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Summary form only given. Optical flow computation is known to be a fundamental step in many applications in image processing, pattern recognition, data compression, and biomedical technology. The goal is to compute an approximation to the projection of the 3D motion field onto the imaging surface. I consider in this talk the problem of real-time computation of dense optical flow for 2D and 3D images by the classical Horn-Schunck model. The basic assumption of this model is that the intensity variations are weak and only due to a movement in the image plan. This constant brightness assumption leads to an ill-posed problem that can only be solved by imposing an additional constraint requiring the flow field to be smooth by means of a standard regularization approach. The Horn-Schuck model is traditionally solved via a coupled point wise relaxation. The performance is generally poor when the image sequence data are strongly textured. I will review and discuss the multigrid components for a fast and robust computation. The parallel implementation of the proposed scheme using domain partitioning shows that the algorithm scales well up to 32 processors on a cluster of AMD Opteron CPUs which consists of four-way nodes connected by an Infiniband network. I will conclude by presenting some experimental results showing the good performance of the proposed algorithm on some classical 2D test images and also for computing 3D motion from cardiac C-arm CT images.