Saliency detection via double nuclear norm maximization and ensemble manifold regularization

Abstract

In recent years, salient object detection via robust principal component analysis (RPCA) has received a significant amount of attention. Existing methods generally replace the rank function by the nuclear norm to obtain low-rank and sparse matrices, ignores the heavy-tailed distributions of singular values and over-penalizes large singular values of low rank matrices. In addition, although the manifold regularization is introduced into RPCA to obtain satisfactory low-rank representation of an original image, the graph hyperparameters selection lacks the ability to approximate the optimal solution for intrinsic manifold estimation. To solve these issues, we propose a novel low-rank matrix recovery model for salient object detection, which integrates double nuclear norm maximization with ensemble manifold regularization and can be formulated as a tractable optimization problem. By virtue of the alternating direction method (ADM), we develop an efficient algorithm to optimize the proposed model, which not only effectively fits the heavy-tailed distribution of singular values of low-rank matrices, but automatically learns the optimal linear combination of a set of predefined graph Laplacians. Experimental results on five challenging datasets show that our model achieves better performance than state-of-the-art unsupervised methods.