 1.71
2 22 1.33 7 3 1.35
3 10 1.62 AVG A.83
AVG 5.1A
8 CLUSTERS
A CLUSTERS 1 32 8.06
1 32 8.27 2 7 1.59
2 11 1.22 3 8 1.58
3 9 1-39 A 5 1.93
A 12 1.28 5 2 1.87
AVG A.78 6 6 1.97
7 2 1.91
5 CLUSTERS 8 2 1.91
1 32 8.05 AVG A.91
2 8 1.39
3 3 1-53
A 6 1.56
5 10 1.26
AVG A.73
6 CLUSTERS
1 32 8.06
2 7 1.A5
3 7 1-63
A 6 1.58
5 7 1.1A
6 5 2.97
AVG A.87

6.6 Segmentation Experiment 2: Gaussian White Noise

This experiment will apply the segmentation procedure to a 128x128
image which is visually perceived to contain a single homogeneous

texture. The gray level at each pixel is generated independently using

12A

a Gaussian distribution with mean 128 and standard deviation 30. The
image is illustrated in Figure 20. The same filtering and segmentation
procedure as in the previous experiment was applied. The segmented
images from 8x8-averaged feature images are shown in Figure 21 and the
results from 16x16-averaged feature images are shown in Figure 22. In
both cases, the images are segmented into irregular patches. The
patches for the 8x8 case are generally smaller than those for the 16x16
case.

The statistics for evaluating the clusterings are given in Table
28 for 8x8 averaging and in Table 29 for l6xl6 averaging. None of the
clusterings pass the threshold test. In fact, none of the individual
clusters appear to be valid. Since all multiple-class solutions are

rejected, we conclude that the image contains a single texture.

6.7 Segmentation Experiment 3: Natural Image Composite

Figure 23 shows the 128x128 image to be used for this experiment.
The image is composed of four natural texture classes: WOOD, PAPE, SCRE
and SAND. The results of segmentation based on 8x8 averaging for the
feature images is shown in Figure 2A, and the results for l6xl6
averaging are Shown in Figure 25.

Different results are obtained by using different averaging
windows. The two-cluster solution using 8x8 averaging groups the W000
and SCRE areas in one cluster and the PAPE and SAND areas in the other.
This clustering appears to be determined by the irregularity of PAPE
and SAND and the directional tendencies of W000 and SCRE. Using 16x16

averaging, the SCRE texture is alone in one cluster in the two-class

125

 

Figure 20: Gaussian White Noise Image for Segmentation
Experiment 2.

126

 

Figure 21: Segmented Images for Gaussian White Noise

Using 8x8 Averaging Windows.
(b) 3-c1uster solution
(d) S-cluster solution

(a) Z—cluster solution
(c) A—cluster solution

127

 

Figure 22: Segmented Images for Gaussian White Noise
Using 16x16 Averaging Windows.
(b) 3-cluster solution
(d) 5—cluster solution

(a) 2-c1uster solution
(c) A-cluster solution

128

 

Figure 23: Natural Image Composite for Segmentation
Experiment 3.

129

 

Figure 24: Segmented Images for Natural Image Composite
Using 8x8 Averaging Windows. (a) 2-c1uster solution
(b) 3-c1uster solution (c) A-cluster solution

(d) 5—cluster solution

130

 

Figure 25: Segmented Images for Natural Image Composite

Using 16x16 Averaging Windows.
(b) 3-cluster solution
(d) 5-cluster solution

(a) 2-cluster solution
(c) A-cluster solution

131

Table 28: Evaluation of Clustering on Gaussian White Noise Image
Using 8x8 Averaging Windows.

