  The research reported in this paper addresses the fundamental task of
separation of locally moving or deforming image areas from a static or globally
moving background. It builds on the latest developments in the field of robust
principal component analysis, specifically, the recently reported practical
solutions for the long-standing problem of recovering the low-rank and sparse
parts of a large matrix made up of the sum of these two components. This
article addresses a few critical issues including: embedding global motion
parameters in the matrix decomposition model, i.e., estimation of global motion
parameters simultaneously with the foreground/background separation task,
considering matrix block-sparsity rather than generic matrix sparsity as
natural feature in video processing applications, attenuating background
ghosting effects when foreground is subtracted, and more critically providing
an extremely efficient algorithm to solve the low-rank/sparse matrix
decomposition task. The first aspect is important for background/foreground
separation in generic video sequences where the background usually obeys global
displacements originated by the camera motion in the capturing process. The
second aspect exploits the fact that in video processing applications the
sparse matrix has a very particular structure, where the non-zero matrix
entries are not randomly distributed but they build small blocks within the
sparse matrix. The next feature of the proposed approach addresses removal of
ghosting effects originated from foreground silhouettes and the lack of
information in the occluded background regions of the image. Finally, the
proposed model also tackles algorithmic complexity by introducing an extremely
efficient "SVD-free" technique that can be applied in most
background/foreground separation tasks for conventional video processing.
