  We discretize a cost functional for image registration problems by deriving
Taylor expansions for the matching term. Minima of the discretized cost
functionals can be computed with no spatial discretization error, and the
optimal solutions are equivalent to minimal energy curves in the space of
$k$-jets. We show that the solutions convergence to optimal solutions of the
original cost functional as the number of particles increases with a
convergence rate of $O(h^{d+k})$ where $h$ is a resolution parameter. The
effect of this approach over traditional particle methods is illustrated on
synthetic examples and real images.
