Fast Multi-labelling for Stereo Matching

  • Yuhang Zhang
  • Richard Hartley
  • Lei Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6313)


We describe a new fast algorithm for multi-labelling problems. In general, a multi-labelling problem is NP-hard. Widely used algorithms like α-expansion can reach a suboptimal result in a time linear in the number of the labels. In this paper, we propose an algorithm which can obtain results of comparable quality polynomially faster. We use the Divide and Conquer paradigm to separate the complexities induced by the label set and the variable set, and deal with each of them respectively. Such a mechanism improves the solution speed without depleting the memory resource, hence it is particularly valuable for applications where the variable set and the label set are both huge. Another merit of the proposed method is that the trade-off between quality and time efficiency can be varied through using different parameters. The advantage of our method is validated by experiments.


Tuning Range Stereo Match Stereo Pair Minimum Cycle Exterior Edge 
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.
    Zabih, R., Veksler, O., Boykov, Y.: Fast approximate energy minimization via graph cuts. In: ICCV 1999, pp. 377–384 (1999)Google Scholar
  2. 2.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23, 1222–1239 (2001)CrossRefGoogle Scholar
  3. 3.
    Komodakis, N., Tziritas, G., Paragios, N.: Performance vs computational efficiency for optimizing single and dynamic mrfs: Setting the state of the art with primal-dual strategies. Comput. Vis. Image Underst. 112, 14–29 (2008)CrossRefGoogle Scholar
  4. 4.
    Komodakis, N., Tziritas, G.: Approximate labeling via graph cuts based on linear programming. PAMI 29, 1436–1453 (2007)Google Scholar
  5. 5.
    Boros, E., Hammer, P.L.: Pseudo-boolean optimization. Discrete Applied Mathematics 123, 155–225 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Carr, P., Hartley, R.: Solving multilabel graph cut problems using multilabel swap. In: DICTA, Melbourne, Australia (2009)Google Scholar
  7. 7.
    Carr, P., Hartley, R.: Minimizing energy functions on 4-connected lattices using elimination. In: ICCV, Kyoto, Japan (2009)Google Scholar
  8. 8.
    Kohli, P., Torr, P.: Dynamic graph cuts for efficient inference in markov random fields. PAMI 29, 2079–2088 (2007)Google Scholar
  9. 9.
    Goldberg, A.V., Rao, S.: Beyond the flow decomposition barrier. J. ACM 45, 783–797 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Rother, C., Kolmogorov, V., Lempitsky, V., Szummer, M.: Optimizing binary mrfs via extended roof duality. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR (2007)Google Scholar
  11. 11.
    Gould, S., Amat, F., Koller, D.: Alphabet SOUP: A framework for approximate energy minimization. In: CVPR (2009)Google Scholar
  12. 12.
    Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., Rother, C.: A comparative study of energy minimization methods for markov random fields with smoothness-based priors. IEEE Trans. Pattern Anal. Mach. Intell. 30, 1068–1080 (2008)CrossRefGoogle Scholar
  13. 13.
    Scharstein, D., Szeliski, R., Zabih, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. SMBV 2001: Proceedings of the IEEE Workshop on Stereo and Multi-Baseline Vision (SMBV 2001), p. 131 (2001)Google Scholar
  14. 14.
    Wang, L., Jin, H., Yang, R.: Search space reduction for mrf stereo. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 576–588. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Veksler, O.: Reducing search space for stereo correspondence with graph cuts. In: BMVC 2006, vol. II, p. 709 (2006)Google Scholar
  16. 16.
    Hirschmuller, H., Scharstein, D.: Evaluation of cost functions for stereo matching. In: CVPR 2007 (2007)Google Scholar
  17. 17.
    Scharstein, D., Pal, C.: Learning conditional random fields for stereo. In: CVPR 2007 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yuhang Zhang
    • 1
  • Richard Hartley
    • 1
    • 2
  • Lei Wang
    • 1
  1. 1.The Australian National University 
  2. 2.NICTA 

Personalised recommendations