Using 2D Topological Map Information in a Markovian Image Segmentation

  • Guillaume Damiand
  • Olivier Alata
  • Camille Bihoreau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)


Topological map is a mathematical model of labeled image representation which contains both topological and geometrical information. In this work, we use this model to improve a Markovian segmentation algorithm. Image segmentation methods based on Markovian assumption consist in optimizing a Gibbs energy function. This energy function can be given by a sum of potentials which could be based on the shape or the size of a region, the number of adjacencies,...and can be computed by using topological map. In this work we propose the integration of a new potential: the global linearity of the boundaries, and show how this potential can be extracted from the topological map. Moreover, to decrease the complexity of our algorithm, we propose a local modification of the topological map in order to avoid the reconstruction of the entire structure.


Markovian segmentation topological maps region segmentation boundaries linearity 


  1. 1.
    Domenger, J.: Conception et implémentation du noyeau graphique d’un environnement 2D1/2 d’édition d’images discrètes. Thèse de doctorat, Université Bordeaux I (1992)Google Scholar
  2. 2.
    Fiorio, C.: A topologically consistent representation for image analysis: the frontiers topological graph. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 151–162. Springer, Heidelberg (1996)Google Scholar
  3. 3.
    Pailloncy, J., Jolion, J.: The frontier-region graph. In: Workshop on Graph based representations. Computing Supplementum, vol. 12, pp. 123–134. Springer, Heidelberg (1997)Google Scholar
  4. 4.
    Braquelaire, J., Desbarats, P., Domenger, J., Wüthrich, C.: A topological structuring for aggregates of 3d discrete objects. In: Workshop on Graph based representations, Austria, IAPR-TC15, pp. 193–202 (1999)Google Scholar
  5. 5.
    Bertrand, Y., Damiand, G., Fiorio, C.: Topological encoding of 3d segmented images. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 311–324. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Braquelaire, J., Desbarats, P., Domenger, J.: 3d split and merge with 3-maps. In: Workshop on Graph based representations, Ischia, Italy, IAPR-TC15, pp. 32–43 (2001)Google Scholar
  7. 7.
    Damiand, G., Resch, P.: Topological map based algorithms for 3d image segmentation. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 220–231. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Gonzales, R.C., Woods, R.E.: Digital Image Processing. Addison-Wesley, Reading (1993)Google Scholar
  9. 9.
    Brun, L., Domenger, J.: A new split and merge algorithm with topological maps and inter-pixel boundaries. In: The fifth International Conference in Central Europe on Computer Graphics and Visualization (1997)Google Scholar
  10. 10.
    Brun, L., Domenger, J., Braquelaire, J.: Discrete maps: a framework for region segmentation algorithms. In: Workshop on Graph based representations, Lyon, IAPR-TC15 (1997) published in Advances in Computing (Springer)Google Scholar
  11. 11.
    Braquelaire, J., Brun, L.: Image segmentation with topological maps and interpixel representation. Journal of Visual Communication and Image Representation 9, 62–79 (1998)CrossRefGoogle Scholar
  12. 12.
    Geman, S., Geman, D.: Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images. IEEE Trans. on Pattern Analysis and Machine Intelligence PAMI 6, 721–741 (1984)zbMATHCrossRefGoogle Scholar
  13. 13.
    Bouman, C., Liu, B.: Multiple Resolutions Segmentation of Textured Images. IEEE Trans. on Pattern Analysis and Machine Intelligence 13, 99–113 (1991)CrossRefGoogle Scholar
  14. 14.
    Kervrann, C., Heitz, F.: A Markov Random Field Model-based Approach to Unsupervised Texture Segmentation using Local and Global Spatial Statistics. IEEE Trans. on Image Processing 4, 856–862 (1995)CrossRefGoogle Scholar
  15. 15.
    Barker, S.A.: Image Segmentation using Markov Random Field Models. Phd thesis, University of Cambridge (1998)Google Scholar
  16. 16.
    Melas, D.E., Wilson, S.P.: Double markov random fields and bayesian image segmentation. IEEE Trans. on Signal Processing 50, 357–365 (2002)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Jacques, A.: Constellations et graphes topologiques. In: Combinatorial Theory and Applications, vol. 2, pp. 657–673 (1970)Google Scholar
  18. 18.
    Cori, R.: Un code pour les graphes planaires et ses applications. In: Astérisque, Paris, France. Soc. Math. de France, vol. 27 (1975)Google Scholar
  19. 19.
    Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Commputer Aided Design 23, 59–82 (1991)zbMATHGoogle Scholar
  20. 20.
    Celeux, G., Diebolt, J.: The SEM Algorithm: a Probabilistic Teacher Algorithm Derived from the EM Algorithm for the Mixture Problem. Computational statistics quarterly 2, 73–82 (1985)Google Scholar
  21. 21.
    Debled-Rennesson, I., Reveilles, J.P.: A linear algorithm for segmentation of digital curves. International Journal of Pattern Recognition and Artificial Intelligence 9, 635–662 (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Guillaume Damiand
    • 1
  • Olivier Alata
    • 1
  • Camille Bihoreau
    • 1
  1. 1.IRCOM-SIC, UMR-CNRS 6615Futuroscope Chasseneuil CedexFrance

Personalised recommendations