Skip to Main content Skip to Navigation
Conference papers

An Equivalence Relation between Morphological Dynamics and Persistent Homology in n-D

Abstract : In Mathematical Morphology (MM), dynamics are used to compute markers to proceed for example to watershed-based image decomposition. At the same time, persistence is a concept coming from Persistent Homology (PH) and Morse Theory (MT) and represents the stability of the extrema of a Morse function. Since these concepts are similar on Morse functions, we studied their relationship and we found, and proved, that they are equal on 1D Morse functions. Here, we propose to extend this proof to n-D, n ≥ 2, showing that this equality can be applied to n-D images and not only to 1D functions. This is a step further to show how much MM and MT are related.
Document type :
Conference papers
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03171063
Contributor : Laurent Najman <>
Submitted on : Tuesday, March 16, 2021 - 4:29:15 PM
Last modification on : Wednesday, June 9, 2021 - 5:28:03 PM

File

paper_1.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03171063, version 1

Collections

Citation

Nicolas Boutry, Thierry Géraud, Laurent Najman. An Equivalence Relation between Morphological Dynamics and Persistent Homology in n-D. Discrete Geometry and Mathematical Morphology (DGMM), May 2021, Uppsala, Sweden. ⟨hal-03171063⟩

Share

Metrics

Record views

29

Files downloads

41