Geometry-based methods for statistics on functions and curves

Project description

How can we define an average closed curve on the plane from a random sample of many such curves, such that it is invariant to certain transformations (e.g. rotations)? Answers to such questions have far-reaching impact on analysis of images arising in numerous discplines (e.g. images of brain tumours). Extending statistical methodology from finite- to infinite-dimensional linear and nonlinear settings requires an improved understanding of probability distributions on constrained function spaces. Employing stochastic processes as a tool to study the interplay between probability and geometry, the project will address some fundamental issues that arise in the development of statistical theory and methodology for data in the form of functions and curves.