A N(k) S(k) k N(k) S(k)
2 CLUSTERS 7 CLUSTERS
I 55 I.26 I 10 I.I3
2 9 1.12 2 5 I.66
AVG I.2A 3 7 1.07
A 7 1.16
3 CLUSTERS 5 I5 -0.923
I 38 0.831 6 7 1.02
2 8 I.22 7 I3 1.03
3 18 0.939 AVG 1.09
AVG 0.91
8 CLUSTERS
A CLUSTERS I 9 I.29
I IA 1.21 2 A I.AA
2 16 1.11 3 6 I.53
3 I8 I.05 A 7 I.0I
A I6 I.07 5 I3 1.18
AVG 1.11 6 9 1.15
7 6 1.06
5 CLUSTERS 8 I0 1.09
I I3 1.18 AVG 1.20
2 I0 I.0A -
3 I7 I.I5
A 10 1.01
5 IA 1.13
AVG 1.11
6 CLUSTERS
I I2 1.08
2 A 1.6A
3 7 1.29
A 8 I.0A
5 23 1.06
6 I0 0.9A6
AVG I.I0

segmentation. The regularity and strong orientation dependence appear
to determine this clustering. The segmentations with three and four
clusters are similar for the two window sizes. The 8x8 window tends to
break up the image into smaller areas and to misclassify more pixels
than the 16x16 window. Edges between textures are more sharply

identified using the 8x8 window, but the 8x8 window is more likely to

132

Table 29: Evaluation of Clustering on Gaussian White Noise Image
Using 16x16 Averaging Windows.

k N (k) S (k) k N (k) S (k)
2 CLUSTERS 7 CLUSTERS
1 39 1.12 1 11 1.25
2 25 0.957 2 11 1.3A
AVG 1.06 3 11 1.2A
A 11 1.3A
3 CLUSTERS 5 10 1.2A
1 2A 0.951 6 3 1.28
2 19 I.0A 7 7 1.20
3 21 0.879 AVG 1.27
AVG 0.95A
8 CLUSTERS
A CLUSTERS 1 10 1.30
1 21 1.06 2 8 1.10
2 15 1.00 3 9 1.37
3 17 0.972 A 11 1.36
A 11 1.03 5 9 1.21
AVG 1.02 6 3 1.28
7 6 1.23
5 CLUSTERS 8 8 1.13
1 13 1.20 AVG 1.25
2 12 1.10
3 15 1.08
A 13 1.2A
5 11 0-973
AVG 1.12
6 CLUSTERS
1 11 1.25
2 1A 1.11
3 11 1.2A
A 11 1.3A
5 10 1.2A
6 7 1.22
AVG 1.23

incorrectly subdivide a homogeneous texture area. One significant
error made using 8x8 averaging is the misclassification of a
low—contrast area of the SCRE panel as WOOD. The same area appears as
a separate segment in the 3 and A class segmentations using l6xl6

averaging.

133

The statistics for evaluating the clusterings are shown in Table
30 for 8x8 'averaging and in Table 31 for 16x16 averaging. The
three-cluster solution is the only one which passes the threshold test
in the 8x8 case. With l6xl6 averaging, the solutions for 3, A, and 5

clusters are found to be acceptable. Using the weighted average of

I3A

Table 30: Evaluation of Clustering on Composite Natural Image
Using 8x8 Averaging Windows.
(* indicates accepted clustering solutions)

k N(k) S(k) k N(k) S(k)
2 CLUSTERS 7 CLUSTERS
I 35 I.3A I IA 1.21
2 29 1.58 2 6 1.52
AVG I.A5 3 I2 2.08
A I0 1.27
3 CLUSTERS 5 A I.32
I 2A 2.II 6 7 I.33
2 28 1.75 7 II 1.32
3 I2 2.22 AVG I.A5
AVG I.97 *
8 CLUSTERS
A CLUSTERS I IA 1.21
I 2I 1.61 2 6 I.52
2 16 1.39 3 12 2.09
3 12 2.19 A 5 I.37
A I5 I.A6 5 A I.32
AVG 1.63 6 7 1.33
7 II I.A3
5 CLUSTERS . 8 5 I.76
I 2I I.A6 AVG I.52
2 I5 I.35
3 I2 2.I7
A 7 1.06
5 9 1.03
AVG I.A6
6 CLUSTERS
I IA 1.21
2 7 I.A7
3 12 2.I3
A IA 1.11
5 I0 1.28
6 7 1.33
AVG I.AI

