A Faithful Discretization of the Verbose Persistent Homology Transform

Understand

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.
• Moreover, we show that this discretization is stable with respect to various perturbations and we provide an algorithm for computing the discretization.