An Equivalence Relation between Morphological Dynamics and Persistent Homology in 1D
Résumé
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.
Domaines
Topologie algébrique [math.AT]Origine | Fichiers produits par l'(les) auteur(s) |
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