S(k) to rank the solutions, we find the three-cluster solution to be
the best, followed in order by the A- and 5-cluster solutions. In the
three-cluster solution, the SAND and PAPE regions are merged in a
single cluster. The irregularity and the contrast of these areas are
similar, so the preference for this solution is plausible. In the

three-class segmentation using 16x16 averaging windows, over 952 of the

135

Table 31: Evaluation of Clustering on Composite Natural Image
Using l6xl6 Averaging Windows.
(* indicates accepted clustering solutions)

k N(k) S(k) k N(k) S(k)
2 CLUSTERS 7 CLUSTERS
I A8 I.AA I 5 2.53
2 I6 2.26 2 12 2.22
AVG I.65 3 I5 2.05
A 6 1.17
3 CLUSTERS 5 12 1.55
I 3I 2.18 6 9 1.09
2 16 2.51 7 5 2.76
3 I7 2.95 AVG 1.86
AVG 2.A7 A
8 CLUSTERS
A CLUSTERS I 5 2.53
I 13 1.92 2 I2 2.22
2 l6 2.A0 3 I5 2.05
3 16 2.59 A .6 1.23
A 19 1.89 5 I2 I.53
AVG 2.20 a 6 6 I.A3
' 7 3 I.A0
5 CLUSTERS 8 5 2.76
I 13 1.92 AVG 1.91
2 I2 2.22
3 15 2.05
A 19 1.89
5 5 2.76
AVG 2.06 A
6 CLUSTERS
I 5 2.53
2 I2 2.22
3 I5 2.05
A I5 1.61
5 I2 I.56
6 5 2.76
AVG I.98

pixels are correctly labelled (assuming the SAND and PAPE panels to be
the same class). The 8x8 window segmentation using 8x8 windows
classifies about 862 of the pixels correctly.

The four-cluster solution, which is the second choice for l6xl6
averaging, reasonably captures the four image types used: the

segmentation based on an 8x8 averaging window correctly labels 812 of

136

the pixels while using a 16x16 window, 912 of the pixels are correctly

labelled.

6.8 Segmentation Experiment A: SCRE

Figure 26 shows the 128x128 SCRE natural image which will be'
segmented using the same procedures as the previous experiments. The
image contains a single texture class, but unlike the Gaussian white
noise image, the SCRE image contains some internal structure. The
segmented images using 8x8 averaging windows are presented in Figure 27
and the results using 16x16 averaging windows are presented in Figure
28. The cluster evaluation statistics are shown in Table 32 for 8x8
averaging and in Table 33 for l6xl6 averaging. None of the clustering
solutions passes the threshold test, but the values of S(k) are larger
than those obtained with Gaussian white noise. There appear to be
emerging clusters, but the presence of some non-isolated clusters in

each solution causes all of the clusterings to be rejected.

6.9 Summary

This chapter presented an algorithm for computing a textural
transform in which the texture of a neighborhood about each pixel is
represented by gray level values in a series of feature images. The
feature images are computed from filtered images using a two-step
procedure in which the second step can be implemented as another
filtering operation. The resulting textural transform was evaluated by
applying a texture segmentation procedure in four experiments. The

segmentation procedure imposed no restrictions on the nature of the

137

 

Figure 26: SCRE Image for Segmentation Experiment A

138

 

Figure 27: Segmented Images for SCRE Using 8x8

Averaging Windows.
(b) 3—cluster solution
(d) 5—c1uster solution

(a) 2-c1uster solution

(c) A-cluster solution

139

 

Figure 28: Segmented Images for SCRE Using 16x16

Averaging Windows. (a) 2-cluster solution
(b) 3-cluster solution (c) A-cluster solution
(d) 5-cluster solution

1A0

Table 32: Evaluation of Clustering on SCRE Image
Using 8x8 Averaging Windows.

