Bayesian Statistics in Computational Anatomy

Computational anatomy is the science of anatomical shape examined by deforming a template organ into a subject organ. It compares and contrasts organ shapes to inspire personalized treatments or find group differences in case-control studies. Independently of the transformation model used, the task of finding deformations between organs is a statistical task concerned with estimating parameters. Recently it has become important to go beyond "best" estimates and quantify the variability of estimates. The variability is caused by noise in the image, model misspecification, or sampling variability in an observational study. Bayesian statistics provides a rigorous framework to build models that can quantify uncertainty. In this book chapter, we will review some of the basics of Bayesian statistics and relate it to our own experience in applying Bayesian ideas in computational anatomy. We will divide the presentation into two parts. First, we formulate image registration using parametric Bayesian statistics and elaborate on some of the practical difficulties that we encountered in our own work. Second, we will give an example of nonparametric Bayesian statistics applied to clustering of deformation fields into parcels of contiguous voxels.