Background Recovery by Fixed-rank Robust Principal Component Analysis

Background recovery is a very important theme in computer vision applications. Recent research shows that robust principal component analysis (RPCA) is a promising approach for solving problems such as noise removal, video background modeling, and removal of shadows and specularity. RPCA utilizes the fact that the background is common in multiple views of a scene, and attempts to decompose the data matrix constructed from input images into a low-rank matrix and a sparse matrix. This is possible if the sparse matrix is sufficiently sparse, which is often not the case in computer vision applications. Moreover, the weighting parameter between the low-rank and sparse matrices greatly affects the accuracy of the results, and tuning this parameter can be tricky. This paper proposes a fixed-rank RPCA algorithm (FRPCA) for solving background recovering problems. Fixing the rank of the low-rank matrix allows FRPCA to better recover the low-rank matrix from the data matrix. Comprehensive tests show that FRPCA produces more stable and accurate results than RPCA.