Date & Time: Monday, November 24, 2014, 16:00-17:00.
Venue: Ramanujan Hall

Title: Riemannian Geometry of the Space of Smooth Planar Loops

Speaker: Jayant Shah, Northeastern University

Abstract: A problem in Computer Vision is how to match or compare shapes and quantify their differences and similarities. A more general question is how to carry out a statistical analysis of variations in shapes. For example, given a statistical sample of, say, images of a brain structure such as the corpus callosum or hippocampus, what is its average shape and what is the standard deviation? The root of the difficulty is the fact that shape spaces are not vector spaces, but infinite dimensional manifolds.

A starting point is to try to compute distances between shapes. This led to attempts to impose a Riemannian structure on shape manifolds and construct geodesics. Peter Michor and David Mumford developed a general theoretical framework so that the standard tools of Differential Geometry may be applied to various versions of shape-related problems in Computer Vision. I will describe the framework and discuss our results in three specific cases of the space of smooth planar loops.