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Mathematics > Algebraic Topology

arXiv:2212.03128 (math)
[Submitted on 6 Dec 2022 (v1), last revised 10 Jul 2024 (this version, v4)]

Title:Chromatic Alpha Complexes

Authors:Sebastiano Cultrera di Montesano, Ondřej Draganov, Herbert Edelsbrunner, Morteza Saghafian
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Abstract:Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided.
Comments: 26 pages; v4 contains minor reviews and clarifications; v3 only updates the title; v2 brings many changes over v1, most notably adds a proof that the chromatic radius function is generalised discrete Morse
Subjects: Algebraic Topology (math.AT); Computational Geometry (cs.CG)
MSC classes: 55N31, 62R40
Cite as: arXiv:2212.03128 [math.AT]
  (or arXiv:2212.03128v4 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.2212.03128

Submission history

From: Ondřej Draganov [view email]
[v1] Tue, 6 Dec 2022 16:51:21 UTC (189 KB)
[v2] Tue, 6 Feb 2024 15:18:12 UTC (2,293 KB)
[v3] Wed, 7 Feb 2024 10:51:39 UTC (2,293 KB)
[v4] Wed, 10 Jul 2024 10:31:44 UTC (2,296 KB)
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