Vision is a natural tool for human-computer interaction, since it pro- vides visual feedback to the user and mimics some human behaviors. It requires however the fast and robust computation of motion primi- tives, which remains a difficult problem. In this work, we propose to apply some recent mathematical results about convex optimization to the TV-L1 optical flow problem. At the cost of a small smoothing of the Total Variation (TV), the convergence speed of the numerical scheme is improved, leading to earlier termination. Furthermore, we successfully implement our algorithm on GPU for realtime perfor- mance using the OpenCL framework.We demonstrate the potential of our optical flow by using it as primary sensor in a remotely con- trolled image browsing software.