Discrete Morse theory is a combinatorial adaptation of Morse theory developed by Robin Forman. The theory has various practical applications in diverse fields of applied mathematics and computer science, such as configuration spaces,[1] homology computation,[2][3] denoising,[4] mesh compression,[5] and topological data analysis.[6]
- ^ Mori, Francesca; Salvetti, Mario (2011), "(Discrete) Morse theory for Configuration spaces" (PDF), Mathematical Research Letters, 18 (1): 39–57, doi:10.4310/MRL.2011.v18.n1.a4, MR 2770581
- ^ Perseus: the Persistent Homology software.
- ^ Mischaikow, Konstantin; Nanda, Vidit (2013). "Morse Theory for Filtrations and Efficient computation of Persistent Homology". Discrete & Computational Geometry. 50 (2): 330–353. doi:10.1007/s00454-013-9529-6.
- ^ Bauer, Ulrich; Lange, Carsten; Wardetzky, Max (2012). "Optimal Topological Simplification of Discrete Functions on Surfaces". Discrete & Computational Geometry. 47 (2): 347–377. arXiv:1001.1269. doi:10.1007/s00454-011-9350-z.
- ^ Lewiner, T.; Lopes, H.; Tavares, G. (2004). "Applications of Forman's discrete Morse theory to topology visualization and mesh compression" (PDF). IEEE Transactions on Visualization and Computer Graphics. 10 (5): 499–508. doi:10.1109/TVCG.2004.18. PMID 15794132. S2CID 2185198. Archived from the original (PDF) on 2012-04-26.
- ^ "the Topology ToolKit". GitHub.io.