INTRODUCTION

Fabric defect detection is one of the most important procedures effecting the manufacturing efficiency and quality in fabric industry. Traditional inspection based on human vision is labor-intensive and lack of consistency and reliability. As the development of image processing technology, many methods base on machine vision are proposed and a good summarization and taxonomy of those methods can be found (Kumar, 2008). Because of the high degree of periodicity of the fabric texture, the spectral approaches are appealing for the task of defect detection. Fourier transform was used for this task in (Chan and Pang, 2000; Tsai and Hsieh, 1999). However, Fourier transform turns out to be suitable for globe defects rather than local ones, because of its poor local resolution in the frequency domain. Therefore, some defect detection algorithms based on Gabor filters were proposed to achieve optimal joint localization in both spatial and frequency domain (Kumar and Pang, 2000a, 2002; Bodnarova et al., 2002; Escofet et al., 1998). As Gabor filter banks are not mutually orthogonal, the outputs of the filter banks are significantly correlated. Wavelet analysis is a good solution to this problem (Nadhim, 2006) which is widely used for and image segmentation (Zhang et al., 2008), image compression (Venkateswaran and Rao, 2007), texture characterization (Loum et al., 2007) and classification (Raju et al., 2008). Several fabric defect defection methods based on wavelet transform were proposed using orthogonal wavelet basis (Jasper et al., 1996; Sari-Sarraf and Goddard Jr., 1999; Yang et al., 2001, 2002).

In this study, fabric defect detection using wavelet transform is further investigated. The undecimated discrete wavelet transform is used to achieve shift-invariant property. Multi-scale analysis of wavelet is used to provide multi-resolution representation of defects. And an adaptive selection scheme of decomposition scales is proposed to enhance the energy distinction between the defective and non-defective regions. The performance of different decomposition scales for each kind of popular defects is also evaluated. Several features based on the energy estimation are extracted and used to discriminate the defect from normal texture.

UNDECIMATED DISCRETE WAVELET TRANSFORM (UDWT)

Standard discrete wavelet transform (DWT) is not suitable for detect detection, as it is not shift-invariant. A defect in different displacement of a fabric image may result in different wavelet coefficients which possibly lead to different detection results. So UDWT is used in this study.

Fig. 1:	2D undecimated wavelet transform

It gives a complete but redundant representation of signal (Unser, 1995). The most important advantage of UDWT is its shift-invariant property which is desirable for fabric defect detection. Compare to DWT, UDWT does not down-sample the wavelet coefficients, instead it up-samples the high-pass and low-pass filters of the wavelet by inserting zeros. The implementation of 2D UDWT is illustrated in Fig. 1, where A_j denotes wavelet approximation at scale j. W_ij denotes wavelet coefficients at scale j along orientation i, where i = 1,2,3 denote horizontal, vertical and diagonal orientation, respectively. h_j[n] and g_j[n] denote the low-pass and high-pass filters at scale j, where:

(1)

(2)

↑denotes up-sample by inserting zeros.

DEFECT DETECTION ALGORITHM

The block diagram of defect detection is shown in Fig. 2. In the proposed algorithm the defect is assumed to be local, not global. The essence of the proposed algorithm is to discriminate the defect from normal texture by examining the defective energy within a sub region. Preprocess is used to make the original fabric image zero mean so that both the dark pixels and bright pixels which defects are usually made up of, have larger energy than the normal background. UDWT, amplitude division and data fusion are used to enhance the energy of the defect and attenuate the energy of normal background. Then the energy features are extracted and defects are detected by thresholding.

Fig. 2:	Block diagram of defect detection

Wavelet selection scheme: For every preprocessed fabric image, UDWT is used for multi-scale decomposition. For almost all the defect detection tasks using wavelet transform, the most important issue is the selection of wavelet. There are two fundamental problems with selection of wavelet. The first is selection of wavelet basis. The second is selection of decomposition scales. Wavelet coefficients at different scales contain different parts of information of fabric image. It is needed to select some scales which can best represent defects in the image. The larger number of scales selected corresponds to higher computational costs, on the other hand insufficient or improper selection of scales may lose some information of certain defects which makes them difficult to detect.

