Fabric Defect Detection in Stockwell Transform Domain

Transcription

1 Sensors & Transducers, Vol. 69, Issue 4, April 4, pp. 4- Sensors & Transducers 4 by IFSA Publishing, S. L. Fabric Defect Detection in Stockwell Transform Domain * Cuifang ZHAO, Yuetong QIN, Changjiang ZHANG, Jiyang HU College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, 34, China Lanxi Quality and Technical Supervision and Inspection Center of Zhejiang Province, 3, China * xx98@zjnu.cn Received: 7 January 4 Accepted: 7 March 4 Published: 3 April 4 Abstract: To improve the accuracy and speed of the fabric defect detection, a novel and automated algorithm is proposed in this paper. The method is based on the Stcokwell transform (or S-transform, ST), a mathematical operation that provides the frequency content at each time point within a time-varying signal. Firstly, gray level integral projection is performed on the fabric image data to obtain a one-dimensional space series. Secondly, the space series for every point at horizontal or vertical direction is subjected to the S transform to obtain a timefrequency spectrum. A function multiplying the S-transform coefficients in low frequencies is defined, which can effectively restrain the texture background, depress the noise and enhance the defect signal. Finally, the adaptive thresholds in the frequency space and the spatial space based on the S-transform coefficients are presented for defect detection. Experimental results show that the proposed algorithm can accurately detect and locate the defects for the real fabric images. The proposed method is simple, robust and easy to implement in real time systems. Copyright 4 IFSA Publishing, S. L. Keywords: S-transform, Time-frequency analysis, Fabric defect detection, Textile industry.. Introduction Inspection is important for the fabric quality control in the textile industries. It usually depends on human, which is limited by some factors such as subjective judgment, inattentiveness, overworked, etc. Sari-Sarraf and Goddard [] have found that only about 7 % of fabric defects could be detected by the most highly trained inspectors. Therefore, in order to lower the cost of the inspection process, to improve products quality and to increase the competitive advantage of the products under the fast production speeds, it is essential to develop an efficient and real-time automated inspection system. In recent years, image-based automated inspection methods have attracted a lot of attention, which can be summarized as four major categories: learning, model-based, statistical and spectral algorithm [, 3]. For leaning-based approach, such as Neural networks [4] and SVM [], has a fatal flaw that their reliability on a large database. For model-based algorithm, such as Autoregressive model and Markov random field model, is insensitive to the translation of pattern on texture, but sensitive to very small width defects and easily affected by the lighting due to similarity between the defects and leather background. In statistical approach, the fabric images are partitioned into the image blocks by various representations, such as auto-correlation function, cooccurrence matrices, the fractal dimension, and Gray Article number P_3 4

