Persistent Homology of Chromatic Alpha Complexes

12/06/2022

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by   Sebastiano Cultrera di Montesano, et al.

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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.