Salient Object Detection via Nonconvex Structured Matrix Decomposition

In the salient object detection, the feature matrix of an image can be represented as a low-rank matrix plus a sparse matrix, corresponding to the background and the salient regions, respectively. Generally, the rank function is approximated by the nuclear norm. However, solving the nuclear norm minimization problem usually leads to a suboptimal solution. To address this problem, we propose a novel nonconvex structure matrix decomposition model, where using a nonconvex surrogate (i.e., the l(1) norm of logistic function) on the singular values of a matrix to approximate the rank function. In addition, our model contains two structural regularizations: a group sparsity induced norm regularization to explore the relationship between each superpixel, making salient object highlighted consistently, and a Laplacian regularization to increase the distance between salient regions and non-salient regions in feature space. Finally, high-level priors are integrated to our model. Experimental results show that our model can achieve better performance compared with the state-of-the-art methods.