基于共焦双曲线的椭圆拟合及其在管道参数估计中的应用
New Confocal Hyperbola-based Ellipse Fitting with Applications to Estimating Parameters of Mechanical Pipes from Point Clouds
摘要：
本文提出了一种用共焦双曲线近似点到椭圆的几何距离来拟合椭圆的新方法。所提出的方法进行了评估，并建立模拟和真实世界的数据集的方法进行比较。首先，它揭示了共焦双曲线距离大大优于其他距离近似，如代数和桑普森。接下来，所提出的椭圆拟合方法与Halir，Taubin，Kanatani，Ahn和Szpak提出的五种可靠和成熟的方法进行了比较。每种方法的性能作为旋转，纵横比，噪声和弧长的函数进行了检查。据观察，所提出的椭圆拟合方法实现了几乎相同的结果（在某些情况下更好）比金标准的几何方法的安和优于其余的方法在所有的模拟实验。最后，该方法优于所考虑的椭圆拟合方法在估计圆柱形机械管道的几何参数从点云。实验结果表明，共焦双曲线是一个很好的近似真实的几何距离，并产生可靠和准确的椭圆拟合在实际设置。
英文摘要：
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.
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