  Foreground detection in a given video sequence is a pivotal step in many
computer vision applications such as video surveillance system. Robust
Principal Component Analysis (RPCA) performs low-rank and sparse decomposition
and accomplishes such a task when the background is stationary and the
foreground is dynamic and relatively small. A fundamental issue with RPCA is
the assumption that the low-rank and sparse components are added at each
element, whereas in reality, the moving foreground is overlaid on the
background. We propose the representation via masked decomposition (i.e. an
overlaying model) where each element either belongs to the low-rank or the
sparse component, decided by a mask. We propose the Masked-RPCA algorithm to
recover the mask and the low-rank components simultaneously, utilizing
linearizing and alternating direction techniques. We further extend our
formulation to be robust to dynamic changes in the background and enforce
spatial connectivity in the foreground component. Our study shows significant
improvement of the detected mask compared to post-processing on the sparse
component obtained by other frameworks.
