Simultaneous Longitudinal Registration with Group-Wise Similarity Prior.

Here we present an algorithm for the simultaneous registration of N longitudinal image pairs such that information acquired by each pair is used to constrain the registration of each other pair. More specifically, in the geodesic shooting setting for Large Deformation Diffeomorphic Metric Mappings (LDDMM) an average of the initial momenta characterizing the N transformations is maintained throughout and updates to individual momenta are constrained to be similar to this average. In this way, the N registrations are coupled and explore the space of diffeomorphisms as a group, the variance of which is constrained to be small. Our approach is motivated by the observation that transformations learned from images in the same diagnostic category share characteristics. The group-wise consistency prior serves to strengthen the contribution of the common signal among the N image pairs to the transformation for a specific pair, relative to features particular to that pair. We tested the algorithm on 57 longitudinal image pairs of Alzheimer's Disease patients from the Alzheimer's Disease Neuroimaging Initiative and evaluated the ability of the algorithm to produce momenta that better represent the long-term biological processes occurring in the underlying anatomy. We found that for many image pairs, momenta learned with the group-wise prior better predict a third time point image unobserved in the registration.