Graph Cut Based Segmentation of Predefined Shapes: Applications to Biological Imaging

  • Emmanuel Soubies
  • Pierre Weiss
  • Xavier Descombes
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 318)


We propose an algorithm to segment 2D ellipses or 3D ellipsoids . This problem is of fundamental importance in various applications of cell biology. The algorithm consists of minimizing a contrast invariant energy defined on sets of non overlapping ellipsoids. This highly non convex problem is solved by combining a stochastic approach based on marked point processes and a graph-cut algorithm that selects the best admissible configuration. In order to accelerate the computing times, we delineate fast algorithms to assess whether two ellispoids intersect or not and various heuristics to improve the convergence rate.


Nuclei segmentation 2D and 3D images Graph-cuts Marked point processes Ellipses and ellipsoids Multiple objects detection Multiple birth and cut Bio-imaging 



This work was partially funded by the Mission pour l’interdisci- plinarité from CNRS, Région Midi Pyrénées, PEPII CASPA3D, ANR SPHIM3D and ANR MOTIMO. The authors wish to thank F. Malgouyres and J. Fehrenbach for interesting discussions. They also thank V. Lobjois, C. Emery, J. Thomazeau, P. Escande and B. Ducommun for their help in this project. They thank L. Aoun and C. Vieu for providing images and interesting discussions regarding micro pillars detection. They thank all the ITAV staff for their warm welcome in a biology laboratory.


  1. 1.
    Baddeley, A., Van Lieshout, M.: Stochastic geometry models in high-level vision. J. Appl. Stat. 20(5–6), 231–256 (1993)CrossRefGoogle Scholar
  2. 2.
    Bertsekas, D.: Nonlinear programming (1999)Google Scholar
  3. 3.
    Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans. Pattern Anal. Mach. Intell. 26(9), 1124–1137 (2004)CrossRefGoogle Scholar
  4. 4.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23, 1222–1239 (2001)CrossRefGoogle Scholar
  5. 5.
    Descombes, X.: Stochastic Geometry for Image Analysis. Wiley/Iste, x.  descombes edition, London (2011)Google Scholar
  6. 6.
    Descombes, X., Minlos, R., Zhizhina, E.: Object extraction using a stochastic birth-and-death dynamics in continuum. J. Math. Imaging Vis. 33(3), 347–359 (2009)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Dong, G., Acton, S.: Detection of rolling leukocytes by marked point processes. J. Electron. Imaging 16, 033013 (2007)CrossRefGoogle Scholar
  8. 8.
    Gamal-Eldin, A., Descombes, X., Charpiat, G., Zerubia, J.: A fast multiple birth  and cut algorithm using belief propagation. In: 18th IEEE International Conference on Image  Processing (ICIP), pp. 2813–2816. IEEE (2011)Google Scholar
  9. 9.
    Gamal Eldin, A., Descombes, X., Charpiat, G., Zerubia, J., et al.: Multiple birth and cut algorithm for multiple object detection. J. Multimed. Process. Technol.(2012)Google Scholar
  10. 10.
    Green, P.J.: Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711–732 (1995)CrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 26, 65–81 (2004)CrossRefGoogle Scholar
  12. 12.
    Nesterov, Y.: Introductory lectures on convex optimization: A  basic course, vol. 87. Springer, Berlin (2004)Google Scholar
  13. 13.
    Perrin, G., Descombes, X., Zerubia, J.: A marked point process model for tree crown extraction in plantations. In: IEEE International Conference on Image Processing, ICIP  2005, vol. 1, pp. I–661. IEEE (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Emmanuel Soubies
    • 1
  • Pierre Weiss
    • 2
  • Xavier Descombes
    • 1
  1. 1.INRIA/I3S/IBVMORPHEME TeamSophia-AntipolisFrance
  2. 2.ITAV-USR3505Université de ToulouseToulouseFrance

Personalised recommendations