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Approximating lower-star persistence via 2D combinatorial map simplification
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DOI：10.1016/j.patrec.2020.01.018.png)
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Abstract
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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 epsilon. 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 epsilon bounds the perturbation in the original persistence diagrams, and we provide experiments demonstrating the computational advantages of the simplification process. (c) 2020 Elsevier B.V. All rights reserved.
Keywords:
Persistent homology computation
2D combinatorial map
Mesh simplification
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