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Algorithms for the Topological Watershed

  • Michel Couprie
  • Laurent Najman
  • Gilles Bertrand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)

Abstract

The watershed transformation is an efficient tool for segmenting grayscale images. An original approach to the watershed [1,4] consists in modifying the original image by lowering some points until stability while preserving some topological properties, namely, the connectivity of each lower cross-section. Such a transformation (and its result) is called a topological watershed. In this paper, we propose quasi-linear algorithms for computing topological watersheds. These algorithms are proved to give correct results with respect to the definitions, and their time complexity is analyzed.

Keywords

Component Tree Weighted Graph Lower Section Grayscale Image Priority Queue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bertrand, G.: On topological watersheds. Journal of Mathematical Imaging and Vision 22, 217–230 (2005)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Beucher, S., Lantuéjoul, C.: Use of watersheds in contour detection. In: Proc. Int. Workshop on Image Processing, Real-Time Edge and Motion Detection/Estimation, Rennes, France (1979)Google Scholar
  3. 3.
    Beucher, S., Meyer, F.: The morphological approach to segmentation: the watershed transformation. In: Dougherty (ed.) Mathematical Morphology in Image Processing, Ch. 12, Marcel Dekker, pp. 433–481 (1993)Google Scholar
  4. 4.
    Couprie, M., Bertrand, G.: Topological grayscale watershed transformation. In: Proc. SPIE Vision Geometry VI, vol. 3168, pp. 136–146 (1997)Google Scholar
  5. 5.
    Couprie, M., Najman, L., Bertrand, G.: Quasi-linear algorithms for the topological watershed. Journal of Mathematical Imaging and Vision 22, 231–249 (2005)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Meyer, F.: Un algorithme optimal de ligne de partage des eaux. In: AFCET Ed., Proc. 8th Conf. Reconnaissance des Formes et Intelligence Artificielle, Lyon, vol. 2, pp. 847–859 (1991)Google Scholar
  7. 7.
    Najman, L., Couprie, M.: Quasi-linear algorithm for the component tree. In: Proc. SPIE Vision Geometry XII, vol. 5300, pp. 98–107 (2004)Google Scholar
  8. 8.
    Najman, L., Couprie, M., Bertrand, G.: Watersheds, extension maps, and the emergence paradigm, report IGM2004-04 of the Institut Gaspard Monge (University of Marne-la-Vallée), to appear in Discrete Applied Mathematics (2004)Google Scholar
  9. 9.
    Roerdink, J., Meijster, A.: The watershed transform: definitions, algorithms and parallelization strategies. In: Fundamenta Informaticae, vol. 41, pp. 187–228 (2000)Google Scholar
  10. 10.
    Tarjan, R.E.: Disjoint sets. In: Data Structures and Network Algorithms, Ch. 2, pp. 23–31. SIAM, Philadelphia (1978)Google Scholar
  11. 11.
    Thorup, M.: On RAM priority queues. In: 7th ACM-SIAM Symposium on Discrete Algorithms, pp. 59–67 (1996)Google Scholar
  12. 12.
    Vincent, L., Soille, P.: Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Trans. on PAMI 13(6), 583–598 (1991)Google Scholar
  13. 13.
    Vincent, L.: Morphological Grayscale Reconstruction in Image Analysis: Application and Efficient Algorithms. IEEE Trans. on PAMI 2(2), 176–201 (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Michel Couprie
    • 1
  • Laurent Najman
    • 1
  • Gilles Bertrand
    • 1
  1. 1.Laboratoire A2SI, Groupe ESIEEIGM, Unité Mixte de Recherche CNRS-UMLV-ESIEE UMR 8049Noisy-le-GrandFrance

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