Hierarchies of Partitions and Morphological Segmentation

  • Fernand Meyer
Conference paper
Part of the Lecture Notes in Computer Science 2106 book series (LNCS, volume 2106)


Segmenting an image amounts to producing a partition, in which each tile represents an object of the image. Given an image, how to segment it into a predetermined number of regions ? How to select the objects to represent or discard when the number of regions varies ? Producing a series of nested partitions, or hierarchy is an answer to this question but is also central to practically all morphological segmentation approaches. In the present paper, we define, study, construct and show how to use for various segmention or filtering tasks such hierarchies.


Minimum Span Tree Gradient Image Dissimilarity Index Regional Minimum Catchment Basin 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Beucher. Segmentation d’Images et Morphologie Mathématique. PhD thesis, E.N.S. des Mines de Paris, 1990.Google Scholar
  2. 2.
    F. Meyer and S. Beucher. Morphological segmentation. 1(1):21–46, September 1990.Google Scholar
  3. 3.
    J.P. Benzécri. L’analyse des données 1. La taxinomie, chapter 3, pages 119–153. Dunod, 1973.Google Scholar
  4. 4.
    T.C. Hu. The maximum capacity route problem. Operation research 9, pages 898–900, 1961.Google Scholar
  5. 5.
    F. Meyer. Topographic distance and watershed lines. Signal Processing, pages 113–125, 1994.Google Scholar
  6. 6.
    F. Meyer. Algorithmes à base de files d’attente hiérarchique. Technical Report NT-46/90/MM, September 1990.Google Scholar
  7. 7.
    M. Grimaud. New measure of contrast: dynamics. Image Algebra and Morphological Processing III, San Diego CA, Proc. SPIE, 1992.Google Scholar
  8. 8.
    C. Vachier. Extraction de Caractéristiques, Segmentation d’Image et Morphologie Mathématique. PhD thesis, E.N.S. des Mines de Paris, 1995.Google Scholar
  9. 9.
    F. Meyer M.F. Zanoguera, B. Marcotegui. An interactive colour image segmentation system. In Wiamis’99: Workshop on Image Analysis for Multimedia Interactive Services, pages 137–141. Heinrich-Hertz Institut Berlin, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Fernand Meyer
    • 1
  1. 1.Centre de Morphologie MathématiqueEcole des Mines de ParisFontainebleauFrance

Personalised recommendations