Project: Time Varying Shape Analysis
Statistical Models and Classification of Time-Varying Shape
This project investigates new methods for nonlinear statistical analysis and classification of time-varying shape. The challenge in this modeling problem is that shape and shape variations are highly nonlinear and high-dimensional, and standard linear statistics cannot be applied. Therefore, our ability to model and understand changes in shape depends on the development of new regression models for data in nonlinear spaces. The research at the University of Utah develops statistical models for dealing with time-varying shape using least-squares principles in shape manifolds, investigates new classification methods for shape sequences, and validates the proposed methodology using synthetic data and tests its efficacy for neuroimaging applications in Alzheimer's disease and Autism.
Schematic of regression analysis on a shape space manifold (left). Application of geodesic regression to analyze age-related shape changes in the corpus collosum (right).
P. T. Fletcher, Geodesic Regression on Riemannian Manifolds, MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA) 2011.