Segmenting Planar Superpixel Adjacency Graphs w.r.t. Non-planar Superpixel Affinity Graphs

  • Bjoern Andres
  • Julian Yarkony
  • B. S. Manjunath
  • Steffen Kirchhoff
  • Engin Turetken
  • Charless C. Fowlkes
  • Hanspeter Pfister
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8081)

Abstract

We address the problem of segmenting an image into a previously unknown number of segments from the perspective of graph partitioning. Specifically, we consider minimum multicuts of superpixel affinity graphs in which all affinities between non-adjacent superpixels are negative. We propose a relaxation by Lagrangian decomposition and a constrained set of re-parameterizations for which we can optimize exactly and efficiently. Our contribution is to show how the planarity of the adjacency graph can be exploited if the affinity graph is non-planar. We demonstrate the effectiveness of this approach in user-assisted image segmentation and show that the solution of the relaxed problem is fast and the relaxation is tight in practice.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
  2. 2.
    Andres, B., Kappes, J.H., Beier, T., Köthe, U., Hamprecht, F.A.: Probabilistic image segmentation with closedness constraints. In: ICCV (2011)Google Scholar
  3. 3.
    Andres, B., Kroeger, T., Briggman, K.L., Denk, W., Korogod, N., Knott, G., Koethe, U., Hamprecht, F.A.: Globally optimal closed-surface segmentation for connectomics. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part III. LNCS, vol. 7574, pp. 778–791. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. TPAMI 33(5), 898–916 (2011)CrossRefGoogle Scholar
  5. 5.
    Bachrach, Y., Kohli, P., Kolmogorov, V., Zadimoghaddam, M.: Optimal coalition structures in graph games. arXiv ePrint (2011)Google Scholar
  6. 6.
    Bagon, S., Galun, M.: Large scale correlation clustering optimization. arXiv ePrint, abs/1112.2903 (2011)Google Scholar
  7. 7.
    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56, 89–113 (2004)MATHCrossRefGoogle Scholar
  8. 8.
    Chopra, S., Rao, M.R.: The partition problem. Math. Program. 59, 87–115 (1993)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Kim, S., Nowozin, S., Kohli, P., Yoo, C.D.: Higher-order correlation clustering for image segmentation. In: NIPS (2011)Google Scholar
  11. 11.
    Kolmogorov, V.: Blossom V: a new implementation of a minimum cost perfect matching algorithm. Mathematical Programming Computation 1(1), 43–67 (2009)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Nowozin, S., Jegelka, S.: Solution stability in linear programming relaxations: graph partitioning and unsupervised learning. In: ICML, pp. 769–776 (2009)Google Scholar
  13. 13.
    Nowozin, S., Lampert, C.H.: Global interactions in random field models: A potential function ensuring connectedness. SIAM J. Img. Sci. 3(4), 1048–1074 (2010)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Shih, W.-K., Wu, S., Kuo, Y.S.: Unifying maximum cut and minimum cut of a planar graph. IEEE Trans. Comput. 39(5), 694–697 (1990)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Vitaladevuni, S.N.P., Basri, R.: Co-clustering of image segments using convex optimization applied to EM neuronal reconstruction. In: CVPR (2010)Google Scholar
  16. 16.
    Yarkony, J.: MAP inference in Planar Markov Random Fields with Applications to Computer Vision. PhD thesis, University of California, Irvine (2012)Google Scholar
  17. 17.
    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-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bjoern Andres
    • 1
  • Julian Yarkony
    • 2
  • B. S. Manjunath
    • 2
  • Steffen Kirchhoff
    • 1
  • Engin Turetken
    • 3
  • Charless C. Fowlkes
    • 4
  • Hanspeter Pfister
    • 1
  1. 1.Harvard UniversityUSA
  2. 2.UC Santa BarbaraUSA
  3. 3.EPFLSwitzerland
  4. 4.UC IrvineUSA

Personalised recommendations