I: N (k) S (k) k N (k) S (k)
2 CLUSTERS 7 CLUSTERS
1 AA I.A5 1 9 1.7A
2 20 1.60 2 12 1.82
AVG 1.50 3 7 1.A3
A 5 2.5A
3 CLUSTERS 5 13 1.71
1 27 1.2A 6 6 1.71
2 15 2.02 7 12 1.1A
3 22 1.57 AVG 1.66
AVG 1.5A
8 CLUSTERS
A CLUSTERS 1 9 1.7A
1 18 I.A6 2 6 1.37
2 1A 1.88 3 5 2.03
3 19 1.89 A 5 2.A6
A 13 1.33 5 11 1.5A
AVG 1.65 6 6 1.71
7 10 1.95
5 CLUSTERS 8 12 1.51
1 19 1.37 AVG 1.7A
2 1A 1.85
3 17 1.70
A 5 2.70
5 9 1-33
AVG 1.73
6 CLUSTERS
1 9 1.7A
2 1A 1.76
3 17 1.70
A 5 2.5A
5 13 1.68
6 6 1.71
AVG 1.78

segmented regions such as a minimum size or connectivity requirement.
A clustering algorithm was applied to some representative pixels, and
the remaining pixels were assigned to the clusters by a minimum
distance classifier.

The segmented images indicate that the feature space is a

reasonable representation of the textures in an image. This conclusion

1A1

Table 33: Evaluation of Clustering on SCRE Image
Using l6xl6 Averaging Windows.

k N(k) S(k) k N(k) S(k)
2 CLUSTERS 7 CLUSTERS
I 57 1.65 I 13 1.73
2 7 1.81 2 A 3.10
AVG 1.66 3 6 1.99
A 12 1.21
3 CLUSTERS 5 A 2.AI
I 32 I.3A 6 16 1.72
2 6 1.99 7 9 1.25
3 26 I.3A AVG 1.72
AVG I.AO
8 CLUSTERS
A CLUSTERS I 13 1.73
1 18 I.A9 2 A 3.10
2 A 3.99 3 A 2.50
3 25 1.36 A II 1.29
A 17 1.59 5 A 2.A1
AVG 1.62 6 16 1.72
7 6 I.AA
5 CLUSTERS 8 6 1.70
1 18 1.53 'AVG 1.80
2 A 3.50
3 1.83
A 9 1.60
5 6 1.6A
AVG 1.73
6 CLUSTERS
1 IA 1.86
2 A 3.63
3 7 1.77
A 17 1.50
5 6 1.28
6 16 1.73
AVG 1.79

was further confirmed by a statistical evaluation of the clusterings.
The evaluation identified reasonable clusterings by requiring all
clusters to be compact and isolated as measured by a test statistic.
Acceptable clusterings were then ranked by an average isolation
statistic. The segmentations corresponding to the preferred

clusterings contained reasonable numbers of clusters and the

1A2

corresponding segmentations generally agree with the image generation
method and visual segmentations of the images.

The experiments used 8x8 and 16x16 windows for computing the
feature images. Both gave satisfactory segmentation results, though
these window sizes are smaller than the subimages used in the
classification experiments. This suggests that a minimum distance
classification algorithm might be more appropriate than a nearest

neighbor algorithm for the channel filtering feature space.

Chapter 7

Summary and Conclusions

7.1 Summary

Texture is characterized by preattentive human visual performance
of segmentation and classification tasks. This form of perception has
many potential applications in computer vision systems, but the
characterization of ”texture" in terms of human performance does not
lead to simple, effective algorithms 'for texture analysis. No
alternative definition of texture independent of human performance has
provided sufficiently precise guidance to enable development of general
texture analysis algorithms.

