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QUANTITATIVE MORPHOLOGICAL CHARACTERIZATION
OF TRIAXIALLY BRAIDED COMPOSITES
USING IMAGE ANALYSIS

presented by

Li Jiang

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MSU I. An Afﬁrmative Adlai/Equal Opportunity Institution
Wain-9.1

 

QUANTITATIVE MORPHOLOGICAL CHARACTERIZATION OF
TRIAXIALLY BRAIDED COMPOSITES USING IMAGE ANALYSIS

By

Li Jiang

A THESIS

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

MASTER OF SCIENCE

Department of Mechanical Engineering

1995

ABSTRACT

QUANTITATIVE MORPHOLOGICAL CHARACTERIZATION OF
TRIAXIALLY BRAIDED COMPOSITES USING IMAGE ANALYSIS

By

Li Jiang

The prediction of mechanical properties of reinforced composites is
strongly inﬂuenced by the morphological features of the reinforcement. In
order to improve the correlation between predicted properties and test proper-
ties, it is essential to have quantitative measures of the composite morpholo-
gies. Methods were developed to quantify braid angle, crimp angle and ﬁber
waviness using computer-aided image processing techniques. The braid angle
and ﬁber waviness at a sample surface are determined non-destructively. Cut-
ting is presently required to determine the crimp angle. The determination of
braid angle is based on the fast Fourier transform (FFT) method, while the
crimp angle determination is accomplished using edge detection and boundary
identiﬁcation. Strategies have been proposed to quantify ﬁber waviness. Cali-
bration tests were conducted to compare computer-based pattern recognition
with human determinations. The reproducibility of the measurements is
quantiﬁed. Extensions of this study have the potential to provide automated,
on-line quantitative measurements of composite geometrical features which

are important for quality control and engineering design.

ACKNOWLEDGMENTS

I would like to thank my major professor Dr. John J. MaGrath for his guid-
ance and support throughout this work.

Thanks are given to Dr. Anil Jain, graduate students Chitra Dorai and
Patchrawat Uthaisombut, Department of Computer Science for their help
with the image acquisition. Also I would like to thank Dr. Dennis Gilliand,
graduate student Hao Zhang, Department of Statistics and Probability and
Dr. Alan Haddow, Department of Mechanical Engineering for their helpful
discussions and suggestions concerning this work.

I am grateful for the ﬁnancial support of this project from the Research
Excellence Fund of the State of Michigan.

Finally, I would like to express my deep appreciation to my family, my hus-

band and my parents for their love and encouragement.

iii

TABLE OF CONTENTS

LIST OF TABLES ................................................ vi

LIST OF FIGURES .............................................. vii

1 INTRODUCTION

2

4

1.1 Motivation ................................................ 1
1.2 Literature Review .......................................... 4
IMAGE PROCESSING
2.1 Introduction ............................................... 10
2.2 Image Enhancement ....................................... 11
2.2.1 Histogram Equalization ............................... 11
2.2.2 Lowpass Filtering .................................... 14
2.2.3 Edge Detection ....................................... 16
2.3 Thresholding .............................................. 23
2.4 Morphological Filters ....................................... 24
2.5 Thinning .................................................. 29
2.6 Fast Fourier Transform ..................................... 29

QUANTIFICATION OF MORPHOLOGICAL FEATURES

3.1
3.2
3.3
3.4

3.5

3.6

Introduction .............................................. 34
Image Analysis System Setup ................................ 35
Errors in Measurements .................................... 38
Braid Angle Determination .................................. 40
3.4.1 Calibration .......................................... 40
3.4.2 Sample Image Analysis ................................ 44
Crimp Angle Determination ................................. 51
3.5.1 Calibration .......................................... 52
3.5.2 Sample Image Analysis ............................... 54
Fiber Waviness Determination ............................... 59

RESULTS AND DISCUSSIONS

4.1

Braid Angle Determination .................................. 62

iv

4.1.1 Calibration .......................................... 62

4.1.2 Sample Image Analysis ................................ 67
4.2 Crimp Angle Determination ................................. 69
4.2.1 Calibration .......................................... 69
4.2.2 Sample Image Analysis ................................ 70
4.3 Image Analysis Speed ....................................... 78

5 CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusions ............................................... 79
5.2 Recommendations for Future Work ........................... 81
LIST OF REFERENCES .......................................... 84

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

LIST OF TABLES

Calculated Results of Ten Measurements of Each

True Angle (Unit: deg) ..................................... 64
Calculated Results from Least-Squares Curve Fit .............. 65
Comparison of the Least-Squares Method with the

Manual Measurement for Test Images (Unit: deg) .............. 65
Braid angles at Different Locations (Unit: deg) ................ 68

Comparison of Braid Angle Measurements between
the Least-Squares Method and the Manual

Measurement (Unit: deg) ................................... 69
Crimp Angles from Test Images (Unit: deg) ................... 70
Crimp Angles from Nine Specimens (Unit: deg) ................ 73
Reproducibility of the Crimp Angle Measurement Tested

by Repeating Imaging on One Specimen (Unit: deg) ............ 77
Reproducibility of the Crimp Angle Measurement Tested by
Repetitions of Measurement on One Image (N =5) (Unit: deg) . . . . 77

vi

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17

Figure 18

LIST OF FIGURES

Deﬁnition of braid angle ................................. 5
Deﬁnition of crimp angle ................................. 7
Deﬁnition of ﬁber waviness ............................... 9
Original image ......................................... 13
Image in Figure 4 after histogram equalization .............. 13
Schematic of digital convolution ........................... 15
Image produced by applying a 3 x 3 lowpass ﬁlter ............ 16
A 3 x 3 Laplacian kernel ................................. 18
Result of applying a 3 x 3 Laplacian ....................... 19
Schematic of Sobel ﬁltering ............................... 20
Sobel kernels ........................................... 21
Image produced by applying Sobel ﬁlter .................... 21
Effect of applying Phase ﬁlter ............................. 22
Image in Figure7 after thresholding ....................... 24
Original test image ...................................... 26
Two repetitions of a 5 x 5 Dilation ......................... 26
'IVvo repetitions of a 5 x 5 Erosion .......................... 26
Original test image ...................................... 28

vii

Figure 19
Figure 20
Figure 21
Figure 22
Figure 23

Figure 24

Figure 25
Figure 26

Figure 27

Figure 28

Figure 29
Figure 30
Figure 31
Figure 32
Figure 33
Figure 34
Figure 35
Figure 36
Figure 37
Figure 38

Figure 39

Image obtained by applying Opening ...................... 28
Image obtained by applying Closing ....................... 28
Example test image ..................................... 32
FFT image ............................................. 32
Schematic of the image analysis system .................... 37

(a) Example test image for calibration of braid angle analysis

(b) The fast Fourier transform of (a) ....................... 42
Test FFT image for calibration of braid angle analysis ........ 43
Final thinned image ..................................... 43

(a) The whole part (~1.5 m long)
(b) A closer picture of the part surface

(c) The cross section of the part (80 x 32 mm2)

The bright section is the foam core ...................... 45
Example image from the sample surface after histogram
equalization ........................................... 47
The FEI‘ of image in Figure 28 ............................ 47

Image produced by applying Dilation and Erosion operations . . 49
Image in Figure 30 after Laplacian edge detection ........... 49
Inverse transformation of the modiﬁed FFT in Figure 29 ...... 51

Polynomial test image for calibration of crimp angle analysis . . 53

Image after thresholding ................................. 53
Image in Figure 34 after thinning ......................... 53
Example raw crimp image for crimp angle determination ..... 56
Image in Figure 36 after histogram equalization ............ 56
Image in Figure 37 after applying a lowpass ﬁlter ............ 56

Image in Figure 38 after applying a Laplacian edge ﬁlter ..... 57

viii

Figure 40
Figure 41
Figure 42

Figure 43

Figure 44

Figure 45

Figure 46
Figure 47

Figure 48

Figure 49

Figure 50

Image in Figure 39 after thresholding ...................... 57
Image in Figure 40 after applying Sobel ﬁlter ............... 57
Image in Figure 40 after thinning ......................... 58
Example raw image of ﬁber waviness after histogram
equalization ............................................ 60
Image in Figure 43 after applying a vertical edge ﬁlter ....... 60
Image in Figure 44 after applying Phase ﬁlter and

thresholding ........................................... 61
Image in Figure 45 after thinning ......................... 61
Example of least—squares line ﬁt to data points .............. 66

Example of 7th order polynomial function ﬁt to the
ﬁber boundary ......................................... 72

Crimp angles measured on different specimens .............. 74

Crimp angle distribution over one sample .................. 75

CHAPTER 1

INTRODUCTION

1.1 Motivation

In the development of new materials, ﬁber-reinforced composites have
occupied an extremely important role. Compared with traditional materials,
these composite materials offer some signiﬁcant advantages, such as larger
strength-to-weight ratios, as well as increased stiffness and tensile strength
in the direction of ﬁber orientation. Such composites are more ﬂexible in bend-
ing and the thermal stability is improved because of their lower coefﬁcients of
thermal expansion. Therefore, ﬁber-reinforced composites have been widely
used in many applications. Speciﬁcally, they have been found to be extremely
suitable for the automotive and aerospace industry.