To detect defects of different kinds, Yang et al. (2001) designed an adaptive wavelet basis for each kind of defects and a set of wavelet bases were used for multiple kinds of the defects which greatly increase computational load. Jasper et al. (1996) and Yang et al. (2002) designed an adaptive wavelet basis to characterize fabric texture and only one scale was used so that multi-resolution representation of the defect was not provided. Sari-Sarraf and Goddard Jr. (1999) used Daubechies D2 (Daubechies, 1988) wavelet basis and selected decomposition scale manually by human observation. The scale at which the normal texture is significantly attenuated while the defect is still visually intact is selected. This involves participation of human vision which may not desirable. In this study we also use Daubechies D2 wavelet basis, because of its low computational complexity as well as its similarity of corresponding 2-D kernel with the fabric weave pattern and the decomposition scale is set adaptive to the fabric texture. The proposed scale selection scheme is based on the following two conceptions. First, the defect, within its boundary, tends to have lower intensity variation than normal texture (Sari-Sarraf and Goddard Jr., 1999) which means the main energy of the defect lies in lower frequency region than the normal texture in the frequency domain. Second, the objective of wavelet transform is to enhance the energy of defective region and attenuate the energy of non-defective region.

Because the normal texture of fabric exhibits high degree of periodicity, it has large energy nearby a certain frequency point which we claimed as Textural Inherent Frequency Point (TIFP), along each orientation in the frequency domain. TIFP is located at the reciprocal of the texture periodicity along each orientation. As the decomposition scale increases, the passband of high-pass filter of UDWT decreases by a step of an octave which is shown in Fig. 3. Let the upper cut-off frequency of high-pass filter of Daubechies wavelet be FC at scale 1, then its upper cut-off frequency at scale j will be FC/(2^j-1). In order to enhance the energy of defective region and attenuate the energy of non-defective region, the frequency region of defects should be in the passband of high-pass filter and the TIFP of normal texture should be in the stopband of high-pass filter along each orientation which means the desirable scales to be selected must meet the following condition:

(3)

which can be written as:

(4)

where, j denotes scale level, FP_i denotes TIFP along orientation i. Equation 4 gives a lower limit of advisable decomposition scale along each orientation. We claim the smallest scale satisfies Eq. 4 as initiation scale, where we start to calculate the wavelet coefficients; the previous scales are ignored to reduce computational load. Different orientations may have different initiation scales depending on TIFP (or texture periodicity) of fabric texture along that orientation.

Fig. 3:	Relationship among the frequency responses of Daubechies wavelet, the defect frequency region and TIFP in one dimension

Figure 3 illustrates the relationship among the frequency responses of Daubechies wavelet from scale 1 to scale 3, the defect frequency region and TIFP in one dimension. In Fig. 3 only scale 3 satisfies Eq. 4, so the initiation scale is scale 3, at which wavelet coefficients are calculated. Wavelet coefficients at scale 1 and 2 are ignored.

Because any scale can only capture the information of certain categories of defects, wavelet coefficients at several successive scales beginning from the initiation scale are used to detect various detects. The number of decomposition scales is an important parameter which greatly affects the detection results. The large number of scales selected corresponds to high computational load, while insufficient number of scales may lead to failure of detection. Proper number of decomposition scales for each kind of defects will be discussed here. The output of UDWT is a set of wavelet coefficients listed as W_1h, W_2v, W_3d,W_1(h+1),W_2(v+1),W_3(d+1),…,W_1(h+n-1),W_2(v+n-1) and W_3(d+n-1), where 1, 2, 3 denote horizontal, vertical and diagonal orientation respectively, h, v and d are their corresponding initiation scales and n denotes the number of scales selected.

