AMS Seminar: Laurent Younes (JHU) @ Whitehead 304

Title:  Shape Spaces of Curves
Abstract:  The talk will discuss results, old and new, on a class of metrics on length-normalized curves in d  dimensions, represented by their unit tangents expressed as a function of arc-length considered as functions from the unit interval to the d-dimensional unit sphere. These metrics are derived from the combined action of diffeomorphisms (change of parameters) and arc-length-dependent rotation acting on the tangent. Minimizing a Riemannian metric balancing a right-invariant metric on diffeomorphisms and an L2 norm on the motion of tangents leads to a special case of “metamorphosis,” for which the computation of geodesic distances can be dramatically simplified after a suitable transformation of the curves into elements of a Hilbert sphere.