Chromatic Alpha Complexes
Algebraic Topology
2025-03-18 v4 Computational Geometry
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.
Cite
@article{arxiv.2212.03128,
title = {Chromatic Alpha Complexes},
author = {Sebastiano Cultrera di Montesano and Ondřej Draganov and Herbert Edelsbrunner and Morteza Saghafian},
journal= {arXiv preprint arXiv:2212.03128},
year = {2025}
}
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