2 Sensors & Transducers, Vol. 69, Issue 4, April 4, pp. 4- Level Co-occurrence Matrix (GLCM). The defect detection is based on the different characters of the image blocks. There are two main weaknesses that sensitivity with block size and intensive computer requirements due to large number of adjacency pixels in calculation. Zuo [6] uses NL-means filtering algorithm for texture enhancement where GLCM is used with Euclidean distance to find defects. He shows overall detection rate of %. Raheja [7] has implemented GLCM based method on DSP kit. The GLCM has been proved to be a promising method for image texture analysis. What s more, there are some methods similar to GLCM have been applied to wood inspection [8], surface defect detection [9], and fabric defect detection. However, GLCM scheme has a disadvantage that it can work only in invariant condition. Spectral methods are particularly suitable for the fabric defect detection such as Fourier analysis [], Wavelet filters [ - 3] and Gabor filters [4, ] due to the high degree of periodicity of yarns in textile fabric. The spatial domain is usually noise sensitive and arduous to locate defects. Fourier-based methods utilize the frequency domain to characterize the defects. As the basis functions of Fourier transform are sinusoids, wavelet transforms are based on small waves of varying frequency, which offers a multi-resolution decomposition information (more local support than Fourier transform). As it is hard for a wavelet base to describe a texture pattern from the wavelet coefficients, Gabor filter attempts the optimal joint localization in spatial and spatialfrequency domains. Gabor filter is a frequency and orientation of selective Gaussian envelope. It can capture a specific band of frequency components from an image and extract directional features. Han [4] uses Gabor filter with GA to detect fabric defects. Shu [] details a method of detecting the fabric defects automatically based on multi-channel and multi-scale Gabor filtering. However, Gabor filter approach has a high computation complexity which limits the application in real time system. The S-transform [6] is an extension of the ideas of the continuous wavelet transform (CWT) and is based on a moving and scalable localizing Gaussian window. It is unique in that it provides frequencydependent resolution while maintaining a direct relationship with the Fourier spectrum. These advantages are due to the fact that the modulating sinusoids are fixed with respect to the time axis, whereas the localizing scalable Gaussian window dilates and translates. In recent years, there has been an increasing number of research articles making use of the S-transform to study applied problems in timefrequency analysis [7, 8]. In this paper, a new spatial frequency spectrum method for the image-based fabric defect detection in S-Transform domain is proposed. This method would reduce the computational time and improve the accuracy for defect detection. It is organized as follows. In the next section, the S-Transform and its time-frequency analysis will be reviewed. The characteristic of the fabric defect in the frequency spectrum using the S-transform will be examined and some defect examples will be described. Then the procedures of the method will be discussed in Section 3. Section 4 presents the experimental results and depicts the evaluation and comparison results of different algorithm. Finally the conclusion of the paper is reported in Section.. S-transform.. Basic Concepts The S-transform, presented in 996 [6], provides a full time-frequency decomposition of a signal. The S-transform of a signal h (t) is defined as the Fourier transform (FT) of the product between h (t) and a Gaussian window function: f ( τ t) f iπft S( τ, f ) = h( t) e e dt, () π where f is the frequency, τ and t are the time variables, and τ controls time axis position of Gaussian window. In this way, the S-transform decomposes a signal into temporal (τ) and frequency components. The inverse of S-transform is defined as + + iπft h t) = ( S( τ, f ) dτ ) e df () ( Using the equivalent frequency-domain definition of the S-transform, the Discrete Stcokwell transform (DST) [9] can be written (making f n / NT andτ jt ): S[ jt, n NT π m N m + n n ] = H[ ] e e M = NT ( j, n, m =,,... N ), iπmj N, n (3) where H[] is the DFT of h[], T is the temporal sampling intervals, N is the temporal sampling point, m is the discrete serial number of frequency shift factors, n is the discrete serial number of frequency values, j is the discrete serial number of τ. If n= voice, it is equal to the constant defined as m S [ jt,] = h[ ] (4) N NT N M = This equation makes the constant average of the time series into the zero frequency voice, so it will make sure that the inverse is exact. 46

3 Sensors & Transducers, Vol. 69, Issue 4, April 4, pp. 4- The discrete form of formula () is iπnk N N N n h[ kt ] = S[ jt, ] e N m= m= NT ().. Time-frequency Analysis Generally, the singular signal has two aspects: frequency change and amplitude change [8]. In time domain, by influence of noise and other signals, it couldn t distinguish singular signal accurately. In frequency domain, it can distinguish different signals but cannot obtain accurate location information. The S-transform is a powerful time-frequency method which represents a significant improvement over existing techniques for localizing spectral information in a wide variety of signal processing environments. It has an advantage in that it provides multi resolution analysis while retaining the absolute phase of each frequency component of the signal. y (t) is a model signal and it is defined as π cos( ( t )) π cos( ( t 6)) π y = cos( ( t )) π cos( ( t 4)) 3 π cos( ( t )) t =,,...,6 t = 6,6,..., t =,,...,4 t = 4,4,..., t =,,...,3 (6) Fig. shows waveform of the model signal y (t) and shows the time-frequency spectral contour map of y (t) in S-transform domain Time.4. Time Fig.. Time-frequency analysis of the model signal in S-transform domain. It can be seen that the S-transform domain timefrequency spectral can clearly distinguish the different frequency signals. It can be concluded that the S-transform domain fully shows the information of original signal corresponding with original signal location. 3. The Proposed Method 3.. Characteristic Analysis of Fabric Defect in S-Transform Domain Faultless fabric is a repetitive and regular global texture. When a defect occurs in the fabric, its regular structure is destroyed so that the corresponding intensity at some specific positions of the frequency spectrum would change. The S-transform can be applied to monitor the spatial frequency spectrum of a fabric. On one hand, it is known that the four-dimensional data would be gotten from the two-dimensional image after the S-transform. However, the four-dimensional frequency spectrum is very difficult to analyze. On the other hand, the singularity of the fabric defect in one line is not obvious. Using the integral projection method to accumulate the gray level can effectively make the singularity outstanding while maintaining the periodic regular global structure of the texture background. At the same time, the twodimensional image changes into the one-dimensional signal, which benefit for detection based on the S-transform. Let a two-dimensional image be f(x, y), which is a real function representing the gray level in x, y spatial coordinates, and let the image width be M and the image height be N. x and y are the horizontal and vertical coordinates of a pixel. The vertical integral projection of f(x, y), denoted by P V (y), is a discrete function: M x= P ( y) = f ( x, y) (7) V The horizontal integral projection of f(x, y), denoted by P H (x), is defined in a similar way: N = P H ( x) f ( x, y) (8) y= In the textile production lines, the broken stitching is relatively the common defect. For the weft-knitted fabrics P V (y) can be selected, and for the warp-knitted fabrics P H (x), can be selected. The warp-knitted fabric images are taken as example for the method mentioned in this paper. Fig. shows the original warp-knitted fabric images with different textures captured from textile production line. Fig. 3 depicts the horizontal integral projection P H (x) obtained from Fig. after gray integral projection. The abscissa indicates row pixel position, and ordinate indicates gray-level 47

