Decomposition into Lowrank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a LargeScale Dataset
Abstract
Recent research on problem formulations based on decomposition into lowrank plus sparse matrices shows a suitable framework to separate moving objects from the background. The most representative problem formulation is the Robust Principal Component Analysis (RPCA) solved via Principal Component Pursuit (PCP) which decomposes a data matrix in a lowrank matrix and a sparse matrix. However, similar robust implicit or explicit decompositions can be made in the following problem formulations: Robust Nonnegative Matrix Factorization (RNMF), Robust Matrix Completion (RMC), Robust Subspace Recovery (RSR), Robust Subspace Tracking (RST) and Robust LowRank Minimization (RLRM). The main goal of these similar problem formulations is to obtain explicitly or implicitly a decomposition into lowrank matrix plus additive matrices. In this context, this work aims to initiate a rigorous and comprehensive review of the similar problem formulations in robust subspace learning and tracking based on decomposition into lowrank plus additive matrices for testing and ranking existing algorithms for background/foreground separation. For this, we first provide a preliminary review of the recent developments in the different problem formulations which allows us to define a unified view that we called Decomposition into Lowrank plus Additive Matrices (DLAM). Then, we examine carefully each method in each robust subspace learning/tracking frameworks with their decomposition, their loss functions, their optimization problem and their solvers. Furthermore, we investigate if incremental algorithms and realtime implementations can be achieved for background/foreground separation. Finally, experimental results on a largescale dataset called Background Models Challenge (BMC 2012) show the comparative performance of 32 different robust subspace learning/tracking methods.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.01245
 Bibcode:
 2015arXiv151101245B
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition
 EPrint:
 121 pages, 5 figures, submitted to Computer Science Review. arXiv admin note: text overlap with arXiv:1312.7167, arXiv:1109.6297, arXiv:1207.3438, arXiv:1105.2126, arXiv:1404.7592, arXiv:1210.0805, arXiv:1403.8067 by other authors, Computer Science Review, November 2016