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The Invariant Representations of a Quadric Cone and a Twisted Cubic
October 2003 (vol. 25 no. 10)
pp. 1329-1332

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. In this paper, 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.

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Index Terms:
Automated theorem proving, computer vision, invariant representation, quadric cone, twisted cubic.
Citation:
Y.H. Wu, Z. Y. Hu, "The Invariant Representations of a Quadric Cone and a Twisted Cubic," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 10, pp. 1329-1332, Oct. 2003, doi:10.1109/TPAMI.2003.1233907
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