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Morse Theory, Discrete Morse Theory and Applications
Theoretical and Natural ScienceBy 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
2012We 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, 2023Jürgen Jost, Dong Zhang
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Merge trees in discrete Morse theory
Research in Mathematical Sciences, 2022Nicholas A Scoville, Scoville Nicholas A
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Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011Vanessa Robins, Adrian P Sheppard
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Random Discrete Morse Theory and a New Library of Triangulations
Experimental Mathematics, 2014Bruno Benedetti, Frank H Lutz
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Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015Olaf Delgado-Friedrichs +2 more
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Membrane parallelism for discrete Morse theory applied to digital images
Applicable Algebra in Engineering, Communications and Computing, 2015Raúl Reina-Molina +2 more
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