Watershed Algorithms and Contrast Preservation

  • Laurent Najman
  • Michel Couprie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

This paper is devoted to the study of watershed algorithms behavior. Through the introduction of a concept of pass value, we show that most classical watershed algorithms do not allow the retrieval of some important topological features of the image (in particular, saddle points are not correctly computed). An important consequence of this result is that it is not possible to compute sound measures such as depth, area or volume of basins using most classical watershed algorithms. Only one watershed principle, called topological watershed, produces correct watershed contours.

Keywords

Mathematical Morphology Watersheds Contours Saliency Topology 

References

  1. 1.
    Najman, L.: Morphologie Mathématique: de la Segmentation d’Images à l’Analyse Multivoque. PhD thesis, Université Paris-Dauphine (1994)Google Scholar
  2. 2.
    Najman, L., Schmitt, M.: Geodesic saliency of watershed contours and hierarchical segmentation. IEEE Trans. on PAMI 18, 1163–1173 (1996)Google Scholar
  3. 3.
    Vachier, C.: Extraction de caractéristiques, segmentation d’images et Morphologie Mathématique. PhD thesis, École Supérieure National des Mines de Paris (1995)Google Scholar
  4. 4.
    Breen, E., Jones, R.: Attribute openings, thinnings and granulometries. Computer Vision and Image Understanding 64, 377–389 (1996)CrossRefGoogle Scholar
  5. 5.
    Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Trans. on Image Proc. 7, 555–570 (1998)CrossRefGoogle Scholar
  6. 6.
    Meijster, A., Wilkinson, M.: A comparison of algorithms for connected set openings and closings. IEEE Trans. on PAMI 24, 484–494 (2002)Google Scholar
  7. 7.
    Meyer, F.: The dynamics of minima and contours. In P. Maragos, R.S., Butt, M., eds.: ISMM 3rd. Computational Imaging and Vision, Kluwer Academic Publishers (1996) 329–336 Google Scholar
  8. 8.
    Lemaréchal, C., Fjørtoft, R., Marthon, P., Cubero-Castan, E.: Comments on geodesic saliency of watershed contours and hierarchical segmentation. IEEE Trans. on PAMI 20, 762–763 (1998)Google Scholar
  9. 9.
    Schmitt, M.: Response to the comment geodesic saliency of watershed contours and hierarchical segmentation. IEEE Trans. on PAMI 20, 764–767 (1998)Google Scholar
  10. 10.
    Roerdink, J., Meijster, A.: The watershed transform: Definitions, algorithms and parallelization strategies. Fundamenta Informaticae 41, 187–228 (2000)MATHMathSciNetGoogle Scholar
  11. 11.
    Couprie, M., Bertrand, G.: Topological grayscale watershed transform. In: SPIE Vision Geometry V Proceedings. vol. 3168, pp. 136–146 (1997)Google Scholar
  12. 12.
    Vincent, L., Soille, P.: Watersheds in digital spaces: An efficient algorithm based on immersion simulations. IEEE Trans. on PAMI 13, 583–598 (1991)Google Scholar
  13. 13.
    Meyer, F.: Un algorithme optimal de ligne de partage des eaux. In: Actes du 8ème Congrès AFCET, Lyon-Villeurbanne, France, pp. 847–859 (1991)Google Scholar
  14. 14.
    Meyer, F.: Topographic distance and watershed lines. Signal Processing 38, 113–126 (1994); Special issue on Mathematical MorphologyGoogle Scholar
  15. 15.
    Najman, L., Schmitt, M.: Watershed of a continuous function. Signal Processing 38, 99–112 (1994); Special issue on Mathematical MorphologyGoogle Scholar
  16. 16.
    Lotufo, R.A., Falcao, A.X., Zampirolli, F.A.: Ift-watershed from gray-scale marker. In: SIBGRAPI, Fortaleza-CE, Brazil, pp. 146–152 (2002)Google Scholar
  17. 17.
    Goetcherian, V.: From binary to grey tone image processing using fuzzy logic concepts. Pattern Recognition 12, 7–15 (1980)CrossRefGoogle Scholar
  18. 18.
    Bertrand, G., Everat, J., Couprie, M.: Image segmentation through operators based upon topology. Journal of Electronic Imaging 6, 395–405 (1997)CrossRefGoogle Scholar
  19. 19.
    Couprie, M., Bezerra, F.N., Bertrand, G.: Topological operators for grayscale image processing. Journal of Electronic Imaging 10, 1003–1015 (2001)CrossRefGoogle Scholar
  20. 20.
    Grimaud, M.: A new measure of contrast: Dynamics. In: SPIE, vol. 1769, Image Algebra and Morphological Processing III, San Diego, 292–305 (1992)Google Scholar
  21. 21.
    Najman, L., Couprie, M.: Topological watershed and contrast preservation. Discrete Applied Mathematics (2003) (in preparation); special issue on DGCI (2003)Google Scholar
  22. 22.
    Andrade, M.: A topological image segmentation method by attributes and applications. PhD thesis, Universidade Federal de Minas Gerais, Brazil (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Laurent Najman
    • 1
  • Michel Couprie
    • 1
  1. 1.Laboratoire A2SIGroupe ESIEE, Cité DescartesNoisy-le-Grand CedexFrance

Personalised recommendations