# A Faithful Discretization of the Augmented Persistent Homology Transform

@inproceedings{Fasy2019AFD, title={A Faithful Discretization of the Augmented Persistent Homology Transform}, author={Brittany Terese Fasy and Samuel Micka and David L. Millman and Anna Schenfisch and Lucia Williams}, year={2019} }

The persistent homology transform (PHT) represents a shape with a multiset of persistence diagrams parameterized by the sphere of directions in the ambient space. In this work, we describe a finite set of diagrams that discretize the PHT such that it faithfully represents the underlying shape. We provide a discretization that is exponential in the dimension of the shape (making it practical for low dimensional shapes immersed in high dimensional spaces). Moreover, we show that this…

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