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DEFECT DETECTION IN FABRIC IMAGES USING SINGULAR VALUE
DECOMPOSITION TECHNIQUE
T.D.Venkateswaran1
Research Scholar, Department of Computer Science, Madurai Kamaraj University, Madurai, India.
G.Arumugam2
Senior Professor and Head, Department of Computer Science, Madurai Kamaraj University, Madurai,
India. [email protected]
Abstract
Defect detection is one of the problems in image processing and many different methods based on
texture analysis have been proposed. In this paper, a
method is proposed for detecting defects in fabric
image textures based on singular value decomposition
technique. The proposed approach applied first in
artificially simulated fabric textures and then real
fabric textures. The proposed algorithm shows good
result to detect all types of defects occurred in fabric
images. High detection rate and low computational
complexity are advantages of this proposed approach.
1. Introduction Visual quality inspection system play an important
role in many industrial and commercial applications
such as tiles, metal, agricultural products, fabric, ceramic, paper and etc. Any hole, damage,
abnormalities and slot in products surfaces are called
defect. Ghazini et al. proposed a defect detection
approach of tiles using combination of two dimensional
wavelet transform and statistical features. Henry et al.
used ellipsoidal region features and min-max technique
on patterned fabric for detecting defects. Ch. Lin et al.,
described a texture defect detection system based on
image deflection compensation. Tolba used a
probabilistic neural network (PNN) for fast defect
classification based on the maximum posterior
probability of the Log-Gabor based statistical features.
Alimohammadi et al., proposed a new method using
optimal Gabor filters to detecting skin defect of fruits
which was usable in agricultural products visual quality
inspection systems (APVQIS). Some of defect
detection approaches are compared by Xie et al. The computational complexity of most of previous
approaches is too high and some of them don’t
guarantee an accurate result for every model of defects.
So in this article, an approach is proposed to defect
detection without these problems.
1.1 Singular Value Decomposition (SVD)
SVD is an effective mathematical tool used to analyze
matrices. In SVD transformation, a matrix can be
decomposed into three matrices that are of the same
size as the original matrix. From the view point of
linear algebra, an image is an array of non-negative scalar entries that can be regarded as a matrix. Without
loss of generality, if A is a square image, denoted as A∈
Rn×n , where R represents the real number domain, then
SVD of A is defined as
A = U S VT
where U ∈ Rn×n
and V ∈ Rn×n
are orthogonal
matrices, and S ∈ Rn×n
is a diagonal matrix, as
Here diagonal elements i.e. σ’ s are singular values
and satisfy
σ1 ≥ σ2 ≥…. σr ≥ σr+1 ≥ =……= σn=0
It is noticeable that the unique property of the SVD
transform is that the potential N2 degrees of freedom or
samples in the original image now get mapped into:
S ⇒ N Degrees of freedom,
U ⇒ N (N -1) / 2 Degrees of freedom,
V ⇒ N (N -1) / 2 Degrees of freedom, totaling N
2 degrees of freedom.
SVD is an optimal matrix decomposition technique
in a least square sense that it packs the maximum signal
energy into as few coefficients as possible. It has the
ability to adapt to the variations in local statistics of an
image.
1.2 SVD Example As an example to clarify SVD transformation,
suppose A
T D Venkateswaran et al, Int.J.Computer Technology & Applications,Vol 5 (2),351-356
IJCTA | March-April 2014 Available [email protected]
351
ISSN:2229-6093
If SVD operation is applied on this matrix, then the
matrix A will be decomposed into equivalent three
matrices as follows:
Here diagonal elements of matrix S are singular
values and we notice that these values satisfy the non
increasing order: 77.9523 ≥ 27.5619 ≥ 1.3349.
1.3 Properties of SVD Generally a real matrix A has many singular values,
some of which are very small, and the number of
singular values which are non-zero equals the rank of
matrix A. SVD has many good mathematical
characteristics. Using SVD in digital image processing
has some advantages:
i) The size of the matrices from SVD transformation
is not fixed and can be a square or a rectangle. ii) The SVs (Singular Values) of an image have very
good stability, i.e. when a small perturbation is added
to an image; its SVs do not vary rapidly;
iii) SVs represent algebraic image properties which are intrinsic and not visual.
As for example, figure 1(a) and 1(b) show an image
and the same image after Gaussian blur of size 9x9
respectively. The highest five singular values of the
original image and the Gaussian blurred image are
presented in the table which clearly shows that the
singular values are almost same i.e. the changes in the
singular values are very small which demonstrate the
good stability of the singular values of an image even
after the manipulation on the image.
Fig1(a)original image Fig 1(b) Gaussian blurred image
Here we have presented an analysis of the effects of
ordinary geometric distortions on the singular values of
an image:
• Transpose: Every real matrix A and its transpose
AT have the same non-zero singular values.
