Background Recovery by Fixed-Rank Robust Principal Component Analysis

  • Wee Kheng Leow
  • Yuan Cheng
  • Li Zhang
  • Terence Sim
  • Lewis Foo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8047)


Background recovery is a very important theme in computer vision applications. Recent research shows that robust principal component analysis (RPCA) is a promising approach for solving problems such as noise removal, video background modeling, and removal of shadows and specularity. RPCA utilizes the fact that the background is common in multiple views of a scene, and attempts to decompose the data matrix constructed from input images into a low-rank matrix and a sparse matrix. This is possible if the sparse matrix is sufficiently sparse, which may not be true in computer vision applications. Moreover, algorithmic parameters need to be fine tuned to yield accurate results. This paper proposes a fixed-rank RPCA algorithm for solving background recovering problems whose low-rank matrices have known ranks. Comprehensive tests show that, by fixing the rank of the low-rank matrix to a known value, the fixed-rank algorithm produces more reliable and accurate results than existing low-rank RPCA algorithm.


Background recovery reflection removal robust PCA 


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  1. 1.
    Babacan, S.D., Luessi, M., Molina, R., Katsaggelos, A.K.: Sparse bayesian methods for low-rank matrix estimation. IEEE Trans. Signal Processing 60(8), 3964–3977 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Candès, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? Journal of ACM 58(3), 11 (2011)CrossRefGoogle Scholar
  3. 3.
    Candès, E.J., Plan, Y.: Matrix completion with noise. In: Proc. IEEE, pp. 925–936 (2010)Google Scholar
  4. 4.
    De la Torre, F., Black, M.: A framework for robust subspace learning. Int. Journal of Computer Vision 54(1-3), 117–142 (2003)zbMATHCrossRefGoogle Scholar
  5. 5.
    Fischler, M., Bolles, R.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of ACM 24(6), 381–385 (1981)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ganesh, A., Lin, Z., Wright, J., Wu, L., Chen, M., Ma, Y.: Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix. In: CAMSAP (2009)Google Scholar
  7. 7.
    Gnanadesikan, R., Kettenring, J.: A framework for robust subspace learning. Robust Estimates, Residuals, and Outlier Detection with Multiresponse Data (check journal title) 28(1), 81–124 (1972)Google Scholar
  8. 8.
    Ke, Q., Kanade, T.: Robust L1 norm factorization in the presence of outliers and missing data by alternative convex programming. In: Proc. CVPR, pp. 739–746 (2005)Google Scholar
  9. 9.
    Lin, Z., Chen, M., Wu, L., Ma, Y.: The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. Technical Report UILU-ENG-09-2215, UIUC (2009), arXiv preprint arXiv:1009.5055Google Scholar
  10. 10.
    Liu, R., Lin, Z., De la Torre, F., Su, Z.: Fixed-rank representation for unsupervised visual learning. In: Proc. CVPR, pp. 598–605 (2012)Google Scholar
  11. 11.
    Wang, N., Yao, T., Wang, J., Yeung, D.-Y.: A probabilistic approach to robust matrix factorization. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part VII. LNCS, vol. 7578, pp. 126–139. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    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: Proc. NIPS, pp. 2080–2088 (2009)Google Scholar
  13. 13.
    Zhou, Z., Li, X., Wright, J., Candès, E.J., Ma, Y.: Stable principal component pursuit. In: Proc. Int. Symp. Information Theory, pp. 1518–1522 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wee Kheng Leow
    • 1
  • Yuan Cheng
    • 1
  • Li Zhang
    • 1
  • Terence Sim
    • 1
  • Lewis Foo
    • 1
  1. 1.Department of Computer ScienceNational University of SingaporeSingapore

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