Fiber-reinforced composites consist of ﬁbers and the surrounding matrix.
The reinforcing ﬁbers can be in continuous lengths or in discontinuous
lengths. In general ﬁbers are the major load-carrying components, while the

roles of the matrix are to transfer stresses between the ﬁbers, provide an

environment to make the ﬁbers in the desired location and protect the ﬁbers
from environmental damages.

One advantage provided by ﬁber-reinforced composites is the ability to be
tailored to meet different requirements. In automotive applications, when
applying composites to structural components, “engineered” architectures are
required. Speciﬁc needs can be satisﬁed by varying the glass ﬁber orientations
and volume fractions.

The morphologies of the reinforcement strongly inﬂuence the material
properties of ﬁber-reinforced composites, although their roles have not been
completely understood. In order to predict material properties it is important
to understand the relationship between manufacturing parameters and geo-
metrical structures.

It has been found that braiding of glass ﬁber offers potential cost effective-
ness. It is good for tubular structures and allows tailoring of preform architec-
ture to adjust strength and stiffness. Investigations of elastic properties of
triaxially braided glass/urethane composites have been performed by Ford
research engineers. Process science models which relate the yarn size, braid
angle, number of yarns and mandrel diameter to the ﬁber volume fraction and
internal geometry etc. have been developed (J aranson et al., 1993).

It was found that during the sample manufacturing process, some prob-
lems were encountered. First, braid angles which were less than 35° were
loose and difﬁcult to handle. Therefore the ﬁnal braid architecture was dis-

torted. Second, all the braids tended to be unstable after they were cut from

the mandrel. This resulted in _+_10° braid angle variations. Third, at the point
of injection, additional distortion occurred and the braid architecture got
worse (J aranson et al., 1993). A comparison of the elastic properties between
experimental results and theoretical results has been made. The correlation
between experimental and theoretical results was not satisﬁed.

In order to improve the correlation between predicted properties and test
properties, it is essential to have accurate quantitative measures of morpholo-
gies of composites. The objective of this study is to develop methods quantify-
ing the morphological features of the triaxially braided composites using
computer-aided image processing techniques. These morphological features
include braid angle, crimp angle and ﬁber waviness. The ﬁnal application of
the techniques being developed could be applied to the production line to pro-
vide a means of engineering design and quality control. Therefore the methods
desired should be non-destructive, accurate, automated, rapid, and economi-
cal. The long term goal of this study is to automate the whole process as much
as possible. Although it seems impossible to give an accurate absolute descrip-
tion of the composite morphology, it has been shown that computer-based
determinations are at least as accurate as human-based determinations and

can give results with an acceptable accuracy for a speciﬁc application.

1.2 Literature Review

Masters et a1. (1993) studied the role of the braid reinforcement microge-
ometry in laminate mechanical behavior. The unnotched tensile properties
and ﬁber volume fractions were investigated for two-dimensional triaxial
braid-reinforced graphite/epoxy composites both experimentally and analyti-
cally. The material sensitivity was tested by varying the braid angle, the yarn
sizes and the longitudinal yarn content. A process science model which relates
the braid architectures to machine parameters was developed.

The deﬁnition of the braid angle which is shown in Figure 1 is the absolute
angle between the longitudinal tow (0° direction tow) direction and the braid
tow direction. Trace yarns were formed by coating graphite yarns with nickel
to determine the locations of yarns. Scanned surface images were produced.
Braid angles were measured using image analysis software by tracing the
nickel-coated yarns. Longitudinal cross sectioning, transverse cross sectioning
and cross sectioning along the braid yarns were conducted to exam the inter-
nal ﬁber architecture.

J ortner (1989) investigated a carbon/carbon laminate reinforced with
plain-woven cloth. He found that tensile strength variations were quite
related to variations in the crimp angle of the interwoven yarns. Small crimp
angles were associated with high strengths. He also found that the ultimate
load per yarn was proportional to the inverse of the sine of the average maxi-
mum crimp angle. Crimp angles were measured manually with the aid of a

protractor scale which was attached to the microscope’s ocular.

Longitudinal Tow Braid Angles

 

Braid Tow

Figure 1. Deﬁnition of braid angle.

The crimp angle can be deﬁned in different ways. One commonly used deﬁ-
nition deﬁnes the crimp angle over one ﬁber yarn peak and trough as the max-
imum absolute angle between the mean yarn direction and the tangent line of
the yarn as shown in Figure 2. This deﬁnition is also used in this study.

Gowayed and Russ (1991) presented the geometrical characterization of
triaxially braided carbon/epoxy composite preforms using computer-based
analysis techniques. Two approaches were conducted to discriminate yarn
locations. One was manual input, the other one was automated image analy-
sis with minimal human inference. The results of ﬁber volume fractions from
each method were compared with the experimental data. A better match with
experimental results was found by using automated image analysis. The
quantiﬁcation of yarn shape was not reported.

Yurgartis et a1. (1993) presented the measurement of the yarn shape in a
carbon/carbon composite reinforced with a plain weave cloth using image pro-
cessing. The inclination angle distribution, crimp angle distribution and angle
match distribution were measured. Manual input was required to identify the
yarn boundaries. Fitting functions were created to match the yarn bound-
aries.

Xu et a1. (1992) quantiﬁed crimp morphology of nylon ﬁbers using image
analysis. They deﬁned the crimp angle as the angle between two lines that
were tangent to two shoulders of a crimp at the points of maximum slope. Pro-
cessing operations were created to transform the original digitized image in

order to enhance the ﬁber boundary. The images they used contained only

Crimp Angles

   

      

 

'IIIIIIIIIIII «IIIIIIIIIII-
V///////./ A

Figure 2. Deﬁnition of crimp angle.

ﬁbers without the presence of any complexity introduced by the background.

Yurgartis (1987) suggested that the ﬁber misalignment in continuous ﬁber
composite had been suspected of having a signiﬁcant inﬂuence on composite
properties such as longitudinal compression strength and longitudinal tensile
modulus etc.. A method to measure small angle ﬁber misalignments (ﬁber
waviness) in continuous non-woven ﬁber composites was developed. Fiber
misalignment distributions were determined. Characterization of the ﬁber
curvature was not given.

Rai et a1. (1992) studied the relationship between lamina stiffness and
ﬁber waviness of carbon-epoxy composites. A unidirectional lamina elastic
model was developed where the ﬁber was assumed to be sinusoidal. It was
found that the stress-strain response to non-zero ﬁber waviness was nonlin-
ear. It was concluded that having quality control of ﬁber waviness in struc-
tural applications was a very critical issue. In their study the ﬁber shape is

represented by a sinusoidal function which is shown in Figure 3:

y = Asin(2n£) (1)

where A is the amplitude and L is the wave length of the sinusoidal function.
The ratio of A to L is deﬁned as ﬁber waviness which can be calculated from
the measured maximum absolute ﬁber angles.

Many efforts have been made by numbers of researchers to study the

effects of geometrical features of reinforcing ﬁbers on composite properties.

Although the inﬂuences can not be completely explained, the conclusion of the
importance of these geometrical features is clear. Accurate and effective meth-

ods for quantitatively characterizing composite morphologies are needed.

yi

 

 

N

 

 

 

Figure 3. Deﬁnition of ﬁber waviness.

CHAPTER 2

IMAGE PROCESSING

2.1 Introduction

Computer-based imaging analysis provides a powerful tool for the charac-
terization of composite materials. Recognizing and measuring features and
structures can be performed very quickly with good reproducibility. Recently
image processing techniques have become increasingly important in the study
of composite materials.

Since computers can only process numerical data an image must be con-
verted to numerical form before computer processing. This conversion process
is called digitization. After an image is captured in digital form it is then sam-
pled into a set of points which can be represented by a matrix. Each point is
called a picture element or a pixel. An integer value called the grey level is
generated at each pixel. This process is called gray-level quantization. For 8-
bit data acquisition as performed here, index values between 0 and 255 (28

2256 grey levels) are used to represent all gray levels between black and

10

11

white.

