Abstract

The joint invariants of a pair of coplanar conics has been widely used in recent vision literature. In this paper, the algebraic invariant of a pair of non-coplanar conics in space is concerned. The algebraic invariant of a pair of non-coplanar conics is first derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space conics. Then, this algebraic invariant is geometrically interpreted in terms of cross-ratios. Finally, an analytical procedure for projective reconstruction of a space conic from two uncalibrated images is developed and the correspondence conditions of the conics between two views are also explicited. Experimentations for the discriminality of the correspondence conditions and the accuracy and stability of the projective reconstruction and of the computation of the invariant are conducted both for simulated and real images. Key words: Invariant, Geometry, Object recognition. 1 Introduction The study of invariant...