Some equivalence relation between persistent homology and morphological dynamics. (arXiv:2205.12546v1 [cs.CV])

In Mathematical Morphology (MM), connected filters based on dynamics are used
to filter the extrema of an image. Similarly, persistence is a concept coming
from Persistent Homology (PH) and Morse Theory (MT) that represents the
stability of the extrema of a Morse function. Since these two concepts seem to
be closely related, in this paper we examine their relationship, and we prove
that they are equal on n-D Morse functions, n $\ge$ 1. More exactly, pairing a
minimum with a …

arxiv cv dynamics