SCI TV - The Study of Shape Change in Organ Motion and Shape Regression
The term shape change generally refers to the variability in conformation of an object corresponding to changes in at least one explanatory continuous variable. Examples include organ motion, in which organs deform with changes in time, and population regression studies in which trends in shape are examined in relation to age or other relevant clinical variables. Important elements of shape change theory are the development of suitable models and the ability to apply those models to real data. The aim of the proposed thesis is to improve both the models and estimation techniques involved in the study of shape change. A new method for estimating organ motion directly from raw imaging data using a popular fluid flow model will be introduced and tested extensively. In addition, a new polynomial model of shape change, extending the common geodesic model, will be used in a series of shape regression studies. In order to provide tools for statistical inference relating to shape regression in this new model, appropriate statistical methods will be developed.