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This paper describes an approach to optical flow computation that combines local and global constraints. A local flow estimate is obtained at each pixel, and is used to segment the image into regions of smooth motion. Within each region, global constraints are applied to reduce noise in local flow estimates while preserving motion boundaries. The main novel contributions in this framework are: (1) the derivation of a consistency measure for local flow computation, and the use of this measure to preserve motion boundary in the estimation; (2) the combined use of global subspace and spatial smoothness constraints to complement local flow estimation. Results on standard test sequences demonstrate improved accuracy in flow estimation, and analyse the role that each contribution plays in this improvement.