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
On the Fitting of Surfaces to Data with Covariances
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rationalising the Renormalisation Method of Kanatani
Journal of Mathematical Imaging and Vision
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
For geometric inference from images, what kind of statistical model is necessary?
Systems and Computers in Japan
Ellipse Fitting with Hyperaccuracy
IEICE - Transactions on Information and Systems
On the Convergence of Fitting Algorithms in Computer Vision
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
Hyper least squares fitting of circles and ellipses
Computational Statistics & Data Analysis
Ellipse fitting with hyperaccuracy
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Renormalization returns: hyper-renormalization and its applications
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Guaranteed ellipse fitting with the sampson distance
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
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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We study the problem of fitting ellipses to observed points in the context of Errors-In-Variables regression analysis. The accuracy of fitting methods is characterized by their variances and biases. The variance has a theoretical lower bound (the KCR bound), and many practical fits attend it, so they are optimal in this sense. There is no lower bound on the bias, though, and in fact our higher order error analysis (developed just recently) shows that it can be eliminated, to the leading order. Kanatani and Rangarajan recently constructed an algebraic ellipse fit that has no bias, but its variance exceeds the KCR bound; so their method is optimal only relative to the bias. We present here a novel ellipse fit that enjoys both optimal features: the theoretically minimal variance and zero bias (both to the leading order). Our numerical tests confirm the superiority of the proposed fit over the existing fits.