automatic inspection of single-system-mélange color fabric density ...

AUTOMATIC INSPECTION OF SINGLE-SYSTEM-MÉLANGE COLOR FABRIC
DENSITY BASED ON FCM ALGORITHM
Gao Weidong 1,2 , Wang Shanyuan 1 , Pan Ruru 2 , Liu Jihong 2 , Wang Xuefang 2 , Lei Hui 2
1 College of Textile, Donghua University, Shanghai, China
2 Key Laboratory of Eco-Textiles, School of Textile and Clothing, Jiangnan University, Wuxi, Jiangsu, China
Abstract: According to the color yarns in the fabric, the fabrics can be divided into three categories: solid color fabrics, single-systemmélange
color fabrics and double-system-mélange color fabrics. In Part I of this study, we have used Hough transform to detect the density
of solid color fabrics successfully. Based on the research, we will discuss the method for detecting the density of single-system-mélange color
fabrics in this paper. By analyzing the pattern and color characters of single-system-mélange color fabrics, FCM algorithm is proposed to
classify the colors in the fabric image based on Lab color space first. With the color segmentation results, the fabric can be divided into
different blocks. The yarns can be located in different blocks with different means, and then the number of yarns can be counted. The fabric
density can be obtained by counting the yarns in a unit length finally. The experiment proved that the algorithm proposed in this study can
inspect the density of single-system-mélange color fabric successfully.
Keywords: FABRIC DENSITY, SINGLE-SYSTEM-MÉLANGE COLOR FABRIC, FCM ALGORITHM, LAB COLOR
SPACE, COLOR CLASSIFICATION.
1. Introduction
In previous study, we proposed to use Hough transform to
detect the skew angles of warp and weft yarns in the fabric. And
then gray-projection method was selected to locate the yarns in the
fabric image. The experiment showed that the density of solid color
fabrics can be inspected automatically [1] . However, the method can
be only applied for solid color fabrics, and it can’t inspect the
density of the fabrics with more than two colors. Figure 1 shows
one sample of the fabric with four colors. It’s obviously that gray-
projection can not be applied to the regions including more that two
color yarns. The methods for measuring the fabric density
mentioned in literature [2-7] can not inspect the density of fabric with
more than two colors.
Fig. 1 Fabric image with several color yarns.
In Part I, we divided the color fabrics into two categories: one
group is single-system-mélange color fabric as shown in Figure 1.
There are more that two colors in the fabric. But one group of yarns,
weft or warps, are constituted by one kind of color yarns. For
example, the warps in the fabric shown in Figure 1 are all white
yarns, while the wefts are composed by four kinds of different color
yarns.
Fig. 2 Double-system-mélange color fabric image.
Another group is double-system-mélange color fabric as
shown in Figure 2. It is also composed by more that two kinds of
color yarns. But both the wefts and warps are made up by more than
two kinds of color yarns. In this study, we just discuss the method
for inspecting the density of the first category. The second category,
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of course, the most complicated fabrics, will be discussed in future
study.
FCM algorithm has been used to analyze the color segmentation
for printed fabrics in RGB color model [8] . By the unsupervised
clustering method, the colors were classified successfully. We have
tried to use an improved FCM algorithm to segment the colors in
yarn-dyed fabrics in HSL color space [9] . But in further study, we
found that RGB and HSL color models have their own fault for
color classification. And the experiment shows that in these two
color spaces, some color fabric images can not be classified with
satisfied results. Take the fabric shown in Figure 1 as an example,
the colors are classified with FCM algorithm in HSL and RGB
color space, and the classification results were shown in Figure 3.
Compared with the original image, it can be seen that the blue
and gray yarns have been segmented, but the green and white yarns
are not segmented successfully in the two color spaces. The borders
of the green and white yarns in the classification results are very
vague, and it is hard to locate the yarns with color classification
results. The expectation results have not been obtained. In order to
find the reasons, we checked the fabric image in Photoshop
software, and found that the white and green yarns in Figure 1 have
similar hue and intensity values. Therefore, it is hard to separate
them from each other in RGB and HSL color spaces. In order to
solve this problem, CIE-Lab color space is proposed to classify the
colors in the fabric image with FCM algorithm. With the color
segmentation results, the fabric image can be segmented into
different blocks, and the yarns are located in different blocks with
different means. The fabric density can be obtained by counting the
yarns in a unit length with an automatic method at last.
