Singular value decomposition combined
with wavelet transform for LCD defect
detection
Jing-Wein Wang, Wen-Yuan Chen and Jiann-Shu Lee
Singular value decomposition is used to obtain the mean value of the first and second singular value ratios of normal and defect LCD images. Then the third and fourth singular values matched with the standard deviation of the first two singular value ratios are used to divide the defect images into two categories: coarse and fine. Finally, 2D discrete wavelet coefficient filtering combined with region growing is adopted to extract defect regions.
Introduction: Mura defects are the most common and difficult to detect LCD defects[1]. Lu and Tsai [2]used singular value decomposition (SVD) to detect defects, first eliminating the singular values at the front to remove the image background and then using the remaining singular values to rebuild the image and reveal the defect regions. However, this method does not reveal the number of singular values that must be eliminated for each defect type to obtain good experimental results. Oh et al. [3] normalised the wavelet approximation signals obtained by the wavelet transform to suppress image background infor-mation. After the wavelet detail signals were strengthened with the con-trast sensitivity function (CSF), they were synthesised, and trimodal thresholding was combined with the Weber constant to determine the defect regions with luminance discrepancies. However, how to calibrate suitable trimodal thresholding remains to be clarified. Lu and Tsai[4]
applied independent component analysis (ICA) to divide TFT-LCD images into independent components and de-mixing matrices. After training, workers chose suitable independent components as image background textures. De-mixing matrices were corrected to become new de-mixing matrices without image background textures. These new matrices were then used to rebuild the image and display defects. Bi et al.[5]used Gabor filters to remove image background textures and presented a level set method improved from the Chan-Vese model to divide defect regions. However, the parameters for this method differ based on contrast and luminance; thus, they are not fixed. Noh et al. [6] used size changes in standard deviations as a basis for differentiating defect pixels and background pixels. However, the method for obtaining suitable numbers of background pixels to calculate the means, matched with a suitable standard deviation for detecting defect regions, still depends on experience. Li and Tsai [7]presented an improved Hough transform for defect detection. The original point to line distance tolerance of the Hough transform was broadened, enabling effective application in defect detection in non-stationary grey-level profiles. However, varying combinations of the distance tolerance parameter values and relevant control parameters still lead to differing output results. In summary, automated detection methods that do not require human intervention to set the parameters have yet to be presented.
Defect detection: According to the contrast between the defect regions and their surrounding backgrounds, we roughly divide defects into coarse and fine images. The leading seven images of Fig. 1a are ones with fine defects, the 8th to 10th images are ones with coarse defects, and the last two images are good images. Among these, coarse defects have a higher contrast and are easier to detect, whereas image preprocessing is required to detect fine defects because of the low contrast level. To resolve these problems, this study uses SVD to decompose all the good and defect images and obtain the means of the ratios of the first two singular values in these images. The two means are then set as a threshold for determin-ing whether the input images are defect images. Suppose that I is an m× n input image, using SVD, the image can be disassembled using the following equation:
I= USVT (1)
where U ¼ [u1, u2, . . . , uk] is the m× m square matrix, V ¼ [v1, v2, . . . ,
vk] is the n× n square matrix, and S ¼ diag(l1,l2, . . . ,lk) is the main
diagonal matrix.l1,l2, . . . ,lkis the singular value, rank I ¼ k. Thus, we
can design the equation for determining defect images as follows: good image, l1 l2≥ mp+mq 2 defect image, l1 l2 ,mp+mq 2 ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ (2)
In this equation,mpandmqare the means of the first and second singular
value ratios of good images and defect images, respectively. Defect images can be further divided into images with fine and coarse defects. Next, we use the third and fourth singular values as a basis for classifying fine and coarse defects. The determining equation is as follows: coarse image, l1 l2≥ mq− l3 l4× sq fine image, l1 l2 ,mq− l3 l4× sq ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ (3)
In this equation,sqis the standard deviation of the means of the first and
second singular value ratios of the defect images. Because the degree of decline between the first two singular value ratios of coarse and fine defects differs significantly from that of the third and fourth singular value ratios, these discrepancies, combined with the standard deviation of the first two singular value ratios, can be used to distinguish the differ-ences between coarse defects and fine defects. Coarse defects can be directly detected, whereas the defect pixels of fine defect images must be enhanced before detection. The first singular value commonly rep-resents the primary texture power of LCD defect images. When the first singular value is removed in the reconstructed image, Ir, the
defect pixels can be enhanced, as shown in the following equation: Ir= I − u1l1nT1 (4) Fig. 1bshows the result of image subtraction. The defect pixels in the white region are enhanced, and the remaining image background infor-mation is suppressed. For defect detection, we use 2D discrete wavelet frame transform (DWFT)[8]as a filter to obtain the general range of defect regions. DWFT can be used to decompose different frequencies in the original images, resulting in the high – high frequency sub-band, HH. The calculation of the HH sub-band used with the DWFT coeffi-cient for detecting defect filtering is as follows:
eDWFT =−1 N2 N−1 x,y=0|HH DWF (x, y)| log |HHDWF(x, y)| (5) where eDWFTrepresents the defect detection distribution value, with the
window size set to 11× 11 (N ¼ 11). After the entire image undergoes filtering and binary thresholding, the defect region can be roughly deter-mined. Next, the region centroid is used as a starting point. Following the principles of 4-connectivity, the point aggregation procedure region growing algorithm is used to detect the region boundary accu-rately[9].
Results: The test samples in this study were 200 8-bit grey level images 256× 256 pixels in size and provided by cooperating businesses. Of these samples, 50 were good images and the rest comprised 10 types of defect images, that is, two types of drop mura, five types of pellet mura, two types of arc mura, and one type of scratch, with 15 images for each defect type. The image shown in Fig. 1c is the result of defect detection, where the defect range is represented using black regions. The authenticity measurements of the defects identified during pixel detection can be divided into the following four categories: accurate acceptance rate (AAR), accurate rejection rate (ARR), false acceptance rate (FAR) and false rejection rate (FRR). The 10 different defect categories occuring in the AAR, ARR, FAR and FRR experimen-tal data are 92.19%, 99.68%, 7.81%, and 0.32%, respectively, where the ground-truth was obtained from the cooperating corporation whose engineers applied manmade definitions based on experience. A com-parison of recall and precision rates demonstrates that our method of 92.19% and 95.93% is superior to those of [2] with 20.19% and 50.93%, respectively. Furthermore, we make a comparison of the result of the related study that used SVD for defect detection, as shown inFig. 1d. The method presented by Lu and Tsai [2]applied SVD with panel image backgrounds to select suitable singular values for image reconstruction and determine whether the panel images had defects. However, the test results we obtained during this study indicate