@INPROCEEDINGS{ClHeRu02,
author = {Clarenz, U. and Henn, S. and Rumpf, M. and 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 = {http://numod.ins.uni-bonn.de/research/papers/public/ClHeRu02.pdf}
}