Performance characterization of fundamental matrix estimation under image degradation
Machine Vision and Applications - Special issue on performance evaluation
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
Robust detection of degenerate configurations while estimating the fundamental matrix
Computer Vision and Image Understanding
The Geometry of Multiple Images: The Laws That Govern The Formation of Images of A Scene and Some of Their Applications
Computer Vision: A Modern Approach
Computer Vision: A Modern Approach
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Estimation of Relative Camera Positions for Uncalibrated Cameras
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Projective Structure from two Uncalibrated Images: Structure from Motion and Recognition
Projective Structure from two Uncalibrated Images: Structure from Motion and Recognition
Modeling the World from Internet Photo Collections
International Journal of Computer Vision
GNU Scientific Library Reference Manual - Third Edition
GNU Scientific Library Reference Manual - Third Edition
Good match exploration using triangle constraint
Pattern Recognition Letters
| Hi-index | 0.14 |
The fundamental matrix (FM) describes the geometric relations that exist between two images of the same scene. Different error criteria are used for estimating FMs from an input set of correspondences. In this paper, the accuracy and efficiency aspects of the different error criteria are studied. We mathematically and experimentally proved that the most popular error criterion, the symmetric epipolar distance, is biased. It was also shown that despite the similarity between the algebraic expressions of the symmetric epipolar distance and Sampson distance, they have different accuracy properties. In addition, a new error criterion, Kanatani distance, was proposed and proved to be the most effective for use during the outlier removal phase from accuracy and efficiency perspectives. To thoroughly test the accuracy of the different error criteria, we proposed a randomized algorithm for Reprojection Error-based Correspondence Generation (RE-CG). As input, RE-CG takes an FM and a desired reprojection error value d. As output, RE-CG generates a random correspondence having that error value. Mathematical analysis of this algorithm revealed that the success probability for any given trial is 1-(2/3)^2 at best and is 1-(6/7)^2 at worst while experiments demonstrated that the algorithm often succeeds after only one trial.