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On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds

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Abstract

We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations. We end this paper by showing how to use the proposed framework in practice on the example of constrained connectivity; in particular it allows to compute such a hierarchy following a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.

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Authors and Affiliations

  1. Laboratoire d’Informatique Gaspard-Monge, Equipe A3SI, ESIEE, Université Paris-Est, Paris, France

    Laurent Najman

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  1. Laurent Najman
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Correspondence to Laurent Najman.

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This work was partially supported by ANR grant SURF-NT05-2_45825.

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Najman, L. On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds. J Math Imaging Vis 40, 231–247 (2011). https://doi.org/10.1007/s10851-011-0259-1

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