论文标题
新的基于共聚焦双曲线的椭圆形拟合，并用应用程序估算点云的机械管道参数
New Confocal Hyperbola-based Ellipse Fitting with Applications to Estimating Parameters of Mechanical Pipes from Point Clouds
论文作者
论文摘要
该手稿提出了一种新方法，将椭圆形拟合到二维数据的新方法使用共焦双曲线近似与点到椭圆的几何距离。评估了所提出的方法并将其与模拟和现实数据集的已建立方法进行了比较。首先，揭示了共聚焦双曲线距离大大优于其他距离近似，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。检查了每种方法作为旋转，纵横比，噪声和弧长的函数的性能。据观察，所提出的椭圆拟合方法比AHN的黄金标准几何方法获得了几乎相同的结果（并且在某些情况下更好），并且在所有仿真实验中均优于其余方法。最后，所提出的方法在估算点云的圆柱机械管的几何参数方面优于考虑的椭圆拟合方法。实验的结果表明，共聚焦双曲线是对真实几何距离的绝佳近似值，并且在实际设置中产生可靠，准确的椭圆拟合。
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.
