Thinning Grayscale Well-Composed Images: A New Approach for Topological Coherent Image Segmentation

  • Jocelyn Marchadier
  • Didier Arquès
  • Sylvain Michelin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)

Abstract

Usual approaches for constructing topological maps on discrete structures are based on cellular complexes topology. This paper aims to construct a coherent topological map defined on a square grid from a watershed transformation. We propose a definition of well-composed grayscale images based on the well-composed set theory and the cross-section topology. Properties of two different thinning algorithms are studied within this scope, and we show how to obtain a thin crest network. We derive an efficient algorithm that permits the construction of a meaningful topological map. Finally, we demonstrate the usefulness of this algorithm for multilevel image segmentation.

Keywords

Topological map thinning well-composed images 

References

  1. 1.
    Arcelli C., Pattern Thinning by Contour Tracing, Computer Graphics and Image Processing, Vol. 17 (1981) 130–144CrossRefGoogle Scholar
  2. 2.
    Bertrand B., Everat J.C., Couprie M., Topological approach to image segmentation, SPIE Vision Geometry V Proceedings, Vol. 2826 (1996)Google Scholar
  3. 3.
    Bertrand B., Everat J.C., Couprie M., Image segmentation through operators based upon topology, Journal of Electronic Imaging, Vol. 6(4) (1997) 395–405CrossRefGoogle Scholar
  4. 4.
    Braquelaire J.-P., Brun L., Image Segmentation with Topological Maps and Interpixel Representation, Journal of Visual Communication and Image Representation, Vol. 9(1) (1998) 62–79CrossRefGoogle Scholar
  5. 5.
    Couprie, M., Bertrand G., Topological Grayscale Watershed Transformation, SPIE Vision Geometry V Proceedings, Vol. 3168 (1997) 136–146Google Scholar
  6. 6.
    Fiorio C., Approche interpixel en analyse d’images, une topologie et des algorithmes de segmentation, PhD Dissertation, Université de Montpellier, France, (1995) 198 pages.Google Scholar
  7. 7.
    Fiorio C., A topologically Consistent Representation for Image Analysis: the Frontiers Topological Graph, DGCI’96, Lectures Notes in Computer Sciences, no. 1176, (1996) 151–162Google Scholar
  8. 8.
    Gangnet M., Hervé J.-C., Pudet T., Van Tong J.-M., Incremental Computation of Planar Maps, SIGGRAPH Proc., Computer Graphics, Vol. 23(3) (1989) 345–354Google Scholar
  9. 9.
    Khalimsky E., Kopperman R., Meyer R., Computer Graphics and Connected Topologies on Finite Ordered Sets, Topology and its Applications, Vol. 36 1–17Google Scholar
  10. 10.
    Kovalevsky V. A., Finite Topology as Applied to Image Analysis, Computer Vision, Graphics and Image Processing, Vol. 46 141–161Google Scholar
  11. 11.
    Kong T. Y., Rosenfeld A., Digital Topology, Introduction and Survey, Computer Vision, Graphics, and Image Processing, Vol. 48 (1989) 357–393CrossRefGoogle Scholar
  12. 12.
    Latecki L., Multicolor Well-Composed pictures, Pattern Recognition Letters, Vol. 16 (1995) 425–431CrossRefGoogle Scholar
  13. 13.
    Latecki L., Discrete Representation of Spatial Objects in Computer Vision, Computational Imaging and Vision Vol. 11, Kluwer Academic Publishers (1999) 216 pagesGoogle Scholar
  14. 14.
    Latecki L., Well-Composed Sets, Advances in Imaging and Electron Physics Vol. 112, Academic Press (2000) 95–163Google Scholar
  15. 15.
    Latecki L., Eckhardt U., Rosenfeld A., Well-Composed Sets, Computer Vision and Image Understanding, Vol. 61 (1995) 70–83CrossRefGoogle Scholar
  16. 16.
    Meyer F., Skeletons and Perceptual Graphs, Signal Processing, Vol. 16 (1989) 335–363CrossRefMathSciNetGoogle Scholar
  17. 17.
    Pierrot Deseilligny M., Stamon G., Suen C., Veinerization: A New Shape Description for Flexible Skeletonization, IEEE Trans. on PAMI, Vol. 20(5) (1998) 505–521Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jocelyn Marchadier
    • 1
  • Didier Arquès
    • 1
  • Sylvain Michelin
    • 1
  1. 1.Institut Gaspard MongeUniversité de Marne-la-Vallée, Equipe ImageChamps sur Marne Cedex

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