In order to get a desired output image, image processing operations are
applied to the digitized image. These operations involve image enhancement,
image segmentation, morphological operations etc. The effect of each opera-
tion can only be described in general. One can not predict the exact result a
particular ﬁlter will have on a particular image. The computer does not
always give the results that a person may expect. The operator has the ulti-
mate authority to judge the quality of an image to decide if a processed image
is good enough for a speciﬁc application. One must go through a trial-and-
error process which means that different types of ﬁlters should be tried until
the satisﬁed results are obtained.

In this study a commercial imaging processing program (Image-Pro Plus)
is used to perform image transformations. The image processing operations

which were applied in this study will be described in the following sections.

2.2 Image Enhancement

2.2.1 Histogram Equalization

The gray level histogram is used to represent the grey level distribution in
an image. It shows whether an image is too bright or too dark. An image is
well scaled when it makes use of all the available gray levels. When the histo-

gram ﬁlls the entire gray value range from 0-255, the grey level distribution is

12

optimal. For a given image, some gray values may not be used due to the poor
contrast of the object or the image acquisition process. This can be improved
using histogram equalization. Histogram equalization alters the contrast of
an image and makes the distribution of grey level uniform by assigning new
intensity values to the original image pixels. The order of the brightness of
each pixel remains unchanged. Only the values change to the new ones. This
forces the peak areas in the histogram to spread out and the trough areas to

compress. The transformation process can be expressed as:
j N’
51:2: j=0,1,2, - . -,k—1 (2)

where k is the number of grey levels, S j is the new assigned value for the jth
gray level, Ni is the number of pixels having ith gray level, and N is the total
number of pixels. After equalization, the original gray values are mapped to
the new values. The modiﬁed image remarkably improves the dynamic range
of the image as well as the visibility of features of interest. Example images
are given below. Figure 4 shows an original image. The image in Figure 4 after

histogram equalization is illustrated in Figure 5.

 

Figure 4. Original image.

 

Figure 5. Image in Figure 4 after histogram equalization.

14

2.2.2 Lowpass Filtering

Based on how the ﬁltering process is performed, spatial ﬁlters can be
divided into two categories: convolution ﬁlters and nonconvolution ﬁlters.
Convolution is commonly used to implement linear operations on signals and
images (Castleman, 1979). A lowpass ﬁlter is a convolution ﬁlter.

Lowpass ﬁlters are used to remove random image noise which may be
caused from the lighting or the camera readout. Lowpass ﬁltering operations
are accomplished by kernel multiplications. A kernel multiplication is the con-
volution of a ﬁlter kernel with the original image. The whole process can be
described as follows: each pixel of the ﬁlter kernel is multiplied by the corre-
sponding pixel of the image kernel, add the results, then divide the sum by the
sum of the ﬁlter kernel. Figure 6 shows the schematic of digital convolution.
Applying a 3 x 3 lowpass ﬁlter to the original image in Figure 4 yields the

image in Figure 7.

 

New Value=(A*K1+B*K2+C*K3+D*K4+E*K5
+F*K6+G*K7+H*K8+I*K9) / Sum of Filter Kernel

 

 

 

 

   
   

 

 

Output Image

 

 

 

 

 

Input Image

Figure 6. Schematic of digital convolution.

 

Figure 7. Image produced by applying a 3 x 3 lowpass ﬁlter.

2.2.3 Edge Detection

There are a variety of edge enhancement ﬁlters which can be used to
accentuate the high frequency information in an image. However, while the
edges are sharpened, the noise may also be enhanced. One of the commonly
used techniques for edge enhancement is differentiation. For a given function

f (x, y) , the gradient off is deﬁned as:

g
_ ax _ 8,:
g[f(x,y)] — if -(g)) (3)

17

For any vector direction I, the directional derivative is:

3f

8-1 = gxcosB + gysmB (4)

where B is the rotation angle from the x axis to direction I . The magnitude of

8 [f(x, )0] isr

Mag(g) = ./g,2+g,.2 (5)

For a digital image, the derivatives in the equations above can be approxi-
mated using difference approximations. Many approximation methods may be

used, such as forward difference approximation which can be expressed as:

31f = f(x + 1, y) -f(x, y)
x

31 = f(x,.v+1) —f(x,y)
)’

(6)

The second derivatives are deﬁned as:

gxx 88+:
1: (7)

a f

g N)‘ —2

18

The reason for using the gradient for edge enhancement is that the direction

of the gradient indicates the direction of the maximum rate of increase of the

function f (x, y) , and the magnitude of the gradient is the maximum rate of

increase of f (x, y) per unit distance in the direction of the gradient (Gonzalez

and Wintz, 1977). In an image, the gradient values will be larger in regions

having rapid variations and smaller in smooth regions.

The Laplacian which is deﬁned as:

(8)

is a second derivative convolution operator. The second derivative will also

identify the maximum gradient because the second derivative changes sign at

a position where the ﬁrst derivative is a maximum. A typical 3 x 3 Laplacian

kernel is shown in Figure 8.

 

 

 

 

 

 

0 -l O
-l 4 -l
0 -l O

 

 

Figure 8. A 3 x 3 Laplacian kernel.

19

As we can see, the kernel has zero weighting (the sum of the kernel ele-
ments is zero). This indicates that the result of applying a Laplacian kernel to
a constant brightness image region will be zero. Also because of the central
weighting in the kernel, the Laplacian will respond strongly to points, lines
and edges. It is direction-invariant. The result of applying a 3 x 3 Laplacian

operator to the image in Figure 4 is shown in Figure 9.

 

Figure 9. Result of applying a 3 x 3 Laplacian.

The Sobel ﬁlter is a nonlinear edge detector and it is strongly directional.
Figure 10 illustrates the process of Sobel ﬁltering. Typical 3 x 3 Sobel kernels
are shown in Figure 11. Figure 12 illustrates the image produced by applying

the Sobel ﬁlter to the original image.

20

 

NewValue = Jng +gy2

(G+2H+I) — (A +ZB+C)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

gy = (C+2F+I) — (A +ZD+G)
A
A B C A #3 C
D E F D f i F
G H I G HT 1
Input Image Output Image

Figure 10. Schematic of Sobel ﬁltering.

21

 

 

 

 

 

 

1 2 1 1 0 -1
0 0 0 2 0 -2
-1 -2 -1 1 0 —1

 

 

 

 

 

 

 

 

 

 

Figure 11. Sobel kernels.

 

Figure 12. Image produced by applying Sobel ﬁlter.

22

Another edge detection ﬁlter called Phase which measures the direction of

the gradient:

Direction = arctan[g—yJ (9)
3x
Phase ﬁltering is the complement of Sobel ﬁltering. For each pixel, the gradi-
ent direction is assigned a value. Then this value is scaled to the gray scale
such that each direction can be represent by a corresponding gray value. The
example image given in Figure 13 is obtained by applying the Phase ﬁlter to

the image in Figure 7 after thresholding.

 

Figure 13. Effect of applying Phase ﬁlter.

23

2.3 Thresholding

After an image is captured and digitized, different image enhancement
operations may be performed in order to get a desired image. The purpose of
doing these operations includes correction of defects in the original image,
removal of noise, increasing the visibility of features of interest and extracting
the useful information. Such improvement will make the image suitable for
further analysis and measurements. Before conducting measurements, image
segmentation should be performed. Segmentation is a process that attempts
to separate touching features in an image. Thresholding is one of the image
segmentation methods. By thresholding, a gray scale image is converted to a
binary (black and white) image where the features of interest in the image are
discriminated from the others. Either the features of interest or the back-
ground can be assigned as black or white. In this study, ﬁbers are set to white,
the matrix is set to black.

Manual setting of threshold values is commonly used. The operator is
responsible for deﬁning the threshold values by inspection of the image.
Changing threshold values (from O to 255), the operator observes each corre-
sponding binary image, a threshold is set when the operator makes the deci-
sion that the regions of interest are well separated from the background.
Unlike other edge detection operations, thresholding processes the entire
image at once. So it is time saving and more efﬁcient. On the other hand,
thresholding may introduce errors to the measurement results. The critical

issue associated with the thresholding operation is to set a proper threshold in

24

order to keep the size of the binary object as close as possible to the one in the
original gray scale image. However it is impossible to get an exact match.
Errors introduced by thresholding and the way to reduce them will be dis-
cussed in section 3.5.2. An example image obtained by thresholding the image

in Figure 7 is shown in Figure 14.

