Persistent Homology of Chromatic Alpha Complexes

Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on 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 mosaics and Alpha complexes.