Image registration: Maximum likelihood, minimum entropy and deep learning

•An information-theoretic framework for pairwise and groupwise registration based on maximum profile likelihood.•The congealing method is derived as a special case of maximum profile likelihood.•A patch-based formulation that links maximum likelihood to deep metric registration.•Using iterative model refinement alleviates the need for registered data in learning a deep metric. [Display omitted] In this work, we propose a theoretical framework based on maximum profile likelihood for pairwise and groupwise registration. By an asymptotic analysis, we demonstrate that maximum profile likelihood registration minimizes an upper bound on the joint entropy of the distribution that generates the joint image data. Further, we derive the congealing method for groupwise registration by optimizing the profile likelihood in closed form, and using coordinate ascent, or iterative model refinement. We also describe a method for feature based registration in the same framework and demonstrate it on groupwise tractographic registration. In the second part of the article, we propose an approach to deep metric registration that implements maximum likelihood registration using deep discriminative classifiers. We show further that this approach can be used for maximum profile likelihood registration to discharge the need for well-registered training data, using iterative model refinement. We demonstrate that the method succeeds on a challenging registration problem where the standard mutual information approach does not perform well.