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Comparison of Matrix Completion Algorithms for Background Initialization in Videos

  • Andrews SobralEmail author
  • Thierry Bouwmans
  • El-hadi Zahzah
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9281)

Abstract

Background model initialization is commonly the first step of the background subtraction process. In practice, several challenges appear and perturb this process such as dynamic background, bootstrapping, illumination changes, noise image, etc. In this context, this work aims to investigate the background model initialization as a matrix completion problem. Thus, we consider the image sequence (or video) as a partially observed matrix. First, a simple joint motion-detection and frame-selection operation is done. The redundant frames are eliminated, and the moving regions are represented by zeros in our observation matrix. The second stage involves evaluating nine popular matrix completion algorithms with the Scene Background Initialization (SBI) data set, and analyze them with respect to the background model challenges. The experimental results show the good performance of LRGeomCG [17] method over its direct competitors.

Keywords

Matrix completion Background modeling Background initialization 

References

  1. 1.
    Balzano, L., Wright, S.J.: On GROUSE and incremental SVD. In: CAMSAP 2013, pp. 1–4 (2013). http://dx.doi.org/10.1109/CAMSAP.2013.6713992
  2. 2.
    Bouwmans, T.: Traditional and recent approaches in background modeling for foreground detection: An overview. Computer Science Review (2014)Google Scholar
  3. 3.
    Bouwmans, T., Zahzah, E.: Robust PCA via principal component pursuit: a review for a comparative evaluation in video surveillance. In: Special Isssue on Background Models Challenge, Computer Vision and Image Understanding. vol. 122, pp. 22–34, May 2014Google Scholar
  4. 4.
    Cai, J.F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. on Optimization 20(4), 1956–1982 (2010)CrossRefzbMATHGoogle Scholar
  5. 5.
    Candès, E.J., Plan, Y.: Matrix completion with noise. CoRR abs/0903.3131 (2009)Google Scholar
  6. 6.
    Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. CoRR abs/0805.4471 (2008). http://arxiv.org/abs/0805.4471
  7. 7.
    Cucchiara, R., Grana, C., Piccardi, M., Prati, A.: Detecting objects, shadows and ghosts in video streams by exploiting color and motion information. In: ICIAP 2001, pp. 360–365, September 2001Google Scholar
  8. 8.
    Keshavan, R.H., Montanari, A., Oh, S.: Matrix completion from noisy entries. The Journal of Machine Learning Research 99, 2057–2078 (2010)MathSciNetGoogle Scholar
  9. 9.
    Lai, A.H.S., Yung, N.H.C.: A fast and accurate scoreboard algorithm for estimating stationary backgrounds in an image sequence. In: IEEE SCS 1998, pp. 241–244 (1998)Google Scholar
  10. 10.
    Lin, Z., Chen, M., Ma, Y.: The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices. Mathematical Programming (2010)Google Scholar
  11. 11.
    Maddalena, L., Petrosino, A.: Background model initialization for static cameras. In: Background Modeling and Foreground Detection for Video Surveillance. CRC Press, Taylor and Francis Group (2014)Google Scholar
  12. 12.
    Maddalena, L., Petrosino, A.: Towards benchmarking scene background initialization. CoRR abs/1506.04051 (2015). http://arxiv.org/abs/1506.04051
  13. 13.
    Meka, R., Jain, P., Dhillon, I.S.: Guaranteed rank minimization via singular value projection. CoRR abs/0909.5457 (2009)Google Scholar
  14. 14.
    Ngo, T., Saad, Y.: Scaled gradients on grassmann manifolds for matrix completion. Advances in Neural Information Processing Systems 25, 1412–1420 (2012)Google Scholar
  15. 15.
    Oliver, N.M., Rosario, B., Pentland, A.P.: A bayesian computer vision system for modeling human interactions. IEEE PAMI 22(8), 831–843 (2000)CrossRefGoogle Scholar
  16. 16.
    Sobral, A., Vacavant, A.: A comprehensive review of background subtraction algorithms evaluated with synthetic and real videos. CVIU 122, 4–21 (2014). http://www.sciencedirect.com/science/article/pii/S1077314213002361 Google Scholar
  17. 17.
    Vandereycken, B.: Low-rank matrix completion by Riemannian optimization. SIAM Journal on Optimization 23(2), 1214–1236 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  18. 18.
    Wang, Z., Lai, M., Lu, Z., Fan, W., Davulcu, H., Ye, J.: Orthogonal rank-one matrix pursuit for low rank matrix completion. SIAM J. Scientific Computing 37(1) (2015). http://dx.doi.org/10.1137/130934271
  19. 19.
    Wen, Z., Yin, W., Zhang, Y.: Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm. Mathematical Programming Computation 4(4), 333–361 (2012). http://dx.doi.org/10.1007/s12532-012-0044-1 CrossRefMathSciNetzbMATHGoogle Scholar
  20. 20.
    Ye, X., Yang, J., Sun, X., Li, K., Hou, C., Wang, Y.: Foreground-background separation from video clips via motion-assisted matrix restoration. IEEE T-CSVT PP(99), 1 (2015)Google Scholar
  21. 21.
    Zhou, X., Yang, C., Zhao, H., Yu, W.: Low-rank modeling and its applications in image analysis. ACM Computing Surveys (CSUR) 47(2), 36 (2014)CrossRefGoogle Scholar
  22. 22.
    Zivkovic, Z.: Improved adaptive gaussian mixture model for background subtraction. In: ICPR 2004, vol. 2, pp. 28–31, Auguet 2004Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Andrews Sobral
    • 1
    • 2
    Email author
  • Thierry Bouwmans
    • 2
  • El-hadi Zahzah
    • 1
  1. 1.Lab. L3IUniversité de La RochelleLa RochelleFrance
  2. 2.Lab. MIAUniversité de La RochelleLa RochelleFrance

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