In this paper we introduce a new framework for image registration.
Our formulation is based on consistent discretization of the optimiza-
tion problem coupled with a multigrid solution of the linear system
which evolve in a Gauss-Newton iteration. We show that our dis-
cretization is h-elliptic independent of parameter choice and therefore
a simple multigrid implementation can be used. To overcome poten-
tial large nonlinearities and to further speed up computation, we use
a multilevel continuation technique. We demonstrate the eﬃciency of
our method on a realistic highly nonlinear registration problem.