This project develops nonlinear statistical models and classification procedures for time-varying shape and investigates their application to biomedical image analysis problems. In biology and medicine it is often critical to understand processes that change the shape of anatomy. For example, a neuroscientist studying the development of the infant brain would be interested in how neurodevelopment is different in healthy children versus those with Autism. An evolutionary biologist studying how a species has evolved to adapt to its environment would be interested in studying changes in the shape of bones found in the fossil record. 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, the ability to model and understand changes in shape depends on the development of new regression models for data in nonlinear spaces. The research activities of this project include: (1) developing statistical models for dealing with time-varying shape using least-squares principles in shape manifolds, (2) investigating new classification methods for shape sequences, and (3) validating the methodology using synthetic data and testing its efficacy for neuroimaging applications in Alzheimer's disease and Autism. In addition to the significant impact to computer vision, biology, and medicine, this project is combining differential geometry, statistics, and computing within the undergraduate and graduate computer science curriculum.
