The twisted cubic and camera calibration
Computer Vision, Graphics, and Image Processing
Projective Reconstruction and Invariants from Multiple Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Degeneracy of Linear Reconstruction From Three Views: Linear Line Complex and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Theory of Reconstruction from Image Motion
Theory of Reconstruction from Image Motion
Invariants of 6 Points from 3 Uncalibrated Images
ECCV '94 Proceedings of the Third European Conference-Volume II on Computer Vision - Volume II
Dualizing Scene Reconstruction Algorithms
SMILE'98 Proceedings of the European Workshop on 3D Structure from Multiple Images of Large-Scale Environments
Duality of reconstruction and positioning from projective views
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
Ambiguity in Reconstruction From Images of Six Points
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Critical Curves and Surfaces for Euclidean Reconstruction
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Degeneracy from twisted cubic under two views
Journal of Computer Science and Technology
A critical configuration for reconstruction from rectilinear motion
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Twisted cubic: degeneracy degree and relationship with general degeneracy
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
Live three-dimensional reconstruction system with stereo vision display
Computers and Electrical Engineering
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The critical configurations for projective reconstruction from three views are discussed. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and cameras uniquely, up to projective transformation. For two views, the classification of critical configurations is well known - the configuration is critical if and only if the points and camera centres all lie on a ruled quadric. For three views the critical configurations have not been identified previously. In this paper it is shown that for any placement of three given cameras there always exists a critical set consisting of a fourth-degree curve - any number of points on the curve form a critical set for the three cameras. Dual to this result, for a set of seven points there exists a fourth-degree curve such that a configuration of any number of cameras placed on this curve is critical for the set of points. Other critical configurations exist in cases where the points all lie in a plane, or one of the cameras lies on a twisted cubic.