Image co-registration by minimizing cumulative distortion

Many applications of medical image processing require co-aligning a set of sample images, followed by their subsequent averaging. In the cases when one of the data images can be designated as a reference, the problem of image co-alignment is trivially reduced to a number of separate image registration problems. Unfortunately, situations exist when all the data images are known to have been corrupted by arbitrary and generally unknown deformations, in which case registering the remaining images to any given one could produce undesirable post-registration errors. In this note, we propose a new solution to the problem of image co-alignment (aka image co-registration) aiming to minimize the cumulative distortion. The proposed method relies on a formal optimization framework, which allows one to incorporate arbitrary a priori information on the averaged image. Moreover, we also introduce a particularly efficient numerical scheme based on alternating direction method of multipliers. The performance of the proposed algorithm is demonstrated in a series of both in silico and in vivo experiments.