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Morse Sequences: A Simple Approach to Discrete Morse Theory

Journal of Mathematical Imaging and Vision
In this paper, we develop the notion of a Morse sequence, which provides an alternative approach to discrete Morse theory, and which is both simple and effective. A Morse sequence on a finite simplicial complex is a sequence composed solely of two elementary operations, that is, expansions (the inverse of a collapse), and fillings (the inverse of a ...
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Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices

, 2012
This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost surely to its
Günther, David +4 more
core

A Discrete Morse Theory for Digraphs

, 2020
Digraphs are generalizations of graphs in which each edge is assigned with a direction or two directions. In this paper, we define discrete Morse functions on digraphs, and prove that the homology of the Morse complex and the path homology are isomorphic for a transitive digraph.
Wang, Chong, Ren, Shiquan
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Discrete Morse Theory, Persistent Homology and Forman-Ricci Curvature [PDF]

, 2020
Emil Saucan
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Discrete Morse theory for totally non-negative flag varieties [PDF]

, 2008
Konstanze Rietsch, Lauren Williams
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On Discrete Morse-Bott Theory