Advertisement

First Results for 3D Image Segmentation with Topological Map

  • Alexandre Dupas
  • Guillaume Damiand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

Abstract

This paper presents the first segmentation operation defined within the 3D topological map framework. Firstly we show how a traditional segmentation algorithm, found in the literature, can be transposed on a 3D image represented by a topological map. We show the consistency of the results despite of the modifications made to the segmentation algorithm and we study the complexity of the operation. Lastly, we present some experimental results made on 3D medical images. These results show the process duration of this method and validate the interest to use 3D topological map in the context of image processing.

Keywords

Topological model 3D Image segmentation Intervoxel boundaries Combinatorial maps 

References

  1. 1.
    Rosenfeld, A.: Adjacency in digital pictures. Information and Control 26, 24–33 (1974)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Kropatsch, W.G., Macho, H.: Finding the structure of connected components using dual irregular pyramids. In: Discrete Geometry for Computer Imagery, pp. 147–158 (September 1995) (invited lecture)Google Scholar
  3. 3.
    Bertrand, Y., Damiand, G., Fiorio, C.: Topological map: Minimal encoding of 3d segmented images. In: Workshop on Graph-Based Representations in Pattern Recognition, Ischia, Italy, IAPR-TC15, pp. 64–73 (May 2001)Google Scholar
  4. 4.
    Braquelaire, J.P., Domenger, J.P.: Representation of segmented images with discrete geometric maps. Image and Vision Computing 17(10), 715–735 (1999)CrossRefGoogle Scholar
  5. 5.
    Damiand, G., Bertrand, Y., Fiorio, C.: Topological model for two-dimensional image representation: definition and optimal extraction algorithm. Computer Vision and Image Understanding 93(2), 111–154 (2004)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Braquelaire, J.P., Brun, L.: Image segmentation with topological maps and inter-pixel representation. Journal of Visual Communication and Image Representation 9(1), 62–79 (1998)CrossRefGoogle Scholar
  8. 8.
    Haxhimusa, Y., Ion, A., Kropatsch, W.G., Brun, L.: Hierarchical image partitioning using combinatorial maps. In: Hanbury, A., Bischof, H. (eds.) 10th Computer Vision Winter Workshop, pp. 43–52 (February 2005)Google Scholar
  9. 9.
    Damiand, G., Resch, P.: Split and merge algorithms defined on topological maps for 3d image segmentation. Graphical Models 65(1-3), 149–167 (2003)zbMATHCrossRefGoogle Scholar
  10. 10.
    Felzenszwalb, P.F., Huttenlocher, D.P.: Image segmentation using local variation. In: Computer Vision and Pattern Recognition, 1998. Proceedings. IEEE Computer Society Conference on, June 1998, pp. 98–104 (1998)Google Scholar
  11. 11.
    Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Computer-Aided Design 23, 59–82 (1991)zbMATHGoogle Scholar
  12. 12.
    Khalimsky, E., Kopperman, R., Meyer, P.R.: Boundaries in digital planes. Journal of Applied Mathematics and Stochastic Analysis 3(1), 27–55 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Damiand, G.: Définition et étude d’un modèle topologique minimal de représentation d’images 2d et 3d. Thèse de doctorat, Université Montpellier II (Décembre 2001)Google Scholar
  14. 14.
    Dupas, A., Damiand, G.: Comparison of local and global region merging in the topological map. In: BrimKov, V.E., et al. (eds.) IWCIA 2008, vol. 4958, pp. 420–431. Springer, Heidelberg (2008)Google Scholar
  15. 15.
    Cormen, T.H., Leiserson, C.E., Rivest, R.: Introduction to Algorithms. MIT Press, Cambridge (1990)Google Scholar
  16. 16.
    Tarjan, R.: Efficiency of a good but not linear set union algorithm. Journal of the ACM 22, 215–225 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient graph-based image segmentation. International Journal of Computer Vision 59(2), 167–181 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alexandre Dupas
    • 1
  • Guillaume Damiand
    • 2
  1. 1.SIC-XLIMUniversité de PoitiersFuturoscope ChasseneuilFrance
  2. 2.LaBRIUniversité de Bordeaux 1, UMR CNRS 5800TalenceFrance

Personalised recommendations