Multigrid methods are well-known to be among the fastest and most accurate numerical schemes for the solution of linear and nonlinear system of equations. By creating a sophisticated coarse-to-fine hierarchy starting from the original equation system they offer much better error reduction properties than frequently used non-hierarchical solvers. Thus, very accurate results are already obtained within a few iterations.
In   we have developed
multigrid schemes for the purpose of real-time optic flow estimation.
As a result up to 42 dense flow fields of size 200 x 200 could be
computed on a standard desktop PC within a single second. Compared to
the frequently used Gauss-Seidel method this equals an acceleration of
two to three orders of magnitude.
Similar speedups can also be obtained for discontinuity-preserving
regularisers  and high accuracy methods with
An overview of multigrid implementations for a variety of variational
optic flow prototypes is given in .
A comparison of the quality and the speed of recent multigrid implementations for several
optic flow protypes can be found
For more information we refer to the correponding paper .