Foreground Segmentation with Tree-Structured Sparse RPCA

Background subtraction is a fundamental video analysis technique that consists of creation of a background model that allows distinguishing foreground pixels. We present a new method in which the image sequence is assumed to be made up of the sum of a low-rank background matrix and a dynamic tree-structured sparse matrix. The decomposition task is then solved using our approximated Robust Principal Component Analysis (ARPCA) method which is an extension to the RPCA that can handle camera motion and noise. Our model dynamically estimates the support of the foreground regions via a superpixel generation step, so that spatial coherence can be imposed on these regions. Unlike conventional smoothness constraints such as MRF, our method is able to obtain crisp and meaningful foreground regions, and in general, handles large dynamic background motion better. To reduce the dimensionality and the curse of scale that is persistent in the RPCA-based methods, we model the background via Column Subset Selection Problem, that reduces the order of complexity and hence decreases computation time. Comprehensive evaluation on four benchmark datasets demonstrate the effectiveness of our method in outperforming state-of-the-art alternatives.