  We propose a method to predict the subject-specific longitudinal progression
of brain structures extracted from baseline MRI, and evaluate its performance
on Alzheimer's disease data. The disease progression is modeled as a trajectory
on a group of diffeomorphisms in the context of large deformation diffeomorphic
metric mapping (LDDMM). We first exhibit the limited predictive abilities of
geodesic regression extrapolation on this group. Building on the recent concept
of parallel curves in shape manifolds, we then introduce a second predictive
protocol which personalizes previously learned trajectories to new subjects,
and investigate the relative performances of two parallel shifting paradigms.
This design only requires the baseline imaging data. Finally, coefficients
encoding the disease dynamics are obtained from longitudinal cognitive
measurements for each subject, and exploited to refine our methodology which is
demonstrated to successfully predict the follow-up visits.
