A unified information-theoretic approach to the correspondence problem in image registration

We consider the correspondence problem associated with the non-rigid registration of a group of images; in par-ticular, the theoretical basis for the derivation of the objec-tive function that defines the ‘best ’ correspondence across a set of images. For intra-subject registration, there is an ac-tual physical deformation process underlying the observed deformation, but for inter-subject registration, there is no such physical process, and hence no hypothetical process that generates the observed data. This leads to the con-clusion that our construction should be based on the data alone. Such a construction is possible using criteria derived from information theory. We show how many commonly used pairwise voxel-based similarity measures can be gen-erated using these criteria, and discuss how this approach can be extended to give a unified theoretical basis for the generation of novel objective functions in the groupwise case, where both image discrepancy and image deformation terms should be included in a principled way.