Statistical Analysis of Images and Parameterized Surfaces

• Activity Number: 64
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Sebastian Kurtek*+
• Companies: Florida State University
• Keywords: shape analysis ; parameterized surfaces ; image registration ; geodesics ; statistical models

Abstract

In this talk I will consider the problems of image registration and shape analysis of three-dimensional objects represented using their boundaries. These boundaries form parameterized surfaces. The main underlying issue in these two problems is the variability in data due to random parameterizations. Our approach is to form the action of parameterization groups on spaces of interest and to remove parameterization variability using algebraic quotient operations. This requires metrics and representations that lead to desired invariances. For this purpose, we use a novel mathematical representation, called a q-map, that allows for simultaneous registration and comparison of images and surfaces. In addition, in the case of shape analysis of parameterized surfaces, an important tool is the computation of geodesics between given objects. The resulting geodesics are used to compute sample statistics and probability models on shape manifolds. I will demonstrate these ideas using multiple applications including medical imaging, graphics and handwriting analysis.