Numerical computation of geometric shape analysis for computer vision
Speaker:Dr. Akil Narayan
University of Massachusetts Dartmouth
Date & Time:3 Jan 2015 (Saturday) 15:00 - 16:00
Venue:E11-1036
Organized by:Department of Mathematics

Abstract

The problems of geometric shape classification, identification, and cliquing are important considerations in pattern theory and computer vision. A standard mathematical approach is to consider the space of shapes as a metrized Riemannian manifold and to subsequently compute distances between points (i.e., shapes) on the manifold. We consider a particular metrization that has the attractive properties of scale and translation invariance: the Weil-Peterson metric on the universal Teichmueller space. The numerical computation of geodesics between planar shapes on this space is very challenging, necessitating numerical algorithms for conformal mapping, nonlinear hyperbolic PDE, and optimization. We present and compare two numerical methods that can successfully compute distances and geodesics on this space. We are able to numerically verify theoretical properties of this space (such as hyperbolicity of the metric). Finally, we identify current shortcomings and discuss in-development solutions to these problems.

Biography

Dr. Akil Narayan received his Bachelor's degree in Electrical Engineering, and Engineering Sciences and Applied Mathematics in 2003 from Northwestern University; and his Ph.D. degree in Applied Mathematics from Brown University in 2009 under the supervision of Jan Hesthaven. From 2009 until 2012 he was a postdoctoral researcher at Purdue University working with Dongbin Xiu.