Lattice-based patterned fabric inspection by using total variation with sparsity and low-rank representations

In this paper, we study an image decomposition model for patterned fabric inspection. It is important to represent fabric patterns effectively so that fabric defects can be separated. One concern is that both patterned fabric (e.g., star- or box-patterned fabrics) and fabric defects contain mainly low frequency components. The main idea of this paper is to use the convolution of a lattice with a Dirac comb to characterize a patterned fabric image so that its repetitive components can be effectively represented in the image decomposition model. We formulate a model with total variation, sparsity, and low-rank terms for patterned fabric inspection. The total variation term is used to regularize the defective image, and the sparsity and the low-rank terms are employed to control the Dirac comb function. The proposed model can be solved efficiently via a convex programming solver. Our experimental results for different types of patterned fabrics show that the proposed model can inspect defects at a higher accuracy compared with some classical methods in the literature.