Foreground Detection via RPCA

Introduction

Foreground detection is the first step in video surveillance system to detect moving objects. Principal Components Analysis (PCA) shows a nice framework to separate moving objects from the background but without a mechanism of robust analysis, the moving objects may be absorbed into the background model. This drawback can be solved by recent researches on Robust Principal Component Analysis (RPCA) [1][2]. 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. First, we evaluate and investigate this RPCA approach [1] and their variants for foreground detection [2][3][4][5]. Second, we propose an IRLS scheme to solve RPCA.

Principle

The video is stocked in a matrix A that is decomposed as follows:

A=L+S (1)

where L and S are the low-rank component and sparse component of A, respectively. The low-rank matrix L contains the background and the sparse matrix S contains the foreground.

From left to right: Original image, low-rank matrix L (background), sparse matrix S (moving objects), moving object mask, ground truth

Contributions

Contributions of our works can be summarized as follows:

• A review regarding RPCA methods solved via PCP: The original PCP [1] , the Stable PCP [2] , the quantization based version of PCP [3],the block based version of PCP [4] and the local PCP [5] are reviewed. For each method, we investigate how they are solved, and if incremental and real-time versions are available for foreground detection. Furthermore, their advantages and drawbacks are discussed in the case of outliers due to dynamic backgrounds or illumination changes. A systematic evaluation and comparative analysis is then provided by comparing and evaluating nine RPCA methods solved via PCP on a recent dataset (Background Models Challenge (BMC) ) which contains various synthetic and realistic videos. For the evaluation, we have usedthe quantitative evaluation framework provided by BMC which allows comparison with the state-of-the-art methods.
• A new approach for solving RPCA methods with IRLS scheme: The aim is to alleviate the limitation of PCP [1] and SPCP [2] by addressing the spatial connexity of the pixel to obtain a robust estimation of the true low-rank and the sparse structure of the matrices L and S. In this copntext, we added spatial constraint into the minimization process and an IRLS alternating scheme for weighted the norm into matrix low rank decomposition.

References

[1] E. Candes, X. Li, Y. Ma, J. Wright, “Robust Principal Component Analysis?”, ACM, Volume 58, No. 3, May 2011.

[2] J. Wright, Y. Peng, Y. Ma, A. Ganesh, S. Rao, “Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices by Convex Optimization”, Neural Information Processing Systems, NIPS 2009, December 2009.

[3] S. Becker, E. Candes, M. Grant, “TFOCS: Flexible First-order Methods for Rank Minimization”, Low-rank Matrix Optimization Symposium, SIAM Conference on Optimization, 2011.

[4] G. Tang, A. Nehorai, “Robust principal component analysis based on low-rank and block-sparse matrix decomposition”, Annual Conference on Information Sciences and Systems, CISS 2011, 2011.

[5] B. Wohlberg, R. Chartrand, J. Theiler, "Local Principal Component Pursuit for Nonlinear Datasets", International Conference on Acoustics, Speech, and Signal

Processing, ICASSP 2012, pages 3925-3928, Kyoto, Japan, 2012.

Publication

Chapter

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. [pdf]

Journal

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

Conferences

C. Guyon, T. Bouwmans. E. Zahzah, “Foreground Detection via Robust Low Rank Matrix Decomposition including Spatio-Temporal Constraint”, International Workshop on Background Model Challenges, ACCV 2012, Daejon, Korea, November 2012. [pdf]

C. Guyon, T. Bouwmans. E. Zahzah, “Foreground Detection via Robust Low Rank Matrix Factorization including Spatial Constraint with Iterative Reweighted Regression”, International Conference on Pattern Recognition, ICPR 2012, Tsukuba, Japan, November 2012. [pdf]

C. Guyon, T. Bouwmans. E. Zahzah, “Moving Object Detection via Robust Low Rank Matrix Decomposition with IRLS scheme”, International Symposium on Visual Computing, ISVC 2012,pages 665–674, Rethymnon, Crete, Greece, July 2012. [pdf]

C. Guyon, T. Bouwmans, E. Zahzah, “Moving Object Detection by Robust PCA solved via a Linearized Symmetric Alternating Direction Method”, International Symposium on Visual Computing, ISVC 2012, pages 427-436, Rethymnon, Crete, Greece, July 2012. [pdf]

C. Guyon, T. Bouwmans, E. Zahzah, "Foreground Detection by Robust PCA solved via a Linearized Alternating Direction Method", International Conference on Image Analysis and Recognition, ICIAR 2012, pages 115-122, Aveiro, Portugal, June 2012. [pdf]

C. Guyon, T. Bouwmans, E. Zahzah, "Foreground detection based on low-rank and block-sparse matrix decomposition", IEEE International Conference on Image Processing, ICIP 2012, pages 1225-1228, Orlando, Florida, USA, September 2012. [pdf]