IEEE Transactions on Pattern Analysis and Machine Intelligence
A note on the least squares fitting of ellipses
Pattern Recognition Letters
Ellipse fitting by accumulating five-point fits
Pattern Recognition Letters
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Assessing error of fit functions for ellipses
Graphical Models and Image Processing
Analysing error of fit functions for ellipses
Pattern Recognition Letters
Ellipse fitting using orthogonal hyperbolae and Stirling's oval
Graphical Models and Image Processing
Fitting Curves and Surfaces With Constrained Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to Data Mining, (First Edition)
Introduction to Data Mining, (First Edition)
Evaluating Harker and O'Leary's distance approximation for ellipse fitting
Pattern Recognition Letters
Direct type-specific conic fitting and eigenvalue bias correction
Image and Vision Computing
A hierarchical approach for fast and robust ellipse extraction
Pattern Recognition
Multiple ellipses detection in noisy environments: A hierarchical approach
Pattern Recognition
Splitting touching cells based on concave points and ellipse fitting
Pattern Recognition
Error Analysis of Geometric Ellipse Detection Methods Due to Quantization
PSIVT '10 Proceedings of the 2010 Fourth Pacific-Rim Symposium on Image and Video Technology
Edge curvature and convexity based ellipse detection method
Pattern Recognition
A Split and Merge Based Ellipse Detector With Self-Correcting Capability
IEEE Transactions on Image Processing
A precise ellipse fitting method for noisy data
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part I
A novel framework for making dominant point detection methods non-parametric
Image and Vision Computing
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A novel ellipse fitting method which is selective for digital and noisy elliptic curves is proposed in this paper. The method aims at fitting an ellipse only when the data points are highly likely belong to an ellipse. This is achieved using the geometric distances of the ellipse from the data points. The proposed method models the non-linear problem of ellipse fitting as a combination of two operators, with one being linear, numerically stable, and easily invertible, while the other being non-linear but unique and easily invertible operator. As a consequence, the proposed ellipse fitting method has several salient properties like unconstrained, stable, non-iterative, and computationally inexpensive. The efficacy of the method is compared against six contemporary and recent algorithms based on the least squares formulation using five experiments of diverse practical challenges, like digitization, incomplete ellipses, and Gaussian noise (up to 30%). Three of the experiments comprise of a total of 44,400 ellipses (positive test data) while the other two are tested on 320,000 non-elliptic conics (negative test data). The results show that the proposed method is quite selective to elliptic shapes only and provides accurate fitting results, indicating potential application in medical, robotics, object detection, and other image processing industrial applications.