Chromatic Alpha Complexes
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2212.03128
- arXiv:
- arXiv:2212.03128
- Bibcode:
- 2022arXiv221203128C
- Keywords:
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- Mathematics - Algebraic Topology;
- Computer Science - Computational Geometry;
- 55N31;
- 62R40
- E-Print:
- 26 pages