Results 131 to 140 of about 1,401 (157)
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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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Critical points with discrete Morse theory
ACM SIGGRAPH 2015 Posters, 2015In 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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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, 2023Juergen Jost, Dong Zhang
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Merge trees in discrete Morse theory
Research in Mathematical Sciences, 2022Nicholas 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 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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