Curve and surface reconstruction methods play an important role in many research and engineering fields. It is an imperative procedure to carry out surface reconstruction from measurement data in reverse engineering, which is complicated with the presence of outliers. To achieve better accuracy and robustness of reconstruction, an improved moving total least squares (MTLS) algorithm based on k-means clustering called a KMTLS method is proposed in this article. Based on MTLS, KMTLS adjusts the weight of discrete points within the support domain by adopting a two-step fitting procedure. Firstly, an ordinary least squares (OLS) method is adopted to obtain the pre-fitting result and calculate the residuals as the input of k-means clustering. In k-means clustering, abnormal nodes are classified into one cluster and a weight function based on clustering information is introduced to deal with these nodes. Secondly, based on the compact weight function in MTLS and the weight obtained in the pre-fitting procedure, a weighted total least squares method is conducted to determine the final estimated value. The process of detecting outliers is automatic without setting threshold artificially. The simulation and experiment show that KMTLS has great robustness and accuracy.

曲线和曲面重建方法在许多研究和工程领域中发挥着重要作用。在逆向工程中根据测量数据进行表面重建是必不可少的过程，由于存在异常值而变得复杂。为了获得更好的重建精度和鲁棒性，本文提出了一种基于 k 均值聚类的改进移动总最小二乘 (MTLS) 算法，称为 KMTLS 方法。KMTLS 在 MTLS 的基础上，通过采用两步拟合程序来调整支持域内离散点的权重。首先采用普通最小二乘法(OLS)得到预拟合结果，计算残差作为k-means聚类的输入。在 k 均值聚类中，将异常节点归为一个簇，引入基于簇信息的权重函数来处理这些节点。其次，基于MTLS中的紧凑权重函数和预拟合过程中得到的权重，进行加权全最小二乘法确定最终估计值。检测异常值的过程是自动的，无需人为设置阈值。仿真和实验表明，KMTLS 具有很强的鲁棒性和准确性。