Rigid velocities compatible with five image velocity vectors

摘要

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 quartics, 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. The fact that as many as ten rigid velocities are obtained indicates that the problem of finding rigid velocities compatible with image velocities is intrinsically difficult.