| Abstract: | We consider the problem of determining motion (3-D 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 ten possible motion values (in rotation and translation) and give many examples. 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. |
