An equivalence relation between morphological dynamics and persistent homology in 1D

DOI10.1007/978-3-030-20867-7_5zbMath1445.68244OpenAlexW2909255296MaRDI QIDQ2189349

Laurent Najman, Thierry Géraud, Nicolas Boutry

Publication date: 15 June 2020

Full work available at URL: https://doi.org/10.1007/978-3-030-20867-7_5

zbMATH Keywords

dynamicsMorse theorypersistencemathematical morphology

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Computing methodologies for image processing (68U10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

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Some equivalence relation between persistent homology and morphological dynamics ⋮ Discrete Morse functions and watersheds ⋮ Component tree loss function: definition and optimization ⋮ Gradient vector fields of discrete Morse functions and watershed-cuts ⋮ An equivalence relation between morphological dynamics and persistent homology in \(n\)-D

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