[1] 
U. Clarenz, S. Henn, and K. Rumpf, M. Witsch.
Relations between optimization and gradient flow methods with
applications to image registration.
In GAMM Seminar on Multigrid and Related Methods for
Optimisation Problems, pages 1130, 2002. [ bib  .pdf 1 ] Fast multiscale and multigrid methods for the matching of images in 2D and 3D are presented. Especially in medical imaging this problem  denoted as the registration problem  is of fundamental importance in the handling of images from multiple image modalities or of image time series. The paper restricts to the simplest matching energy to be minimized, i.e., E[φ] = (1)/(2) _{Ω} T o φ R^{2}, where T, R are the intensity maps of the two images to be matched and φ is a deformation. Matching of images, i.e., finding an optimal deformation φ which minimizes E is known to be an illposed problem. Here, the focus is on regularization methods. We compare different iterative methods where the necessary regularization is incorporated via an additional convex energy functional. Furthermore we give a new interpretation of these methods in the framework of gradient flows. Hence, a regularization is interpreted as a regular metric used to measure length on the descent path in the gradient flow method. Typically regularizing energies appear together with a small coefficient. We obtain an interpretation of this coefficient as a timestep parameter. Examples on 2D and large 3D image matching problems prove the robustness and efficiency of the proposed approach.
