Parallel Multicut Segmentation via Dual Decomposition

  • Julian Yarkony
  • Thorsten Beier
  • Pierre Baldi
  • Fred A. Hamprecht
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8983)


We propose a new outer relaxation of the multicut polytope, along with a dual decomposition approach for correlation clustering and multicut segmentation, for general graphs. Each subproblem is a minimum \(st\)-cut problem and can thus be solved efficiently. An optimal reparameterization is found using subgradients and affords a new characterization of the basic LP relaxation of the multicut problem, as well as informed decoding heuristics. The algorithm we propose for solving the problem distributes the computation and is amenable to a parallel implementation.


Dual decomposition Multi-cut segmentation Correlation clustering 


  1. 1.
    Andres, B., Kappes, J.H., Beier, T., Köthe, U., Hamprecht, F.A.: Probabilistic image segmentation with closedness constraints. In: ICCV (2011)Google Scholar
  2. 2.
    Andres, B., Yarkony, J., Manjunath, B.S., Kirchhoff, S., Turetken, E., Fowlkes, C.C., Pfister, H.: Segmenting planar superpixel adjacency graphs w.r.t. non-planar superpixel affinity graphs. In: Heyden, A., Kahl, F., Olsson, C., Oskarsson, M., Tai, X.-C. (eds.) EMMCVPR 2013. LNCS, vol. 8081, pp. 266–279. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  3. 3.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. TPAMI 33(5), 898–916 (2011)CrossRefGoogle Scholar
  4. 4.
    Barahona, F., Mahjoub, A.: On the cut polytope. Math. Program. 36(2), 157–173 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Chopra, S., Rao, M.R.: The partition problem. Math. Program. 59, 87–115 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Deza, M.M., Grotschel, M., Laurent, M.: Complete descriptions of small multicut polytopes. In: Gritzmann, P., Sturmfels, B. (eds.) Applied Geometry and Discrete Mathematics, The Victor Klee Festschrift, vol. 4 (1991)Google Scholar
  7. 7.
    Deza, M.M., Laurent, M.: Geometry of Cuts and Metrics. Springer, New York (1997)CrossRefzbMATHGoogle Scholar
  8. 8.
    Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23, 864–894 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Franc, V., Sonnenburg, S., Werner, T.: Cutting-plane methods in machine learning. In: Sra, S., Nowozin, S., Wright, S.J. (eds.) Optimization for Machine Learning, Chap. 7, pp. 185–218. MIT Press, Cambridge (2012)Google Scholar
  10. 10.
    Kohli, P., Torr, P.H.S.: Dynamic graph cuts for efficient inference in markov random fields. TPAMI 29(12), 2079–2088 (2007)CrossRefGoogle Scholar
  11. 11.
    Kolmogorov, V., Wainwright, M.J.: On the optimality of tree-reweighted max-product message-passing. CoRR abs/1207.1395 (2005)Google Scholar
  12. 12.
    Komodakis, N., Paragios, N., Tziritas, G.: MRF energy minimization and beyond via dual decomposition. TPAMI 33(3), 531–552 (2011)CrossRefGoogle Scholar
  13. 13.
    Laurent, M.: A comparison of the Sherali-Adams, Lovasz-Schrijver and Lasserre relaxations for 0–1 programming. Math. Oper. Res. 28, 470–496 (2001)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Martin, D., Fowlkes, C.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, pp. 416–423 (2001)Google Scholar
  15. 15.
    Rother, C., Kolmogorov, V., Lempitsky, V., Szummer, M.: Optimizing binary MRFs via extended roof duality. In: CVPR, pp. 1–8, June 2007Google Scholar
  16. 16.
    Sontag, D., Globerson, A., Jaakola, T.: Introduction to dual decomposition for inference (2010)Google Scholar
  17. 17.
    Sontag, D., Meltzer, T., Globerson, A., Jaakkola, T., Weiss, Y.: Tightening LP relaxations for MAP using message passing. In: UAI, pp. 503–510 (2008)Google Scholar
  18. 18.
    Yarkony, J., Ihler, A., Fowlkes, C.C.: Fast planar correlation clustering for image segmentation. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part VI. LNCS, vol. 7577, pp. 568–581. Springer, Heidelberg (2012) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Julian Yarkony
    • 1
    • 2
  • Thorsten Beier
    • 1
  • Pierre Baldi
    • 2
  • Fred A. Hamprecht
    • 1
  1. 1.Heidelberg Collaboratory for Image Processing (HCI)University of HeidelbergHeidelbergGermany
  2. 2.Department of Computer ScienceUniversity of California, IrvineIrvineUSA

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