New Confocal Hyperbola-based Ellipse Fitting with Applications to Estimating Parameters of Mechanical Pipes from Point Clouds

TL;DR

This paper introduces a novel ellipse fitting method using confocal hyperbola approximation, demonstrating superior accuracy and robustness over existing methods in both simulated and real-world datasets, especially for mechanical pipe analysis.

Contribution

The paper proposes a new ellipse fitting technique based on confocal hyperbola approximation, outperforming established methods in accuracy and robustness.

Findings

Confocal hyperbola distance outperforms algebraic and Sampson distances.

The proposed method matches or exceeds the accuracy of the geometric Ahn method.

It effectively estimates parameters of mechanical pipes from point clouds.

Abstract

This manuscript presents a new method for fitting ellipses to two-dimensional data using the confocal hyperbola approximation to the geometric distance of points to ellipses. The proposed method was evaluated and compared to established methods on simulated and real-world datasets. First, it was revealed that the confocal hyperbola distance considerably outperforms other distance approximations such as algebraic and Sampson. Next, the proposed ellipse fitting method was compared with five reliable and established methods proposed by Halir, Taubin, Kanatani, Ahn and Szpak. The performance of each method as a function of rotation, aspect ratio, noise, and arc-length were examined. It was observed that the proposed ellipse fitting method achieved almost identical results (and in some cases better) than the gold standard geometric method of Ahn and outperformed the remaining methods in all simulation experiments. Finally, the proposed method outperformed the considered ellipse fitting methods in estimating the geometric parameters of cylindrical mechanical pipes from point clouds. The results of the experiments show that the confocal hyperbola is an excellent approximation to the true geometric distance and produces reliable and accurate ellipse fitting in practical settings.