Nonconvex Low-Rank Sparse Factorization for Image Segmentation

In this paper, we present a new color image segmentation model based on nonconvex low-rank and nonconvex sparse (NLRSR) factorization of the feature matrix. The main difference between our model and the recently developed methods like the sparse subspace clustering (SSC) and low-rank representation (LRR) based subspace clustering is that they use the data matrix as the dictionary while we learn a dictionary. In order to better cater to the low-rankness of the dictionary and the sparsity of the represent coefficients, we use the nonconvex penalty functions rather than the convex ones. The variable splitting technique and the alternative minimization method are applied for solving the proposed NLRSR model. The sparse representation coefficient matrix is utilized to construct an affinity matrix and then the normalized cut (Ncut) is applied to obtain the segmentation result. Experimental results show our method can achieve visually better segmentation results than the SSC and LRR method. Objective metrics further confirms this.