Geometric invariance in computer vision
Geometric invariance in computer vision
Algorithms in invariant theory
Algorithms in invariant theory
Projective Reconstruction and Invariants from Multiple Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Invariants of 6 points from 3 uncalibrated images
ECCV '94 Proceedings of the third European conference on Computer Vision (Vol. II)
Invariants of Six Points and Projective Reconstruction From Three Uncalibrated Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algebraic and Geometric Tools to Compute Projective and Permutation Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics
Generalized homogeneous coordinates for computational geometry
Geometric computing with Clifford algebras
The Geometry of Multiple Images: The Laws That Govern The Formation of Images of A Scene and Some of Their Applications
Applications of Invariance in Computer Vision: Second Joint European-U. S. Workshop, Ponta Delgada, Azores, Portugal, October 9-14, 1993
A Geometric Approach for the Theory and Applications of 3D Projective Invariants
Journal of Mathematical Imaging and Vision
Proceedings of the 7th International Conference on Computer Analysis of Images and Patterns
CAIP '97 Proceedings of the 7th International Conference on Computer Analysis of Images and Patterns
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
A Six Point Solution for Structure and Motion
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
A New Methodology for Computing Invariants in Computer Vision
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
The invariant representations of a quadric cone and a twisted cubic
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detecting and Handling Unreliable Points for Camera Parameter Estimation
International Journal of Computer Vision
Detecting critical configuration of six points
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part II
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Projective geometric invariants play an important role in computer vision. To set up the invariant relationships between spatial points and their images from a single view, at least six pairs of spatial and image points are required. In this paper, we establish a unified and complete framework of the invariant relationships for six points. The framework covers the general case already developed in the literature and two novel cases. The two novel cases describe that six spatial points and the camera optical center lie on a quadric cone or a twisted cubic, called quadric cone case or twisted cubic case. For the general case and quadric cone case, camera parameters can be determined uniquely. For the twisted cubic case, camera parameters cannot be determined completely; this configuration of camera optical center and spatial points is called a critical configuration. The established unified framework may help to effectively identify the type of geometric information appearing in certain vision tasks, in particular critical geometric information. An obvious advantage using this framework to obtain geometric information is that no any explicit estimation on camera projective matrix and optical center is needed.