Camera Calibration and Direct Reconstruction from Plane with Brackets
Journal of Mathematical Imaging and Vision
Detecting and Handling Unreliable Points for Camera Parameter Estimation
International Journal of Computer Vision
Degeneracy from twisted cubic under two views
Journal of Computer Science and Technology
Detecting critical configuration of six points
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part II
A unified and complete framework of invariance for six points
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
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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.