Two main results are established in this paper. First, we show that seven point
correspondences are sufficient to uniquely determine from two perspective views the three-
dimensional motion parameters (within a scale factor for the translations) of a rigid object
with curved surfaces. The seven points should not be traversed by two planes with one
plane containing the origin, nor by a cone containing the origin. Second, a set of``essential
parameters''are introduced which uniquely determine the motion parameters up to a scale …

In this thesis, several fundamental breakthroughs have been made on the uniqueness and
estimation of 3-D motion parameters of rigid objects, both on theoretical and computational
aspects. When the object surface is restricted to be planar, we show that given two image
frames, one can determine uniquely eight" pure parameters" which are nonlinear functions
of the actual motion parameters. There are two different ways to estimate these pure
parameters. The first is the direct method and the second, two-step method. The direct …