Title: An Introduction to Elastic Shape Analysis of Curves
Speaker: Tom Needham (The Ohio State University)
Abstract: Consider the following basic question: what is the correct notion of distance between a pair of closed curves in Euclidean space? The question is subtle if we require the distance metric to be invariant under choice of parameterization and alignment; that is, if we want to measure the distance between the “shapes” of the curves. The field of elastic shape analysis answers this question by defining a Riemannian metric on the infinite-dimensional manifold of closed curve shapes and measuring shape similarity by geodesic distance. In this talk I will give an introduction to elastic shape analysis. I will also describe my own work on the shape space of framed curves, which more generally has a natural Kähler structure. Time permitting, I will describe recent work of Anirudh et. al. which applies these ideas to topological data analysis.
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html