 

Figure 14. Image in Figure 7 after thresholding.

2.4 Morphological Filters

Morphological processing provides a different way to modify both gray
scale images and binary images. There are two basic morphology operators:
Dilation and Erosion (Russ, 1990). In a binary image there are only two pos-

sible values (1 or 0) for each pixel. Dilation processing can be described as

25

follows. A binary pixel having value 0 will be changed to 1 if any of its neigh-
bors are 1. This results in adding one layer of pixels around boundaries of
objects. Therefore Dilation will expand the object size and connect discontinu-
ous regions. Erosion is a complementary operation relative to Dilation. If a
pixel is 1, then it will be set to 0 if any of its neighbors are 0. Therefore one
layer of pixels will be removed from around boundaries of objects. As a result
of Erosion, the object will be reduced in size, and some continuous features
may be broken. Figure 15 shows an example test image. The result of perform-
ing two repetitions of a 5 x 5 Dilation to the original image is illustrated in
Figure 16. Two repetitions of a 5 x 5 Erosion on the original image produce the

image in Figure 17.

26

 

Figure 15. Original test image.

 

Figure 16. Two repetitions of a 5 x 5 Dilation.

 

Figure 17. Two repetitions of a 5 x 5 Erosion.

27

The Opening operation is formed by performing an Erosion followed by a
Dilation respectively. It separates connected objects or opens the large
enclosed holes near object borders. Since Erosion reduces the original object
size while the following Dilation adds more pixels to the eroded object, the
object dimension will be restored somewhat. However the overall size of the
object will tend to be slightly smaller than the original one.

The Closing operation is formed by performing a Dilation followed by an
Erosion respectively. Thus, Closing ﬁlls small holes and joins gaps in the
object. The difference between the processed and original object size is smaller
compared with using Opening. Since both Opening and Closing tend to
remove small features from the object, the ﬁnal image will look smooth and
clean.

The applications of Dilation and Erosion may introduce distortion of the
object shape. It is recommended to use the same kernel shape and the same
number of cycles for both Dilation and Erosion for the purpose of reducing
image distortion. An example test image is shown in Figure 18. The result of
applying a 5 x 5 Opening is shown in Figure 19. Figure 20 illustrates the

image obtained by applying a 5 x 5 Closing to the original image.

 

Figure 18. Original test image.

 

Figure 19. Image obtained by applying Opening.

 

Figure 20. Image obtained by applying Closing.

29

2.5 Thinning

Thinning removes the exterior border pixels layer by layer until the object
has a single pixel width. The connectivity of the image should be maintained
after thinning. There are different thinning techniques. One method is to com-
pute the shortest distance between each point in the object and a boundary
point (Hussain, 1991). If more than one boundary points have the same mini-
mum distance, then the corresponding object point is called a medial axis
transformation point. During processing, all the pixels are removed except
those which are medial axis transformation points. The ﬁnal thinned object is
called the medial axis of the object.

Thinning is very sensitive to changes of the object shape. Even a little
change may produce some additional branches, loops or other complicated fea-
tures. This will make the quantitative analysis difﬁcult and the results may
be unreliable. If the thinned image is too complicated, it will be impossible to
interpret it. Therefore it is very important to produce an image with nice

shaped objects before performing thinning.

2.6 Fast Fourier Transform

The image processing operations described in the previous sections are
performed in the spatial domain, while the Fourier transform is a frequency

domain operation. It plays an important role in the image processing analysis.

30

Speciﬁcally, it has been found to be quite a useful tool for non-destructive eval-
uation (Blake, 1987). In the frequency domain, an image is represented by the
energy spectrum represented as “white spots” which are symmetric about the
origin. For each point, the brightness is proportional to the amplitude of the
waveform. The direction from the origin indicates the direction of the wave-
forms.

For a two-dimensional continuous function f (x, y), the Fourier transform is

deﬁned as:

F(u, v) = r r f(x,y) e_j2n(ux+vy)dxdy (10)

And, the inverse Fourier transform of F (u, v) is:

f(x,y) = r r F(u,v)ej2n(ux+vy)dudv (11)

where u and v are frequency variables which correspond to the x and y direc-
tions.

For the discrete case, the image is divided into a M x N grid with a dimen-
sion of Ax x Ay for each unit cell. The two-dimensional discrete Fourier trans-

form is given as:

M-lN—I _-2,, ﬂ+g
I J (M N)
F(u,V) _ W2 2f(x7y)e (12)
x=0y=0
u=0,1,2, - - ~,M—I v=0,1,2, - - -,N—I

and the inverse transform of F( u, v) is:

M-lN-I 12,, LIME")
A! N
f(x,)» - 2 2F(H,V)e (13)
u=0v=0
x=0,1,2, - - .,M—I y=0,1,2, . - -,N-l

Here, f (x, y) represents an image and F (u, v) is its spectrum. From the sepa-
rability property of the two-dimensional Fourier transform, F (u, v) and f (x, y)
can be obtained by applying one-dimensional Fourier transforms and the cor-
responding inverse transforms.

The fast Fourier transform algorithm is a decomposition procedure which
reduces the numbers of multiply and add operations involved in the above
equations. Especially when M and N are large, a great amount of time can be
saved for the computation. More details about the Fourier transform and the
fast Fourier transform can be found in Gonzalez and Wintz (197 7 ). Figure 21
and Figure 22 show an example test image and its FFT respectively.

In the spatial domain, a convolution operation is performed by kernel mul-
tiplication. While in the frequency domain, the spectrum may also be modiﬁed

using ﬁlters. A convolution operation can be achieved by multiplying the

 

Figure 21. Example test image.

 

Figure 22. FFT image.

33

transformed image by the kernel. Applying different ﬁlters allows low fre-
quencies or high frequencies to be enhanced to smooth or sharpen the image
and remove the other frequencies.

In the FFT, a certain pattern may be recognized from the spectrum direc-
tion. For example, if the ﬁbers are aligned horizontally, then in the FFT the
spectrum will distribute vertically and vice versa. This suggests the possibil-
ity of using FFT for the braid angle determination in this study and it has
been proved to work well. Frequencies correspond to the noise and undesired
background with known patterns in the FFT image can be easily cut off. After

ﬁltering operations, the image can be restored using the inverse transform.

CHAPTER 3

QUANTIFICATION OF
MORPHOLOGICAL FEATURES

3.1 Introduction

The image processing method provides a means of performing pattern rec-
ognition and measurement. It has been proved to be an especially useful tool
to conduct the morphological analysis and quantiﬁcation of composite materi-
als with good reproducibility.

The object of this study is to develop methods for quantifying morphologi-
cal features of triaxially braided glass/urethane composites using computer-
aided image processing techniques and automate the whole process as much
as possible. The approach to braid angle determination used here is non-
destructive and is based on the Fast Fourier transform method, while the
approach to crimp angle determination involves edge detection and boundary
identiﬁcation. Cutting samples is required presently for the latter.

It should be noted that the quality of the image is very important in the

34

35

application of image analysis. It will directly affect the reliability of measure-
ment results. A good quality image can minimize or eliminate problems later
in the image processing. One can not totally rely on image operations. In other
words, if problems associated with an image can be solved by the choice of
cameras, optics or lighting systems, one should solve those problems directly

and not by applying image operations.

3.2 Image Analysis System Setup

Image analysis procedures start with the image acquisition. The image is
captured by a video camera which converts an optical image into an electrical
signal. This analog signal is sent to the analog-to-digital converter (frame
grabber) where the analog signal is converted into numerical data in the form
of an array of numbers. Then these numbers are stored in the computer mem-
ory and they are ready for image processing.

Figure 23 shows the schematic of the image analysis system. Some of the
images used in this study were captured in our lab using a Javelin Mos Sensor
camera and a Sony DXC-151A CCD video camera. A Canon 16-100 mm TV
Zoom lens and a Navitar Zoom 6000 lens were used to get different magniﬁca-
tions. Some of the images were captured in Dr. Anil J ain’s lab in the Depart-
ment of Computer Science, Michigan State University using a Panasonic GP-
KR202 CCD video camera. The image digitization is done with a DT2861

image board which has a resolution of 512 x 480 pixels and provides 256 gray

36

levels. Image processing is performed using commercial software (Image-Pro
Plus Version 2.0 and Version 1.2 for Windows) installed in a Gateway 2000
4DX2-66E PC. Images are displayed on a Electrohome No. 38-D05IMA-UP
RGB monitor. A Conner backup hard disk tape drive is used to archive
images. A 200MB magnetic tape can store about 800 images (512 x 480 pix-
els). It takes approximately one minute and forty seconds to store a 0.25MB

image.

