Low-rank decomposition fabric defect detection based on prior and total variation regularization

Low-rank decomposition model is widely used in fabric defect detection, where a feature matrix is decomposed into a low-rank matrix that represents defect-free regions of the image and a sparse matrix that represents defective regions. Two shortcomings, however, still exist in the traditional low-rank decomposition models. First, they cannot detect the position and shape of the defect very well, and they are usually misjudge the textured background as a defect. Second, they cannot detect some large homogeneous defective block. To solve those problems, we propose a low-rank decomposition model with defect prior and total variation regular term, we call it PTVLR. And it is consisted of the following parts. (1) Defect prior, which characterizes the autoencoder residual image, is used as a prior consideration of detect for improving the separation effect of low-rank texture and defect, (2) total variation regular of term constrains the defect according to the spatial continuity of the defect, (3) LF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L_F}$$\end{document} norm characterizes the image noise part. The performance of PTVLR is evaluated on the box-, star- and dot- patterned fabric databases. And its superior results are shown compared with state-of-the-art methods, that is, 55.58% f-measure and 77.89% true positive rate (TPR) for box-patterned fabrics, 53.20% f-measure and 86.75% TPR for star-patterned fabrics, 69.78% f-measure and 88.33% TPR for dot-patterned fabrics.