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 descriptorsnecessary 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.
Topological descriptors , such as persistence diagrams and Euler characteristic curves, have been shown to be useful for summarizing and differentiating shapes , both empirically and theoretically. The theoretical justification for their use is based on the fact that shapes can be fully reconstructed using just the descriptors . In this work, we provide the first algorithm using directional persistence diagrams to reconstruct simplicial complexes in arbitrary finite dimension.
A
, such as persistence diagrams and Euler characteristic curves,
R
. Related work uses persistence diagrams and Euler characteristic curves to differentiate between shapes and quantifies the number of descriptorsnecessary for shape reconstruction, given certain assumptions such as minimum curvature
, both empirically and theoretically. The theoretical justification for their use is based on the fact that shapes can be fully reconstructed using just the descriptors
D
deterministic