We describe a method for computing a dense estimate of motion and disparity, given a stereo video sequence containing moving non-rigid objects. In contrast to previous approaches, motion and disparity are estimated simultaneously from a single coherent probabilistic model that correctly accounts for all occlusions, depth discontinuities, and motion discontinuities. The model is a Markov random field (MRF) whose label space incorporates every possible occlusion status for every pixel. Hence, the MRF’s data likelihoods are physically realistic. The results demonstrate that simultaneous estimation of motion and disparity is superior to estimating either in isolation, and show the promise of the technique for accurate, probabilistically justified, scene analysis.