• Flip: A, row-flipped Arf, and column-flipped Acf
have the same non-zero singular values.
• Rotation: A and Ar (A rotated by an arbitrary
degree) have the same non-zero singular values.
• Scaling: B is a row-scaled version of A by
repeating every row for L1 times. For each non-zero
singular value λ of A, B has square root of L1λ
. C is a column-scaled version of A by repeating
every column for L2 times. For each non-zero singular value λ of A, C has square root of L2λ
. If D is row-scaled by L1 times, and column-scaled
by L2 times, for each non-zero singular value λ of A, D
has square root of L1 L2λ
• Translation: A is expanded by adding rows and
columns of black pixels. The resulting matrix Ae has the
same non-zero singular values as A. Because of these
properties, SVD may be used as a tool to develop semi-
blind watermarking schemes.
This paper is organized as follows. In section II, we
review the literature in the area of defect detection in
fabric image. In section III, we give the proposed defect
detection algorithm using singular value decomposition
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technique. In section IV, we give the results and discussions and in section V we provide the conclusion
for this paper.
2. LITERATURE REVIEW Methods that are found in literature for the
inspection of patterned texture images include the
traditional image subtraction methods [6-10], the
method of golden image subtraction (GIS) [1], the
method of wavelet-preprocessed golden image
subtraction (WGIS) [1], the method of Direct-
Thresholding (DT) based on wavelet transform [1], the
Bollinger Bands method [2], the Regular Bands
method, the Local Binary Pattern (LBP) method [3],
and the motif-based methods [4, 5].
The basic GIS method involves a training stage with lot of defect-free samples and a testing stage [1]. In the
training stage, the energy of the golden image
subtraction, which is defined as the sum of absolute
difference between the golden image (a template unit of
size that is more than that of the periodic unit) and a
histogram-equalized reference image (defect-free
image) over a given window, is obtained at every pixel
location. Thresholds are obtained from several defect-
free images. In the testing stage, energies obtained from
the golden image and the defective test images are
compared with the thresholds obtained from the
training stage to find the defects after using a median
filter or Weiner filter to perform filtering. The method
was tested with 30 defect-free and 30 defective pmm
images. The detection success rates obtained for the
pmm images are 100% for defect-free images and
56.67% for defective images. The overall success rate was found to be 78.33%. In order to conquer the
sensitivity of this method to noise, the WGIS method
was developed [1]. This is similar to the GIS method
expect that a Haar wavelet transform is applied over all
the images and the sub-images (in level-1
approximation) are utilized instead of the original
image. The overall success rate was improved to
96.7%.
The traditional image subtraction method developed
by Chin and Harlow for the examination of printed
circuit boards involves a direct subtraction of the image
that is under inspection with a defect-free template
image [6]. Since this method involves pixel to pixel
comparison, it is sensitive to noises and distortions.
Khalaj et al. developed a method of inspecting
patterned wafers based on periodicity estimation using
a gray value projection and a reference image that is constructed from the input image itself using the
average gray values of all the periodic units [7].
Pixel-to-pixel comparison between the test image
and the reference or template image, which is based on
an assumed threshold, helps in identifying the defects.
Xie and Guan presented a similar method, wherein the building block needed for constructing a reference
image is extracted based on linear interpolation [8].
However, when the defect size in the image is too
large, the building block constructed based on the
methods recommended in [7, 8] can never be a good
estimate of the true value.
In the method of DT [1], the Haar wavelet transform
is applied to the reference images and the fourth level
horizontal and vertical details are extracted. Lower and
upper bound values of the three horizontal details in
level-4 and also vertical details are extracted and their
averages are calculated after filtering. Thresholds
obtained using these horizontal and vertical details in
the training stage with defect-free images are utilized in
the testing stage for finding the defects in pmm images.
The detection success rates were found to be 86.77%
for defect-free images and 90% for defective images.
The overall detection success rate was found to be 88.3%.
