Further Five-Point Fit Ellipse Fitting

Abstract

The least squares method is the most commonly used technique for fitting an ellipse through a set of points. However, it has a low breakdown point, which means that it performs poorly in the presence of outliers. We describe various alternative methods for ellipse fitting which are more robust: the Theil-Sen, least median of squares, Hilbert curve, and minimum volume estimator approaches. Testing with synthetic data demonstrates that the least median of squares is the most suitable method in terms of accuracy and robustness.

Global Contour and Region Based Shape Analysis and Similarity Measures

“…Rosin 61 and Roth and Levine 62 proposed a least median of squares approaches to feature fitting. Minimal subsets (i.e.…”

2D Shape Measures for Computer Vision

“…For instance, to fit ellipses, Rosin [48] used the Least Median of Squares (LMedS) approach which is robust to outliers, and enables the ellipse to be fitted reliably even in the presence of outliers. The LMedS enables outliers to be rejected, and then a more accurate (and ellipse-specific) least squares fit to the inliers was found [15].…”

Ellipse Fitting Using Orthogonal Hyperbolae and Stirling's Oval

“…This enables a higher level representation of, for example, edge data, which is useful for many applications of computer vision. A large body of work has been developed on ellipse fitting techniques, mostly using least squared error [1,2] but also other criteria such as the least median of squares [7,8]. The majority of these fitting methods operate by minimizing some function of the errors between the data points and the ellipse.…”