Persistent Homology of Chromatic Alpha Complexes

Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, Morteza Saghafian

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.