We propose a novel multiscale approach for the image registration problem, i.e., to find a deformation that maps one image onto another. The image registration problem is confirmed to be mathematical ill-posed due to the fact that determining the unknown components of the displacements merely from the images is an underdetermined problem. The approach presented here utilizes an auxiliary regularization term based on the energy of a plate with free edges, which incorporates smoothness constraints into the deformation field. One of the important aspects of this approach is that the energy does not penalize affine-linear functions. Consequently, the kernel of the Euler - Lagrange equation is spanned by all rigid motions. Hence, the presented approach is invariant under planar rotation and translation. In order to find an optimal deformation, we solve a sequence of subproblems with decreasing regularization parameter. In this framework the regularization parameter can be regarded as a scale parameter, which captures information at multiple spatial scales. We analyze the multiscale nature of a solution.
