基于最小二乘的正交距离拟合方法研究

计算机工程与应用 ›› 2015, Vol. 51 ›› Issue (11): 27-30.

基于最小二乘的正交距离拟合方法研究

崔佳洁，崔希民，王强，李聪

中国矿业大学（北京）地球科学与测绘工程学院，北京 100083

出版日期:2015-06-01 发布日期:2015-06-12

Research of orthogonal distance fitting method based on least-squares

CUI Jiajie, CUI Ximin, WANG Qiang, LI Cong

College of Geoscience and Surveying Engineering, China University of Mining & Technology（Beijing）, Beijing 100083, China

Online:2015-06-01 Published:2015-06-12

摘要/Abstract

摘要： 对点云进行拟合以获得信息模型是许多工程应用领域的一个核心问题，其目的是根据设计模型和规范的要求，高精度地对三维部件、工件进行检查、检核。在最小二乘原理的基础上，阐述了一种新的拟合方法——几何正交距离拟合，运用这种方法的算法处理标准几何体测量数据，并与一般代数拟合方法处理结果进行比较，分析了同一几何体运用不同方法对拟合结果的影响。得出在测量点误差较大的情况下和进行曲线曲面拟合时，几何正交距离拟合方法优于一般代数拟合方法。

关键词: 最小二乘原理, 一般代数拟合, 几何正交距离拟合, 拟合精度

Abstract: Fitting point cloud to achieve the information of model is a central issue in many fields of engineering applications. Its purpose is to inspect and check workpiece and three-dimensional parts according to the design model and the requirement of specification. The paper introduces a new fitting method on the basis of the least squares principle——the geometrical orthogonal distance fitting. It uses the orthogonal distance fitting algorithm to process measurement data of the geometry, and compares the fitting precision of the data with the result of general algebraic fitting method. Then the paper analyzes the result of fitting using different methods on the same geometry. It proves that larger error in the measurement point and to carry on the curve and surface fitting, orthogonal distance fitting is better than the general algebra method of least squares fitting.

Key words: least squares principle, algebraic fitting, geometrical orthogonal distance fitting, fitting precision

崔佳洁，崔希民，王强，李聪. 基于最小二乘的正交距离拟合方法研究[J]. 计算机工程与应用, 2015, 51(11): 27-30.

CUI Jiajie, CUI Ximin, WANG Qiang, LI Cong. Research of orthogonal distance fitting method based on least-squares[J]. Computer Engineering and Applications, 2015, 51(11): 27-30.