4 Sensors & Transducers, Vol. 69, Issue 4, April 4, pp. 4- accumulated amplitude. As can be seen from Fig. 3, the gray-level accumulation signal at normal texture exhibits a certain periodicity and mutation occurs at the defect points. background. It is well known that lower frequencies have longer periods, it stands to reason that lower frequencies can cope with lower sampling rates. That is to say, there are great difference magnitude of frequency spectrum between the defects and the texture background under low-frequency. As illustrated in Fig. 4, the S-transform coefficient modulus under the higher frequencies appear a certain periodicity at normal texture points, and the S-Transform coefficient modulus under the lower frequencies appear significant differences between the defects and the normal texture. Based on the above characteristics, the S-transform temporal frequency analysis can be introduced to the defects detection Fig.. The original fabric images x x x Fig. 4. The S-transform coefficient modulus S(x, f) of Fig Thresholding 3... Space 3 3 Fig. 3. The horizontal integral projection P H (x) obtained from Fig.. Fig. 4 illustrates the three-dimensional timefrequency diagrams of S-transform coefficient modulus S (x, f) of the signals shown in Fig. 3. The abscissa indicates row pixel position, and ordinate indicates frequency. The lightness of the diagrams means the amplitude of the S-transform coefficient. In general, the fabric defects occur infrequently and have no periodicity comparing with the texture Based on the preceding discussion, the S- transform coefficients of low-frequency can be used to distinguish the defects and the texture background. Fig. shows the modulus S(x, f) of Fig. 4 under single frequency fp and Fig. 6 show the multifrequency products S ft (x) of Fig. 4, where: S ft ( x) = ft f = S( x, f ) (9) As can be seen from Fig., it is difficult to find out signal break point from the modulus under a single frequency. And Fig. 6 shows that the texture background can be suppress and the odd and break 48

5 Sensors & Transducers, Vol. 69, Issue 4, April 4, pp. 4- points of defect positions are amplified by multiplying the modulus in low frequencies. It is possible to improve the signal to noise ratio by finetuning the ft. f= f= f= f= Fig.. S(x, f) under a fixed frequency. f, ft = f, ft = Fig. 7. The frequency level histogram of Fig. 4. f, ft = f, ft = Fig. 6.The multi-frequency products SfT (x). The frequency threshold ft selection is critically important, which cannot be too small for the detection performance and cannot be too larger for the computational complexity. An adaptive frequency threshold method is adopted by using a frequencylevel histogram in ST domain, which represents the number of frequency corresponding to modulus maxima at each point. The histogram with frequency levels in the range [, N-] is a discrete function h (fk) = nk, where fk is the k th frequency level and nk is the number of points having frequency level fk. The frequency level fk can be listed as follows: f k = arg max S( x, f ), f [, M ] () where S(x, f) is the modulus at spatial point x(x=,,m-). Fig. 7 shows the frequency level histogram of Fig. 4. Obviously, two dominant modes characterizes the frequency level histograms. The frequency threshold ft can be decided based on the first bottom Spatial Space Multiplying a variety of frequency coefficients based on ST domain can highlight the defect signal. The thresholding segmentation is used for defect signal detection. A thresholded signal g(x) is defined as ifs ft ( x) > T g( x) = () ifs ft ( x) < T We computed the spatial domain signal segmentation threshold T using the following expression: T = μ + λσ, () where µ represents the global mean of the signal S ft (x) and σ represents the standard deviation. We chose the factor λ somewhat by trial and error to determine the strictness of the defect detection test Implementation of the Method The proposed scheme for detecting defects in fabric images may be summarized by the following procedure: ) Apply the median filter method into the image preprocessing. Let F( x, y) replaces the value of a pixel by the median of the gray levels in the neighborhood of that pixel. { f ( s, t) } F( x, y) = Median (3) ( s, t) S x, y ) Computer the horizontal integral projection P(x) of F(x, y) according to Equation (8) for the warpknitted fabric images. 3) Take the S-transform of P(x). Let S(x, f) denote the (x, f) th S-transform coefficient. 4) Calculate the frequency threshold ft using the frequency-level histogram. 49

