Shape Analysis of Functional Data
Speaker: Anuj Srivastava
Title: Shape Analysis of Functional Data
Abstract: This tutorial style presentation is on recent advances in functional and shape data analysis that emphasizes the following ideas: (1) Shapes of interest are represented by continuous objects (curves, surfaces, etc) rather than discrete representations of the past; (2) the registration problem, i.e. the correspondence of points across objects, considered a difficult problem in shape analysis, is handled during analysis rather then treated as pre-processing; and (3) the goal is to derive statistical inferences about shapes, relative to underlying probability distributions. The central idea is to choose metrics (or energies) with appropriate invariance properties and physical interpretations, and use them for analyzing shapes.
Additionally, one uses certain square-root representations to simplify these complex metrics into more standard mathematical tools, to enable implementation involving large datasets. I will motivate these ideas using a number of problems from biology, medical imaging, and computer vision.