Abstract: We introduce a new non-linear registration model based on a curvature type regularizer. We show that affine linear transformations belong to the kernel of this regularizer. Consequently, an additional global registration is superfluous. Furthermore, we present an implementation of the new scheme based on the numerical solution of the underlying Euler-Lagrange equations. The real DCT is the backbone of our implementation and leads to a stable and fast O(n log n) algorithm, where n denotes the number of voxels. We demonstrate the advantages of the new technique for synthetic data sets. Moreover, first convincing results for the registration of MR-mammography images are presented.