Robust Fitting of Ellipses and Spheroids

TL;DR

This paper introduces robust algorithms for fitting ellipses and spheroids that maintain high accuracy even under high noise and eccentricity, outperforming traditional methods.

Contribution

The paper presents novel robust fitting algorithms based on geometric and statistical properties, effective in high-noise and high-eccentricity scenarios.

Findings

Algorithms perform well in high-noise conditions

Effective for high-eccentricity ellipses and spheroids

Validated through simulation results

Abstract

Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise level or the ellipse eccentricity are high. A series of robust fitting algorithms are proposed that perform well in high-noise, high-eccentricity ellipse/spheroid (a special class of ellipsoid) cases. The new algorithms are based on the geometric definition of an ellipse/spheroid, and improved using global statistical properties of the data. The efficacy of the new algorithms is demonstrated through simulations.