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APPLIED PROBLEMS Defect Detection in Textile Fabric Images Using Wavelet Transforms and Independent Component Analysis1 A. Serdaroglu*, A. Ertuzun*, and A. Ercil** *Bogazici University, Turkey e-mail: serdaroa@boun.edu.tr; ertuz@boun.edu.tr **Sabanci University, Turkey e-mail: aytulercil@sabanciuniv.edu Abstract—In this paper, a new method based on the use of wavelet transformation prior to independent com- ponent analysis for solving the problem of defect detection in textile fabric images is presented. Different sub- bands of the wavelet packet tree scheme of the defect-free subwindows are obtained and independent compo- nents of these subbands are calculated as basis vectors. The true feature vectors corresponding to these basis vectors are computed. The test subwindow is labeled as defective, or not according to the Euclidean distance between the true feature vector representing the non-defective regions and the feature vector of the subwindow under test. The advantage of adding wavelet analysis prior to the independent component analysis is presented. DOI: 10.1134/S1054661806010196 1 1. INTRODUCTION the data. The representation achieved by ICA facilitates the analysis of the data encountered in such ﬁelds like, Automated industrial inspection systems based on data compression, pattern recognition, de-noising [5]. hardware and/or software tools are increasingly being The basic ICA model is shown as installed in factories in order to increase the quality and speed of production of the products. One of the industry x = As, (2.1) ﬁelds where automated visual inspection systems are where x is the random vector containing the mixtures, s most needed is the textile industry. In this work, a new is the random vector containing the sources, and A is method that combines the concepts of wavelet transfor- the mixing matrix. No a priori information about the mation and Independent Component Analysis (ICA) mixing matrix and sources are known. In order to make for defect detection problem in textile images, is pre- the problem of estimating the independent components sented. Both of the above concepts are proved to pos- by observing only the mixtures x solvable, the sources sess good performance capacities in various ﬁelds such s must be assumed to be independent from each other as biomedical engineering, signal and speech process- with each having a nongaussian probability distribu- ing. The aim of this study is to ﬁnd the independent tion. The sources s can be estimated after ﬁnding the components of the wavelet transform of textile fabric de-mixing matrix B given in Eq. (2.2): images for the purpose of defect detection. It is intended to be a continuum of the studies done on the s = Bx. (2.2) detection defects in textile fabric images by Atalay [1], Meylani et al. [2] who used adaptive two-dimensional The demixing matrix can be estimated by maximi- lattice ﬁlters, Latif-Amet et al. [3] who used subband zation of the nongaussianity of the sources. As the non- domain co-occurrence matrices and Sezer et al. [4] who gaussianity of the mixtures is increased, they become used ICA based methods. statistically more independent from each other [6]. Hurri et al. [7] have presented some results in apply- ing ICA to image data. The aim of ICA is to make the 2. INDEPENDENT COMPONENT ANALYSIS image pixels as mutually independent as possible. ICA aims to ﬁnd a linear transformation of the orig- An image subwindow I(x, y) can be represented as a inal data such that the new representation is one that linear sum of its basis functions (i.e., independent com- minimizes the statistical dependence of the components ponents) which can be extracted by ICA. present in the representation. ICA tries to ﬁnd the hid- n ∑ a ( x, y )s. den components that capture the essential structure of I ( x, y ) = i (2.3) 1 The text was submitted by the authors in English. i=1 Here, ai (x, y) are called basis functions, and the si con- stitute the feature vector that will be used in the pro- Received October 25, 2004 posed defect detection system. ISSN 1054-6618, Pattern Recognition and Image Analysis, 2006, Vol. 16, No. 1, pp. 61–64. © Pleiades Publishing, Inc., 2006. 62 SERDAROGLU et al. number of desired independent components. Dimen- AA AH HA HH sion reduction decreases the computation time. Dimen- AV AD HV HD sion reduction is performed by Principal Component Analysis (PCA). Let m represent the number of desired VA VH DA DH independent components. In PCA, m eigenvectors with the m highest eigenvalues of the covariance matrix of X VV VD DV DD are chosen. In such a way, the size of X is reduced to m × 10000. Fig. 1. 