(a) RGB color model (b)HSL color model
Fig. 3 Color classification results of fabric image.
2. CIE-Lab Color Model
Compared with RGB and HSL color models, Lab color model is
designed to approximate human vision. Its model is shown in
Figure 4. Lab model aspires to perceptual uniformity, and its L
component closely matches human perception of lightness. It can

thus be used to make accurate color balance correction by
modifying output curves with a and b components, or adjusting the
lightness contrast using L component. But in RGB color model or
HSL color model, it is hard to realize these.
Fig. 4 Lab Color Space.
2.1 Conversation From RGB to Lab
In the computer, the image is expressed or saved in RGB color
model. To use Lab color model, the first step is to convert the image
from RGB to Lab color space in the experiment. To complete the
conversion, the fabric image should first be changed to XYZ color
model. The conversion method is given as follows:
(1)r=R/255
(2)
⎛r+ 0.055 ⎞
if(
r > 0.04045) r = ⎜ ⎟
⎝ 1.055 ⎠
r
else r =
12.92
To obtain g, b, the G, B components are processed in the same
way.
⎡X⎤ ⎡0.4124 0.3576 0.1805⎤
⎡r⎤ (3) ⎢Y ⎥ = ⎢0.2106 0.7125 0.0722⎥⋅⎢g⎥
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎢⎣Z⎥⎦ ⎢⎣0.0193 0.1192 0.9505⎥⎦
⎢⎣b⎥⎦ After then, the image can be converted to Lab from RGB color
space with the help of XYZ color model in follow steps:
(1) f( X 0.008856) x X
else
16
x = 7.787 × X +
116
1
3
i > = ,
(2)Y, Z components are processed as X component in step 1, and we
can get y, z.
⎧ L = 116 × y−16
(3) ⎪
⎨a
= 500 × ( x− y)
⎪
⎩b
= 200 × ( y− z)
After the conversion, L, a, b are all belong to [-128, 128],
thus cluster method can be used to classify the colors in the singlesystem-mélange
color fabric image with Lab color space. The Lab
image of the sample fabric is shown in Figure 5. The green and
white yarns which are difficult to classify in RGB and HSL color
space, are now easily to distinguish in Lab image. And it provides
the foundation of segmentation for the color yarns in single-systemmélange
color fabrics.
2.2 Conversion from Lab to RGB
To show the segmentation results, the fabric image should be
changed back from Lab to RGB color space. The method is similar
as mentioned above. It is the inverse process. The fabric image
2.4
,
52
should first be changed to XYZ color model, and then converted
back to RGB color model to shown on the screen.
Fig. 5 Lab Image of Figure 1.
3. Fuzzy C-Means Clustering Method
In the color segmentation and pattern recognition, clustering is
one of the most important processes. Among the clustering
methods, Fuzzy C-Means clustering method (FCM) is most famous.
FCM algorithm [10] is an unsupervised clustering method. The
clustering method attempts to minimize the objective function by
organizing the data into different clusters. The objective function is
as follow:
c n
∑∑
m
JUV ( , ) = uij x −v
i= 1 j=
1
j i
where n is the number of data; c is the cluster number; U is the
memberships degree matrix; V is the cluster centers matrix; u ij
expresses the membership degree of the data point x j belonging to
the ith fuzzy group. u ij satisfies these two conditions:
u ∈ [0,1], i = 1,2,..., c and
ij
c
∑
i=
1
u = 1, j = 1,2,..., n.
m ∈ (1, +∞ ) is a weighting exponent that influences the
fuzziness of the clusters. It controls the sharing degree between
different cluster groups.
