A Survey Approach

1) Survey on a category

Robust Principal Component Analysis for Background Subtraction: Systematic Evaluation and Comparative Analysis

Principal Component Analysis (PCA) has been used to model the background by significantly reducing the data’s dimension. To perform PCA, different Robust Principal Components Analysis (RPCA) models have been recently developped in the literature. The background sequence is then modeled by a low rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. However, authors compare their algorithm only with the PCA (Oliver et al. (1999)) or another RPCA model. Furthermore, the evaluation is not made with the datasets and the measures currently used in the field of background subtraction. Considering all of this, we propose to evaluate RPCA models in the field of video surveillance. Contributions of this chapter can be summarized as follows: 1) A survey regarding robust principal component analysis, and 2) An evaluation and comparison on different video surveillance datasets.

C. Guyon, T. Bouwmans, E. Zahzah, “Robust Principal Component Analysis for Background Subtraction: Systematic Evaluation and Comparative Analysis”, INTECH, Principal Component Analysis, Book 1, Chapter 12, page 223-238, March 2012.

Robust PCA via Principal Component Pursuit: A Review for a Comparative Evaluation in Video Surveillance

Foreground detection is the first step in video surveillance system to detect moving objects. Recent research on subspace estimation by sparse representation and rank minimization represents a nice framework to separate moving objects from the background. Robust Principal Component Analysis (RPCA) solved via Principal Component Pursuit decomposes a data matrix A in two components such that A= L+S, where L is a low-rank matrix and S is a sparse noise matrix. The background sequence is then modeled by a low-rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. To date, many efforts have been made to develop Principal Component Pursuit (PCP) methods with reduced computational cost that perform visually well in foreground detection. However, no current algorithm seems to emerge and to be able to simultaneously address all the key challenges that accompany real-world videos. This is due, in part, to the absence of a rigorous quantitative evaluation with synthetic and realistic large-scale dataset with accurate ground truth providing a balanced coverage of the range of challenges present in the real world. In this context, this work aims to initiate a rigorous and comprehensive review of RPCA-PCP based methods for testing and ranking existing algorithms for foreground detection. For this, we first review the recent developments in the field of RPCA solved via Principal Component Pursuit. Furthermore, we investigate how these methods are solved and if incremental algorithms and real-time implementations can be achieved for foreground detection. Finally, experimental results on the Background Models Challenge (BMC) dataset which contains different synthetic and real datasets show the comparative performance of these recent method. (more information)

T. Bouwmans, E. Zahzah, “Robust PCA via Principal Component Pursuit: A Review for a Comparative Evaluation in Video Surveillance”, Special Isssue on Background Models Challenge, Computer Vision and Image Understanding, CVIU 2014, Volume 122, pages 22–34, May 2014.

T. Bouwmans, E. Zahzah,"Robust Principal Component Analysis via Decomposition into Low-rank and Sparse Matrices: An overview", Handbook on "Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing", CRC Press, Taylor and Francis Group, May 2016.

2) Survey on all the categories

Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset

Recent research on problem formulations based on decomposition into low-rank plus sparse matrices shows a suitable framework to separate moving objects from the background. 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 low-rank 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 Low-rank 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 real-time implementations can be achieved for background/foreground separation. Finally, experimental results on a large-scale dataset called Background Models Challenge (BMC 2012) show the comparative performance of 32 different robust subspace learning/tracking methods. (more information)

T. Bouwmans, A. Sobral, S. Javed, S. Jung, E. Zahzah, "Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset", Computer Science Review, Volume 23, pages 1-71, February 2017.

Robust Principal Component Analysis, Subspace Learning, and Tracking

This work provides an overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via low-rank+sparse matrix decomposition (L+S), RST via L+S, and robust subspace recovery (RSR). RSR assumes that an entire data vector is either an outlier or an inlier. The L+S formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions. Finally, experimental results on a large-scale dataset called CD.net 2014 are provided.

N. Vaswani, T. Bouwmans, S. Javed, P. Narayanamurthy, “Robust Principal Component Analysis, Subspace Learning, and Tracking ”, IEEE Signal Processing Magazine, 2018.

N. Vaswani, T. Bouwmans, S. Javed, P. Narayanamurthy, “Robust PCA and Robust Subspace Tracking: A Comparative Evaluation”, IEEE Statistical Signal Processing Workshop, SSP 2018, Freiburg, Germany, June 2018.