Fast-Robust PCA

  • Markus Storer
  • Peter M. Roth
  • Martin Urschler
  • Horst Bischof
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5575)


Principal Component Analysis (PCA) is a powerful and widely used tool in Computer Vision and is applied, e.g., for dimensionality reduction. But as a drawback, it is not robust to outliers. Hence, if the input data is corrupted, an arbitrarily wrong representation is obtained. To overcome this problem, various methods have been proposed to robustly estimate the PCA coefficients, but these methods are computationally too expensive for practical applications. Thus, in this paper we propose a novel fast and robust PCA (FR-PCA), which drastically reduces the computational effort. Moreover, more accurate representations are obtained. In particular, we propose a two-stage outlier detection procedure, where in the first stage outliers are detected by analyzing a large number of smaller subspaces. In the second stage, remaining outliers are detected by a robust least-square fitting. To show these benefits, in the experiments we evaluate the FR-PCA method for the task of robust image reconstruction on the publicly available ALOI database. The results clearly show that our approach outperforms existing methods in terms of accuracy and speed when processing corrupted data.


Principal Component Analysis Outlier Detection Reconstruction Error Pepper Noise Active Appearance Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  2. 2.
    Murase, H., Nayar, S.K.: Visual learning and recognition of 3-d objects from appearance. Intern. Journal of Computer Vision 14(1), 5–24 (1995)CrossRefGoogle Scholar
  3. 3.
    Kirby, M., Sirovich, L.: Application of the karhunen-loeve procedure for the characterization of human faces. IEEE Trans. on Pattern Analysis and Machine Intelligence 12(1), 103–108 (1990)CrossRefGoogle Scholar
  4. 4.
    Turk, M., Pentland, A.: Eigenfaces for recognition. Journal of Cognitive Neuroscience 3(1), 71–86 (1991)CrossRefGoogle Scholar
  5. 5.
    Wang, Y., Huang, K., Tan, T.: Human activity recognition based on r transform. In: Proc. CVPR (2008)Google Scholar
  6. 6.
    Tai, Y.W., Brown, M.S., Tang, C.K.: Robust estimation of texture flow via dense feature sampling. In: Proc. CVPR (2007)Google Scholar
  7. 7.
    Lee, S.M., Abbott, A.L., Araman, P.A.: Dimensionality reduction and clustering on statistical manifolds. In: Proc. CVPR (2007)Google Scholar
  8. 8.
    Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models - their training and application. Computer Vision and Image Understanding 61, 38–59 (1995)CrossRefGoogle Scholar
  9. 9.
    Cootes, T.F., Edwards, G.J., Taylor, C.J.: Active appearance models. IEEE Trans. on Pattern Analysis and Machine Intelligence 23(6), 681–685 (2001)CrossRefGoogle Scholar
  10. 10.
    Huber, P.J.: Robust Statistics. John Wiley & Sons, Chichester (2004)Google Scholar
  11. 11.
    Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A.: Robust Statistics: The Approach Based on Influence Functions. John Wiley & Sons, Chichester (1986)zbMATHGoogle Scholar
  12. 12.
    Xu, L., Yuille, A.L.: Robust principal component analysis by self-organizing rules based on statistical physics approach. IEEE Trans. on Neural Networks 6(1), 131–143 (1995)CrossRefGoogle Scholar
  13. 13.
    Torre, F.d., Black, M.J.: A framework for robust subspace learning. Intern. Journal of Computer Vision 54(1), 117–142 (2003)CrossRefzbMATHGoogle Scholar
  14. 14.
    Roweis, S.: EM algorithms for PCA and SPCA. In: Advances in Neural Information Processing Systems, pp. 626–632 (1997)Google Scholar
  15. 15.
    Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. Journal of the Royal Statistical Society B 61, 611–622 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Skočaj, D., Bischof, H., Leonardis, A.: A robust PCA algorithm for building representations from panoramic images. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2353, pp. 761–775. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Rao, R.: Dynamic appearance-based recognition. In: Proc. CVPR, pp. 540–546 (1997)Google Scholar
  18. 18.
    Black, M.J., Jepson, A.D.: Eigentracking: Robust matching and tracking of articulated objects using a view-based representation. In: Proc. European Conf. on Computer Vision, pp. 329–342 (1996)Google Scholar
  19. 19.
    Leonardis, A., Bischof, H.: Robust recognition using eigenimages. Computer Vision and Image Understanding 78(1), 99–118 (2000)CrossRefzbMATHGoogle Scholar
  20. 20.
    Edwards, J.L., Murase, J.: Coarse-to-fine adaptive masks for appearance matching of occluded scenes. Machine Vision and Applications 10(5–6), 232–242 (1998)CrossRefGoogle Scholar
  21. 21.
    Geusebroek, J.M., Burghouts, G.J., Smeulders, A.W.M.: The Amsterdam Library of Object Images. International Journal of Computer Vision 61(1), 103–112 (2005)CrossRefGoogle Scholar
  22. 22.
    Storer, M., Roth, P.M., Urschler, M., Bischof, H., Birchbauer, J.A.: Active appearance model fitting under occlusion using fast-robust PCA. In: Proc. International Conference on Computer Vision Theory and Applications (VISAPP), February 2009, vol. 1, pp. 130–137 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Markus Storer
    • 1
  • Peter M. Roth
    • 1
  • Martin Urschler
    • 1
  • Horst Bischof
    • 1
  1. 1.Institute for Computer Graphics and VisionGraz University of TechnologyGrazAustria

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