2-D wavelet packet tree decomposition. As mentioned previously, the feature vectors used are nothing but coefﬁcients of the independent compo- nents; namely, the si’s in Eq. (2.3) constitute the feature 3. WAVELET PACKETS vectors. By multiplying each 10000 subwindow by the The decomposition of a signal can be done via the k de-mixing matrices, which are found by the ICA algo- conventional method of wavelet transform and is called rithm, 10000 feature vectors, s, are extracted for each pyramid structured wavelet transform [8]. Each time subband. This makes a total of k feature vectors for a the low frequency band is split, the other bands are not subwindow. The size of s is m × 1. In order to ﬁnd the used. This is suitable for signals with most of their strue vector, which is the true feature vector representing energy concentrated in the low frequency regions. the clean regions, the mean of those 10000 feature vec- However, for some signals, energy is concentrated in tors (coefﬁcients of the independent components) are the middle frequencies. In this case, we have to split all taken for each subband. This makes a total of k strue vec- the bands. This is called wavelet packet decomposition. tors. A two-dimensional wavelet packet tree decomposition In the detection part, the de-mixing matrix found in and the terminology used in this paper are shown in Fig. 1. the feature extraction part is used. The image to be tested is divided into N × N non-overlapping subwin- dows making a total of 2562/N2 subwindows, since the 4. METHODOLOGY size of each fabric image is 256 × 256. Each subwin- Our defect detection system consists mainly of two dow is multiplied by k de-mixing matrices, and the cor- parts: feature extraction and detection. In the feature responding s vectors (feature vectors) are obtained. The extraction part, a true feature vector is aimed to be Euclidean distances between these vectors and the k extracted by training the system with clean regions of strue vectors are found. If the mean of the k distances is the fabric images. The feature vector of a test subwin- above the threshold value determined by Eq. (4.1), the dow is compared with the true feature vector in the corresponding subwindow is said to be defective, oth- detection part. The general methodology is as follows: erwise it is said to be non-defective. This procedure is As a ﬁrst preprocessing step, the mean of every done for all the test windows. image is subtracted from itself, and then every image is divided by its variance in order to make the ICA estima- α = D m + η ( D u – D l ), (4.1) tion better conditioned [5–6]. The aim of this project is where Dm is the median value of distances, (Du – Dl) is to apply subband analysis prior to ICA. The procedure the inter-quartile range and η is a constant determined is as follows: 10000 subwindows of size N × N are experimentally. Mahalanobis distance measure is also taken from random points of the defect free images, and tried, and it is observed that both distance measures these subwindows are converted into column vectors lead to similar detection rates. each of size N2 × 1. After the subwindows of the defect- free image(s) are extracted, the subbands of these The performance rate of defect detection is calcu- image subwindows are decomposed. These subbands lated by the following formula: are extracted by 2-level wavelet transformation. Detection Rate (%) = 100 × (NCC + NDD)/Ntolal. (4.2) According to the application, one or more subbands can be taken from the possible 16 subbands of the 2-level Here, NCC is the number of subwindows classiﬁed as wavelet packet tree scheme. Writing those column vec- being non-defective when they are actually non-defec- tors as the columns of a matrix forms a data matrix X of tive; NDD is the number of subwindows classiﬁed as size N2 × 10000. Let k represent the number of sub- being defective when they are indeed defective, and bands taken during the algorithm. There will be k X Ntotal is the total number of subwindows. matrices each composed by a different subband of the image subwindows. Since 2-level wavelet transforma- 5. IMPLEMENTATION AND RESULTS tion is used, this means that the resulting size of the subband will be (N/4) × (N/4). This makes the size of In all the experiments, 16 non-defective and 18 defec- each X matrix (N2/16) × 10000. tive images are used. After the data acquisition part, the dimension of the Experiment 1: First the defects are detected using data may be reduced to a number that is equal to the only an ICA. 16 independent components are extracted PATTERN RECOGNITION AND IMAGE ANALYSIS Vol. 16 No. 1 2006 DEFECT DETECTION IN TEXTILE FABRIC IMAGES USING WAVELET TRANSFORMS 63 with a window size of 16 × 16. The extracted indepen- dent components are shown (Fig. 2). Experiment 2: Subband analysis prior to ICA is performed. The data matrix X is formed by the AA sub- bands of the subwindows. The wavelet transformation is performed by 16-tap Daubachies wavelet ﬁlters. Bat- tle–Lémarie wavelet ﬁlters, symlets, coiﬂets, Haar, dis- crete Meyer, and biorthogonal wavelets are also tried. However, the best performance is provided by 16-tap Fig. 2. Independent components of defect free textile fabric Daubachies wavelet ﬁlters. 