On the optimality of mutual information as an image registration objective function

We model images and the anatomy that they are derived from as stationary and jointly ergodic random processes. Using an empirically-observed property of anatomy, and data processing inequality arguments, we arrive at optimality criteria for mutual information in the ensemble domain. Using ergodicity, we transfer the criteria to single pairs of images in the spatial domain, where it applies to the popular mutual information-based registration approach that is used in practice.