Globally Optimal Closed-Surface Segmentation for Connectomics

  • Bjoern Andres
  • Thorben Kroeger
  • Kevin L. Briggman
  • Winfried Denk
  • Natalya Korogod
  • Graham Knott
  • Ullrich Koethe
  • Fred A. Hamprecht
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7574)

Abstract

We address the problem of partitioning a volume image into a previously unknown number of segments, based on a likelihood of merging adjacent supervoxels. Towards this goal, we adapt a higher-order probabilistic graphical model that makes the duality between supervoxels and their joint faces explicit and ensures that merging decisions are consistent and surfaces of final segments are closed. First, we propose a practical cutting-plane approach to solve the MAP inference problem to global optimality despite its NP-hardness. Second, we apply this approach to challenging large-scale 3D segmentation problems for neural circuit reconstruction (Connectomics), demonstrating the advantage of this higher-order model over independent decisions and finite-order approximations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.
    Chopra, S., Rao, M.R.: The partition problem. Math. Program. 59, 87–115 (1993)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Alt, H., Fuchs, U., Kriegel, K.: On the Number of Simple Cycles in Planar Graphs. In: Möhring, R.H. (ed.) WG 1997. LNCS, vol. 1335, pp. 15–24. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  4. 4.
    Grötschel, M., Wakabayashi, Y.: A cutting plane algorithm for a clustering problem. Math. Program. 45, 59–96 (1989)MATHCrossRefGoogle Scholar
  5. 5.
    Costa, M.-C., Letocart, L., Roupin, F.: Minimal multicut and maximal integer multiflow: A survey. European J. of Oper. Res. 162, 55–69 (2005)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56, 89–113 (2004)MATHCrossRefGoogle Scholar
  7. 7.
    Demaine, E.D., Emanuel, D., Fiat, A., Immorlica, N.: Correlation clustering in general weighted graphs. Theoretical Computer Science 361, 172–187 (2006)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)MATHGoogle Scholar
  9. 9.
    Sontag, D., Jaakkola, T.: New outer bounds on the marginal polytope. In: NIPS (2008)Google Scholar
  10. 10.
    Barahona, F., Grötschel, M., Jünger, M., Reinelt, G.: An application of combinatorial optimization to statistical physics and circuit layout design. Oper. Res. 36, 493–513 (1988)MATHCrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Kim, S., Nowozin, S., Kohli, P., Yoo, C.D.D.: Higher-order correlation clustering for image segmentation. In: NIPS (2011)Google Scholar
  13. 13.
    Nowozin, S., Jegelka, S.: Solution stability in linear programming relaxations: graph partitioning and unsupervised learning. In: ICML (2009)Google Scholar
  14. 14.
    Vicente, S., Kolmogorov, V., Rother, C.: Graph cut based image segmentation with connectivity priors. In: CVPR (2008)Google Scholar
  15. 15.
    Nowozin, S., Lampert, C.H.: Global connectivity potentials for random field models. In: CVPR (2009)Google Scholar
  16. 16.
    Lempitsky, V., Kohli, P., Rother, C., Sharp, T.: Image segmentation with a bounding box prior. In: ICCV (2009)Google Scholar
  17. 17.
    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
  18. 18.
    Hatcher, A.: Algebraic Topology. Cambridge Univ. Press (2002)Google Scholar
  19. 19.
    Helmstaedter, M., Briggman, K.L., Denk, W.: High-accuracy neurite reconstruction for high-throughput neuro-anatomy. Nature Neuroscience 14, 1081–1088 (2011)CrossRefGoogle Scholar
  20. 20.
    Denk, W., Horstmann, H.: Serial block-face scanning electron microscopy to reconstruct three-dimensional tissue nanostructure. PLoS Biology 2, e329 (2004)Google Scholar
  21. 21.
    Briggman, K.L., Helmstaedter, M., Denk, W.: Wiring specificity in the direction-selectivity circuit of the retina. Nature 471, 183–188 (2011)CrossRefGoogle Scholar
  22. 22.
    Sommer, C., Straehle, C., Koethe, U., Hamprecht, F.A.: Ilastik: Interactive Learning and Segmentation Toolkit. In: ISBI (2011)Google Scholar
  23. 23.
    Meilǎ, M.: Comparing clusterings – an information based distance. J. of Multivariate Anal. 98, 873–895 (2007)CrossRefGoogle Scholar
  24. 24.
    Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66, 846–850 (1971)CrossRefGoogle Scholar
  25. 25.
    Knott, G., Marchman, H., Wall, D., Lich, B.: Serial section scanning electron microscopy of adult brain tissue using focused ion beam milling. J. Neurosci. 28, 2959–2964 (2008)CrossRefGoogle Scholar
  26. 26.
    Lucchi, A., Smith, K., Achanta, R., Knott, G., Fua, P.: Supervoxel-based segmentation of mitochondria in em image stacks with learned shape features. IEEE Transactions on Medical Imaging 31, 474–486 (2012)CrossRefGoogle Scholar
  27. 27.
    Straehle, C.N., Köthe, U., Knott, G., Hamprecht, F.A.: Carving: Scalable Interactive Segmentation of Neural Volume Electron Microscopy Images. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part I. LNCS, vol. 6891, pp. 653–660. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bjoern Andres
    • 1
  • Thorben Kroeger
    • 1
  • Kevin L. Briggman
    • 2
  • Winfried Denk
    • 3
  • Natalya Korogod
    • 4
  • Graham Knott
    • 4
  • Ullrich Koethe
    • 1
  • Fred A. Hamprecht
    • 1
  1. 1.HCI University of HeidelbergGermany
  2. 2.NIHBethesdaUSA
  3. 3.MPI for Medical ResearchHeidelbergGermany
  4. 4.EPFLLausanneSwitzerland

Personalised recommendations