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Morse Theory, Discrete Morse Theory and Applications

Theoretical and Natural Science
By employing a specific class of smooth functions to study a space, Morse theory establishes deep connections between analysis and topology. It is a classical subject of pure mathematics, originally pioneered by Marston Morse in the 1920s. In this article, we use Morse theory to present a proof of an interesting result on the knots, known as the Fáry ...
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Discrete Morse theory for filtrations

2012
We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations of cell complexes.
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Discrete-to-Continuous Extensions: Lovász Extension and Morse Theory

Discrete and Computational Geometry, 2023
Jürgen Jost, Dong Zhang
exaly  

Merge trees in discrete Morse theory

Research in Mathematical Sciences, 2022
Nicholas A Scoville, Scoville Nicholas A
exaly  

Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011
Vanessa Robins, Adrian P Sheppard
exaly  

Random Discrete Morse Theory and a New Library of Triangulations

Experimental Mathematics, 2014
Bruno Benedetti, Frank H Lutz
exaly  

Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015
Olaf Delgado-Friedrichs   +2 more
exaly  

Membrane parallelism for discrete Morse theory applied to digital images

Applicable Algebra in Engineering, Communications and Computing, 2015
Raúl Reina-Molina   +2 more
exaly  

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