New Confocal Hyperbola-based Ellipse Fitting with Applications to Estimating Parameters of Mechanical Pipes from Point Clouds
Date
2021-03-14
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Calgary
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 arclength
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.
Description
manuscript
Keywords
Geomatics
Citation
Maalek, R., Lichti, D.D. (2021). New confocal hyperbola-based ellipse fitting with applications to estimating parameters of mechanical pipes from point clouds. University of Calgary.