37

 

  

Video Camera

Photostand

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RGB Monitor

 

 

 

 

 

 

Computer
Frame Grabber
Image Processing Software

Figure 23. Schematic of the image analysis system.

38

3.3 Errors in Measurements

No measurement can be completely free of uncertainties. When a measure-
ment is made, it is desired to know if the result is good enough. To be able to
evaluate the uncertainties and keep them to a minimum is very important for
any measurement.

“Error” by deﬁnition is the inevitable uncertainty that attends all mea-
surements. It can not be avoided by being careful (Taylor, 1982). Errors can be
grouped as random and systematic. Random errors can be estimated using
statistical methods, while systematic errors can be hard to detect or evaluate,
and can not be discovered by repeating measurements or increasing the sam-
ple sizes. They tend to accumulate and bias the measurement results. How-
ever if they are identiﬁed they can be corrected or reduced to magnitudes as
small as possible. For a large reduction of both random errors and systematic
errors, it is required to improve the techniques and the equipment used in the
measurement.

For any experimental result, it is also desired to have a quantitative esti-
mation of the measured mean. A large sample size is needed for high conﬁ-
dence. For a large sample size (n .>_ 30), the conﬁdence limits for the population

mean can be expressed as (Spiegel, 1975):

(14)

39

For a small sample size (n<30), conﬁdence levels can be obtained using the t

distribution. The conﬁdence limits are given by:

><|
H-

('5
§1IG

(15)

where )7 is the sample mean, 6 is the sample standard deviation, and the

term 3 is the standard deviation of the mean. The values of Z C and t c corre-

J72

spond to different conﬁdence levels (99.73%, 99.45%, 68.27%, etc.). For exam-

ple, one can be 68.27% conﬁdent that the true mean lies between the interval

2
./r_t

The possible sources of systematic error in this study can be generalized as

of )—(.+. (Z 6 =1).
follows:
(1) Specimen preparation
(2) Image acquisition
0 Alignment of specimen
0 Lighting
0 Cameras and lenses
(3) Image processing and analysis
0 Operations applied
0 Setting threshold values
0 Separating touching features
0 Setting spatial calibrations to change spatial measurement units

(4) Mathematical calculations

4O

Errors encountered in the measurements will be discussed in this Chapter

and Chapter 4.

3.4 Braid Angle Determination

3.4.1 Calibration

Test images with known braid angles were created for calibration tests.
Since test images are noise free and their complexities are under controlled,
they can be used to understand how well computer-based pattern recognition
compares to human-based pattern recognition for ideal situations. This is
helpful to deﬁne the capabilities of performance and the inﬂuences on the real
situations which are non-ideal. Also with test images systematic errors which
may be introduced by the image acquisition, the image processing software
and the calculations involved can be detected.

Test images with angles arbitrarily chosen from 30°to 80°were created
and digitized. These digitized images are called test raw images. Then the test
raw images were transformed into the frequency domain using the FFT opera-
tion. The images after applying the FFT operation are called FFT images. Fig-
ure 24 shows an example of these images where x1 and x2 are raw angles, x3
and x4 are the corresponding FFT angles.

Another test image which consists of ten non-parallel lines corresponding

to ten braid angles (from 426" to 510° ) was created. The average of these ten

41

braid angles is 469°. Figure 25 shows the corresponding FFT image of this
test image. It can be seen that the energy spectrum is more widely spread out
compared with the one in Figure 24. Image operations were performed on the
FFT image to deﬁne the inﬂuences of the image processing on measurement
results and determine the adequacy of the proposed method. Image operations
involved will be discussed in section 3.3.2. The FFT image after thinning is
shown in Figure 26. Angle measurements were conducted on the ﬁnal thinned
images. Comparison was made between least-squares determinations and
manual determinations.

The resolution limits of the measurements are determined by the resolu-
tion of the frame grabber (512 x 418 pixels) and the magniﬁcations of the
optics. The highest resolution for the angle measurement limited by image
digitizing is approximately 0.1°(atan(—I-) 2 01°). A spatial resolution of 0.1

512

mm can be obtained with the magniﬁcations used in this study.

42

Test Image FFT Image
(a) (b)
x1 ——- x3
x2 ——I> X4

 

Figure 24. (a) Example test image for calibration of braid angle analysis.
(b) The fast Fourier transform of (a).

43

 

Figure 25. Test FFT image for calibration of braid angle analysis.

 

Figure 26. Final thinned image.

44

3.4.2 Sample Image Analysis

Specimen Preparation

The composite components under investigation are triaxially braided
glass/urethane parts (crossmembers) provided by Ford Motor Company. Fig-
ure 27 shows photographs taken from the real composite part. The method for
braid angle analysis considered in the present work is non-destructive. The
sample was aligned manually on the baseboard of the photostand (Figure 23).
The x and y directions can be adjusted with the aid of the sample edge, rulers,
the frame grabber and the image processing program. Images were captured
at different locations over the sample ﬂat surface along the entire length of
the sample. The domain size of the sample represented by the image can be
varied depending on the magniﬁcation of the optics. It was found that in gen-

eral a higher magniﬁcation will produce better image quality.

45

 

(b)

 

(C)

Figure 27. (a) The whole part (~1.5 m long).
(b) A closer picture of the part surface.
(c) The cross section of the part (80 x 32 mmz).
The bright section is the foam core.

46

Image Processing

Image processing operations were performed on the raw image in order to
get the desired information needed to determine braid angles. The operations

applied are as follows:

Raw Image --> Equalization --> FFT --> Lowpass --> Dilation -->

Erosion --> Laplacian --> Threshold --> Thinning --> Final Image

An example raw image after histogram equalization which represents a
sample area of about 33 x 24 mm2 is shown in Figure 28. Histogram equaliza-
tion attempts to give the best possible gray level distribution to the image.
The contrast of the image and the visibility of the features in the image are
improved after applying histogram equalization.

Then the image is transformed into the frequency domain using the FFT
operation. Due to the complexities of the structure which include variations of
the longitudinal tow direction and the braid tow direction as well as the ﬁber
curvature and the noise from the background, the energy spectrum in the FFT
is spread out for the image from the real sample. These introduce difﬁculties
for the determination of ﬁber directions. Figure 29 shows the FFT image of
the image in Figure 28.

Next a lOWpaSS ﬁlter is performed on the image to remove the noise. Low-
pass ﬁltering will produce a blurred effect on the image. Then two morphology

operators: Dilation and Erosion are applied to the image successively. The

47

 

Figure 28. Example image from the sample surface after
histogram equalization.

 

Figure 29. The FFT of the image in Figure 28.

48

purpose of using Dilation is to connect discontinuous features in the image. As
mentioned in section 2.4, as a result of Dilation the object size will be
expanded while the following Erosion will reduce the object size. Therefore the
overall size of the object can be restored somewhat. The image after applying
Dilation and Erosion operations is shown in Figure 30.

The ﬁber directions are detected using the Laplacian edge detector. The
FFT image after Laplacian edge detection is shown in Figure 31. Two main
directions which correspond to crossed ﬁber (braid tow) directions can be rec-
ognized from the image.

By thresholding, a gray scale image is converted to a binary image where
the features of interest in the image are discriminated from the others. And
ﬁnally the object in the image are reduced to a single pixel width using the

thinning operation.

49

 

Figure 30. Image produced by applying Dilation and Erosion
operations.

 

Figure 31. Image in Figure 30 after Laplacian edge detection.

50

Investigations have been conducted to identify the spectrum distribution of
the noise in the FFT image. N o deﬁnite pattern has been found. This can be
done in two ways. One is to apply the FFT to the background. The result
shows that the spectrum is randomly distributed over the frequency space.
Another way is to remove the frequencies in the deﬁned areas between the
main directions, then restore the image using the inverse FFT operation. An
image with smooth background is obtained. Figure 32 shows one image after
applying the inverse FFT.

When the same processing operations are performed on different images or
repeated on one image, the Script Mode of the image processing software can
be used to enhance the processing speed. When Script Mode switches on, it
records all the operations into a .SCR ﬁle. By using Play Script the next time,

the selected previously recorded script ﬁle will be played back automatically.

