Complete Projective Semi-Di erential Invariants

It is well known that given four point correspondences under perspectivity, we uniquely can determine a projectively invariant reference frame for planar scenes. We extend this result to all semi-diierential data correspondences having enough degrees of freedom to perform resection. For example, three points together with rst and second curve derivatives in one of them suuce for unique frame determination. The coordinates of points in the scene with respect to this reference frame constitute a complete system of invariants. Rather than solving the Lie prolongations, we arrive at these results by exhaustively exploiting all available relationships between the given semi{diierential data in two perspective views. The generalization of the method to the 3D projective group is straightforward , thus covering the case of nonplanar scenes under stereo as well.