Robust Low-Rank Approximation of Images for Background and Foreground Separation

Background and foreground separation is the major task in video surveillance system to detect moving or suspicious objects. Robust Principal Component Analysis, whose formulation relies on low-rank plus sparse matrices decomposition, shows an interestingly suitable framework to separate moving objects from the background. The optimization problem is transformed to a sequence of convex programs that minimize the sum of L1-norm and nuclear norm of the two component matrices, which are efficiently resolved by an Augmented Lagrangian Multiplierss based solver. In this paper, we propose two new robust schemas for low rank approximation of numerical matrices. The proposed algorithms allow batch and incremental robust low-rank approximal of matrices used in static and real-time foreground extraction to detect moving objects. Experiments reveal that the proposed method are both deterministic, converge decently and quickly; besides, they achieve an accurate background and foreground separation outcome.