Fabric defect detection using the modified local
binary pattern (LBP) [3] involves two stages, namely,
the training stage and the defect detection stage. In the
training stage, the LBP operator is applied to an image
of defect-free fabric pixel-by-pixel, and a reference
feature vector is computed. The defect-free fabric is
then divided into several windows of size that are
slightly more than that of periodic unit and an LBP
operator is applied to each of these windows to get a
suitable threshold from the defect-free image. In the
detection stage the defective fabric is divided into
several windows (as in the training stage) and LBPs are
obtained. Defects are then located in the fabric based
on the threshold. The method was tested on pmm, p2,
and p4m images and the detection success rate was
found to be 96.7%. Ngan et al. [4, 5] developed motif-based methods
for detecting defective lattices from 16 out of 17
wallpaper groups based on energy and the variance of
the hand-located lattices. Minimum- maximum
decision boundaries (rectangular boundaries) are
obtained in an energy variance space from several
defect-free test images using hand-located defect-free
and defective lattices that are said to be composed of
motifs[4]. The energy of the moving subtraction
between a motif and its circular shift matrices is
derived using a norm-metric measurement and the
variance of the energies for all motifs is obtained. By
learning the distribution of these values over a number
of defect-free lattices, boundary conditions for
discerning defective and defect free lattices are
obtained. As the 16 wallpaper groups of patterned
fabric can be transformed into three major groups, namely, pmm, p2, and p4m, the method was evaluated
T D Venkateswaran et al, Int.J.Computer Technology & Applications,Vol 5 (2),351-356
IJCTA | March-April 2014 Available [email protected]
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ISSN:2229-6093
over these three major wallpaper groups. Decision boundaries were obtained using 160 defect-free lattices
samples and the method was tested with 140 defect-free
and 113 defective samples. An overall detection
success rate of 93.3% was achieved.
3. PROPOSED ALGORITHM
The steps for proposed Defect Detection Algorithm are
as follows:
Load the Test Texture image in BMP or JPEG Format.
Reduce the noises in Test Texture image using
median filter.
Convert the Test Texture image to Gray scale
image.
Find the first singular value using singular
value decomposition technique.
Compare the singular value with the reference
image.
If the difference is greater than detection
sensitivity level (D), declare that test fabric
image is defective; otherwise test fabric image
is defect free.
The flowchart of the Algorithm is shown in Figure I.
4. RESULTS AND DISCUSSIONS
Table I shows the values of first singular value of a
synthetic fabric texture image for different types of
defects presence in fabrics. . The value of D is within
20 for fabric texture image to declare defect free;
otherwise the fabric texture image declared defective. Figure II shows the pictorial representation of Table I
The real fabric texture images show vast difference in
singular values if the defect presence in the fabrics
compare to synthetic fabric images. Figure III shows
the pictorial representation of Table II
5. CONCLUSION
In this paper, singular value decomposition technique
has been effectively used for the development of the
automated defect detection scheme for fabric texture
images. Experiments on real fabric images with defects
show that the proposed method is robust in finding
fabric defects. Thus, the proposed method can
contribute to the development of computerized defect detection in fabric industries.
Figure I Flowchart of Defect Detection algorithm
REFERENCES
[1] H.Y.T. Ngan, G.K.H. Pang, S.P. Yung and M.K.
Ng, “Wavelet based methods on patterned fabric defect detection,” Pattern Recognit., Vol.38, No.4, 2005,
pp.559-576.
[2] H.Y.T. Ngan and G.H.K. Pang, “Novel method for
patterned fabric inspection using Bollinger bands,”
Opt. Eng., Vol.45, No.8, 2006, pp.087202-1-15.
[3] F. Tajeripour, E. Kabir and A. Sheikhi, “Fabric
Defect Detection Using Modified Local Binary
Patterns,” Proc. of the Int. Conf. on Comput. Intel. and
Multimed. Appl., Sivakasi, Tamilnadu, India,
December, 2007, pp.261-267.
[4] H.Y.T. Ngan, G.H.K. Pang and N.H.C. Yung,
“Motif-based defect detection for patterned fabric,”
Pattern Recognit., Vol.41, No.6, 2008, pp.1878-1894.
[5] H.Y.T. Ngan and G.H.K. Pang, “Ellipsoidal
decision regions for motif-based patterned fabric defect
detection,” Pattern Recognit., Vol.43, No.6, 2010,
pp.2132-2144. [6] R.T. Chin and C.A. Harlow, “Automated visual
inspection: A survey,” IEEE Trans. on Pattern Anal.
and Mach. Intel., Vol.4, No.6, 1982, pp.557-573.
[7] B.H. Khalaj and T. Kailath, “Patterned wafer
inspection by high resolution spectral estimation
LOAD THE TEST TEXTURE IMAGE
NOISE REDUCTION USING MEDIAN FILTER
COMPARE THE FIRST SINGULAR VALUE WITH
REFERENCE IMAGE
CONVERT THE RGB IMAGE TO GRAY SCALE IMAGE
FIN D THE FIRST SINGULAR VALUE USING SINGULAR
VALUE DECOMPOSITION
IF DEFECT
DETECTED?
DEFECT FREE TEST TEXTURE
IMAGE
DEFECTIVE TEST TEXTURE
IMAGE
END
NO YES
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IJCTA | March-April 2014 Available [email protected]
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ISSN:2229-6093
techniques,” Mach. Vision and Appl., Vol.7, 1994, pp.178-185.
[8] P. Xie and S.U. Guan, “A golden-template self-
generating method for patterned wafer inspection,”
Mach. Vision and Appl., Vol.12, 2000, pp.149-156.
[9] Gonzalez, R., R. Woods and S. Eddins, 2004.
