ABSTRACT
As discussed in detail in the initial chapters of this book, the Robust PCA (RPCA) problem
argmin L,S
‖L‖∗ + λ‖S‖1 s.t. D = L+ S , (11.1)
which decomposes a matrix D into a low-rank, L, and sparse component, S, has been shown to give very good performance for video background modeling, in which context the stationary background is represented by the low-rank component, and the moving foreground is represented by the sparse component. This chapter introduces two distinct types of enhancements to the standard RPCA problem, (i) the development of more computationally efficient algorithms for solving this problem (or a variant thereof), including an incremental algorithm that is able to process a single video one frame at a time, and (ii) modifying the problem form to make it invariant to transformations such as translation and rotation, so that it can be applied to video captured by a non-stationary camera. These two enhancements are combined in the final section of the chapter.
