Advertisement

Abstract

This paper defines floodings on edge weighted and on node weighted graphs. Of particular interest are the highest floodings of a graph below a ceiling function defined on the nodes. It is shown that each flooding on a node weighted graph may be interpreted as a flooding on an edge weighted graphs with appropriate weights on the edges. The highest flooding of a graph under a ceiling function is then interpreted as a shortest distance on an augmented graph, using the ultrametric distance function. Thanks to this remark, the classical shortest distance algorithms may be used for constructing floodings.

Keywords

Neighboring Node Edge Weight Weighted Graph Outgoing Edge Node Weight 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gondran, M., Minoux, M.: Graphes et Algorithmes. Eyrolles (1995)Google Scholar
  2. 2.
    Klein, J.: Conception et Réalisation d’une unité logique pour l’analyse quantitative d’images. PhD thesis, University of Nancy (1976)Google Scholar
  3. 3.
    Meyer, F.: The levelings. In: Heijmans, H., Roerdink, J. (eds.) Mathematical Morphology and Its Applications to Image Processing, pp. 199–207. Kluwer (1998)Google Scholar
  4. 4.
    Meyer, F.: Flooding and segmentation. In: Goutsias, J., Vincent, L., Bloomberg, D.S. (eds.) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol. 18, pp. 189–198 (2002)Google Scholar
  5. 5.
    Moore, E.F.: The shortest path through a maze. In: Proc. Int. Symposium on Theory of Switching, vol. 30, pp. 285–292 (1957)Google Scholar
  6. 6.
    Salembier, P., Serra, J.: Flat zones filtering, connected operators and filters by reconstruction. IEEE Transactions on Image Processing 3(8), 1153–1160 (1995)CrossRefGoogle Scholar
  7. 7.
    Serra, J. (ed.): Image Analysis and Mathematical Morphology. II: Theoretical Advances. Academic Press, London (1988)Google Scholar
  8. 8.
    Vincent, L.: Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms. IEEE Trans. in Image Procesing, 176–201 (1993)Google Scholar
  9. 9.
    Vachier, C., Vincent, L.: Valuation of image extrema using alternating filters by reconstruction. In: Proc. SPIE Image Algebra and Morphological Processing, San Diego CA (July 1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fernand Meyer
    • 1
  1. 1.CMM-Centre de Morphologie Mathématique, Mathématiques et SystèmesMINES ParisTechFrance

Personalised recommendations