Chapter 11 - Elastic Matching: Continuum Mechanical and Probabilistic Analysis

Abstract

A computational framework has evolved in which individual anatomies are modeled as warped versions of a canonical representation of the anatomy. To realize this framework, the method of elastic matching was invented for determining the spatial mapping between a three-dimensional image pair in which one image volume is modeled as an elastic continuum that is deformed to match the appearance of the second volume. This chapter describes the basic concepts underlying the original method and their probabilistic generalization within a Bayesian framework. For brain warping, a number of effective similarity metrics exist, whereas there is comparatively little known about the kinds of prior models that are specifically suited to the problem (and its applications) or how their influence on the solution, relative to the likelihood, should be determined. The resolution of these issues directly impacts the viability of any matching procedure, Bayesian or otherwise, but is best addressed within a probabilistic setting. To reduce the likelihood of false matches that arise when the local variations in anatomy are very large in magnitude, a standard approach is to solve the problem at different spatial scales.