DEFECT DETECTION IN FABRIC IMAGES USING SINGULAR VALUE DECOMPOSITION TECHNIQUE

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1 DEFECT DETECTION IN FABRIC IMAGES USING DECOMPOSITION TECHNIQUE T.D.Venkateswaran 1 Research Scholar, Department of Computer Science, Madurai Kamaraj University, Madurai, India. thadanvenkateswaran@gmail.com G.Arumugam2 Senior Professor and Head, Department of Computer Science, Madurai Kamaraj University, Madurai, India. gurusamyarumugam@gmail.com 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 R n n, where R represents the real number domain, then SVD of A is defined as A = U S V T where U R n n and V R n n are orthogonal matrices, and S R n n is a diagonal matrix, as Here diagonal elements i.e. σ s are singular values and satisfy σ 1 σ 2. σ r σ r+1 = = σ n =0 It is noticeable that the unique property of the SVD transform is that the potential N 2 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 351

2 If SVD operation is applied on this matrix, then the matrix A will be decomposed into equivalent three matrices as follows: 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. Here diagonal elements of matrix S are singular values and we notice that these values satisfy the non increasing order: 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; 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 A T have the same non-zero singular values. Flip: A, row-flipped A rf, and column-flipped A cf have the same non-zero singular values. Rotation: A and A r (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 L 1 λ. 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 L 2 λ. If D is row-scaled by L 1 times, and column-scaled by L 2 times, for each non-zero singular value λ of A, D has square root of L 1 L 2 λ Translation: A is expanded by adding rows and columns of black pixels. The resulting matrix A e has the same non-zero singular values as A. Because of these properties, SVD may be used as a tool to develop semiblind 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 352

3 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 defectfree 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 353

4 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 LOAD THE TEST TEXTURE IMAGE NOISE REDUCTION USING MEDIAN FILTER CONVERT THE RGB IMAGE TO GRAY SCALE IMAGE FIN D THE FIRST USING DECOMPOSITION DEFECT FREE TEST TEXTURE IMAGE COMPARE THE FIRST WITH REFERENCE IMAGE NO IF DEFECT DETECTED? END YES DEFECTIVE TEST TEXTURE IMAGE [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 [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 [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 [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 [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 [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 [7] B.H. Khalaj and T. Kailath, Patterned wafer inspection by high resolution spectral estimation 354

5 techniques, Mach. Vision and Appl., Vol.7, 1994, [10] Jain A K, Image Analysis and Computer Vision, pp PHI, New Delhi, 1997 [8] P. Xie and S.U. Guan, A golden-template selfgenerating method for patterned wafer inspection, Mach. Vision and Appl., Vol.12, 2000, pp [9] Gonzalez, R., R. Woods and S. Eddins, Digital Image Processing Using MATLAB. 1st Edn., Prentice Hall, TABLE I S OF SYNTHETIC FABRIC IMAGES SYNTHETIC FABRIC TEXTURES FIRST DIFFERENCE TRADITIONAL INSPECTION PROPOSED METHOD CLEAN REFERENCE FABRIC DEFECT FREE DEFECT FREE HOLE DEFECT DEFECTIVE DEFECTIVE STAIN DEFECT DEFECTIVE DEFECTIVE MISS-PICK DEFECT DEFECTIVE DEFECTIVE MISS-END DEFECT DEFECTIVE DEFECTIVE DOUBLE-PICK DEFECT DEFECTIVE DEFECTIVE DOUBLE-END DEFECT DEFECTIVE DEFECTIVE WEFT-FLOAT DEFECT DEFECTIVE DEFECTIVE WARP-FLOAT DEFECT DEFECTIVE DEFECTIVE COURSE-PICK DEFECT DEFECTIVE DEFECTIVE COURSE-END DEFECT DEFECTIVE DEFECTIVE THIN-PICK DEFECTIVE DEFECTIVE THIN-END DEFECTIVE DEFECTIVE IRREGULAR WEFT DENSITY DEFECTIVE DEFECTIVE CLEAN REFERENCE FABRIC HOLE DEFECT STAIN DEFECT MISS-PICK DEFECT MISS-END DEFECT DOUBLE-PICK DEFECT DOUBLE-END DEFECT WEFT-FLOAT DEFECT WARP-FLOAT DEFECT COURSE-PICK DEFECT COURSE-END DEFECT THIN-PICK THIN-END Figure II Pictorial representation of Table I IRREGULAR WEFT DENSITY Series1 355

6 TABLE II S OF REAL FABRIC IMAGES REAL FABRIC TEXTURES FIRST DIFFERENCE TRADITIONAL INSPECTION PROPOSED METHOD DEFECT FREE REFERENCE DEFECT FREE DEFECT FREE HOLE DEFECT DEFECTIVE DEFECTIVE STAIN DEFECTIVE DEFECTIVE MISS-PICK DEFECTIVE DEFECTIVE MISS-END DEFECTIVE DEFECTIVE DOUBLE-PICK DEFECTIVE DEFECTIVE DOUBLE-END DEFECTIVE DEFECTIVE WARP-FLOAT DEFECTIVE DEFECTIVE COURSE-PICK DEFECTIVE DEFECTIVE WEFT DENSITY DEFECTIVE DEFECTIVE TEAR DEFECTIVE DEFECTIVE CONTAMINATION DEFECTIVE DEFECTIVE SNARL DEFECTIVE DEFECTIVE DEFECT FREE FABRIC DEFECT FREE DEFECT FREE DEFECT FREE REFERENCE HOLE DEFECT STAIN MISS-PICK MISS-END DOUBLE-PICK DOUBLE-END WARP-FLOAT COURSE-PICK WEFT DENSITY TEAR CONTAMINATION SNARL DEFECT FREE FABRIC Figure III Pictorial representation of Table II Series1 356