A finite sample of directions and filtration values of the persistent homology transform can be extended to the whole sphere with interleaving-distance error at most twice the sampling radius plus the height sampling error.
Operations on constructible functions
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Kan Approximations of the Persistent Homology Transform
A finite sample of directions and filtration values of the persistent homology transform can be extended to the whole sphere with interleaving-distance error at most twice the sampling radius plus the height sampling error.