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Approximating lower-star persistence via 2D combinatorial map simplification

Guillaume Damiand 1 Eduardo Paluzo-Hidalgo 2 Ryan Slechta 3 Rocio Gonzalez-Diaz 2 
1 Origami - Origami
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
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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Submitted on : Monday, March 2, 2020 - 2:34:16 PM
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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, Elsevier, 2020, 131, pp.314-321. ⟨10.1016/j.patrec.2020.01.018⟩. ⟨hal-02495726⟩



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