  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.
