In this paper, we present an algorithm to approximate a set of data points with G1 continuous arcs, using points' covariance data. To the best of our knowledge, previous arc spline approximation approaches assumed that all data points contribute equally (i.e. have the same weights) during the approximation process. However, this assumption may cause serious instability in the algorithm, if the collected data contains outliers. To resolve this issue, a robust method for arc spline approximation is suggested in this work, assuming that the 2D covariance for each data point is given. Starting with the definition of models and parameters for single arc approximation, the framework is extended to multiple-arc approximation for general usage. Then the proposed algorithm is verified using generated noisy data and real-world collected data via vehicle experiment in Sejong City, South Korea.

翻译：本文提出了一种利用数据点协方差信息对离散点集进行G1连续圆弧逼近的算法。据我们所知，以往的圆弧样条逼近方法均假设所有数据点在逼近过程中具有同等贡献（即权重相同），然而当采集数据包含异常值时，该假设可能导致算法出现严重不稳定性。为解决此问题，本研究提出一种鲁棒的圆弧样条逼近方法，其前提是每个数据点的二维协方差矩阵已知。从单圆弧逼近的模型与参数定义出发，将框架扩展至适用于一般场景的多圆弧逼近。最后通过生成含噪数据与韩国世宗市实车实验采集的真实数据验证了所提算法的有效性。