Chromatic Alpha Complexes
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
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| _version_ | 1866912277688483840 |
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| author | di Montesano, Sebastiano Cultrera Draganov, Ondřej Edelsbrunner, Herbert Saghafian, Morteza |
| author_facet | di Montesano, Sebastiano Cultrera Draganov, Ondřej Edelsbrunner, Herbert Saghafian, Morteza |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_03128 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Chromatic Alpha Complexes di Montesano, Sebastiano Cultrera Draganov, Ondřej Edelsbrunner, Herbert Saghafian, Morteza Algebraic Topology Computational Geometry 55N31, 62R40 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. |
| title | Chromatic Alpha Complexes |
| topic | Algebraic Topology Computational Geometry 55N31, 62R40 |
| url | https://arxiv.org/abs/2212.03128 |