A Bayesian Generative Model for Surface Template Estimation

3D surfaces are important geometric models for many objects of interest in image analysis and Computational Anatomy. In this paper, we describe a Bayesian inference scheme for estimating a template surface from a set of observed surface data. In order to achieve this, we use the geodesic shooting approach to construct a statistical model for the generation and the observations of random surfaces. We develop a mode approximation EM algorithm to infer the maximum a posteriori estimation of initial momentum μ, which determines the template surface. Experimental results of caudate, thalamus, and hippocampus data are presented.