Globally Optimal Image Partitioning by Multicuts

  • Jörg Hendrik Kappes
  • Markus Speth
  • Björn Andres
  • Gerhard Reinelt
  • Christoph Schn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6819)


We introduce an approach to both image labeling and unsupervised image partitioning as different instances of the multicut problem, together with an algorithm returning globally optimal solutions. For image labeling, the approach provides a valid alternative. For unsupervised image partitioning, the approach outperforms state-of-the-art labeling methods with respect to both optimality and runtime, and additionally returns competitive performance measures for the Berkeley Segmentation Dataset as reported in the literature.


image segmentation partitioning labeling multicuts multiway cuts multicut polytope cutting planes integer programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kleinberg, J., Tardos, É.: Approximation algorithms for classification problems with pairwise relationships: Metric labeling and Markov random fields. In: FOCS (1999)Google Scholar
  2. 2.
    Wainwright, M.J., Jordan, M.I.: Graphical models, exponential families, and variational inference. FTML 1, 1–305 (2008)zbMATHGoogle Scholar
  3. 3.
    Sontag, D., Jaakkola, T.: New outer bounds on the marginal polytope. In: NIPS (2007)Google Scholar
  4. 4.
    Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. TPAMI 28, 1568–1583 (2006)CrossRefGoogle Scholar
  5. 5.
    Deza, M., Grötschel, M., Laurent, M.: Complete descriptions of small multicut polytopes. In: Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift. American Mathematical Society, Providence (1991)Google Scholar
  6. 6.
    Chopra, S., Rao, M.R.: On the multiway cut polyhedron. Networks 21, 51–89 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chopra, S., Rao, M.R.: The partition problem. Mathematical Programming 59, 87–115 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Boykov, Y., Veksler, O., Zabih, R.: Markov random fields with efficient approximations. In: CVPR (1998)Google Scholar
  9. 9.
    Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? TPAMI 26, 147–159 (2004)CrossRefzbMATHGoogle Scholar
  10. 10.
    Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiway cuts (extended abstract). In: STOC (1992)Google Scholar
  11. 11.
  12. 12.
    Călinescu, G., Karloff, H., Rabani, Y.: An improved approximation algorithm for multiway cut. JCSS 60, 564–574 (2000)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. TPAMI 23, 1222–1239 (2001)CrossRefGoogle Scholar
  14. 14.
    Andres, B., Kappes, J.H., Beier, T., Köthe, U., Hamprecht, F.: Probabilistic image segmentation with closedness constraints (submitted to ICCV 2011)Google Scholar
  15. 15.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)zbMATHGoogle Scholar
  16. 16.
    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. TPAMI 30, 1068–1080 (2008)CrossRefGoogle Scholar
  17. 17.
    Lellmann, J., Kappes, J., Yuan, J., Becker, F., Schnörr, C.: Convex multi-class image labeling by simplex-constrained total variation. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 150–162. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: ICCV (2001)Google Scholar
  19. 19.
    Arbeláez, P.: Boundary extraction in natural images using ultrametric contour maps. In: CVPRW (2006)Google Scholar
  20. 20.
    Maire, M., Arbeláez, P., Fowlkes, C., Malik, J.: Using contours to detect and localize junctions in natural images. In: CVPR (2008)Google Scholar
  21. 21.
    Ren, X.: Multi-scale improves boundary detection in natural images. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 533–545. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jörg Hendrik Kappes
    • 1
  • Markus Speth
    • 1
  • Björn Andres
    • 1
  • Gerhard Reinelt
    • 1
  • Christoph Schn
    • 1
  1. 1.Image & Pattern Analysis Group, Discrete and Combinatorial Optimization Group, Multidimensional Image Processing GroupUniversity of HeidelbergGermany

Personalised recommendations