Since texture analysis algorithms attempt to model preattentive
human vision, insights from vision science and from intuition have been
used to guide the development of algorithms. The lack of precise
guidance from a definition of texture and the lack of generality in
existing algorithms has resulted in a profusion of diverse approaches
to texture analysis.

A recent theory concerning the early information processing
strategies in human vision was used to motivate a new approach to
texture analysis. A feature space which measures average local energy

was defined from filtered images and used in texture classification

1A3

1AA

problems. The features were applied to artificial images, natural
images, and preprocessed natural images. The performance of the
feature space in various classification tasks was investigated and
compared with the power spectral and co-occurrence methods.

A method for computing a texture feature vector over a small
neighborhood about each pixel in an image was developed for texture
segmentation. A clustering algorithm was applied to the feature
vectors, and a segmented image was produced by labelling each pixel
according to the cluster in which the pixel's feature vector lies.

Since each clustering solution corresponds to a segmented image, a
means for seleCting acceptable clusterings is required. A cluster
validity statistic was used to determine which, if any, of a set of
clusterings provided an acceptable representation of the data. A
related statistic was used to rank the, accepted solutions. Four
texture segmentation experiments were performed using both composite

and homogeneous images.

7.2 Conclusions

7.2.1 Classification

The channel filtering features were used to classify subimages of
eight natural textures. The results using 6Ax6A and 32x32 subimages
were good. The features performed poorly when presented l6xl6
subimages. These results indicate that the features are suitable for

classification of natural images based on 32x32 or larger subimages.

1A5

The effect of histogram equalization on the evaluation of natural
textures by the channel filtering features was investigated in a series
of experiments. We found that almost all of the histogram equalized
images were perceived as having different textures from the original
classes. Histogram equalization was also observed to confuse image'
classes which were originally separable. The results suggest that
histogram equalization should be used carefully, if at all, with
channel filtering features.

The channel filtering features were found to be insensitive to
global, constant gray level changes. This implies that histogram
equalization to remove differences in average brightness is
unnecessary.

A procedure for determining whether two images portray the same
texture at different magnifications was developed. The procedure was
tested for 2X magnifications only. Certain aspects of the procedure
might be simplified by using a different classification algorithm, but
the results obtained were good.

A procedure for detecting orientation differences was developed
which gave excellent performance for 90 degree orientation changes but
was less reliable for A5 degree orientation changes due to fundamental
differences in A5 degree rotated patterns caused by the rectangular
quantization grid and the square image shape.

The effect of phase modification was investigated. The experiment
demonstrated that images with identical power spectra could be
discriminated by channel filtering features based on differences in the

phase spectra.

1A6

An experiment comparing the co-occurrence method with the channel
filtering method demonstrated that selection of displacement vectors
for co-occurrence matrices is a serious problem. Even displacement
vectors selected specifically to discriminate micropatterns can fail to
discriminate images composed of the micropatterns. On the other hand,
the channel filtering features were applied in the same way as in other
experiments and produced excellent classification accuracy.

Experiments to test computational simplifications of the channel
filtering procedure showed that the method is "robust" in that the
classification accuracy is not degraded by using ideal band-pass

channels or by eliminating certain channels.

7.2.2 Segmentation

Four experiments were performed to test the utility of the channel
filtering approach for texture segmentation. In the first experiment,
an image composed of a regular dot pattern and a random dot pattern
were segmented. The statistical evaluation of the clustering solutions
indicated that two clusters existed in the feature space. The
labellings of the pixels corresponded closely to the actual image
areas.

Segmentation of a Gaussian white noise image yielded irregularly
shaped, non-contiguous segments throughout the image. The cluster
validity statistic found no acceptable clustering solution, so the

image was correctly identified as portraying a single texture.

1A7

A composite image composed of four natural textures was segmented.
The statistical evaluation indicated that the best solution involved
three clusters. This result was considered reasonable due to the
visual similarity of two of the actual texture classes. The second
best solution involved four clusters and the segmentation generally
corresponded to the actual textures in the image.

