Foreground detection is the first step in video surveillance system to detect moving objects. Recent research on subspace estimation by sparse representation and rank minimization represents a nice framework to separate moving objects from the background. Robust Principal Component Analysis (RPCA) solved via Principal Component Pursuit decomposes a data matrix A in two components such that A = L + S , where L is a low-rank matrix and S is a sparse noise matrix. The background sequence is then modeled by a low-rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. To date, many efforts have been made to develop Principal Component Pursuit (PCP) methods with reduced computational cost that perform visually well in foreground detection. However, no current algorithm seems to emerge and to be able to simultaneously address all the key challenges that accompany real-world videos. This is due, in part, to the absence of a rigorous quantitative evaluation with synthetic and realistic large-scale dataset with accurate ground truth providing a balanced coverage of the range of challenges present in the real world. In this context, this work aims to initiate a rigorous and comprehensive review of RPCA-PCP based methods for testing and ranking existing algorithms for foreground detection. For this, we first review the recent developments in the field of RPCA solved via Principal Component Pursuit. Furthermore, we investigate how these methods are solved and if incremental algorithms and real-time implementations can be achieved for foreground detection. Finally, experimental results on the Background Models Challenge (BMC) dataset which contains different synthetic and real datasets show the comparative performance of these recent methods. 
Robust PCA via Principal Component Pursuit: A review for a comparative evaluation in video surveillance