Presentation
Persistent Homology Computation Using Combinatorial Map Simplification
Author/s | Damiand, Guillaume
González Díaz, Rocío ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2019 |
Deposit Date | 2021-10-07 |
Published in |
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ISBN/ISSN | 978-3-030-10827-4 0302-9743 |
Abstract | We propose an algorithm for persistence homology computation of orientable 2-dimensional (2D) manifolds with or without boundary (meshes) represented by 2D combinatorial maps. Having as an input a real function h on the ... We propose an algorithm for persistence homology computation of orientable 2-dimensional (2D) manifolds with or without boundary (meshes) represented by 2D combinatorial maps. Having as an input a real function h on the vertices of the mesh, we first compute persistent homology of filtrations obtained by adding cells incident to each vertex of the mesh, The cells to add are controlled by both the function h and a parameter δ . The parameter δ is used to control the number of cells added to each level of the filtration. Bigger δ produces less levels in the filtration and consequently more cells in each level. We then simplify each level (cluster) by merging faces of the same cluster. Our experiments demonstrate that our method allows fast computation of persistent homology of big meshes and it is persistent-homology aware in the sense that persistent homology does not change in the simplification process when fixing δ . |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España |
Project ID. | MTM2015-67072-P
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Citation | Damiand, G. y González Díaz, R. (2019). Persistent Homology Computation Using Combinatorial Map Simplification. En CTIC 2019: 7th International Workshop on Computational Topology in Image Context (26-39), Málaga, España: Springer. |
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