Discrete morse theory - Open Access .click

Topology and Its Applications
A classical result in Morse theory is the determination of the homotopy type of the loop space of a manifold. In this paper, we study this result through the lens of discrete Morse theory. This requires a suitable simplicial model for the loop space. Here, we use Milnor's $\textrm{F}^+\textrm{K}$ construction to model the loop space of the sphere $S^2$,
Kevin P Knudson
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Denoising with discrete Morse theory

The Visual Computer, 2021
Denoising noisy datasets is a crucial task in this data-driven world. In this paper, we develop a persistence-guided discrete Morse theoretic denoising framework. We use our method to denoise point-clouds and to extract surfaces from noisy volumes. In addition, we show that our method generally outperforms standard methods.
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Critical points with discrete Morse theory

ACM SIGGRAPH 2015 Posters, 2015
In this work, we present some of the unexpected observations resulted from our recent research. We, recently, needed to identify a small number of important critical points, i.e. minimum, maximum and saddle points, on a given manifold mesh surface. All critical points on a manifold triangular mesh can be identified using discrete Gaussian curvature ...
Peihong Guo +4 more
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fos: mathematics
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mathematics - combinatorics
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fos: computer and information sciences
morse theory
computational geometry cs.cg