Invariant of a Pair of non-Coplanar Conics in Space: Definition, Geometric Interpretation and Computation

Long Quan (1, 2)

1 MOVI - Modeling, localization, recognition and interpretation in computer vision
2 LIFIA - Laboratoire d'Informatique Fondamentale et d'Intelligence Artificielle

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 the computation of the invariant are conducted both for simulated and real images.

Mots clés: Invariant; geometry; object recognition

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Long Quan. Invariant of a Pair of non-Coplanar Conics in Space: Definition, Geometric Interpretation and Computation. 5th International Conference on Computer Vision (ICCV '95), Jun 1995, Cambridge, United States. pp.926--931, ⟨10.1109/ICCV.1995.466836⟩. ⟨inria-00590054⟩