Multigrid solution of the optical flow system using a combined diffusion- and curvature-based regularizer

Optical flow techniques are used to compute an approximate motion field in an image sequence. We apply a variational approach for the optical flow using a simple data term but introducing a combined diffusion- and curvature-based regularizer. The same data term arises in image registration problems where a deformation field between two images is computed. For optical flow problems, usually a diffusion-based regularizer should dominate, whereas for image registration a curvature-based regularizer is more appropriate. The combined regularizer enables us to handle optical flow and image registration problems with the same solver and it improves the results of each of the two regularizers used on their own. We develop a geometric multigrid method for the solution of the resulting fourth-order systems of partial differential equations associated with the variational approach for optical flow and image registration problems. The adequacy of using (collective) pointwise smoothers within the multigrid algorithm is demonstrated with the help of local Fourier analysis. Galerkin-based coarse grid operators are applied for an efficient treatment of jumping coefficients. We show some multigrid convergence rates, timings and investigate the visual quality of the approximated motion or deformation field for synthetic and real-world images. Copyright (c) 2008 John Wiley & Sons, Ltd.