Star Shape Prior for Graph-Cut Image Segmentation

  • Olga Veksler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5304)


In recent years, segmentation with graph cuts is increasingly used for a variety of applications, such as photo/video editing, medical image processing, etc. One of the most common applications of graph cut segmentation is extracting an object of interest from its background. If there is any knowledge about the object shape (i.e. a shape prior), incorporating this knowledge helps to achieve a more robust segmentation. In this paper, we show how to implement a star shape prior into graph cut segmentation. This is a generic shape prior, i.e. it is not specific to any particular object, but rather applies to a wide class of objects, in particular to convex objects. Our major assumption is that the center of the star shape is known, for example, it can be provided by the user. The star shape prior has an additional important benefit - it allows an inclusion of a term in the objective function which encourages a longer object boundary. This helps to alleviate the bias of a graph cut towards shorter segmentation boundaries. In fact, we show that in many cases, with this new term we can achieve an accurate object segmentation with only a single pixel, the center of the object, provided by the user, which is rarely possible with standard graph cut interactive segmentation.


Image Segmentation Object Segment Shape Constraint Shape Prior Geodesic Active Contour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. IJCV 2, 321–331 (1998)Google Scholar
  2. 2.
    Falaco, A.X., Udupa, J., Samarasekara, S., Sharma, S.: User-steered image segmentation paradigms: Live wire and live lane. In: Graphical Models and Image Processing, vol. 60, pp. 233–260 (1998)Google Scholar
  3. 3.
    Mortensen, E.N., Barrett, W.A.: Interactive segmentation with intelligent scissors. In: Graphical Models and Image Processing (GMIP), vol. 60, pp. 349–384 (1998)Google Scholar
  4. 4.
    Osher, S., Sethian, J.: Fronts propagating with curvature dependent speed: Algorithm based on hamilton jacobi formulations. Journal of Computational Physics 79, 12–49 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Boykov, Y., Jolly, M.P.: Interactive graph cuts for optimal boundary and region segmentation. In: ICCV 2001, vol. I, pp. 105–112 (2001)Google Scholar
  6. 6.
    Blake, A., Rother, C., Brown, M., Perez, P., Torr, P.: Interactive Image Segmentation Using an Adaptive GMMRF Model. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3021, pp. 428–441. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Boykov, Y., Funka Lea, G.: Graph cuts and efficient n-d image segmentation. International Journal of Computer Vision 69(2), 109–131 (2006)CrossRefGoogle Scholar
  8. 8.
    Wu, Z., Leahy, R.: An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation. PAMI 15(11), 1101–1113 (1993)CrossRefGoogle Scholar
  9. 9.
    Cox, I., Rao, S.B., Zhong, Y.: ”ratio regions”: A technique for image segmentation. In: ICPR 1996, pp. 557–565 (1996)Google Scholar
  10. 10.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. In: IEEE Conference on Computer Vision(ICCV), pp. 731–737 (1997)Google Scholar
  11. 11.
    Veksler, O.: Image segmentation by nested cuts. In: CVPR 2000, vol. I, pp. 339–344 (2000)Google Scholar
  12. 12.
    Jermyn, I., Ishikawa, H.: Globally optimal regions and boundaries as minimum ratio weight cycles. PAMI 23(10), 1075–1088 (2001)CrossRefGoogle Scholar
  13. 13.
    Felzenszwalb, P., Huttenlocher, D.: Efficient graph-based image segmentation. IJCV 59(2), 167–181 (2004)CrossRefGoogle Scholar
  14. 14.
    Wang, S., Kubota, T., Siskind, J., Wang, J.: Salient closed boundary extraction with ratio contour. PAMI 27(4), 546–561 (2005)CrossRefGoogle Scholar
