The optical flow field for an observer moving through a static environment depends on the observer's translational and rotational motion along with the distances to each surface point. We previously introduced `subspace methods' for recovering 3D motion and depth from optical flow. These methods solve first for the observer's translation, independent of rotation and depth. In this paper, we discuss a particular implementation of this general theory, utilizing `center-surround motion-opponent operators' that prefer motion in one direction in the center and motion in the opposite direction in the surround. Cells in visual area MT of the primate brain are known to have velocity-selective receptive fields with a similar center-surround spatial organization. We propose a theoretical framework for analyzing MT cell responses.