The role of non-overlap in image registration

Here we model the effect of non-overlapping voxels on image registration, and show that a major defect of overlap-only models--their limited capture range--can be alleviated. Theoretically, we introduce a maximum likelihood model that combines histograms of overlapping and non-overlapping voxels into a common joint distribution. The convex problem for the joint distribution is solved via iterative application of replicator equations that converge monotonically. We then focus on rigidly aligning images with unknown translation, where we present a fast FFT-based method for computing joint histograms for all relative translations of an image pair. We then apply this method to standard overlap-only information theoretic registration criteria such as mutual information as well as to our variants that exploit non-overlap. Our experimental results show that global optima correspond to the correct registration generally only when non-overlapping image regions are included.