Rigid Velocities Compatible with Five Image Velocity Vectors

tions yield two quartic polynomial constraints, gi(v) = 52() = 0, on the translational velocity, v, of the rigid body. We show that gi(v) and ?2(v) have, in general, exactly 16 distinct common zeros, and we show that, in general, ten of these common zeros yield values of v compatible with the 2D motion field. An alternative proof that there are ten values of v, based on the theory of ambiguous surfaces, is sketched. Finally some questions are raised concerning the connections between the theory of image velocities and the theory of image displacements. The problem of obtaining rigid velocities compatible with a given set of image velocity vectors is algebraic in that it depends on the solution of simultaneous polynomial equations. We show that five image velocity vectors yield two quartic polynomial constraints on the translational part of the rigid velocity, and that of the 16 common zeros of these two quariics, exactly ten yield rigid velocities compatible with the image velocities. An alternative argument that there are in general exactly ten rigid velocities compatible with five given image velocities is briefly sketched.