Another experiment on a homogeneous natural image resulted in a
correct identification of the image as a homogeneous texture. Emerging
clusters were found, but they were not well-defined enough to pass the

statistical validity test.

7.2.3 General

The channel filtering feature space has been evaluated on a
variety of texture classification and segmentation problems. The
results indicate that the feature space is a good representation of
texture for these problems. Equivalently, the feature space has been
validated as a model for preattentive human vision on a variety of
stimuli. The investigation of this feature space has involved tests in
which visually discriminable image classes were expected to be
discriminated by the features and in which visually indiscriminable
image classes generated in different ways were expected to be confused
by the features.

The classification and segmentation procedures used to evaluate
the feature space did not involve sophisticated heuristics: the results

are consequences of the structure of the feature space. Some results,

1A8

in particular the magnification experiment and the results of the
segmentation experiments, suggest that a minimum distance classifier
may be more appropriate than a nearest neighbor classifier for the
channel filtering feature space. Further investigation of the feature
space may suggest that a different clustering procedure may be more
appropriate for texture segmentation.

The performance of the channel filtering feature demonstrates that
a global filtering model of vision is capable of reasonably
approximating human preattentive vision. This contrasts to results of
previous studies which discounted the value of phase information for
texture analysis and which suggested that the Fourier transform is not
an appropriate tool for texture analysis. This study shows that phase
information provides critical information on the distribution of
spectral energy through the image plane. The use of phase information
enables spatially local analysis of different spectral energy bands.
This information was measured by the channel filtering features and

provided good results.

7.3 Advantages of the Channel Filtering Method

1. The channel filtering features have a satisfying intuitive
basis. Unlike some ad hoc procedures, the significance of the channel
filtering features are explainable in terms of image properties such as
contrast, edge density, local energy, and directionality. The
explanations are a consequence of the intuitive interpretations of the

channels and of the spatial filtering operation.

1A9

2. The channel filtering method provides classification results
superior to those obtained by the power spectral method. The
performance is attributed to the utilization of phase information in
the channel filtering procedure.

3. The channel filtering method has no critical parameters
similar to the choice of displacement vectors for the co-occurrence
method.

A. A method for computing features for texture segmentation
exists which does not require recomputation of the entire filtering
procedure over every subimage of interest. This means that only a
simple feature computation needs to be repeated to evaluate the
textures in different regions. In fact, the texture features for every
pixel can be computed by a procedure, easily amenable to parallel
execution.

5. Simple procedures for classification and for segmentation
produce good results. This indicates that the results are due to the
structure of the feature space and not to a clever classification or
segmentation procedure.

6. There are many opportunities for parallelism in computing the
filtered images and the texture features. This could enable fast
hardware implementations of the channel filtering procedure to be

constructed with a high degree of modularity and at fairly low cost.

7.A Disadvantages of the Channel Filtering Method

1. The computational and storage requirements for sequential,

digital implementation of the channel filtering approach are too

150

demanding for many applications. Other implementation methods using
parallel hardware or optical/digital methods may make fast
implementations possible. Among the current difficulties are the
number of Fourier transforms, inverse transforms, and image
multiplications required in the channel filtering procedure. These
operations are very demanding when implemented sequentially.

2. A simple method for generating images which have specified
characteristics in the texture feature space is not known. Such a
procedure would enable further validation of the feature space by
enabling generation of images which are "close" to a given image. This
capability would enable a quantitative determination of how well the
feature space models human preattentive perception. The major
obstacles to development of such a method are the overlapping of the
channels in the spatial frequency domain and the dependence of the

feature values on phase spectrum information.

7.5 Suggestions for Further Research

1. Segmentation results have suggested that the minimum distance
classification algorithm is more appropriate than the nearest-neighbor
algorithm for the channel filtering feature space. Further research is
needed to confirm this hypothesis and to investigate the applicability
of other decision rules.

2. Different clustering algorithms for use in the segmentation
procedure should be investigated. CLUSTER is known to perform poorly
in certain situations, and statistics similar to those used to evaluate

the clusterings in this study can be defined for other algorithms.

