Solving Minimum Cost Lifted Multicut Problems by Node Agglomeration

  • Amirhossein KardoostEmail author
  • Margret Keuper
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11364)


Despite its complexity, the minimum cost lifted multicut problem has found a wide range of applications in recent years, such as image and mesh decomposition or multiple object tracking. Its solutions are decompositions of a graph into an optimal number of segments which are optimized w.r.t. a cost function defined on a superset of the edge set. While the currently available solvers for this problem provide high quality solutions in terms of the task to be solved, they can have long computation times for more difficult problem instances. Here, we propose two variants of a heuristic solver (primal feasible heuristic), which greedily generate solutions within a bounded amount of time. Evaluations on image and mesh segmentation benchmarks show the high quality of these solutions.



We acknowledge funding by the DFG project KE 2264/1-1. We also acknowledge the NVIDIA Corporation for the donation of a Titan Xp GPU.


  1. 1.
    Keuper, M., Levinkov, E., Bonneel, N., Lavoué, G., Brox, T., Andres, B.: Efficient decomposition of image and mesh graphs by lifted multicuts. In: 2015 IEEE International Conference on Computer Vision (ICCV). pp. 1751–1759 (2015)Google Scholar
  2. 2.
    Tang, S., Andriluka, M., Andres, B., Schiele, B.: Multi people tracking with lifted multicut and person re-identification. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2017)Google Scholar
  3. 3.
    Keuper, M.: Higher-order minimum cost lifted multicuts for motion segmentation. In: The IEEE International Conference on Computer Vision (ICCV) (2017)Google Scholar
  4. 4.
    Beier, T., Andres, B., Köthe, U., Hamprecht, F.A.: An efficient fusion move algorithm for the minimum cost lifted multicut problem. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9906, pp. 715–730. Springer, Cham (2016). Scholar
  5. 5.
    Beier, T., et al.: Multicut brings automated neurite segmentation closer to human performance. Nat. Methods 14, 101 (2017)CrossRefGoogle Scholar
  6. 6.
    Chopra, S., Rao, M.: The partition problem. Math. Programm. 59, 87–115 (1993)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Deza, M.M., Laurent, M.: Geometry of Cuts and Metrics. AC, vol. 15. Springer, Heidelberg (1997). Scholar
  8. 8.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE TPAMI 33(5), 898–916 (2011)CrossRefGoogle Scholar
  9. 9.
    Alush, A., Goldberger, J.: Ensemble segmentation using efficient integer linear programming. TPAMI 34, 1966–1977 (2012)CrossRefGoogle Scholar
  10. 10.
    Andres, B., Kappes, J.H., Beier, T., Köthe, U., Hamprecht, F.A.: Probabilistic image segmentation with closedness constraints. In: ICCV (2011)Google Scholar
  11. 11.
    Andres, B., et al.: Globally Optimal Closed-Surface Segmentation for Connectomics. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012. LNCS, vol. 7574, pp. 778–791. Springer, Heidelberg (2012). Scholar
  12. 12.
    Andres, B., et al.: 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). Scholar
  13. 13.
    Bagon, S., Galun, M.: Large scale correlation clustering optimization. CoRR abs/1112.2903 (2011)Google Scholar
  14. 14.
    Beier, T., Hamprecht, F.A., Kappes, J.H.: Fusion moves for correlation clustering. In: CVPR (2015)Google Scholar
  15. 15.
    Beier, T., Kroeger, T., Kappes, J., Köthe, U., Hamprecht, F.: Cut, glue, & cut: a fast, approximate solver for multicut partitioning. In: CVPR (2014)Google Scholar
  16. 16.
    Kappes, J.H., Speth, M., Andres, B., Reinelt, G., Schnörr, C.: Globally optimal image partitioning by multicuts. In: Boykov, Y., Kahl, F., Lempitsky, V., Schmidt, F.R. (eds.) EMMCVPR 2011. LNCS, vol. 6819, pp. 31–44. Springer, Heidelberg (2011). Scholar
  17. 17.
    Kappes, J.H., Speth, M., Reinelt, G., Schnörr, C.: Higher-order segmentation via multicuts. CoRR abs/1305.6387 (2013)Google Scholar
  18. 18.
    Kappes, J.H., Swoboda, P., Savchynskyy, B., Hazan, T., Schnörr, C.: Probabilistic correlation clustering and image partitioning using perturbed multicuts. In: Aujol, J.-F., Nikolova, M., Papadakis, N. (eds.) SSVM 2015. LNCS, vol. 9087, pp. 231–242. Springer, Cham (2015). Scholar
  19. 19.
    Kim, S., Nowozin, S., Kohli, P., Yoo, C.D.: Higher-order correlation clustering for image segmentation. In: NIPS (2011)Google Scholar
  20. 20.
    Kim, S., Yoo, C.D., Nowozin, S.: Image segmentation using higher-order correlation clustering. IEEE TPAMI 36, 1761–1774 (2014)CrossRefGoogle Scholar
  21. 21.
    Nowozin, S., Jegelka, S.: Solution stability in linear programming relaxations: graph partitioning and unsupervised learning. In: ICML (2009)Google Scholar
  22. 22.
    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. LNCS, vol. 7577, pp. 568–581. Springer, Heidelberg (2012). Scholar
  23. 23.
    Yarkony, J., Zhang, C., Fowlkes, C.C.: Hierarchical planar correlation clustering for cell segmentation. In: Tai, X.-C., Bae, E., Chan, T.F., Lysaker, M. (eds.) EMMCVPR 2015. LNCS, vol. 8932, pp. 492–504. Springer, Cham (2015). Scholar
  24. 24.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. TPAMI 22, 888–905 (2000)CrossRefGoogle Scholar
  25. 25.
    Horňáková, A., Lange, J.H., Andres, B.: Analysis and optimization of graph decompositions by lifted multicuts. In: ICML (2017)Google Scholar
  26. 26.
    Chen, X., Golovinskiy, A., Funkhouser, T.: A benchmark for 3D mesh segmentation. ACM Trans. Graph. (Proc. SIGGRAPH) 28, 73 (2009)Google Scholar
  27. 27.
    Demaine, E.D., Emanuel, D., Fiat, A., Immorlica, N.: Correlation clustering in general weighted graphs. Theor. Comput. Sci. 361, 172–187 (2006)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Kappes, J.H., et al.: A comparative study of modern inference techniques for structured discrete energy minimization problems. In: IJCV (2015)Google Scholar
  29. 29.
    Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 49, 291–307 (1970)CrossRefGoogle Scholar
  30. 30.
    Kappes, J., et al.: A comparative study of modern inference techniques for structured discrete energy minimization problems. Int. J. Comput. Vis. 115, 155–184 (2015)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Cardona, A., et al.: An integrated micro- and macroarchitectural analysis of the drosophila brain by computer-assisted serial section electron microscopy. PLOS Biol. 8, 1–17 (2010)CrossRefGoogle Scholar
  32. 32.
    Carreras, I., et al.: Crowdsourcing the creation of image segmentation algorithms for connectomics. Frontiers Neuroanat. 9, 1–13 (2015)Google Scholar
  33. 33.
    Andres, B.: Lifting of multicuts. CoRR abs/1503.03791 (2015)Google Scholar
  34. 34.
    Meilă, M.: Comparing clusterings-an information based distance. J. Multivar. Anal. 98, 873–895 (2007)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Data and Web Science GroupUniversity of MannheimMannheimGermany

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