A robust multigrid solver for the Euler-Lagrange equations with non-smooth coefficients

Ulrich Ruede

Lehrstuhl fuer Informatik 10 (Systemsimulation)
FAU Erlangen-Nuernberg
Cauerstrasse 6
D-91058 Erlangen

Harald Koestler

Optical flow and non-rigid registration of medical datasets lead to a variational minimization problem that requires robust and efficient numerical solvers. Existing multigrid solvers for these problems depend highly on the smoothness of the given image data. Therefore the images are often smoothed before the computations. This can lead to difficulties, e.g. when one tries to detect the motion of very small objects. In order to handle non-smoothed image data we apply several multigrid techniques, such as Galerkin coarsening and matrix-dependent transfer operators. Further improvements can be obtained by developing suitable line-wise and block-smoothers. Our synthetic and real world results demonstrate that we can relax the restrictions on the smoothness of the image data without loosing the fast multigrid convergence rate. For high resolution 3D data it is necessary to parallelize the algorithms.