Chromatic alpha complexes
Motivated by applications in 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.
Authors
- Morteza Saghafian (ORCID: https://orcid.org/0000-0002-4201-5775)
- Ondřej Draganov (ORCID: https://orcid.org/0000-0003-0464-3823)
- Herbert Edelsbrunner (ORCID: https://orcid.org/0000-0002-9823-6833)
- Sebastiano Cultrera di Montesano (ORCID: https://orcid.org/0000-0001-6249-0832)
Institutions
- Institute of Science and Technology Austria (AT)
Publication Details
- Journal
- Foundations of Data Science
- Published
- 2025-03-17
- DOI
- https://doi.org/10.3934/fods.2025003
- Citations
- 2
- Primary Topic
- Topological and Geometric Data Analysis
- Type
- article
- Field-Weighted Citation Impact
- 3.01