A Discrete Homotopic Deformable Model Dealing with Objects with Different Local Dimensions

  • Yann Cointepas
  • Isabelle Bloch
  • Line Garnero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)


In this paper we introduce a deformable model based on cellular complexes. This model allows the representation of objects with different local dimensions, and has good topological properties.We define homotopic deformation on this model and prove that a local criterion can be used to characterize simple elements of the model. This criterion is used to build an homotopic deformable model that can be used for image processing.


Cellular Model Local Criterion Abstract Graph Simple Cell Deformable Model 
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  1. 1.
    E. Artzy, G. Frieder, and G.T. Herman. The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm. Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, 15:1–24, 1981.Google Scholar
  2. 2.
    Gilles Bertrand and Michel Couprie. Some structural properties of discrete surfaces. In Proceedings of DGCI’97, volume 1347 of LNCS, pages 113–124, 1997.Google Scholar
  3. 3.
    Gilles Bertrand and Grégoire Malandain. A new characterization of three-dimensional simple points. Pattern Recognition Letters, 15:169–175, February 1994.zbMATHCrossRefGoogle Scholar
  4. 4.
    Yann Cointepas, Isabelle Bloch, and Line Garnero. Cellular complexes: A tool for 3d homotopic segmentation in brain images. In Proceedings of ICIP’98, volume 3, pages 832–836, Chicago, 1998.Google Scholar
  5. 5.
    J. Françon. Discrete combinatorial surfaces. Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, 57:20–26, 1995.Google Scholar
  6. 6.
    Claude Godbillon. Eléments de topologie algébrique. Hermann, 1971.Google Scholar
  7. 7.
    Gabor T. Herman. Discrete multidimensional Jordan surfaces. Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, 54(6):507–515, 1992.MathSciNetGoogle Scholar
  8. 8.
    T.Y. Kong and A. Rozenfeld. Digital topology: Introduction and survey. Computer Vision, Graphics, and Image Processing, 48:357–393, 1989.CrossRefGoogle Scholar
  9. 9.
    V.A. Kovalevsky. Discrete topology and contour definition. Pattern Recognition Letters, 2(5):281–288, 1984.CrossRefGoogle Scholar
  10. 10.
    V.A. Kovalevsky. Finite topology as applied to image analysis. Computer Vision, Graphics, and Image Processing, 46:141–146, 1989.CrossRefGoogle Scholar
  11. 11.
    Grégoire Malandain, Gilles Bertrand, and Nicolas Ayache. Topological segmentation of discrete surfaces. International Journal of Computer Vision, 10(2):183–197, 1993.CrossRefGoogle Scholar
  12. 12.
    Réy Malgouyres. A definition of surfaces of Z 3. In Conference on Discrete Geometry for Computer Imaging, pages 23–34, 1994.Google Scholar
  13. 13.
    D.G. Morgenthaler and A. Rosenfeld. Surfaces in three-dimensional images. Information and control, 51:227–247, 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    J.R. Munkers. Elements of Algebraic Topology. Addison-Wesley, Menlo Park. CA, 1984.Google Scholar
  15. 15.
    T. Pavlidis. Structural Pattern Recognition. Springer-Verlag, New York, 1977.zbMATHGoogle Scholar
  16. 16.
    Y.F. Tsao and K.S. Fu. A parallel thinning algorithm for 3-d pictures. Computer Vision, Graphics, and Image Processing, 17:315–331, 1981.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Yann Cointepas
    • 1
  • Isabelle Bloch
    • 1
  • Line Garnero
    • 2
  1. 1.Département TSI - CNRS URA 820ENSTParis Cedex 13FRANCE
  2. 2.LENA - CNRS URA 654Paris Cedex 13FRANCE

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