Weighted Double-Low-Rank Decomposition With Application to Fabric Defect Detection (2020)

Recently, many methods based on low-rank representation have been proposed for fabric defect detection. Most of them relax the low-rank decomposition problem to a nuclear norm minimization (NNM) problem to pursue the convexity of the objective function. When solving the standard NNM problem, matrix singular values have to be treated equally. This, however, would be impractical in the scenario of fabric defect detection as the matrix singular values have clear physical meanings, and thus, they should be treated differently. In this article, we propose a weighted double-low-rank decomposition method (WDLRD) to treat the matrix singular values differently by assigning different weights. Thus, the most important/distinguishing characteristics of a fabric image can be preserved. Another difference between WDLRD and the other existing low-rank-based methods is that WDLRD considers a defective fabric image being decomposed to two low-rank matrices, i.e., low-rank defect-free matrix and low-rank defect matrix, as the defect-free and defective regions are usually composed of homogeneous objects that have a high correlation. Besides, WDLRD is more robust for defect detection in various situations by adding a noise term to avoid noise or other interference on the fabric surface. In addition, a defect prior is incorporated into the objective function of WDLRD to guide locating the defective regions. The proposed optimization problem can be easily solved by an iterative algorithm based on augmented Lagrange multipliers. Experimental results on TILDA, periodically patterned fabric, and Textile & Apparel Artificial Intelligence databases show that the proposed WDLRD obtains better performance than state-of-the-art methods in locating the defective regions on fabric images. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the problem that the performance of fabric defect detection in the textile industry is poor. It is necessary to develop an effective method to improve the defect detection accuracy and reduce overall manufacturing cost. Existing automatic defect detection approaches usually contain two stages: first, capture fabric images from the weaving machine and then use a defect detection algorithm in a host computer to conduct a real-time inspection and give an alarm if defects occur. This article focuses on locating defects for given defective images after the procedure of binary classification (which determines an image as defective or defect free). The article proposes an objective function to mathematically interpret the optimization problem between fabric images and predictive defects. The optimal solution can be obtained by employing the alternating direction method of multipliers (ADMMs). The proposed method is described as a new defect detection algorithm. Extensive experiments were conducted to evaluate the algorithm, and the experimental results indicate that the proposed method is superior to many existing fabric defect detection methods. Preliminary experiments suggest that this method is feasible but has not yet been really used in production. In future research, we will collect more fabric images from the textile industry and develop large-scale databases for verifying the proposed method for real-life applications.