Nonparametric Inference on Shape Spaces

• Activity Number: 504
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2008 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Abhishek Bhattacharya*+
• Companies: The University of Arizona
• Keywords: shape space of k-ads ; Riemannian manifold ; Frechet analysis ; extrinsic and intrinsic analysis ; mean and variation ; nonparametric inference

Abstract

The statistical analysis of shape distributions based on random samples is important in many areas. To measure the shape of an object, one may pick a suitable ordered set of points on an image of the object under consideration. The equivalence class of that set of points identified modulo size, translation and rotation is called its similarity shape. In case we consider the equivalence class modulo all affine transformations, we get the affine shape of that configuration. Another notion of shape is the projective shape which is particularly appropriate in machine vision. All these shape spaces can be made into Riemannian manifolds. In my talk, I present certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds and apply them to the shape spaces to estimate shape parameters and compare different shape distributions.