A novel low-rank constraint method with the sparsity model for moving object analysis

Abstract

This thesis presents a new Robust Principal Components Analysis(RPCA) method that decompose data matrix into low-rank and sparse error matrix given deficient samples. From recently developed RPCA, many accomplishments have been presented in computer vision problems, such as face recognition, background subtraction, photometric stereo and so on. Especially, RPCA that decompose data matrix into low-rank and sparse error matrix in polynomial-time was proposed, and has been shown to provide promising results. However, the conventional RPCA could fail to estimate low-rank and sparse error matrix properly, because the RPCA assumes that enough observations to construct data matrix and to support a major sub-space are given. To overcome the limitation, an additional constraint is needed. This paper proposes an effective method to decompose low-rank and sparse matrix with deficient samples via rank-N soft constraint, in case that an input data matrix originally comes from a certain rank-N matrix. Particularly, when sample vectors in a data matrix are linearly dependent, the rank of the data matrix becomes one. We discuss about a special case of rank-1 soft constraint condition, and apply the proposed RPCA method with rank-1 soft constraint to computer vision applications. In the latter of our research, we present two applications using the proposed decomposition method. Firstly, we present a new ghost-free High Dynamic Range(HDR) method as an application. For a scene, taken photographs with different exposures are linearly dependent for scene radiance which consist of rank one matrix. HDR is suitable for rank-1 assumption, and relatively deficient samples are given. By utilizing this observation, we model undesired moving objects or saturation regions as additive sparse error and sensor irradiance as low-rank structure. As the second application, we present a moving object boundary detection method by the proposed RPCA with rank-1 soft constraint. Und...