  We study the problem of diffeomorphometric geodesic landmark matching where
the objective is to find a diffeomorphism that via its group action maps
between two sets of landmarks. It is well-known that the motion of the
landmarks, and thereby the diffeomorphism, can be encoded by an initial
momentum leading to a formulation where the landmark matching problem can be
solved as an optimisation problem over such momenta. The novelty of our work
lies in the application of a derivative-free Bayesian inverse method for
learning the optimal momentum encoding the diffeomorphic mapping between the
template and the target. The method we apply is the ensemble Kalman filter, an
extension of the Kalman filter to nonlinear observation operators. We describe
an efficient implementation of the algorithm and show several numerical results
for various target shapes.