151

3. Further investigation of the performance of the segmentation
procedure is needed. The averaging windows used to compute the feature
images could be implemented as another filtering operation, perhaps
using a sequence of filters as in the original channel filtering
procedure. The validity of the feature space for images which involve-
distinct forms should also be investigated.

A. The use of channel filtering for receding surfaces should be
investigated. Since the apparent size of the texture on a receding
surface shrinks progressively with distance, the spectral information
from the surface should move steadily toward high-frequency channels.
This would cause the feature vectors for pixels depicting the surface
to be strung out though the feature space. A clustering procedure
which can detect long, stringy clusters, such as the single-link
algorithm, might be useful for analyzing surface structure.

5. Since the feature space developed in chapter A is based on a
theory of human visual information processing, it may be useful to
determine how faithfully the feature space reproduces human texture
vision. Psychophysical experiments could help to guide the selection
of classification and clustering algorithms which would duplicate human
performance.

6. Spatial frequency domain filtering has been used to provide at
least partial solutions for several computational vision problems, now
including texture analysis. Revision of procedures for solving other
computational vision problems using channel filtering as a framework

could enable development of unified computational vision systems.

APPENDICES

Appendix A: A Catalog of Texture Definitions

1. ”We may regard texture as what constitutes a macroscopic region.
Its structure is simply attributed to the repetitive patterns in which
elements or primitives are arranged according to a "placement rule"."
[Tamura et al, 1978]

2. "We suggest the following operational definition of 'texture'.
A region in an image has a constant texture if a set of local
statistics or other local properties of the picture function are
constant, slowly varying, or approximately periodic." [Sklansky, 1978]

3. "A texture will be considered to be a random field X(n,m)
where n and m are integers." (They later specialize to Markov random
fields.) [Conners and Harlow, l980a]

A. ”The image texture we consider is nonfigurative and
cellular.... An image texture is described by the number and types of
its (tonal) primitives and the spatial organization or layout of its
(tonal) primitives... a fundamental characteristic of texture: it
cannot be analyzed without a frame of reference of tonal primitive
being stated or implied. For any smooth gray-tone surface, there
exists a scale such that when the surface is examined, it has no
texture. Then as resolution increases, it takes on a fine texture and
then a coarse texture.“ [Haralick, 1979]

5. “Image texture refers to the visual sensation that one

receives about the structure arrangement of an image region. The

152

153

textural properties of a scene are often qualitatively described as
coarse, grainy, striated, or rough. Computer simulations .have been
done in which overlapping particles have been placed at random
locations. When only a few particles are present, the visual
impression is of discrete, countable objects. However, when the number
of objects is increased, the visual impression is of texture rather
than countable objects.‘| [Hall et al, 1977] 1

6. "Texture is defined for our purposes as an attribute of a
field having no components that appear enumerable. The phase relations
between the components are thus not apparent. Nor should the field
contain an obvious gradient. The intent of this definition is to
direct the attention of the observer to the global properties of the
display - i.e. its overall "coarseness", "bumpiness", or "fineness".
Physically, nonenumerable (aperiodic) patterns are generated by
stochastic as opposed to deterministic processes. Perceptually,
however, the set of all patterns without obvious enumerable components
will include many deterministic (and even periodic) textures. Because
our criterion for enumerability was subjective rather than objective,
many of our patterns actually contained repetitive elements which were
not immediately obvious but could be identified when the observer
specifically looked for these components. To further minimize very
obvious enumerable periodic components of the patterns, all displays
contained only components whose spatial frequencies were proportional
to prime numbers. We would like to stress that the above constraints
imposed on our textures are all designed to minimize the importance of
phase information - a variable we consider more important for pattern

recognition than for texture perception." [Richards and Polit, I97A]