Amplitude division: It is found that defects, within their boundaries, tend to have more dark pixels (e.g., big-knot, dirty yarn, etc.) or light pixels (e.g., mispick, broken yarn, etc.) than the normal texture. In turn large quantities of dark pixels or light pixels within a local region indicate a defect in that region. Preprocess is used to make the original fabric image zero mean so that the dark pixels within a defective region have larger negative amplitudes than normal texture while light pixels within a defective region have larger positive amplitudes than normal texture and UDWT is used to enhance both positive and negative amplitude distinctions while keeps the output zero mean. In order to know whether the defect is made up of dark pixels or light pixels the output of UDWT is divided into two parts, each of which contains only positive amplitudes or negative amplitudes, respectively:

(5)

(6)

where, WN denotes the negative coefficients containing the energy from dark pixels, WP denotes the positive coefficients containing the energy from light pixels. Both of two parts are further processed separately.

Data fusion: UDWT decomposes the original image into wavelet coefficients of several scales and orientations. Each scale and orientation only captures parts of information of defects in the fabric image, so it is needed to fuse the information gathered from different scales and orientations to provide relatively complete representation of the defects which makes them easy to discriminate from normal texture. Some data fusion schemes were used by Kumar and Pang (2000b) and Sari-Sarraf and Goddard Jr. (1999) to fuse the information from different scales and orientations into a single image. In this study only data from different scales are fused and a simple fusion scheme is used:

(7)

(8)

The fusion scheme is similar to Kumar and Pang (2000a), except that data from different orientations are not fused, because different orientations may have different initiation scales, it is not proper to fuse them together. Besides it is found that most defects are horizontal, vertical or diagonal and wavelet coefficients of the UDWT along a certain orientation are enough to detect the defects along that orientation. For a defect along a certain orientation, the output of UDWT along other orientations give little information about it, so fusing data from different orientations will not notably improve the detection result but add extra computational load. The positive and negative amplitudes of wavelet coefficients are fused separately for the same reason discussed here and geometric mean is used to fuse the data at adjacent scales. Since lots of elements in CN_i and CP_i are set to zero by amplitude division, only the real defects which emerge on both adjacent scales are preserved and random noise is depressed. This is useful to reduce false alarm.

Energy feature calculation: The fused images of each orientation and of both positive and negative amplitudes are subjected to the energy estimation to extract energy features. And these features are used to discriminate the defects from normal texture. The fused images are divided into non-overlapping subregions. Within these subregions six energy features are computed as:

(9)

(10)

(11)

(12)

(13)

(14)

In the symbols of six features H, V, D denote horizontal, vertical, diagonal orientation, respectively and P, N denote positive and negative amplitudes, respectively, e.g., EHP denotes the energy of horizontal positive amplitudes in the subregion.

The extraction of the features can be explained as following procedure: The amplitudes within a subregion are accumulated along each orientation which can be considered as a 2D-to-1D projection toward that orientation, to form an accumulation vector and then the energy of the accumulation vector is calculated and used for defect detection by thresholding. Compared with direct calculation of energy of wavelet coefficient matrix, the proposed method uses more addition operations instead of multiplication operations which needs less computational time on most computational platform (except some specialized DSPs).

Fig. 4 (a-c):	(a) Sample fabric without defect, (b) CP2 and (c) EVP of a

More important, because the accumulation vector of corresponding feature accumulates the defective amplitude a long a certain orientation, so if the subregion containing a real defect along that orientation, the amplitudes of accumulation vector will be greatly enhanced which makes the defect much easy to detect by thresholding. The size of the subregion is an important parameter. Large size corresponds to less detection error while small size provides more precise location of defects. In this study the size of 32x32 subregion is used to achieve a desirable result.

Thresholding: The six features measure the defective energy of positive and negative amplitudes along horizontal, vertical and diagonal orientations within a subregion, respectively. If any of them exceeds the thresholding limit, then the subregion is considered as a defective region. The thresholding limits are determined from defect-free sample fabric images. The features of sample images are calculated. Figure 4 illustrates a sample image, its fused image CP₂ (x, y) and the feature EVP. The thresholding limits of features are set to μ+λσ, where μ and σ are mean and standard deviation of features extracted from sample fabric images, λ is a parameter compromising between false positive and false negative rate and set to 4 in this study.

Different from most defect detection algorithms which can only detect the defect giving its location, this method, by examining which feature exceeds the thresholding limit, can also provide some detailed information of the defect: whether the defect is horizontal, vertical or diagonal, whether the defect is mainly made up of dark pixels or light pixels.