In this paper we discuss a hybrid technique for piecewise-smooth optical flow estimation. We first pose optical flow estimation as a gradient-based local regression problem and solve it under a high-breakdown robust criterion. Then taking the output from the first step as the initial guess, we recast the problem in a robust matching-based global optimization framework. We have developed novel fast-converging deterministic algorithms for both optimization problems and incorporated a hierarchical scheme to handle large motions. This technique inherits the good sub-pixel accuracy from the local gradient approach and the insensitivity to local perturbation and derivative quality from the global matching approach, and it overcomes the limitations of both. Significant advantages over competing techniques are demonstrated on various standard synthetic and real image sequences.