The twisted cubic and camera calibration
Computer Vision, Graphics, and Image Processing
Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A stability analysis of the fundamental matrix
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
Determining the Epipolar Geometry and its Uncertainty: A Review
International Journal of Computer Vision
On accurate and robust estimation of fundamental matrix
Computer Vision and Image Understanding
Robust detection of degenerate configurations while estimating the fundamental matrix
Computer Vision and Image Understanding
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Theory of Reconstruction from Image Motion
Theory of Reconstruction from Image Motion
Ambiguous Configurations for 3-View Projective Reconstruction
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Ambiguity in Reconstruction From Images of Six Points
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Nonlinear Estimation of the Fundamental Matrix with Minimal Parameters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two-View Geometry Estimation Unaffected by a Dominant Plane
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Critical Configurations for Projective Reconstruction from Multiple Views
International Journal of Computer Vision
RANSAC for (Quasi-)Degenerate data (QDEGSAC)
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Globally Optimal Estimates for Geometric Reconstruction Problems
International Journal of Computer Vision
Detecting and Handling Unreliable Points for Camera Parameter Estimation
International Journal of Computer Vision
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Fundamental matrix, drawing geometric relationship between two images, plays an important role in 3-dimensional computer vision. Degenerate configurations of space points and two camera optical centers affect stability of computation for fundamental matrix. In order to robustly estimate fundamental matrix, it is necessary to study these degenerate configurations. We analyze all possible degenerate configurations caused by twisted cubic and give the corresponding degenerate rank for each case. Relationships with general degeneracies, the previous ruled quadric degeneracy and the homography degeneracy, are also reported in theory, where some interesting results are obtained such as a complete homography relation between two views. Based on the result of the paper, by applying RANSAC for degenerate data, we could obtain more robust estimations for fundamental matrix.