Double Structured Nuclear Norm-Based Matrix Decomposition for Saliency Detection

Saliency detection aims at identifying the most important and informative area in a scene. Recently low rank matrix recovery (LR) theory becomes an effective tool for saliency detection. The existing LR-based methods all work under the popular low rank and sparsity pursuit framework and perform well for images with small or homogeneous objects. However, if the image is with heterogeneous objects, the sparsity property of the object cannot be guaranteed. Moreover, as a useful tool for depicting a spatially structured matrix variable, nuclear norm (corresponding to the low rank) considers only the global structure but overlooks the inherent local structure of the data. We address these problems by proposing a double structured nuclear norm-based matrix decomposition (DSNMD) model for saliency detection. In the model, a tree-structured nuclear (TSN) norm is firstly introduced to constraint both the background and foreground regions. We also empirically demonstrate that TSN norm provides stronger performance at capturing the underlying structural information of the image regions including global structure, local structure, and internal structure of each node of the tree, and it deservedly inherits the advantages of both nuclear norm and sparsity-related norms (e.g., $\ell _{1}$ -norm, group sparsity norm) for saliency detection. Comprehensive evaluations on six benchmark datasets indicate that our method universally surpasses state-of-the-art unsupervised methods and performs favorably against supervised approaches.