Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Theory of Reconstruction from Image Motion
Theory of Reconstruction from Image Motion
A Geometric Approach for the Theory and Applications of 3D Projective Invariants
Journal of Mathematical Imaging and Vision
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
The Dou8ble Algebra: An Effective Tool for Computing Invariants in Computer Vision
Proceedings of the Second Joint European - US Workshop on Applications of Invariance in Computer Vision
Relation between 3D invariants and 2D invariant
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
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
The invariant representations of a quadric cone and a twisted cubic
IEEE Transactions on Pattern Analysis and Machine Intelligence
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When space points and camera optical center lie on a twisted cubic, no matter how many corresponding pairs there are from space points to their image points, camera projection matrix cannot be uniquely determined, in other words, the configuration of camera and space points in this case is critical for camera parameter estimation. In practice, it is important to detect this critical configuration before the estimated camera parameters are used. In this work, a new method is introduced to detect this critical configuration, which is based on an effective criterion function constructed from an invariant relationship between six space points and their corresponding image points. The advantage of this method is that no explicit computation on camera projection matrix or optical center is needed. Simulations show it is quite robust and stable against noise. Experiments on real data show the criterion function can be faithfully trusted for camera parameter estimation.