Algebraic Methods in 3-D Motion Estimation From Two-View Point Correspondences.

We consider the problem of determining motion (3D-rotation and translation) of rigid objects from their images taken at two time instants. We assume that the locations of the perspective projection on the image plane of n points from the surface of the rigid body are known at two time instants. For n = 5, we show that there are at most 10 possible motions values (in rotation and translation) and give many real examples in which the bound of 10 is actually achieved. For n >= 6, we show that the solution is generally unique. We derive a variety of necessary and sufficient conditions a solution must satisfy, show their equivalence and use algebraic geometry to derive the bound on the number of solutions. A homotopy method is then used to compute all the solutions. Several examples are worked out and our computational experience is summarized.