Summary: Complete Projective SemiDifferential Invariants
Lehrstuhl f¨ur Mustererkennung und Bildverarbeitung
D79110 Freiburg i.Br., Germany
Abstract. It is well known that given four point correspondences under
perspectivity, we uniquely can determine a projectively invariant refer
ence frame for planar scenes.
We extend this result to all semidifferential data correspondences hav
ing enough degrees of freedom to perform resection. For example, three
points together with first and second curve derivatives in one of them
suffice 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--differential data in two perspective views.
The generalization of the method to the 3D projective group is straight
forward, thus covering the case of nonplanar scenes under stereo as well.
The use of quantities that are not dependend upon the acquisition geometry