Braid Angle Measurement

Images after thinning are used to represent the mean ﬁber directions.
These images are saved as .BIT ﬁles in Image-Pro Plus. In a .BIT ﬁle an image
is represented by a two-dimensional array where each cell in the array has an
intensity value that describes the pixel of the image. Least-squares lines were

found to approximate the ﬁber directions in order to calculate braid angles.

51

 

Figure 32. Inverse transformation of the modiﬁed FFT in
Figure 29.

3.5 Crimp Angle Determination

The general process for the crimp angle measurement includes:
(1) edge detection;
(2) identifying the ﬁber boundary;
(3) ﬁtting a model function to the ﬁber boundary;

(4) using the information from the ﬁtting function to calculate crimp angles.

52

3.5.1 Calibration

Sinusoidal and polynomial test images with known crimp angle were cre-
ated and digitized. Without applying any image operation, these images were
used to compare results obtained from a polynomial curve ﬁtting with known
values. Figure 33 illustrates another polynomial test image. The portion
which is set to white is chosen as the representation of the ideal crimp, and
the remaining areas are set to black as the background. Image operations
were performed on the test image. The operations applied are the same as
those applied to the real sample images in order to explore the inﬂuence of
image processing on the ideal situation which is necessary for investigating
the inﬂuence of processing operations applied on the quantiﬁcation of crimp
angle when the situation is non-ideal. Discussions will be given concerning
the operations involved in the following section. Figure 34 shows the image
produced by thresholding. The image in Figure 34 after thinning is shown in
Figure 35. This thinned image is used to represent the centerline of the crimp
shape in the raw image. A 7th order polynomial was found to approximate the

crimp curve.

53

 

Figure 33. Polynomial test image for calibration of crimp angle analysis.

 

Figure 34. Image after thresholding.

 

Figure 35. Image in Figure 34 after thinning.

54

3.5.2 Sample Image Analysis

Specimen Preparation

A ﬂat plaque composite sample 48A (one of the three architectures investi-
gated by Ford Motor Company) was used for crimp angle analysis (Jaranson
et al., 1993). For each specimen, two cuts were made along the braid tow
direction of the sample. The sizes of specimens are different from one to
another. Manual polishing was carried out until the desired quality of side
surfaces was obtained. Manual alignment of the specimen is required. The
mean yarn direction can be determined using the edge of the specimen as a

reference and with the aid of the frame grabber and the image processing pro-

gram.

Image Processing

The crimp images were taken in Dr. Anil J ain’s lab. It has been found that
properly lighting the sample including the top and bottom illumination has
beneﬁcial effects on the image quality. A series of image operations were found
to be necessary to process the raw image in order to make it suitable for doing

measurements. The operations involved are given below:

Raw Image --> Equalization -->Lowpass -->

Laplacian --> Threshold --> Thinning (Sobel) --> Final Image

Figures 36-42 show a series of image transformations. The actual size of each

55

image displayed is for a sample size of about 32.2 x 5.5 mm2. An example raw
image used to determine crimp angle is shown in Figure 36. First histogram
equalization is applied to the raw image. It can be seen from Figure 37 that
signiﬁcant improvement of the ﬁber visibility is obtained after histogram
equalization. Then applying a lowpass ﬁlter to the image in Figure 37 pro-
duces the image in Figure 38. The Laplacian edge detector is used to detect
the ﬁber edges. As a result of applying the Laplacian edge detection ﬁlter, the
regions with low contrast in the image will be removed and edges will be
enhanced. This effect is shown in Figure 39. After thresholding (Figure 40),
the Sobel nonlinear edge ﬁlter may be used to detect both top and bottom
boundaries of the ﬁbers (Figure 41). The result of applying the thinning opera-
tion to the image in Figure 40 is illustrated in Figure 42.

This is a general process. Due to the variation of image complexities, for a
speciﬁc image, repetitions of some operations may be required. When setting
the threshold, problems may be encountered associated with separating
touching features that have similar gray values. The correct threshold to
detect the ﬁbers of interest may also detect other features which are touching
the ﬁbers. Therefore in order to separate these features from the ﬁbers, the
threshold may be set to a value where the ﬁbers are underdetected. In the
case when touching features can not be entirely separated from the ﬁbers by
thresholding, then the Sub operation in the image processing software which
performs substraction of the speciﬁed operand from the image is needed to

accomplish this in order to get a nice thinned image. This operation requires

56

 

Figure 36. Example raw image for crimp angle determination.

 

Figure 37. Image in Figure 36 after histogram equalization.

 

Figure 38. Image in Figure 37 after applying a lowpass ﬁlter.

57

 

Figure 39. Image in Figure 38 after applying a Laplacian edge ﬁlter.

 

Figure 40. Image in Figure 39 after thresholding.

 

Figure 41. Image in Figure 40 after applying Sobel ﬁlter.

58

 

Figure 42. Image in Figure 40 after thinning.

human determination. Otherwise branches and loops may appear at touching
points which make the thinned image complicated. Errors may occur during
this process. A way to reduce the errors is to observe the closeness of ﬁt
between the binary image and the gray level image. This can be done using
the Diff operation in the image processing software which gives the absolute

value of the difference between the two speciﬁed images.

Crimp Angle Measurement

Data from .BIT ﬁles were used to calculate the crimp angles. 7th order
polynomials were found to approximate the curves. The number of points used
to ﬁnd a polynomial ﬁt is determined by the step size and the horizontal width
of the crimp. The portions near the two ends of the curve in the image may be
overestimated by the polynomial which does not correctly represent the curve
shape. To avoid inaccurate results data from near the ends should not be used
for the calculation. For each crimp two crimp angles, one positive and one neg-
ative were calculated. The average crimp angle can be obtained by averaging
the absolute values of these two angles. This may compensate the initial mis-

alignment of the specimen.

59

3.6 Fiber Waviness Determination

The determination of ﬁber waviness is non-destructive. Part of the work
has been done for the determination of ﬁber waviness. It is proposed that sim-
ilar test images as those used for the crimp angle analysis will be applicable
for the calibration work of ﬁber waviness analysis.

Image operations have been deﬁned to transform the raw image. The tech-
niques involved are quite similar to those used in processing the crimp

images. Operations applied are given as follows:

Raw Image --> Equalization --> Vertical Edge -->

Lowpass --> Phase --> Threshold --> Thinning --> Final Image

Vertical Edge is an edge detector which enhances the vertical edges in the
image. Other operations involved have been described in the previous sec-
tions. Figures 43—46 show an example of such transformations. The curves in
the thinned image are used to represent the shapes of the ﬁber curvature.
For the quantitative determination of ﬁber waviness, polynomials (6th
order) were generated to approximate the ﬁber curves in Figure 46. It seems
that the polynomial approximation or the Fourier series is more suitable than
the sinusoidal function for ﬁber waviness characterization for the real situa-

tion. More work needs to be done to quantify the ﬁber waviness.

60

 

Figure 43. Example raw image of ﬁber waviness after
histogram equalization.

 

Figure 44. Image in Figure 43 after applying a vertical edge ﬁlter.

61

 

 

Figure 45. Image in Figure 44 after applying Phase ﬁlter and
thresholding.

 

Figure 46. Image in Figure 45 after thinning.

CHAPTER 4

RESULTS AND DISCUSSION

4.1 Braid Angle Determination

4.1.1 Calibration

For the test images with angles arbitrarily chosen from 30°to 80° , ten
repetitions of manual angle measurement were performed on each of the test
raw images and the corresponding FFT images. The uncertainty is approxi-
mately 02° for the raw angle measurement and 0.4°for the FFT angle mea-
surement. Results for the test images with the angle range of 30°to 35° are
given in Table 1. For each of the ten data sets, a least- squares line was con-
structed by linear regression analysis of “processed” angle as a function of raw
angle. The linear correlation coefficient, r , and the standard error of estimate,

S, were calculated. r and S are given by (Spiegel, 197 5):

r2 = 2(Oest—6)2

2 (16)
2(9—6)

 

62

63

 

 

2
S : JZ(9—9est) (17)

n

where 9 is the measured angle, Best is the estimated value of 0 using least-
squares ﬁt, 0 is the mean value of the measured angles, and n is the number
of measurements. Results are given in Table 2. The linear correlation coefﬁ-
cient measures how well the least-squares regression line ﬁts the data. From
Table 2, it can be seen that good linear correlations are found, since all the cor-
relation coefﬁcients are nearly equal to 1. The standard error of estimate mea-
sures the data scatter about the regression curve. An example of ﬁtting a
least-squares line to the data points is illustrated in Figure 47. The two bro-
ken lines were constructed parallel to the regression line at the vertical dis-
tance of S. If the sample points are large enough, then it should be found that
68% of the points would be included between the pair of lines.

