Estimating three-dimensional motion parameters of a rigid planar patch, III: Finite point correspondences and the three-view problem

Two results are presented in this paper. First, it is shown that in estimating three-dimensional motion of a rigid planar patch, the eight pure parameters used in [1] and [2] are uniquely determined from the image correspondences of four points, no three collinear, and can be estimated by solving a set of linear equations. The second result concerns the three-view problem. It is proved that given four image point correspondences in three perspective views of a planar patch undergoing general three-dimensional rigid body motion, the number of solutions for the motion parameters is one, as opposed to two [2] when only two perspective views are given.