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On the equivalence between hierarchical segmentations and ultrametric watersheds

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 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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Contributor : Laurent Najman Connect in order to contact the contributor
Submitted on : Friday, December 17, 2010 - 4:50:12 PM
Last modification on : Saturday, January 15, 2022 - 3:56:08 AM
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Laurent Najman. On the equivalence between hierarchical segmentations and ultrametric watersheds. Journal of Mathematical Imaging and Vision, Springer Verlag, 2011, 40 (3), pp.231-247. ⟨10.1007/s10851-011-0259-1⟩. ⟨hal-00419373v2⟩



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