For another test image which consists of ten non-parallel lines, measure-
ments were performed on the FFT image after thinning (Figure 26). Two
methods, least-squares method and manual measurement were compared.
For each case ten measurements were conducted using different threshold
values. Results are displayed in Table 3. It can be seen from the table that
results from the two methods are in good agreement. The relative errors are
comparable. The least-squares method gives a closer result to the known
value. It is revealed that the thinned image gives a mean direction in this

ideal case. This is expected. The method has been extended to apply to the

64

 

 

 

 

 

 

 

 

 

 

 

real sample analysis. Signiﬁcant inﬂuences on performance have been dis-

cussed in section 3.3.2.

 

 

 

 

 

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Table 2: Calculated Results from Least-Squares Curve Fit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

# of Linegr Correlation Standard Error of Estimate
Data oefficrent (deg)
Set Raw Angle FFT Angle Raw Angle FFT Angle
1 0.9979 0.9803 0.10 0.32
2 0.9966 0.9704 0.13 0.37
3 0.9973 0.9727 0.12 0.37
4 0.9976 0.9910 0.11 0.23
5 0.9970 0.9753 0.12 0.34
6 0.9948 0.9928 0.16 0.17
7 0.9964 0.9811 0.13 0.31
8 0.9957 0.9920 0.15 0.19
9 0.9956 0.9836 0.15 0.27
10 0.9955 0.9627 0.14 0.41

 

 

 

Table 3: Comparison of the Least-Squares Method with the Manual
Measurement for Test Images (Unit: deg)

 

 

 

 

 

 

 

Method Measured Standard Known Percentage

Mean Angle Deviation Angle Error (%)
Least-Squares 46.66 0.26 46.9 0.5
Manual Measurement 46.40 0.13 46.9 11

 

 

Percentage error=(Measured angle-Known angle)/ Known angle.

 

36

66

 

I

35

Measured Angle (deg)
on 0
co 4:

1 I

(A
N

31

 

  
  
  

 

 

ESolid Least-Squares Line
1 1 g 1 i
30.5 31 31.5 32 32.5 33 33.5 34 34.5 35

True Angle (deg)

Figure 47. Example of least-squares line ﬁt to data points.

67

4.1.2 Sample Image Analysis

Images were taken at six different locations along the sample ﬂat surface.
Since measurements were conducted over relatively small areas, it is assumed
that the waviness of longitudinal ﬁbers is negligible. The FFT only transforms
a certain part of the image, within the transformed area of each image about
5-8 braid angles were measured. The right angle corresponds to 0, and the left
angle corresponds to the absolute value of -0. Braid angles, the mean values of
right and left angles are given in Table 4. The results suggest that the braid
angles vary from location to location. The absolute value of variation is up to
11.14°for the mean values within the measured domain of approximately
1200 x 80 mmz. Comparison of the least-squares method with the manual
measurement was made. Results are reported in Table 5. The mean of the
measurements from the six locations is 45.47° with a standard deviation of
338°. This is comparable to the mean of 466° and a 32° standard deviation
obtained from direct manual measuring on the sample surface.

The reproducibility of the braid angle measurement for the real sample
has been examined at a single location by investigating the variability intro-
duced by:

(1) the image transformations with a speciﬁed threshold value;
(2) the image transformations with different threshold values.

Since the shape and the size of the object will change with different thresh-

old values, the result produced by thresholding will directly affect the thin-

ning result. As discussed in section 2.5, thinning is very sensitive to changes

68

of the object shape. A little change may introduce additional branches, loops
or other complicated features. This will make the quantitative analysis difﬁ-
cult and the result may be unreliable. Therefore it is desired to know the inﬂu-
ence of the setting of thresholds on the measurement results. Five
measurements were conducted for each of the two cases. A mean of
44.13 °with a standard deviation of 0.16°for case (1) and a mean of 43.60°
with a standard deviation of 0.7 2° for case (2) are observed. The results sug-
gest that the variation of the braid angle measurement produced by using a
ﬁxed threshold value is less than the variation of the braid angle measure-
ment produced by using different threshold values. Compared to the variation

of 338° observed at different locations in a single sample, the variation level

of 016° -0.72° is small.

Table 4: Braid Angles at Different Locations (Unit: deg)

 

 

 

 

 

 

 

 

 

 

 

 

Braid Angle
Location Mean Value
Right Left
1 43.28 45.25 44.27
2 46.48 44.09 45.29
3 53.47 48.93 51.20
4 42.79 40.58 41.69
5 47.01 42.59 44.80
6 46.02 45.25 45.64

 

 

69

Table 5: Comparison of Braid Angle Measurements between the
Least-Squares Method and the Manual Measurement (Unit: deg)

 

 

 

 

 

 

 

Method Mean Braid Standard 95% Conﬁdence
Angle Deviation Limits ( i)
Least-Squares 45.47 3.38 . 1.05
Manual Measurement 45.6 3.2 2.3

 

4.2 Crimp Angle Determination

4.2.1 Calibration

Angles measured from test images using the polynomial ﬁt method with-
out applying image operations were compared with known angles. Results are

displayed in Table 6. It is suggested that the polynomial ﬁt can yield a rather

good approximation to the true value (to within approximately 1%).

Ten measurements were performed on another test image (Figure 35). The
mean for the measured angle is 12.63° with a standard deviation of 020°.
Compared with the known angle of 12.95° , a 2.5% percentage error is deﬁned.

No signiﬁcant systematic error which biases the measurement results is

found from the image processing.

 

Table 6: Crimp Angles from Test Images (Unit: deg)

 

 

 

 

 

 

 

Test Function Measured Known Percentage Error
Angle Angle (%)
Sinusoidal Function 45.49 4500 1,1
Polynomial Function 13.06 12.95 0.8

 

Different results were found by using different orders of polynomial and

different numbers of points to determine the polynomial functions. Investiga-
tions were conducted based on the test images. The uncertainty from the
choice of polynomial orders (5th, 6th and 7th) is approximately 045° . And the
uncertainty from changing numbers of ﬁtting points (15-30 points) is approxi-
mately 0.13°. It was found that a 7th order polynomial gave a more accurate
approximation to the curve shape, since a minimum value of the summation of
the square of the errors was obtained for the 7 th order polynomial, where the

error is the difference between the original value and the corresponding esti-

mated value using polynomial ﬁt.

4.2.2 Sample Image Analysis

Crimp angles were measured on nine specimens. There are typically 2-5
crimps in each specimen. Figure 48 shows an example of polynomial ﬁt to the

data points of the ﬁber boundary. The mean value of the crimp angle (a),

 

71

standard deviation (6) and the coefficient of variation (the ratio of o to a (CS/a»
were calculated for each specimen. N is the number of crimp angles measured
for each specimen. Results are given in Table 7. It can be seen from the table
that the crimp angles vary by 6%-36% for different specimens. For a speciﬁc
specimen the crimp angles change from one location to another along the
braid tow direction with a maximum standard deviation of about 4°. The
mean crimp angle for the nine specimens is 11.86° with a mean standard devi-
ation of 3.11 ° . A plot of crimp angles from different specimens is illustrated in
Figure 49. The error bars shown in the plot are standard deviations of the
mean.

Figure 50 displays the sample crimp angle distribution over a single sam-
ple. Sixty-nine crimp angles were measured. The measured mean is 11.75°
with a standard deviation of 330°. The 95% conﬁdence limits for the mea-
sured mean of one sample is 11.75° i 0.78°which was calculated using equa-
tion (14). This mean crimp angle is comparable to the average crimp angle of
106° reported by Jaranson et a1. (1993) who found the result by averaging
the crimp angles measured from four specimens.

From the above results it is revealed that the variability of crimp angle
determinations observed in different specimen (11.86° i 3.11°) is almost iden-
tical to the variability observed for different locations on a single specimen

(11.75° 3: 330°).

Y Axis (mm)

72

 

I

1.8 . 1'1“.“ . gData

Solid ? Polynomial Fit

.5 _s —L
d N h a)
l I ﬁ I

.0
on
I

0.4- ~ ; .1

 

i
L
l.‘
t

 

 

0.2
0 2 4 6 8 10 12 14 16 18

X Axis (mm)

Figure 48. Example of 7 th order polynomial ﬁinction ﬁt to the
ﬁber boundary.

