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.

该手稿提出了一种使用共聚焦双曲线逼近点到椭圆的几何距离将椭圆拟合到二维数据的新方法。对提出的方法进行了评估，并将其与模拟和真实数据集上的已建立方法进行了比较。首先，我们发现共焦双曲线距离大大优于其他距离近似值，例如代数和桑普森。接下来，将提出的椭圆拟合方法与Halir，Taubin，Kanatani，Ahn和Szpak提出的五种可靠且已建立的方法进行了比较。检查了每种方法的性能与旋转，纵横比，噪声和弧长的关系。可以看出，所提出的椭圆拟合方法与Ahn的金标准几何方法取得了几乎相同的结果（在某些情况下还更好），并且在所有模拟实验中均优于其余方法。最后，在从点云估计圆柱机械管道的几何参数方面，所提出的方法优于考虑的椭圆拟合方法。实验结果表明，共焦双曲线非常适合真实的几何距离，并且在实际环境中可产生可靠且准确的椭圆拟合。