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Journal Articles Pattern Recognition Letters Year : 2020

Approximating lower-star persistence via 2D combinatorial map simplification

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 for orientable 2-dimensional (2D) manifolds with or without boundary (meshes) represented by 2D 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 the computational advantages of the simplification process.
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Dates and versions

hal-02495726 , version 1 (02-03-2020)

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Guillaume Damiand, Eduardo Paluzo-Hidalgo, Ryan Slechta, Rocio Gonzalez-Diaz. Approximating lower-star persistence via 2D combinatorial map simplification. Pattern Recognition Letters, 2020, 131, pp.314-321. ⟨10.1016/j.patrec.2020.01.018⟩. ⟨hal-02495726⟩
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