Discontinuity-preserving computation of variational optic flow in real-time

Abstract. Variational methods are very popular for optic flow computation: They yield dense flow fields and perform well if they are adapted such that they respect discontinuities in the image sequence or the flow field. Unfortunately, this adaptation results in high computational complexity. In our paper we show that it is possible to achieve real-time performance for these methods if bidirectional multigrid strategies are used. To this end, we study two prototypes: i) For the anisotropic imagedriven technique of Nagel and Enkelmann that results in a linear system of equations we derive a regular full multigrid scheme. ii) For an isotropic flow-driven approach with total variation (TV) regularisation that requires to solve a nonlinear system of equations we develop a full multigrid strategy based on a full approximation scheme (FAS). Experiments for sequences of size 160 × 120 demonstrate the excellent performance of the proposed numerical schemes. With frame rates of 6 and 12 dense flow fields per second, respectively, both implementations outperform corresponding modified explicit schemes by two to three orders of magnitude. As a consequence, real-time performance of these high quality methods becomes possible for the first time