Fast Dual-Graph Regularized Background Foreground Separation

Foreground-background separation is a crucial task in various applications such as computer vision, robotics, and surveillance. Robust Principal Component Analysis (RPCA) is a popular method for this task, which considers the static background as the low-rank component and the moving objects in the foreground as the sparse component. To enhance the performance of RPCA, graph regularization is typically used to incorporate the sophisticated geometry of the background and temporal correlation. However, handling the graph Laplacians can be challenging due to the substantial number of data points. In this study, we propose a novel dual-graph regularized foreground-background separation model based on Sobolev smoothness. Our model is solved using a fast numerical algorithm based on the matrix CUR decomposition. Experimental results on real datasets demonstrate that our proposed algorithm achieves state-of-the-art computational efficiency.