An Equivalence Relation between Morphological Dynamics and Persistent Homology in 1D

Abstract : We state in this paper a strong relation existing between Mathematical Morphology and Discrete Morse Theory when we work with 1D Morse functions. Specifically, in Mathematical Morphology, a classic way to extract robust markers for segmentation purposes, is to use the dynamics. On the other hand, in Discrete Morse Theory, a well-known tool to simplify the Morse-Smale complexes representing the topo-logical information of a Morse function is the persistence. We show that pairing by persistence is equivalent to pairing by dynamics. Furthermore, self-duality and injectivity of these pairings are proved.
Type de document :
Pré-publication, Document de travail
2019
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https://hal.archives-ouvertes.fr/hal-01978607
Contributeur : Laurent Najman <>
Soumis le : vendredi 11 janvier 2019 - 16:05:11
Dernière modification le : jeudi 17 janvier 2019 - 01:15:39

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boutry.ismm.2019-2019-01-11-2....
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  • HAL Id : hal-01978607, version 1

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Nicolas Boutry, Thierry Géraud, Laurent Najman. An Equivalence Relation between Morphological Dynamics and Persistent Homology in 1D. 2019. 〈hal-01978607〉

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