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Denoising with discrete Morse theory
The Visual Computer, 2021Denoising 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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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 Fry ...
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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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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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Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015Vanessa Robins, Adrian P Sheppard
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Existence results for double-phase problems via Morse theory
Communications in Contemporary Mathematics, 2018Kanishka Perera, Marco Squassina
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Morse Theory for Filtrations and Efficient Computation of Persistent Homology
Discrete and Computational Geometry, 2013Konstantin Mischaikow, Vidit Nanda
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