Statistical Shape Analysis Using the Persistent Homology Transform

Explore statistical shape analysis through the lens of persistent homology in this 51-minute lecture by Katharine Turner. Delve into the Persistent Homology Transform and its applications within the field of Applied and Computational Algebraic Topology. Learn about classical shape statistics, related variants, and TDA approaches. Examine approximation techniques, multidimensional scaling, and alignment methods. Investigate boundary considerations and motivation examples. Gain insights into recent progress, generic provisos, and the process of defining pairwise distances using Persistent Homology Transforms. This comprehensive talk, presented at the Hausdorff Center for Mathematics, offers a deep dive into cutting-edge techniques for analyzing and comparing shapes statistically.

Introduction
Classical Shape Statistics
The Persistent Homology Transform
Related variants
TDA
Approximation
Sanity Check
Multidimensional scaling
Alignment
Boundary
Motivation Example
Recent Progress
Generic provisos
Persistent Homology Transforms
Defining Pairwise Distance
Discussion