On the equivalence between hierarchical segmentations and ultrametric watersheds

Details On the equivalence between hierarchical segmentations and ultrametric watersheds On the equivalence between hierarchical segmentations and ultrametric watersheds

2010-02-09

arxiv.org/abs/1002.1887v2

Journal of Mathematical Imaging and Vision 40, 3 (2011) 231-247

Computer Science

Discrete Mathematics

19 pages, double-column

Scientific paper

10.1007/s10851-011-0259-1

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 in 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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