On Morphological Hierarchical Representations for Image Processing and Spatial Data Clustering

  • Pierre Soille
  • Laurent Najman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7346)


Hierarchical data representations in the context of classification and data clustering were put forward during the fifties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satisfied. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing.


image representation segmentation clustering ultrametric hierarchy graphs connected components constrained connectivity watersheds min-tree alpha-tree 


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pierre Soille
    • 1
  • Laurent Najman
    • 2
  1. 1.Joint Research Centre, European CommissionInstitute for the Protection and Security of the CitizenIspraItaly
  2. 2.Laboratoire d’Informatique Gaspard-Monge, Equipe A3SI, ESIIEUniversité Paris-EstFrance

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