We consider the correspondence problem associated with the non-rigid registration of a group of images; in particular, the theoretical basis for the derivation of the objective function that defines the 'best' correspondence across a set of images. For intra-subject registration, there is an actual 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 conclusion 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 generated 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.