The nonlinear equation that relates the optical-flow field to 3-D motion and depth can be split by an exact algebraic manipulation to form three sets of equations. The first set relates the image velocities to the translational component of the 3-D motion alone. Thus, the depth and the rotational velocity need not be known or estimated prior to solving for the translational velocity. Once the translation has been recovered, the second set of equations can be used to solve for the rotational velocity. Finally, depth can be estimated with the third set of equations, given the recovered transaction and rotation. The algorithm applies to the general case of arbitrary motion with respect to an arbitrary scene. The authors show that the performance of the algorithm compares quite favorably with other proposed approaches.