Summary: This paper presents an approach to obtain a deformation which matches two images acquired from different medical imaging modalities. This problem arises in the investigation of human brains. Two distance functionals for the images are proposed with different pros and cons. These functionals are to be minimized. We add a smoothing term to the minimization problem which retains certain desired elastic features in the solution. At each minimization step an approximate solution for the linearized problem is computed with a multigrid method as an inner iteration.
Furthermore, we use a multiresolution minimization approach to obtain a suitable initial guess. Finally, we present some experimental results for registration problems of synthetic images and for a real computer tomography-magnetic resonance imaging registration.