  This paper presents a novel mathematical framework for representing
uncertainty in large deformation diffeomorphic image registration. The Bayesian
posterior distribution over the deformations aligning a moving and a fixed
image is approximated via a variational formulation. A stochastic differential
equation (SDE) modeling the deformations as the evolution of a time-varying
velocity field leads to a prior density over deformations in the form of a
Gaussian process. This permits estimating the full posterior distribution in
order to represent uncertainty, in contrast to methods in which the posterior
is approximated via Monte Carlo sampling or maximized in maximum a-posteriori
(MAP) estimation. The frame-work is demonstrated in the case of landmark-based
image registration, including simulated data and annotated pre and
intra-operative 3D images.
