This work presents a real-time, data-parallel approach for global label assignment on regular grids. The labels are selected according to a Markov ran-dom field energy with a Potts prior term for binary interactions. We apply the proposed method to accelerate the clean-up step of a real-time dense stereo method based on plane sweeping with multi-ple sweeping directions, where the label set directly corresponds to the employed directions. In this set-ting the Potts smoothness model is suitable, since the set of labels does not possess an intrinsic metric or total order. The observed run-times are approximately 30 times faster than the ones obtained by graph cut approaches.