Inherent ambiguities in recovering 3-D motion of a planar surface from a noisy flow field

The inherent ambiguities in recovering 3-D motion information of a planar surface from a single optical flow field are studied using a statistical model. These ambiguities are quantified using the Cramer-Rao lower bound, which is a lower bound for the error variances of motion parameter estimates. Motion-estimation algorithms which give unbiased estimates of motion parameters are considered. The bound is independent of the rotational motion parameters. It is studied for the motion of 3-D rigid planar surfaces. The dependence of the bound on several factors (such as the underlying motion, surface position, surface orientation, the field of view, and the density of available pixels) is derived in the form of closed-form expressions and can be computed by inverting a 5×5 positive-definite matrix