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math.AT2024
Decomposing the Persistent Homology Transform of Star-Shaped Objects
Shreya Arya, Barbara Giunti, Abigail Hickok +3
In this paper, we study the geometric decomposition of the degree- Persistent Homology Transform (PHT) as viewed as a persistence diagram bundle. We focus on star-shaped objects…
math.AT2022
Computing Persistence Diagram Bundles
Abigail Hickok
Persistence diagram (PD) bundles, a generalization of vineyards, were introduced as a way to study the persistent homology of a set of filtrations parameterized by a topological sp…
math.AT2022
Persistence Diagram Bundles: A Multidimensional Generalization of Vineyards
Abigail Hickok
I introduce the concept of a persistence diagram (PD) bundle, which is the space of PDs for a fibered filtration function (a set o…