15A

7. "Images composed of numerous binary pixels which are only
weakly correlated with their neighbors form one extreme in a continuum
of scene types whose opposite extreme is exemplified by simple line
drawings against a uniform background. In the latter case the image
pixels are highly redundant and the image consequently carries little
information in the sense of Shannon, whereas in the former case,
redundancy is low and the information content is high: normally so high
that the vision system must selectively disregard information in order
to process the scene. The limiting extremes of this continuum of
images are the uniform ("constant”) image all of whose pixels are
identical, and the random image, whose pixel arrangement is completely
determined by a probability distribution. The random image appears to
be homogeneous (and therefore completely redundant) in a global sense:
that is, different subregions large enough to contain many pixels
convey an equivalent subjective impression. This type of homogeneity,
which is different from a locally highly redundant image, is usually
called "texture", and is characteristic of the structure of the
probability distribution of the random image.” [Resnikoff, 1981]

8. ”Texture is an apparently paradoxical notion. 0n the one
hand, it is commonly used in the early processing of visual
information, especially for practical classification purposes. 0n the
other hand, no one has succeeded in producing a commonly accepted
definition of texture. The resolution of this paradox, we feel, will
depend on a richer, more developed model for early visual information
processing, a central aspect of which will be representational systems

at many different levels of abstraction. These levels will most

155

probably include actual intensities at the bottom and will progress
through edge and orientation descriptors to surface, and perhaps
volumetric, descriptors. Given these multi-level structures, it seems
clear that they should be included in the definition of, and in the
computation of, texture descriptors." [Zucker and Kant, 1981]

9. ”The notion of texture appears to depend upon three
ingredients: (1) some local 'order' is repeated over a region which is
large in comparison to the order's size, (2) the order consists in the
nonrandom arrangement of elementary parts, and (3) the parts are
roughly uniform entities having approximately the same dimensions
everywhere within the textured region." [Hawkins, 1969]

10. "Although these descriptions of texture seem perceptually
reasonable, they do not immediately lead to simple quantitative
textural measures in the sense that lthe description of edge
discontinuity leads to the quantitative definition of an edge in terms

of its location, slope angle, and height.” [Pratt, I978]

APPENDIX 8: Definition of Channel Filters

The transfer function of a 2Nx2N spatial frequency channel filter
Fk(u,v), where -N+I (. u,v <= N, is defined as follows:
Imag [ Fk(u,v) ] = 0 for all u,v,k,
Real [ Fk(0,0) ] = l for all k,

and for (u,v) $ (0,0) ,

2
[10(D(U.v)) - 10941) 1
Real [ Fk(u,v) ] = exp [ -.5 * ------------- 5' --------- ]
6'
2 2 1/2 k-l
where D(u,v) - [u +v ] , 5 - .275. and f‘k- 2 .

For a 2Nx2N image, we will use spatial frequency channels for
k=I,...(logz N + I). This definition yields a series of filters one

octave apart whose widths are slightly more than one octave on each
side of the center frequency. The value of O" was selected to
produce filters whose widths are within the constraints for human

visual filters given in [Ginsburg, I978].

156

157

The transfer function for a 2Nx2N orientation channel filter Gk(u,v)
where -N+I <- u,v <- N is defined as follows:
Imag [ Gk(u,v) ] I 0 for all u,v,k,
Real [ Gk(0,0) ] 8 1 for all k,

and for (u,v);E(0,0),
2

Real [ Gk(u,v) ] - exp [ -,5 A ----32---- ]

(71
where ak- Min { l/J‘K- arctan(v/u)| , | (Ink-18°) - arctan(v,u)| },
6 - 17.8533, 1 <- k <- A, and the values of [AK are given in the
table below for each value of k. The value of (5 is chosen to produce
the same overlap between channels as in the spatial frequency channels.
Note that the orientation channels defined here are slightly wider
then the 30 degree wide channels proposed for human vision in

[Ginsburg, 1978].

Values ofIAk(in degrees) for each k

k M

l 0 (horizontal)
2 A5

3 90

A 135

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