Article
Approximating lower-star persistence via 2D combinatorial map simplification
Author/s | Damiand, Guillaume
Paluzo Hidalgo, Eduardo Slechta, Ryan González Díaz, Rocío |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2020 |
Deposit Date | 2020-06-22 |
Published in |
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Abstract | Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in the associated persistence diagrams. In this paper, we propose a filtration simplification algorithm ... Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in the associated persistence diagrams. In this paper, we propose a filtration simplification algorithm for orientable 2-dimensional (2D) manifolds with or without boundary ( meshes ) represented by2D combinatorial maps. Given a lower-star filtration of the mesh, faces are added into contiguous clusters according to a “height” function and a parameter . Faces in the same cluster are merged into a single face, resulting in a lower resolution mesh and a simpler filtration. We prove that the parameter bounds the perturbation in the original persistence diagrams, and we provide experiments demonstrating thecomputational advantages of the simplification process. |
Citation | Damiand, G., Paluzo Hidalgo, E., Slechta, R. y González Díaz, R. (2020). Approximating lower-star persistence via 2D combinatorial map simplification. Pattern Recognition Letters, 131 (march 2020), 314-321. |
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