20

Table 7: Crimp Angles from Nine Specimens (Unit: deg)

73

 

 

 

 

 

 

 

 

 

 

 

Specimen Mean Cirgnp Angle Standardcgeviation o/E (%) N
1 11.48 3.08 27 6
2 10.46 3.72 36 8
3 12.04 3.93 33 8
4 12.52 2.60 21 8
5 11.66 3.23 28 6
6 11.41 3.24 28 9
7 12.80 3.90 30 10
8 13.80 0.87 6 4
9 10.58 3.38 32 10

 

 

 

 

 

 

—L —L —L -L .3 N
O) O N 15 O) (D 0

Mean Value of Crimp Angle (deg)

O)

74

 

 

 

l I l L 4 L l I J

 

 

1 2 3 4 5 6 7 8 9
Specimen Number

Figure 49. Crimp angles measured on different specimens.

10

75

 

0.16 , 1 1 F
o.14~-~- -

o.12~~

1
1

Frequency
9
0
0
i

0.04b“' ., . .. ., . . ,, .....

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O

0 5 9 10 15
Crimp Angle (deg)

Figure 50. Crimp angle distribution over one sample.

25

76

The investigation of the reproducibility of the crimp angle measurement
for the real specimen has been conducted by examining the following situa-
tions:

(1) the inﬂuence of multiple imaging on one specimen;
(2) the inﬂuence of the setting of thresholds examined at a single location for a
given specimen.

Results revealed by Table 8 show that the reproducibility found for one
specimen being imaged three times is about 10° -1.9° (4%-23% variation). The
higher variation of 23% is associated with the lower mean crimp angle (8.32° ).
It should be possible to reduce this by using higher magniﬁcation optics
(increasing the resolution of the images).

Table 9 shows the results of the second situation. The standard deviation
(o=0.19°) produced by the crimp angle measurement with a ﬁxed threshold
value is smaller than the one (o=0.44° ) produced by the crimp angle measure-
ment with different threshold values. Five measurements were taken for each
situation. It is suggested that using a deﬁned threshold value yields more
reproducible results. The variation level of 0.19°-0.44°is small compared to
the variation of 3.30°observed within one sample. As mentioned in section
3.5.2, for the crimp angle determination human involvement is needed to sep-
arate touching features. The measurement is insensitive to human interaction

judging by the reproducibility results.

77

Table 8: Reproducibility of the Crimp Angle Measurement Tested by
Repeating Imaging on One Specimen (Unit: deg)

 

 

 

 

 

 

 

Crimp Mean GEE-Sip Angle StandardO-Deviation o/a (%)
#1 22.48 1.01 4
#2 8.32 1.89 23
#3 10.12 1.16 11

 

 

 

Table 9: Reproducibility of the Crimp Angle Measurement Tested by
Repetitions of Measurement on One Image (N =5) (Unit: deg)

 

Mean Crimp Angle

Standard Deviation

 

 

 

 

 

 

Threshold (3) (6) Glen (%)
Fixed 12.79 0.19 1.5
N on-Fixed 12.59 0.44 3.5

 

 

78

4.3 Image Analysis Speed

It takes about 5 minutes to capture and transform the image. More time is
needed for data processing and quantitative calculations. Presently the total
analysis time required is about 14 minutes per image. The time required for
the crimp angle analysis is approximately 1-2 minutes longer than for the
braid angle analysis due to the human involvement for the determination of
crimp angle. The processing speed can be increased with faster equipment (a
120MHz pentium PC and a DT3851 image board). Also the analysis time can
be reduced when software subroutines are linked with the existing software to
provide curve ﬁtting and quantitative determinations of the morphologies.
With such improvement the total time required from imaging the sample to

obtaining the quantitative results is expected to be about 8-9 minutes.

CHAPTER 5

CONCLUSIONS AND
RECOMNIENDATIONS

5.1 Conclusions

The morphological features including braid angle and crimp angle were
quantiﬁed using computer-aid image processing techniques. Image operations
were deﬁned to process the image for the analyses of braid angle, crimp angle
and ﬁber waviness. Calibration results show that braid angles can be mea-
sured to within 0.5% and that crimp angles can be measured to within 2.5%. It
is suggested that the present methods can produce accurate angle determina-
tions for ideal cases. Based on test images, good correlation is found between
computer-based and human-based determinations.

For real sample analyses, the braid angle variation within one sample is
found to be about 7% and the crimp angle variation within one sample is
found to be about 28%. The results of reproducibility for both braid angle and

crimp angle measurements tested by changing threshold values suggest that

79

80

using a deﬁned threshold value yields more reproducible results (0.4% for
braid angle determinations and 1.5% for crimp angle determinations) than
using different threshold values (1.7% for braid angle determinations and
3.5% for crimp angle determinations). Also the reproducibility of the crimp
angle measurement tested by multiple imaging on a single specimen is within
the range of 4%-23%.

The braid angle determination is non-destructive and based on the fast
Fourier transform method. Linear least-squares curve ﬁtting is used to deter-
mine the ﬁber directions. Cutting is presently required to determine the crimp
angle. The ﬁber shape is approximated by a 7th order polynomial function.
The quantitative description of ﬁber waviness has not been entirely accom-
plished. No signiﬁcant systematic error was detected for the present methods.

With the Image-Pro Plus version 1.2 for Windows, operator input is elimi-
nated. This is desirable for the automation purpose. Scripting has been used
to automate a part of the image transformations. The total time required from
imaging the sample to obtaining the ﬁnal quantitative results is about 14 min-
utes per image.

The present method is limited to characterizing braid angles at the sample
surface regions where the ﬁber visibility is relatively good. The interior fea-
tures can not be detected non-destructively with the present approach.

In order to get good statistical representations of the results, good quality
images and a relatively large number of measurements are required. Speciﬁ-

cally, for braid angle analysis approximately ten images which are taken from

81

each side of the cross member ﬂat surface at different locations are needed.
But in some surface regions the ﬁber visibility is poor. In this case, the image

can not provide any useful information.

5.2 Recommendations for Future Work

Recommendations for the Equipment

Due to the limitations of the present equipment, images being taken using
the current video camera (a Javelin Mos Sensor camera with a resolution of
485 x 384 pixels) and lens (a Canon 16-100 mm TV Zoom lens) we can not
achieve the desired image resolution and quality level. A CCD B/W video cam-
era (a resolution of 768 x 493 pixels or higher is preferred), a high quality
zoom lens and a photostand with top and bottom illumination are required to
improve the image quality. The storage space provided by the current PC com-
puter system is far from enough and the time for image analysis needs to be
reduced. The situation should be improved with a new pentium PC and the
image board. It is suggested that the workstation could provide much greater
computational capabilities (Yurgartis, 1994) for digital image analysis. A hard
disk tape drive is being used for image backups. The data storage and
retrieval are cumbersome and time inefﬁcient. It seems that optical disks

might be a better choice for fast data storage, data retrieval and cost-effective.

82

Recommendations for Quantitative Determinations

Similar strategies as used in the determinations of braid angle and crimp
angle including the calibration test and the sample image analysis should be
employed to investigate the ﬁber waviness.

For braid angle and crimp angle determinations, measurements need to be
taken to examine the variation of the measurements on different samples. The
variability which may be introduced by sampling the same specimen at a spec-
iﬁed location by different operators should be investigated.

Presently a ﬂat plaque sample is used for the crimp angle determination
due to the poor contrast between ﬁbers and the matrix of the actual structural
part, but it is desired to perform analysis on the real crossmember sample in
future work. To enhance the contrast it may be useful to include some opaque
“tracer” ﬁbers in the braiding process. Also some modiﬁcations of the imaging
method may be helpful such as using color ﬁlters or polarizing ﬁlters.

Preliminary work on the braid angle determination has been done using x-
ray photographs which were provided by Ford research engineers. The photo-
graphs were imaged, then these images were transformed into the frequency
domain. One problem associated with using the photographs is the quality of
the image. More work needs to be done to investigate the feasibility of using
photographs as the source to quantify braid angles. Other techniques could be
investigated such as an ultrasonic nondestructive evaluation method or IR
imaging radiometry technique to explore the possibilities for determining the

interior braid angles and crimp angles non-destructively.

83

Automating the entire analysis process is the long term goal of this study.
A part of the ﬁiture work will be writing subroutines and linking with the

existing software to provide automated morphological feature determinations.

LIST OF REFERENCES

84

LIST OF REFERENCES

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Castleman, K. R. (1979), “Digital Image Processing”, Prentice-Hall, Inc., New
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Cole, G. S. (1991), “Practical Examples of Useful Algorithms in Computer-
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