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Moving Object Detection by Robust PCA Solved via a Linearized Symmetric Alternating Direction Method

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Book cover Advances in Visual Computing (ISVC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7431))

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Abstract

Robust Principal Components Analysis (RPCA) gives a suitable 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 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. This convex optimization is commonly solved by an Alternating Direction Method (ADM) that is not applicable in real application, because it is computationally expensive and needs a huge size of memory. In this paper, we propose to use a Linearized Symmetric Alternating Direction Method (LSADM) to achieve RPCA for moving object detection. LSADM in its fast version requires less computational time than ADM. Experimental results on the Wallflower and I2R datasets show the robustness of the proposed approach.

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References

  1. Bouwmans, T.: Recent advanced statistical background modeling for foreground detection: A systematic survey. RPCS 4, 147–176 (2011)

    Google Scholar 

  2. Oliver, N., Rosario, B., Pentland, A.: A bayesian computer vision system for modeling human interactions. In: ICVS 1999 (1999)

    Google Scholar 

  3. Bouwmans, T.: Subspace learning for background modeling: A survey. RPCS 2, 223–234 (2009)

    Google Scholar 

  4. Torre, F.D.L., Black, M.: A framework for robust subspace learning. International Journal on Computer Vision, 117–142 (2003)

    Google Scholar 

  5. Candes, E., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? International Journal of ACM 58 (2011)

    Google Scholar 

  6. 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 (2009)

    Google Scholar 

  7. 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 (2009)

    Google Scholar 

  8. Lin, Z., Chen, M., Wu, L., Ma, Y.: The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. UIUC Technical Report (2009)

    Google Scholar 

  9. Yuan, X., Yang, J.: Sparse and low-rank matrix decomposition via alternating direction methods. Optimization Online (2009)

    Google Scholar 

  10. Ma, S.: Algorithms for sparse and low-rank optimization: Convergence, complexity and applications. Thesis (2011)

    Google Scholar 

  11. Goldfarb, D., Ma, S., Scheinberg, K.: Fast alternating linearization methods for minimizing the sum of two convex function. Preprint, Mathematical Programming Series A (2010)

    Google Scholar 

  12. Wren, C., Azarbayejani, A., Darrell, T., Pentland, A.: Pfinder: Real-time tracking of the human body. IEEE Transactions on PAMI 19, 780–785 (1997)

    Article  Google Scholar 

  13. Stauffer, C., Grimson, W.: Adaptive background mixture models for real-time tracking. In: CVPR 1999, pp. 246–252 (1999)

    Google Scholar 

  14. Toyama, K., Krumm, J., Brumitt, B., Meyers, B.: Wallflower: Principles and practice of background maintenance. In: ICCV 1999, pp. 255–261 (1999)

    Google Scholar 

  15. Li, L., Huang, W., Gu, I., Tian, Q.: Statistical modeling of complex backgrounds for foreground object detection. IEEE T-IP, 1459–1472 (2004)

    Google Scholar 

  16. 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)

    Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Guyon, C., Bouwmans, T., Zahzah, EH. (2012). Moving Object Detection by Robust PCA Solved via a Linearized Symmetric Alternating Direction Method. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2012. Lecture Notes in Computer Science, vol 7431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33179-4_41

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  • DOI: https://doi.org/10.1007/978-3-642-33179-4_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33178-7

  • Online ISBN: 978-3-642-33179-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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