Efficient background subtraction with low-rank and sparse matrix decomposition

Decomposition of a video scene into background and foreground is an old problem, for which novel approaches in the last years have been proposed. The robust subspace approach based on a low-rank plus sparse matrix decomposition has shown a great ability to identify static parts from moving objects in video sequences. However, those models are still insufficient in realistic environments. In this paper, we propose a modified approximated robust PCA algorithm that can handle moving cameras and takes advantage of the block sparse structure of the pixels corresponding to the moving objects. Additionally, we propose a novel SVD-free algorithm for the case of rank-1 background that outperforms current state-of-the-art methods in computation cost/time as well as performance. Finally, experiments and numerical results evaluating the proposed methods are demonstrated.