author = {Clarenz, U. and Henn, S. and Rumpf, M. Witsch, K.},
  title = {Relations between optimization and gradient flow methods with applications
	to image registration},
  booktitle = {GAMM Seminar on Multigrid and Related Methods for Optimisation Problems},
  year = {2002},
  pages = {11--30},
  abstract = {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., $E[\phi] = \frac{1}{2} \int_\Omega |T \circ
	\phi - R|^2$, where $T$, $R$ are the intensity maps of the two images
	to be matched and $\phi$ is a deformation. Matching of images, i.e.,
	finding an optimal deformation $\phi$ which minimizes $E$ is known
	to be an ill-posed 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 time-step parameter. Examples on 2D and large
	3D image matching problems prove the robustness and efficiency of
	the proposed approach.},
  pdf = { 1}