Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Self-Calibration of Stationary Cameras
International Journal of Computer Vision
Lines and Points in Three Views and the Trifocal Tensor
International Journal of Computer Vision
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Bayesian Modeling of Uncertainty in Low-Level Vision
Bayesian Modeling of Uncertainty in Low-Level Vision
Computer Vision: A Modern Approach
Computer Vision: A Modern Approach
Parameter Estimates for a Pencil of Lines: Bounds and Estimators
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
In defence of the 8-point algorithm
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Robust detection of degenerate configurations for the fundamental matrix
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
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In general, feature points and camera parameters can only be estimated with limited accuracy due to noisy images. In case of collinear feature points, it is possible to benefit from this geometrical regularity by correcting the feature points to lie on the supporting estimated straight line, yielding increased accuracy of the estimated camera parameters. However, regarding Maximum-Likelihood (ML) estimation, this procedure is incomplete and suboptimal. An optimal solution must also determine the error covariance of corrected features. In this paper, a complete theoretical covariance propagation analysis starting from the error of the feature points up to the error of the estimated camera parameters is performed. Additionally, corresponding Fisher Information Matrices are determined and fundamental relationships between the number and distance of collinear points and corresponding error variances are revealed algebraically. To demonstrate the impact of collinearity, experiments are conducted with covariance propagation analyses, showing significant reduction of the error variances of the estimated parameters.