  15. 15.
    Grady, L., Schwartz, E.L.: Isoperimetric graph partitioning for image segmentation. PAMI 28(3), 469–475 (2006)CrossRefGoogle Scholar
  16. 16.
    Schoenemann, T., Cremers, D.: Globally optimal image segmentation with an elastic shape prior. In: ICCV 2007, pp. 1–6 (2007)Google Scholar
  17. 17.
    Kolmogorov, V., Zabih, R.: What energy function can be minimized via graph cuts? IEEE Transaction on PAMI 26(2), 147–159 (2004)CrossRefzbMATHGoogle Scholar
  18. 18.
    Leventon, M., Grimson, W., Faugeras, O.: Statistical shape influence in geodesic active contours. In: CVPR 2000, vol. I, pp. 316–323 (2000)Google Scholar
  19. 19.
    Tsai, A., Yezzi Jr., A., Wells III, W., Tempany, C., Tucker, D., Fan, A., Grimson, W., Willsky, A.: Model-based curve evolution technique for image segmentation. In: CVPR, vol. I, pp. 463–468 (2001)Google Scholar
  20. 20.
    Rousson, M., Paragios, N.: Shape priors for level set representations. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 78–92. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  21. 21.
    Cremers, D., Osher, S., Soatto, S.: Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. IJCV 69(3), 335–351 (2006)CrossRefGoogle Scholar
  22. 22.
    Slabaugh, G., Unal, G.: Graph cuts segmentation using an elliptical shape prior. In: ICIP 2005, vol. II, pp. 1222–1225 (2005)Google Scholar
  23. 23.
    Funka-Lea, G., Boykov, Y., Florin, C., Jolly, M., Moreau-Gobard, R., Ramaraj, R., Rinck, D.: Automatic heart isolation for ct coronary visualization using graph-cuts. In: ISBI 2006, pp. 614–617 (2006)Google Scholar
  24. 24.
    Das, P., Veksler, O., Zavadsky, S., Boykov, Y.: Semiautomatic segmentation with compact shapre prior. In: CRV 2006, pp. 28–36 (2006)Google Scholar
  25. 25.
    Vicente, S., Kolmogorov, V., Rother, C.: Graph cut based image segmentation with connectivity priors. In: CVPR (2008)Google Scholar
  26. 26.
    Freedman, D., Zhang, T.: Interactive graph cut based segmentation with shape priors. In: CVPR, vol. I, pp. 755–762 (2005)Google Scholar
  27. 27.
    Kumar, M., Torr, P., Zisserman, A.: Obj cut. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. I, pp. 18–25 (2005)Google Scholar
  28. 28.
    Ford, L., Fulkerson, D.: Flows in Networks. Princeton University Press, Princeton (1962)zbMATHGoogle Scholar
  29. 29.
    Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. PAMI 26(9), 1124–1137 (2004)CrossRefzbMATHGoogle Scholar
  30. 30.
    Kolmogorov, V., Boykov, Y.: What metrics can be approximated by geo-cuts, or global optimization of length/area and flux. In: ICCV, vol. I, pp. 564–571 (2005)Google Scholar
  31. 31.
    Kolmogorov, V., Boykov, Y., Rother, C.: Applications of parametric maxflow in computer vision. In: ICCV, pp. 1–8 (2007)Google Scholar
  32. 32.
    Kohli, P., Torr, P.: Dynamic graph cuts for efficient inference in markov random fields. PAMI 29(12), 2079–2088 (2007)CrossRefGoogle Scholar
  33. 33.
    Cohen, L., Cohen, I.: Finite-element methods for active contour models and balloons for 2-d and 3-d images. PAMI 15(11), 1131–1147 (1993)CrossRefGoogle Scholar
  34. 34.
    Appleton, B., Talbot, H.: Globally optimal geodesic active contours. JMIV 23(1), 67–86 (2005)MathSciNetCrossRefGoogle Scholar
  35. 35.
    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, vol. 2, pp. 416–423 (July 2001)Google Scholar
  36. 36.
    Rother, C., Kolmogorov, V., Blake, A.: ”grab-cut”- interactive foreground extraction using iterated graph cuts. ACM Transaction on Graphics 23(3), 309–314 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Olga Veksler
    • 1
  1. 1.University of Western OntarioLondonCanada

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