This work presents a real-time, data-parallel approach for global label assignment on regular grids. The labels are selected according to a Markov random field energy with a Potts prior term for binary interactions. We apply the proposed method to accelerate the cleanup step of a real-time dense stereo method based on plane sweeping with multiple sweeping directions, where the label set directly corresponds to the employed directions. In this setting 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.