FCM algorithm often starts with an initial guess for the cluster
centers [11] which is intended to mark the mean location of each
cluster. The initial guess for these cluster centers will most likely be
incorrect. So in the experiment we choose to initial the membership
matrix. The FCM algorithm is implemented as follows [12] :
(1)Choose the cluster number c, the weighting exponent m and the
terminative precision ε .
(2)Initialize the membership degree matrix U (0) and set the iteration
counter t=1.
(3)Update the cluster center matrix using membership degree
matrix:
n
i = ∑
m
ij
n
m
j / ∑ ij , = 1,2,...,
j= 1 j=
1
v u x u i c
(4)Update the membership degree matrix U, and set t=t+1..
u
ij
2
−1
⎡ ⎤
c m−1
⎢ ⎛ d ⎞ ij ⎥
∑
=
⎢ ⎜
⎟
k = 1 d ⎟ ⎥
⎝ kj ⎢ ⎠
⎣ ⎥⎦
If d = 0 , u = 1,
and u = 0( i ≠ k)
.
kj
kj
ij
Here
d x v
2
ij = || i − j || .
ij
2

( t+ 1) ( t)
(5)If U −U ≤ ε , stop the iteration, otherwise go to step 3.
4. Experiments
4.1 Fabric Image Acquisition
A Microtek flat scanner was used to digitize the single-systemmélange
color fabric image with a resolution of 1200 DPI. Just as
the solid color fabric, in order to reduce the color differentiation on
the fabric’s appearance, the capture region was selected far from the
edge of the fabric, and the surface of fabric should be clarity in the
experiment.
4.2 Detect The Skew Angle of Yarns
According to the method discussed in previous study, Hough
transform is used to detect the skew angles of warps and wefts, and
they are marked as θ warp and θ weft , where θ warp represents the
skew angle of warps while θ weft is the skew angle of wefts.
4.3 Color Classification in Lab Color Space
As discussed above, the fabric image is converted from RGB to
Lab color model, and then FCM algorithm is used to classify the
colors in fabric image. Take the fabric image shown in Figure 1 as
an example, set the cluster number c =4, weighting exponent m =2,
the terminative precision ε =0.001. The color classification result is
shown in Figure 6.
Fig. 6 Color classification result in Lab color space.
From Figure 6, it can be found that Lab color space has its
inherent advantages in color classification. Compared with the
results in RGB and HSL color spaces as shown in Figure 3, the
color segmentation result in Lab color space is more superior.
However, there still are some gray pixels in the white yarn block in
the result. It may be caused by undulating weave structure or other
reasons. In order to eliminate these pixels, the image was converted
from RGB model to gray model. Closed operation was used to
process the image in gray model. A 3× 3 filter was selected in the
experiment. The processing result was shown in Figure 7. From the
figure, it can be seen that the noise has been removed successfully.
Fig. 7 Closed operation processing result.
4.4 Divide The Fabric Image into Different Blocks
With the color classification results, the fabric can be divided
into several blocks which include one kind of weft yarns. As one
group of the yarns is composed of one color, it is easy to locate the
yarns in different blocks. The warps in the fabric shown in Figure 1
are all white yarns. With the skew angles which have been detected,
53
the fabric image can be divided into eleven blocks as shown in
Figure 8.
Fig. 8 Eleven blocks of the fabric image.
From the figure, it is observed that the blocks can be divided
into two categories. One group is A, E, K, the wefts and the warps
are the same color in these blocks. Another group is B, D, F, G, H,
I, J, the warps and wefts have different colors. The yarns can be
located in different blocks with different means, and then fabric
density can be inspected.
5. Results and Discussion
5.1 Weft Segmentation
The regions where the wefts and warps have the same color can
be seen as solid color fabric. This kind of fabric has been discussed
in Part I. With the gray-projection method, the yarns can be
segmented successfully.
The gray-projection can not be applied for the blocks where
wefts and warps have different colors, such as Block I. In order to
locate the yarns in these blocks, correlation coefficient method is
introduced into the inspection process. Suppose X, Y are two
independent vectors, the correlation coefficient r of X, Y can be
defined as:
( X − X) ⋅( Y −Y)
r =
,
D( X) ⋅ DY ( )
where X , DX ( ) is the mean value and variance value of vector
X , and Y , DY ( ) is the mean value and variance value of vector
Y .
r ∈− [ 1,1] is the correlation coefficient of X, Y , it represents
correlation degree between the two vectors .
