A note on the least squares fitting of ellipses
Pattern Recognition Letters
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Fitting of Surfaces to Data with Covariances
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Revisiting Hartley's Normalized Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Convergence of Fitting Algorithms in Computer Vision
Journal of Mathematical Imaging and Vision
Performance evaluation of iterative geometric fitting algorithms
Computational Statistics & Data Analysis
Analysis and recognition of touching cell images based on morphological structures
Computers in Biology and Medicine
Splitting touching cells based on concave points and ellipse fitting
Pattern Recognition
Conic fitting using the geometric distance
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
IEEE Transactions on Pattern Analysis and Machine Intelligence
RANSAC based ellipse detection with application to catadioptric camera calibration
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: models and applications - Volume Part II
Hyper least squares fitting of circles and ellipses
Computational Statistics & Data Analysis
Robust ellipse and spheroid fitting
Pattern Recognition Letters
Computational Statistics & Data Analysis
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When faced with an ellipse fitting problem, practitioners frequently resort to algebraic ellipse fitting methods due to their simplicity and efficiency. Currently, practitioners must choose between algebraic methods that guarantee an ellipse fit but exhibit high bias, and geometric methods that are less biased but may no longer guarantee an ellipse solution. We address this limitation by proposing a method that strikes a balance between these two objectives. Specifically, we propose a fast stable algorithm for fitting a guaranteed ellipse to data using the Sampson distance as a data-parameter discrepancy measure. We validate the stability, accuracy, and efficiency of our method on both real and synthetic data. Experimental results show that our algorithm is a fast and accurate approximation of the computationally more expensive orthogonal-distance-based ellipse fitting method. In view of these qualities, our method may be of interest to practitioners who require accurate and guaranteed ellipse estimates.