Performance evaluation of iterative geometric fitting algorithms
Computational Statistics & Data Analysis
International Journal of Computer Vision
Development of a 3D High-Precise Positioning System Based on a Planar Target and Two CCD Cameras
ICIRA '08 Proceedings of the First International Conference on Intelligent Robotics and Applications: Part II
Precise ellipse estimation without contour point extraction
Machine Vision and Applications
Hyper least squares fitting of circles and ellipses
Computational Statistics & Data Analysis
Temporal super resolution from a single quasi-periodic image sequence based on phase registration
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part I
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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For fitting an ellipse to a point sequence, ML (maximum likelihood) has been regarded as having the highest accuracy. In this paper, we demonstrate the existence of a "hyperaccurate" method which outperforms ML. This is made possible by error analysis of ML followed by subtraction of high-order bias terms. Since ML nearly achieves the theoretical accuracy bound (the KCR lower bound), the resulting improvement is very small. Nevertheless, our analysis has theoretical significance, illuminating the relationship between ML and the KCR lower bound.