Evaluating Harker and O’Leary’s distance approximation for ellipse fitting

Abstract

Harker and O'Leary's [3] recently proposed a new distance measure for conics. This paper compares its accuracy and effectiveness against several other error of fits (EOFs) for ellipses using: 1/ visualisations of the distortions with respect to the Euclidean distance; 2/ a set of evaluation measures specifically designed for assessing ellipse EOFs [7,8]; 3/ the accuracy of LMedS ellipse fitting using the various EOFs.

Image processing and data evaluation algorithms for reproducible optical in-plane permeability characterization by radial flow experiments

“…61 They are specifically efficient in terms of numerical costs as well as robust with respect to incomplete scattered data as was confirmed by Rosin. 62 The mathematical relations most relevant for this work are briefly revised in the appendix as part of a uniform strategy for fitting geometric models to given sets of noisy data points. In the work at hand, two different types of elliptic geometry models were investigated: (1) a complete geometry model involving all five available degrees of freedom (DoF) of an ellipse, i.e.…”

“…For the analyses presented in this paper, geometric model fitting algorithms were implemented following the principles published by O'Leary and Zsombor-Murray, 58 Harker et al 60 and O'Leary et al 61 They are specifically efficient in terms of numerical costs as well as robust with respect to incomplete scattered data as was confirmed by Rosin. 62 The mathematical relations most relevant for this work are briefly revised in the appendix as part of a uniform strategy for fitting geometric models to given sets of noisy data points. In the work at hand, two different types of elliptic geometry models were investigated:…”

New confocal hyperbola-based ellipse fitting with applications to estimating parameters of mechanical pipes from point clouds

“…Hence, the confocal hyperbola distance is speculated to possess similar geometric properties to the true geometric distance of a point to the ellipse. In fact, Rosin had compared 16 different geometric distance approximation methods, including algebraic, Sampson, Harker and O'Leary, and the confocal hyperbola, in terms of properties such as linearity, curvature bias, asymmetry and general goodness [21,28,29]. Overall, the confocal hyperbola was the best in every category, especially for larger noise levels (see Table 2 of [21,28,29]).…”

“…In fact, Rosin had compared 16 different geometric distance approximation methods, including algebraic, Sampson, Harker and O'Leary, and the confocal hyperbola, in terms of properties such as linearity, curvature bias, asymmetry and general goodness [21,28,29]. Overall, the confocal hyperbola was the best in every category, especially for larger noise levels (see Table 2 of [21,28,29]). In Section 5.1, we will demonstrate that the confocal hyperbola method provides almost identical results to that of Chernov [11], which is the current state-of the-art.…”