With the skew angle which has been detected, the coordinate of
the pixels in the fabric image can be transformed according to the
method that has been discussed in Part I of the study. Suppose ij P
is the gray level of the pixel ( i, j ) , set X = ( P , P , P , ⋅⋅⋅ , P ) ,
i0 i1 i 2 iw
Y = ( P , P , P , ⋅⋅⋅ , P ), j = i+
1.
X, Y represent the adjacent
j 0 j1 j 2 jw
rows of pixels in the fabric image. The correlation coefficient of
X, Y then would be calculated. Take the Block I as an example,
the correlation coefficients are shown in Figure 9.
It is obvious that if the two rows are in the same yarn, r is
closed to 1. If the two rows lied in the interstices between two
yarns, the correlation coefficient r must be the minimum value
among the adjacent points in Figure 9. Compare with Block I, the
valley points in Figure 9 are corresponding to the interstices in the

fabric image. The yarns can be located by finding the local
minimums in Figure 9.
Fig. 9 Correlation coefficients of the adjacent rows.
However, there are some error local minimums in the curve. In
order to eliminate these points, a 1× 5 filter [0, 0,1, 0, 0] was used
in the experiment. If the point is the minimum among the adjacent
five points, it was considered as the true minimum which represents
the interstice between yarns. Blocks B, D, F, G, H, J are processed
with the same method then. Combine with segmentation results of
blocks A, E, K, the wefts in the fabric image are all segmented
successfully as shown in Figure 10(a).
5.2 Warp Segmentation
The segmentation of warps can also be divided into two cases.
Just as the weft segmentation, the block as A, E, K is considered as
solid color fabric. It can be extended into the entire image. The
block which composed by different color yarns can be inspected
with the correlation coefficient method. The warps of the fabric
shown in Figure 1 are segmented successfully in Figure 10(b).
(a) Weft segmentation result (b)Warp segmentation result
Fig. 10 Yarn segmentation results.
5.3 Inspect Fabric Density
As the wefts and warps are all located in the fabric image, the
fabric density can be obtained by counting the yarns in a unit
length. The fabric density is also measured with a textile analysis
magnifying glass manually. The results measured by these two
methods are compared in Table 1. From the table, it can be seen the
error is just 0.1 thread. The result measured by image analysis is
very close to manual measuring result. This fact proves that the
method proposed in this study can be used to measure the fabric
density instead of the traditional means.
Table 1: The measurement of fabric density
Warp density[thd/inch] Weft density[thd/inch] Error[%]
Automatic Manual Automatic Manual Warp Weft
82.6 82.5 128.6 128.5 0.12 0.1
6. Conclusions
The method for inspecting the single-system-mélange color
fabric density was discussed in this study. The fabric sample shown
in this study has same color warps and different color wefts. The
density of the fabric with same color wefts and different color
warps can also be detected with this method by adjusting the
algorithm.
In this study, FCM algorithm is proposed to classify the colors
for the fabric in Lab color space. By the color classification results,
the fabric image can be divided into different blocks with same
54
color or different colors. And the gray-projection and correlation
coefficient methods are used to locate the yarns in different blocks.
The wefts and warps were located and the density was obtained by
counting the yarns in a unit length finally. The experiment result
proved the algorithm proposed can inspect the density of singlesystem-mélange
color fabric successfully.
Till then, we have completed the measurement of the density for
solid color fabrics and single-system-mélange color fabrics.
According to the classification of fabrics mentioned in Part I, we
still have to inspect the density of double-system-mélange color
fabrics. It is the most complicated fabric which discussed in this
study, and the method will be described with detail in Part III of this
study.
Acknowledgement
The authors are grateful for the financial supported by the
Fundamental Research Funds for the Central Universities
(No.JUSRP21105) and the National Natural Science Foundation of
China (No.61040046).
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