Generalized Hard Constraints for Graph Segmentation

  • Filip Malmberg
  • Robin Strand
  • Ingela Nyström
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6688)


Graph-based methods have become well-established tools for image segmentation. Viewing the image as a weighted graph, these methods seek to extract a graph cut that best matches the image content. Many of these methods are interactive, in that they allow a human operator to guide the segmentation process by specifying a set of hard constraints that the cut must satisfy. Typically, these constraints are given in one of two forms: regional constraints (a set of vertices that must be separated by the cut) or boundary constraints (a set of edges that must be included in the cut). Here, we propose a new type of hard constraints, that includes both regional constraints and boundary constraints as special cases. We also present an efficient method for computing cuts that satisfy a set of generalized constraints, while globally minimizing a graph cut measure.


Image segmentation Graph cuts Regional constraints Boundary constraints 


  1. 1.
    Audigier, R., Lotufo, R.A.: Seed-relative segmentation robustness of watershed and fuzzy connectedness approaches. In: Falcão, A.X., Lopes, H. (eds.) Proceedings of the 20th Brazilian Symposium on Computer Graphics and Image Processing, pp. 61–68. IEEE Computer Society, Los Alamitos (2007)Google Scholar
  2. 2.
    Boykov, Y., Jolly, M.-P.: Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images. In: Proceedings of the 8th IEEE International Conference on Computer Vision (ICCV), vol. 1, pp. 105–112 (2001)Google Scholar
  3. 3.
    Couprie, C., Grady, L., Najman, L., Talbot, H.: Power watersheds: A unifying graph-based optimization framework. IEEE Transactions on Pattern Analysis and Machine Intelligence 99(PrePrints) (2010), doi:10.1109/TPAMI.2010.200.Google Scholar
  4. 4.
    Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: Thinnings, shortest path forests, and topological watersheds. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(5), 925–939 (2010)CrossRefGoogle Scholar
  5. 5.
    Falcão, A.X., Bergo, F.P.: Interactive volume segmentation with differential image foresting transforms. IEEE Transactions on Medical Imaging 23(9), 1100–1108 (2004)CrossRefGoogle Scholar
  6. 6.
    Falcão, A.X., Stolfi, J., Lotufo, R.A.: The image foresting transform: Theory, algorithms, and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(1), 19–29 (2004)CrossRefGoogle Scholar
  7. 7.
    Falcão, A.X., Udupa, J.K., Miyazawa, F.K.: An ultra-fast user-steered image segmentation paradigm: Live wire on the fly. IEEE Transactions on Medical Imaging 19(1), 55–62 (2000)CrossRefGoogle Scholar
  8. 8.
    Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient graph-based image segmentation. International Journal of Computer Vision 59(2) (2004)Google Scholar
  9. 9.
    Grady, L.: Random walks for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(11), 1768–1783 (2006)CrossRefGoogle Scholar
  10. 10.
    Grady, L.: Minimal surfaces extend shortest path segmentation methods to 3D. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(2), 321–334 (2010)CrossRefGoogle Scholar
  11. 11.
    Malmberg, F., Lindblad, J., Sladoje, N., Nyström, I.: A graph-based framework for sub-pixel image segmentation. Theoretical Computer Science (2010), doi:10.1016/j.tcs.2010.11.030.Google Scholar
  12. 12.
    Malmberg, F., Vidholm, E., Nyström, I.: A 3D live-wire segmentation method for volume images using haptic interaction. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 663–673. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Miranda, P.A., Falcão, A.X.: Links between image segmentation based on optimum-path forest and minimum cut in graph. Journal of Mathematical Imaging and Vision 35(2), 128–142 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)CrossRefGoogle Scholar
  15. 15.
    Udupa, J.K., Saha, P.K., Lotufo, R.A.: Relative fuzzy connectedness and object definition: Theory, algorithms, and applications in image segmentation. IEEE Transactions on Pattern Anaysis and Machine Intelligence 24(11), 1485–1500 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Filip Malmberg
    • 1
  • Robin Strand
    • 1
  • Ingela Nyström
    • 1
  1. 1.Centre for Image AnalysisUppsala UniversityUppsalaSweden

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