A Comprehensive Framework for Registration and Shape Analysis of Functional Data

• Activity Number: 568
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Anuj Srivastava*+
• Companies: Florida State University
• Keywords: functional data analysis ; shape analysis ; registration ; image metrics ; shape statistics ; elastic shape analysis

Abstract

It is often necessary to align and register imaging data during analysis. The registration step not only preserves important structures but also leads to parsimonious statistical models for capturing data variability. In case of shape analysis, the registration is akin to removing the parameterization variability present in mathematical representations of functions, curves and surfaces. Taking three examples: (1) real-valued function data, (2) parameterized curves in Euclidean spaces, and (3) parameterized surfaces, I will describe a Riemannian framework that achieves the following goals. It provides an analysis of shapes of curves and surfaces that is invariant to standard similarity transformations and, additionally, to parameterizations of these objects. It incorporates registration of objects while providing proper metrics, geodesics, and sample statistics. These sample statistics are further useful in statistical modeling of shapes in different shape classes. It also provides distance-based tools for registration of image data. I will present examples from medical image analysis, protein structure analysis, 3D face recognition, and human activity recognition in videos.