Persistence Diagrams for Efficient Simplicial Complex Reconstruction

12/29/2019

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by   Brittany Terese Fasy, et al.

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Topological descriptors have been shown to be useful for summarizing and differentiating shapes. Related work uses persistence diagrams and Euler characteristic curves to differentiate between shapes and quantifies the number of descriptors necessary for shape reconstruction, given certain assumptions such as minimum curvature. In this work, we provide the first deterministic algorithm using directional persistence diagrams to reconstruct simplicial complexes in arbitrary finite dimension.