Measurement error models
Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter
Image and Vision Computing - Special issue: 5th Alvey vision meeting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ellipse detection and matching with uncertainty
Image and Vision Computing - Special issue: BMVC 1991
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
A note on the least squares fitting of ellipses
Pattern Recognition Letters
A buyer's guide to conic fitting
BMVC '95 Proceedings of the 6th British conference on Machine vision (Vol. 2)
The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
On the Optimization Criteria Used in Two-View Motion Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
International Journal of Computer Vision - Special issue on a special section on visual surveillance
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonparametric Segmentation of Curves into Various Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Role of Total Least Squares in Motion Analysis
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Motion analysis with a camera with unknown, and possibly varying intrinsic parameters
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
On the Fitting of Surfaces to Data with Covariances
IEEE Transactions on Pattern Analysis and Machine Intelligence
Revisiting Hartley's Normalized Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
From FNS to HEIV: A Link between Two Vision Parameter Estimation Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the complexity of curve fitting algorithms
Journal of Complexity
Least Squares Fitting of Circles
Journal of Mathematical Imaging and Vision
Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Convergence of Fitting Algorithms in Computer Vision
Journal of Mathematical Imaging and Vision
On the Consistency of the Normalized Eight-Point Algorithm
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
Optimal Parameter Estimation with Homogeneous Entities and Arbitrary Constraints
Proceedings of the 31st DAGM Symposium on Pattern Recognition
Revisiting the brightness constraint: probabilistic formulation and algorithms
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Computational Statistics & Data Analysis
Renormalization returns: hyper-renormalization and its applications
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Optimization techniques for geometric estimation: beyond minimization
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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The renormalisation technique of Kanatani is intended to iteratively minimise a cost function of a certain form while avoiding systematic bias inherent in the common method of minimisation due to Sampson. Within the computer vision community, the technique has generally proven difficult to absorb. This work presents an alternative derivation of the technique, and places it in the context of other approaches. We first show that the minimiser of the cost function must satisfy a special variational equation. A Newton-like, fundamental numerical scheme is presented with the property that its theoretical limit coincides with the minimiser. Standard statistical techniques are then employed to derive afresh several renormalisation schemes. The fundamental scheme proves pivotal in the rationalising of the renormalisation and other schemes, and enables us to show that the renormalisation schemes do not have as their theoretical limit the desired minimiser. The various minimisation schemes are finally subjected to a comparative performance analysis under controlled conditions.