Abstract We consider the problem of computing optical flflow in monocular video taken from a moving vehicle. In this setting, the vast majority of image flflow is due to the vehicle’s ego-motion. We propose to take advantage of this fact and estimate flflow along the epipolar lines of the egomotion. Towards this goal, we derive a slanted-plane MRF model which explicitly reasons about the ordering of planes and their physical validity at junctions. Furthermore, we present a bottom-up grouping algorithm which produces over-segmentations that respect flflow boundaries. We demonstrate the effectiveness of our approach in the challenging KITTI flflow benchmark [11] achieving half the error of the best competing general flflow algorithm and one third of the error of the best epipolar flflow algorithm.