Image matching has emerged as an important area of investigation in medical image analysis. In particular, much attention has been focused on the atlas problem, in which a template representing the structural anatomy of the human brain is deformed to match anatomic brain images from a given individual. The problem is made difficult because there are important differences in both the gross and local morphology of the brain among normal individuals. We have formulated the image matching problem under a Bayesian framework. The Bayesian methodology facilitates a principled approach to the development of a matching model. Of special interest is its capacity to deal with uncertainty in the estimates, a potentially important but generally ignored aspect of the solution. In the construction of a reference system for the human brain, the Bayesian approach is well suited to the task of modeling variation in morphology. Statistical information about morphological variability, accumulated over past samples, can be formally introduced into the problem formulation to guide the matching or normalization of future data sets.