“Digital Image Processing Using MATLAB”. 1st Edn.,
Prentice Hall,
[10] Jain A K,”Image Analysis and Computer Vision”, PHI, New Delhi, 1997
TABLE I SINGULAR VALUES OF SYNTHETIC FABRIC IMAGES SYNTHETIC FABRIC
TEXTURES
FIRST
SINGULAR
VALUE
SINGULAR
VALUE
DIFFERENCE
RESULT OF
TRADITIONAL
INSPECTION
RESULT OF
PROPOSED
METHOD
CLEAN REFERENCE FABRIC 44236 0 DEFECT FREE DEFECT FREE
HOLE DEFECT 43200 1036 DEFECTIVE DEFECTIVE
STAIN DEFECT 44216 20 DEFECTIVE DEFECTIVE
MISS-PICK DEFECT 45941 1705 DEFECTIVE DEFECTIVE
MISS-END DEFECT 45635 1399 DEFECTIVE DEFECTIVE
DOUBLE-PICK DEFECT 46203 1967 DEFECTIVE DEFECTIVE
DOUBLE-END DEFECT 46208 1972 DEFECTIVE DEFECTIVE
WEFT-FLOAT DEFECT 44425 189 DEFECTIVE DEFECTIVE
WARP-FLOAT DEFECT 44406 170 DEFECTIVE DEFECTIVE
COURSE-PICK DEFECT 44622 386 DEFECTIVE DEFECTIVE
COURSE-END DEFECT 44876 640 DEFECTIVE DEFECTIVE
THIN-PICK 44591 355 DEFECTIVE DEFECTIVE
THIN-END 44451 215 DEFECTIVE DEFECTIVE
IRREGULAR WEFT DENSITY 44069 167 DEFECTIVE DEFECTIVE
4150042000425004300043500440004450045000455004600046500
CLEA
N R
EFE
RENCE F
ABRIC
HO
LE D
EFE
CT
STAIN
DEFE
CT
MIS
S-P
ICK D
EFECT
MIS
S-E
ND D
EFECT
DO
UBLE
-PIC
K DEFE
CT
DO
UBLE
-END D
EFE
CT
WEFT-F
LOAT D
EFEC
T
WARP-F
LOAT D
EFE
CT
CO
URSE-P
ICK D
EFE
CT
CO
URSE-E
ND D
EFE
CT
THIN
-PIC
K
THIN
-END
IRREGULA
R W
EFT DENSIT
Y
Series1
Figure II Pictorial representation of Table I
T D Venkateswaran et al, Int.J.Computer Technology & Applications,Vol 5 (2),351-356
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ISSN:2229-6093
TABLE II SINGULAR VALUES OF REAL FABRIC IMAGES
REAL FABRIC TEXTURES FIRST
SINGULAR
VALUE
SINGULAR
VALUE
DIFFERENCE
RESULT OF
TRADITIONAL
INSPECTION
RESULT OF
PROPOSED
METHOD
DEFECT FREE REFERENCE 47175 0 DEFECT FREE DEFECT FREE
HOLE DEFECT 45272 1903 DEFECTIVE DEFECTIVE
STAIN 46383 792 DEFECTIVE DEFECTIVE
MISS-PICK 47387 212 DEFECTIVE DEFECTIVE
MISS-END 44730 2445 DEFECTIVE DEFECTIVE
DOUBLE-PICK 42983 4192 DEFECTIVE DEFECTIVE
DOUBLE-END 47631 456 DEFECTIVE DEFECTIVE
WARP-FLOAT 47506 331 DEFECTIVE DEFECTIVE
COURSE-PICK 46849 326 DEFECTIVE DEFECTIVE
WEFT DENSITY 45818 1357 DEFECTIVE DEFECTIVE
TEAR 44757 2418 DEFECTIVE DEFECTIVE
CONTAMINATION 46647 528 DEFECTIVE DEFECTIVE
SNARL 45504 1671 DEFECTIVE DEFECTIVE
DEFECT FREE FABRIC 47182 7 DEFECT FREE DEFECT FREE
40000
41000
42000
43000
44000
45000
46000
47000
48000
DEFE
CT F
REE R
EFE
RENCE
HO
LE D
EFE
CT
STAIN
MIS
S-P
ICK
MIS
S-E
ND
DO
UBLE
-PIC
K
DO
UBLE
-END
WARP-F
LOAT
CO
URSE-P
ICK
WEFT D
ENSIT
Y
TEAR
CO
NTA
MIN
ATIO
N
SNARL
DEFE
CT F
REE F
ABR
IC
Series1
Figure III Pictorial representation of Table II
T D Venkateswaran et al, Int.J.Computer Technology & Applications,Vol 5 (2),351-356
IJCTA | March-April 2014 Available [email protected]
356
ISSN:2229-6093