Image registration is central to many challenges in medical imaging today. It has a vast range of applications. The purpose of this note is twofold. First, we review some of the most promising non-linear registration strategies currently used in medical imaging. We show that all these techniques may be phrased in terms of a variational problem and allow for a unified treatment. Second, we introduce, within the variational framework, a new non-linear registration model based on a curvature type smoother. We show that affine linear transformations belong to the kernel of this regularizer. As a result, the approach becomes more robust against poor initializations of a pre-registration step. Furthermore, we develop a stable and fast implementation of the new scheme based on a real discrete cosine transformation. We demonstrate the advantages of the new technique for synthetic data sets and present an application of the algorithm for registering MR-mammography images.