Total Variation and Rank-1 Constraint RPCA for Background Subtraction

Background subtraction (BS) in video sequences is a main research field, and the aim is to separate moving objects in the foreground from stationary background. Using the framework of schemes-based robust principal component analysis (RPCA), we propose a novel BS method employing the more refined prior representations for the static and dynamic components of the video sequences. Specifically, the rank-1 constraint is exploited to describe the strong low-rank property of background layer (temporal correlation of static component), and 3-D total variation measure and $L_{1}$ norm are used to model the spatial-temporal smoothness of foreground layer and sparseness of noise (dynamic component). This method introduces rank-1, smooth, and sparse properties into the RPCA framework for BS task, and it is dubbed TR1-RPCA. In addition, an efficient algorithm based on the alternating direction method of multipliers is designed to solve the proposed BS model. Extensive experiments on simulated and real videos demonstrate the superiority of the proposed method.