Segmentation is a low-level vision cue often deployed by stereo algorithms to assume that disparity within superpixels varies smoothly. In this paper, we show that constraining, on a superpixel basis, the cues provided by a recently proposed technique, which explicitly models local consistency among neighboring points, yields accurate and dense disparity fields. Our proposal, starting from the initial disparity hypotheses of a fast dense stereo algorithm based on scanline optimization, demonstrates its effectiveness by enabling us to obtain results comparable to top-ranked algorithms based on iterative disparity optimization methods.