Image Segmentation by Branch-and-Mincut

  • Victor Lempitsky
  • Andrew Blake
  • Carsten Rother
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5305)


Efficient global optimization techniques such as graph cut exist for energies corresponding to binary image segmentation from low-level cues. However, introducing a high-level prior such as a shape prior or a color-distribution prior into the segmentation process typically results in an energy that is much harder to optimize. The main contribution of the paper is a new global optimization framework for a wide class of such energies. The framework is built upon two powerful techniques: graph cut and branch-and-bound. These techniques are unified through the derivation of lower bounds on the energies. Being computable via graph cut, these bounds are used to prune branches within a branch-and-bound search.

We demonstrate that the new framework can compute globally optimal segmentations for a variety of segmentation scenarios in a reasonable time on a modern CPU. These scenarios include unsupervised segmentation of an object undergoing 3D pose change, category-specific shape segmentation, and the segmentation under intensity/color priors defined by Chan-Vese and GrabCut functionals.


Image Segmentation Active Front Optimal Segmentation Shape Prior Image Segmentation Problem 
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.

Supplementary material

978-3-540-88693-8_2_MOESM1_ESM.avi (13.1 mb)
Supplementary material(13,411 KB)
978-3-540-88693-8_2_MOESM2_ESM.avi (11.8 mb)
Supplementary material(12,110 KB)


  1. 1.
    Agarwal, S., Chandaker, M., Kahl, F., Kriegman, D., Belongie, S.: Practical Global Optimization for Multiview Geometry. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951. Springer, Heidelberg (2006)Google Scholar
  2. 2.
    Boros, E., Hammer, P.: Pseudo-boolean optimization. Discrete Applied Mathematics 123(1-3) (2002)Google Scholar
  3. 3.
    Boykov, Y., Jolly, M.-P.: Interactive Graph Cuts for Optimal Boundary and Region Segmentation of Objects in N-D Images. In: ICCV 2001 (2001)Google Scholar
  4. 4.
    Boykov, Y., Kolmogorov, V.: Computing Geodesics and Minimal Surfaces via Graph Cuts. In: ICCV 2003 (2003)Google Scholar
  5. 5.
    Boykov, Y., Kolmogorov, V.: An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision. PAMI 26(9) (2004)Google Scholar
  6. 6.
    Bray, M., Kohli, P., Torr, P.: PoseCut: Simultaneous Segmentation and 3D Pose Estimation of Humans Using Dynamic Graph-Cuts. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3952. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Chan, T., Vese, L.: Active contours without edges. Trans. Image Process 10(2) (2001)Google Scholar
  8. 8.
    Clausen, J.: Branch and Bound Algorithms - Principles and Examples. Parallel Computing in Optimization (1997)Google Scholar
  9. 9.
    Cremers, D., Osher, S., Soatto, S.: Kernel Density Estimation and Intrinsic Alignment for Shape Priors in Level Set Segmentation. IJCV 69(3) (2006)Google Scholar
  10. 10.
    Cremers, D., Schmidt, F., Barthel, F.: Shape Priors in Variational Image Segmentation: Convexity, Lipschitz Continuity and Globally Optimal Solutions. In: CVPR 2008 (2008)Google Scholar
  11. 11.
    Greig, D., Porteous, B., Seheult, A.: Exact maximum a posteriori estimation for binary images. Journal of the Royal Statistical Society 51(2) (1989)Google Scholar
  12. 12.
    Felzenszwalb, P.: Representation and Detection of Deformable Shapes. PAMI 27(2) (2005)Google Scholar
  13. 13.
    Freedman, D., Zhang, T.: Interactive Graph Cut Based Segmentation with Shape Priors. In: CVPR 2005 (2005)Google Scholar
  14. 14.
    Gavrila, D., Philomin, V.: Real-Time Object Detection for ”Smart” Vehicles. In: ICCV 1999 (1999)Google Scholar
  15. 15.
    Huang, R., Pavlovic, V., Metaxas, D.: A graphical model framework for coupling MRFs and deformable models. In: CVPR 2004 (2004)Google Scholar
  16. 16.
    Kim, J., Zabih, R.: A Segmentation Algorithm for Contrast-Enhanced Images. ICCV 2003 (2003)Google Scholar
  17. 17.
    Kohli, P., Torr, P.: Effciently Solving Dynamic Markov Random Fields Using Graph Cuts. In: ICCV 2005 (2005)Google Scholar
  18. 18.
    Kolmogorov, V., Zabih, R.: What Energy Functions Can Be Minimized via Graph Cuts. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352. Springer, Heidelberg (2002)Google Scholar
  19. 19.
    Kolmogorov, V., Boykov, Y., Rother, C.: Applications of Parametric Maxflow in Computer Vision. In: ICCV 2007 (2007)Google Scholar
  20. 20.
    Pawan Kumar, M., Torr, P., Zisserman, A.: OBJ CUT. In: CVPR 2005 (2005)Google Scholar
  21. 21.
    Lampert, C., Blaschko, M., Hofman, T.: Beyond Sliding Windows: Object Localization by Efficient Subwindow Search. In: CVPR 2008 (2008)Google Scholar
  22. 22.
    Leibe, B., Leonardis, A., Schiele, B.: Robust Object Detection with Interleaved Categorization and Segmentation. IJCV 77(3) (2008)Google Scholar
  23. 23.
    Lempitsky, V., Blake, A., Rother, C.: Image Segmentation by Branch-and-Mincut. Microsoft Technical Report MSR-TR-2008-100 (July 2008)Google Scholar
  24. 24.
    Leventon, M., Grimson, E., Faugeras, O.: Statistical Shape Influence in Geodesic Active Contours. In: CVPR 2000 (2000)Google Scholar
  25. 25.
    Rother, C., Kolmogorov, V., Blake, A.: ”GrabCut”: interactive foreground extraction using iterated graph cuts. ACM Trans. Graph. 23(3) (2004)Google Scholar
  26. 26.
    Schoenemann, T., Cremers, D.: Globally Optimal Image Segmentation with an Elastic Shape Prior. In: ICCV 2007 (2007)Google Scholar
  27. 27.
    Wang, Y., Staib, L.: Boundary Finding with Correspondence Using Statistical Shape Models. In: CVPR 1998 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Victor Lempitsky
    • 1
  • Andrew Blake
    • 1
  • Carsten Rother
    • 1
  1. 1.Microsoft Research Cambridge 

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