Masked-RPCA: Moving Object Detection with an Overlaying Model

Moving object detection in a given video sequence is a pivotal step in many computer vision applications such as video surveillance. Robust Principal Component Analysis (RPCA) performs low-rank and sparse decomposition to accomplish such a task when the background is stationary and the foreground is dynamic and relatively small. A fundamental issue with the RPCA is the assumption that the low-rank and sparse components are added at each pixel, whereas in reality, the moving foreground is overlaid on the background. We propose the masked decomposition (i.e. an overlaying model) where each element either belongs to the low-rank or the sparse component, decided by a mask. We introduce the Masked-RPCA (MRPCA) algorithm to recover the mask (hence the sparse object) and the low-rank components simultaneously, via a non-convex formulation. An adapted version of the Douglas-Rachford splitting algorithm is utilized to solve the proposed formulation. Our experiments using real-world video sequences show consistently better performance for both cases of static and dynamic background videos compared to RPCA and its variants based on the additive model. Additionally, we show that utilizing non-convex priors in our formulation leads to improved results without any added complexity compared to a relaxed formulation using convex surrogates and methods based on the additive model.