16 independent compo- images. nents are extracted, and the subwindow size is taken as 16 × 16. In order to prevent overlearning and increase the defect detection rate, the number of independent components is reduced to 8 by PCA. Experiment 3: Many reasonable combinations of subbands from the 2-level wavelet packet tree scheme are used. The best results are obtained by taking the AA subband. This is due to the fact that most of the energy is stored in this band. Taking all of the four subbands in the left quarter of the wavelet packet tree (i.e. the AA, Fig. 3. Intensity defects obtained by using 1 subband (left), AH, AV, and AD subbands) gave a satisfactory detec- and 4 subbands (right) with 16 ICs. tion rate, yet not as good as that of the case where only the AA subband was taken. There are mainly two types of defects: intensity defects, where the gray level values of the defective parts are different from those of the overall image and geometrical defects, where not the gray level value but the textural characteristics are dif- ferent from those of the general fabric image. It is found that while the method where only the AA subband is used leads to better detection rates for intensity defects, in order to obtain a satisfactory defect detection rate for geometrical defects, the aforementioned 4 subbands Fig. 4. Geometrical defects obtained by using 1 subband must be used. This phenomenon can be observed in (left), and 4 subbands (right) with 16 ICs. Figs. 3 and 4 where defect detection is performed for intensity defects and for geometrical defects, respec- tively. So, the best parts of both methods are taken by Application 2: WICA_1SB_16IC_WS 16 decision fusion. Decision fusion of the two methods are Application 3: WICA_4SB_16IC_WS16 performed by combining the detected defects of the two methods by the logical OR operator. In this manner, we Application 4: W_1SB_WS16 obtained the best results among all the other methods. Application 5: W_4SB WS16 Below is the summary of the experiments that give Application 6: WICA_1SB_8IC_WS16 thorough information about what subband analysis Application 7: WICA_4SB_8IC_WS16 adds upon ICA. The following abbreviations are used in order to name the applications in short hand: Application 8: WICA_1SB_5IC_WS16 Application 9: WICA_4SB_5IC_WS16 WS: Window Size; SB: Number of Subbands used; Application 10: DecFus_16IC_WS16 IC: Number of Independent Components; ICA: Inde- Application 11: DecFus_8IC_WS16 pendent Component Analysis; W: Wavelet Transform; Application 12: WICA_1SB_8IC_WS32 WICA: Wavelet applied prior to ICA; DecFus: Deci- sion Fusion of two methods where in one method only Application 13: WICA_4SB_8IC_WS32. the AA subband is used, and in the other method all the In applications 4 and 5 only wavelet transformation AA, AH, AV, and AD subbands are used. is used. This is accomplished by building the feature vector of a subwindow by the energies of the chosen subbands. In the last two applications, the window size The applications are as follows: is chosen as 32 × 32. A comparison of the defect detec- Application 1: ICA_16IC WS 16 tion rates of all the methods is shown in Fig. 5a. The PATTERN RECOGNITION AND IMAGE ANALYSIS Vol. 16 No. 1 2006 64 SERDAROGLU et al. Defect detection rate, % 6. CONCLUSIONS 100 (a) Defect detection rates of applications 1–13, A new method, which combines concepts of wavelet 99 η is optimized per method transformation and ICA for defect detection, is pre- 98 sented. It can be concluded that applying wavelet anal- 97 ysis prior to ICA increases the defect detection rate compared to the use of wavelet transformation or ICA 96 alone. 95 94 REFERENCES 93 1. A. Atalay, “Automated Defect Inspection of Textile Fab- 92 rics Using Machine Vision Techniques,” MS Thesis 91 ° (Bo g aziçi University, 1995). 90 2. R. Meylani, C. Öden, A. Ertüzün, A. Erçil,“2-D Itera- 1 2 3 4 5 6 7 8 9 10 11 12 13 tively Reweighted Algorithm for Adaptive Detection of Application number Defects in Textured Images,” to appear in IEICE Trans- (b) actions on Fundamentals of Electronics Communica- 1.0 Probability of defect detection versus tions and Computer Sciences (2006). Application 1 probability of false alam 0.9 Application 2 “Texture Analysis Using Adaptive Two-Dimensional Lattice 0.8 Application 3 ° Filters,” MS Thesis (Bo g aziçi University, Istanbul, Tur- Application 4 0.7 key, 1997). Application 5 0.6 Application 6 3. A. Latif Amet, A. Ertüzün, and A. Erçil, “An Efﬁcient 0.5 Application 7 Method for Texture Defect Detection: Subband Domain Application 8 0.4 Co-Occurrence Matrices,” Image Vis. Comput., 6, 543– Application 9 0.3 Application 10 553 (2000). 0.2 Application 11 4. O. G. Sezer, A. Ertuzun, and A. Ercil, “Independent 0.1 Application 12 Component Analysis for Texture Defect Detection,” Pat- Application 13 tern Recognition and Image Analysis 14 (2), 303–307 0 0.1 0.2 0.3 0.4 0.5 (2004). Fig. 5. (a) Defect Detection Rates of applications. 5. A. Hyvarinen and E. Oja, “Independent Component (b) Receiver Operating Curves. Analysis: Algorithms and Applications,” Neural Net- works, 411–430 (2000). Receiver Operating Curves (ROCs) are plotted 6. A. Hyvarinen, “Survey on Independent Component (Fig. 5b) for the sake of comparison. Analysis,” Neural Computing Surveys, 94–128 (1999). For practical purposes, the η value used in determin- 7. J. Hurri, A. Hyvarinen, J. Karhunen, and E. Oja, “Image ing the decision threshold given by Eq. (4.1) is opti- Feature Extraction Using Independent Component Anal- mized per method. That is to say, the optimum value for ysis,” http://citeseer.nj.nec.com/hurri96image.html. η is found for a method. The user of this system can 8. T. Chang and J. Kuo, “Texture Analysis and Classiﬁca- simply substitute this optimum η value for the method tion with Tree-Structured Wavelet Transform,” IEEE he uses no matter what the fabric images are. Trans. Image Process. 2 (4), 429–441 (1993). PATTERN RECOGNITION AND IMAGE ANALYSIS Vol. 16 No. 1 2006

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