6 Sensors & Transducers, Vol. 69, Issue 4, April 4, pp. 4- ) Computer the multi-frequency products S ft (x) according to Equation (9). 6) Calculate the spatial threshold value T from Equation (). 7) Use Equation () to get g(x). 8) Judgment: the fabric image has defect points when the sum of g(x) is larger than zero, and no defect points when the sum of g(x) is equal to zero. N x= n X = g( x) > g( x) = have no (4) Fig. 8~ shows the characteristic extracted from the warp-knitted fabric images shown in Fig. by the different methods. As it can be seen that the features selected by our method can better characterize the difference between the defect and the background, which is more conducive to defect detection. Fig. ~3 illustrates the detection results of the methods. It is shown that the proposed method outperforms the rest.. Note that the processing for the weft- knitted fabric images should change the second step: to solve the vertical integral projection P (y) of F (x, y) according to Equation (7). When detecting the defects such as the broken hole, dirty spot etc., it should synthesis the results obtained in two orthometric directions Experimental Results 4 To verify the effectiveness of the proposed algorithm, some fabric images taken from real situations are selected, the size of which is 6 8. This new algorithm is compared to two earlier algorithms (the Wavelet-based method proposed in the paper [3], the GLCM-based method proposed in the paper [8]). The performances are shown in Fig. 8~3. 3 Fig. 9. The characteristic extracted from the warp-knitted fabric images shown in Fig. by the Wavelet-based method x x x 3 3 x 37 3 x x 43 Fig. 8. The characteristic extracted from the warp-knitted fabric images shown in Fig. by the proposed method x Fig.. The characteristic extracted from the warp-knitted fabric images shown in Fig. by the GLCM-based method (The window size is 3 3).

7 Sensors & Transducers, Vol. 69, Issue 4, April 4, pp. 4- The Wavelet-based method is heuristically selected to capture the most outstanding features of defects, the accuracy rate of which is not high enough compared with the others. It can not correctly detect the defects shown in Fig. and Fig.. The Wavelet-based method has a weakness that poor performance in textures constructed by large-sized primitive. In GLCM-based method, the samples are of size and all images in the paper [8] are of good quality, but all images in our paper are not so good. The defect detection results are shown in Fig. 3 with size 3 3. Fig. 3. The results of the images shown in Fig. by the GLCM-based method (λ=3). Table. Computed time. Fig.. The results of the images shown in Fig. 8 by the proposed method (λ=3). DWT (ms) GLCM (ms) ST (ms) Fabric Fabric Fabric Fabric Fabric Fabric Table lists the computer costs of the different methods. It is obvious that the computer time of the proposed method in this paper is the least, and GLCM is the largest. As S-transform can be calculated using the Fourier transform, it is easy to realize in real time system. 6. Conclusions Fig.. The results of the images shown in Fig. 9 by the wavelet-based method (λ=3). It is obvious that the window size of GLCM has poor ability to adapt the structure of different fabric images, which is the most important factor for the detection results. In this paper, we have explored some alternatives for improving both the speed and accuracy of the traditional fabric defect detection method. The spectral information of the S-transform is, with slight modification, extracted to characterize the features of the fabric defects from real image samples. It has been shown that these features can be used to correctly classify the normal and abnormal textures, as these features are based on magnitude, frequency, and time of the disturbance signal. The excellent time-frequency resolution characteristic of the S-transform makes it an attractive candidate for analysis of the fabric defects detection. Some fabric defects are detected using the proposed method, the wavelet method and GLMS method, showing clearly the advantage of the S-transform in detecting and localizing the defect detection problem.

