The invariant representations of a quadric cone and a twisted cubic

Author

Wu, Y.H. ; Hu, Z.Y.

Author_Institution

Nat. Lab. of Pattern Recognition, Inst. of Autom. Chinese Acad. of Sci., Beijing, China

Volume

25

Issue

10

fYear

2003

Firstpage

1329

Lastpage

1332

Abstract

Up to now, the shortest invariant representation of a quadric has 138 summands and there has been no invariant representation of a twisted cubic in 3D projective space, which limit to some extent the applications of invariants in 3D space. We give a very short invariant representation of a quadric cone, a special quadric, which has only two summands similar to the invariant representation of a planar conic, and give a short invariant representation of a twisted cubic. Then, a completely linear algorithm for generating the parametric equations of a twisted cubic is provided also. Finally, we exemplify some applications of our proposed invariant representations in the fields of computer vision and automated geometric theorem proving.

Keywords

computational geometry; computer vision; theorem proving; 3D projective space; 3D space; automated geometric theorem proving; computer vision; invariant representations; linear algorithm; parametric equations; planar conic; quadric cone; special quadric; summands; twisted cubic; Application software; Computer vision; Equations; Kernel; Symmetric matrices;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/TPAMI.2003.1233907

Filename

1233907