Rank-constrained PCA for intrinsic images decomposition

Intrinsic image decomposition is an important topic in computer vision and computer graphics applications. However, this is a challenging problem by adopting the information of a single image. Therefore, additional priors or supplementary information such as multiply images or user interactions are necessary to address this problem. In this paper, we propose a novel scheme to use multiple images for intrinsic image decomposition, based on a similar strategy in robust principal component analysis (RPCA). RPCA utilizes the fact that the reflectance layer is common in multiple lights 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 rank-constrained PCA algorithm (RCPCA) for solving background recovering problems. Fixing the rank of the low-rank matrix to be 1 allows RCPCA to better recover the low-rank matrix from the data matrix. Comprehensive tests show that RCPCA produces more stable and accurate results than RP-CA.