8 Sensors & Transducers, Vol. 69, Issue 4, April 4, pp. 4- Finally, we are working on applying the technique to different types of the fabric images from the current real-world. We are actively working with some textile industries to integrate our image detection system into manufacturing lines. Acknowledgements The authors wish to thank the Education Department of Zhejiang Province in China for supporting this research through grand number Z334, and the Science and Technology Department of Zhejiang Province in China for also supporting this research through grand number C3. References []. S. H. Sari-Sarraf, J. S. Goddard, Vision systems for on-loom fabric inspection, IEEE Transactions on Industry Applications, Vol. 3, Issue 6, 999, pp. -9. []. S. K. L. Mak, P. Peng, K. F. C. Yiu, Fabric defect detection using morphological filters, Image and Vision Computing, Vol. 7, Issue, 9, pp [3]. Henry Y. T. Ngan, Grantham K. H. Pang, Nelson H. C. Yung, Automated fabric defect detection-a review, Image and Vision Computing, Vol. 9, Issue 7,, pp [4]. S. J. K. Chandra, P. K. Banerjee, A. K. Datta, Neural network trained morphological processing for the detection of defects in woven fabric, Journal of the Textile Institute, Vol., Issue 8,, pp []. T. D. Shumin, L. Zhoufeng, L. Chunlei, Ada Boost Learning for Fabric Defect Detection Based on HOG and SVM, in Proceedings of the International Conference on Multimedia Technology (ICMT'), 6-8 July, pp [6]. T. W. Zhang, Q. Zhao, L Liao, Development of a real-time machine vision system for detecting defeats of cord fabric, in Proceeding of the International Conference on Computer Application and System, -4 October, pp [7]. T. H. Zuo, Y. Wang, X. Yang, X. Wang, Fabric defect detection based on texture enhancement, in Proceedings of the th International Congress on Image and Signal Processing (CISP), 6 8 October, pp [8]. S. J. L. Raheja, B. Ajay, A. Chaudhary, Real time fabric defect detection system on an embedded DSP platform, Optik, Vol. 4, 3, pp [9]. S. R. W. Conners, C. A. Harlow, A theoretical comparison of texture algorithms, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-, Issue. 3, 98, pp. 4. []. S. C. H. Chan, G. K. H. Pang, Fabric defect detection by Fourier analysis, IEEE Transactions on Industry Applications, Vol. 36, Issue,, pp []. Y. Han, P. Shi, An adaptive level-selecting wavelet transform for texture defect detection, Image and Vision Computing, Vol., Issue 8, 7, pp []. S. Stephane Mallat, Wen Liang Hwang, Singularity Detection and processing with wavelets, IEEE Transactions on Information Theory, Vol. 38, Issue, 99, pp [3]. S. D. Bin, B. Rui-Lin, L. Ying, C. Wen-Da, On-line Vision-based Fabric Inspection Algorithm, Journal of Jiangnan University (Natural Science Edition), Vol., Issue,. [4]. T. H. Runping, Z. Lingmin, Fabric defect detection method based on Gabor filter mask, WRI Global Congress on Intelligent Systems, 9 May 9, pp []. T. Y. Shu, Z. Tan, Fabric defects automatic detection using Gabor filters, in Proceedings of the th World Congress on Intelligent Control and Automation, Hangzhou, China, -9 June, 4, pp [6]. S. R. G. Stockwell, L. Mansinha, R. P. Lowe, Localization of the complex spectrum: the S-transform, IEEE Transactions on Signal Processing, Vol. 44, Issue 4, 996, pp [7]. S. A. Benammar, R. Drai, A. Guessoum, Ultrasonic flaw detection using threshold modified S-transform, Ultrasonics, Vol. 4, Issue, 4, pp [8]. S. P. Sanchez, F. G. Montoya, F. Manzano- Agugliaro, C. Gil, Genetic algorithm for S-transform optimization in the analysis and classification of electrical signal perturbations, Expert Systems with Applications, Vol. 4, Issue 7, 3, pp [9]. S. R. G. Stockwell, Why use the S-transform? Fields Institute Communications Series, American Mathematical Society, Vol., 7, pp Copyright, International Sensor Association (IFSA) Publishing, S. L. All rights reserved. (