It has been suggested that perceived three-dimensional (3D) structure-from-motion can be accounted for by a 2-frame orthographic approximation of the flow field. This study investigated the extent to which higher order cues (perspective and acceleration) are used in addition to first-order flow. Participants matched the 3D dihedral angle of a hinged plane (probe) defined by multiple-depth cues to one defined by motion only, for stimulus sizes of 8 and 33 degrees, using perspective and orthographic projection. The results show that perspective effects can be important even for relatively small stimuli (8 degrees) and that accelerations contribute to perceived shape. In all conditions, large biases were found. These are well accounted for by a model in which all relevant flow measurements (first-order, perspective, and acceleration) are used together with estimates of the noise in each. The model has no built-in bias toward particular 3D shapes. Instead, the visual system may act as an optimal estimator of 3D structure-from-motion.