Abstract
Robust Principal Components Analysis (RPCA) shows a nice framework to separate moving objects from the background. 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. RPCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the l 1-norm. To solve this convex program, an Alternating Direction Method (ADM) is commonly used. However, the subproblems in ADM are easily solvable only when the linear mappings in the constraints are identities. This assumption is rarely verified in real application such as foreground detection. In this paper, we propose to use a Linearized Alternating Direction Method (LADM) with adaptive penalty to achieve RPCA for foreground detection. LADM alleviates the constraints of the original ADM with a faster convergence speed. Experimental results on different datasets show the pertinence of the proposed approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bouwmans, T.: Recent advanced statistical background modeling for foreground detection: A systematic survey. RPCS 4(3), 147–176 (2011)
Bouwmans, T.: Subspace learning for background modeling: A survey. RPCS 2(3), 223–234 (2009)
Oliver, N., Rosario, B., Pentland, A.: A bayesian computer vision system for modeling human interactions. In: ICVS 1999 (January 1999)
De La Torre, F., Black, M.: A framework for robust subspace learning. International Journal on Computer Vision, 117–142 (2003)
Candes, E., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? International Journal of ACMÂ 58(3) (May 2011)
Chandrasekharan, V., Sanghavi, S., Parillo, P., Wilsky, A.: Rank-sparsity incoherence for matrix decomposition (2009) (preprint)
Cai, J., Candes, E., Shen, Z.: A singular value thresholding algorithm for matrix completion. International Journal of ACM (May 2008)
Wright, J., Peng, Y., Ma, Y., Ganesh, A., Rao, S.: Robust principal component analysis: Exact recovery of corrupted low-rank matrices by convex optimization. In: NIPS 2009 (December 2009)
Lin, Z., Ganesh, A., Wright, J., Wu, L., Chen, M., Ma, Y.: Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix. UIUC Technical Report (August 2009)
Lin, Z., Chen, M., Wu, L., Ma, Y.: The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. UIUC Technical Report (November 2009)
Yuan, X., Yang, J.: Sparse and low-rank matrix decomposition via alternating direction methods. Optimization Online (November 2009)
Lin, Z., Liu, R., Su, Z.: Linearized alternating direction method with adaptive penalty for low-rank representation. In: NIPS 2011 (December 2011)
Sheikh, Y., Shah, M.: Bayesian modeling of dynamic scenes for object detection. IEEE T-PAMI 27, 1778–1792 (2005)
Toyama, K., Krumm, J., Brumitt, B., Meyers, B.: Wallflower: Principles and practice of background maintenance. In: ICCV 1999, pp. 255–261 (September 1999)
Maddalena, L., Petrosino, A.: A fuzzy spatial coherence-based approach to background foreground separation for moving object detection. Neural Computing and Applications, 1–8 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guyon, C., Bouwmans, T., Zahzah, EH. (2012). Foreground Detection by Robust PCA Solved via a Linearized Alternating Direction Method. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2012. Lecture Notes in Computer Science, vol 7324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31295-3_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-31295-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31294-6
Online ISBN: 978-3-642-31295-3
eBook Packages: Computer ScienceComputer Science (R0)