Invariant of a pair of non-coplanar conics in space: definition, geometric interpretation and computation

Author

Quan, Long

Author_Institution

Inst. Nat. de Recherche en Inf. et Autom., Grenoble, France

fYear

1995

fDate

20-23 Jun 1995

Firstpage

926

Lastpage

931

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

Keywords

algebra; calibration; computational geometry; image recognition; image reconstruction; algebraic invariant; computer vision; coplanar conics; cross-ratios; geometric computation; geometric interpretation; invariant algebra; joint invariants; noncoplanar conics; quaternary quadratic forms; uncalibrated images; Algebra; Books; Computational geometry; Computer vision; Differential equations; Image reconstruction;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Vision, 1995. Proceedings., Fifth International Conference on

Conference_Location

Cambridge, MA

Print_ISBN

0-8186-7042-8

Type

conf

DOI

10.1109/ICCV.1995.466836

Filename

466836