空间圆形物体的共形几何代数拟合方法  

Conformal Geometric Algebraic Fitting Method for Circular Objects in Space

作　　者：焦卫东[1] 庞艳丽 JIAO Wei-dong;PANG Yan-li(Tianjin Key Laboratory of Intelligent Signal and Image Processing,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]中国民航大学天津市智能信号与图像处理重点实验室,天津300300

出　　处：《计算机仿真》2023年第8期376-381,494,共7页Computer Simulation

基　　金：国家重点研发计划(2020YFB1600101)。

摘　　要：针对传统空间圆拟合方法不稳定、拟合精度不高的问题,提出一种空间圆形物体的共形几何代数拟合方法。首先,将实验数据点集映射到共形空间,利用内积算子给出了拟合球最小二乘法的共形空间表达。在共形空间求最小非负特征解,即两个最佳拟合球的方程。利用共形空间Meet算子对这两个最小非负特征解求交得到拟合空间圆。实验结果表明,上述算法受噪声影响小、鲁棒性较高,特别适用于解决噪声复杂的数据点问题,运行速度比欧氏空间方法快2.9倍以上。同时,经应用实例验证所提方法在保证测量精度的前提下,有效提高了算法运行效率,可在工程中实际应用。A conformal geometric algebraic fitting method for space circular objects was proposed to solve the problems of instability and low fitting accuracy of traditional space circular fitting methods.Firstly,the experimental data point set was mapped to conformal space,and the conformal space expression of the fitting spherical least square method was given by using the inner product operator.Then,the minimum nonnegative eigen solution was found in conformal space,that is,the equations of the two best-fitting spheres.Finally,the conformal space Meet operator was used to cross the two minimum nonnegative eigen solutions to obtain the fitting space circle.Experimental results show that the proposed algorithm is less affected by noise and has high robustness.It is especially suitable for solving data point problems with complex noise,and the running speed is more than 2.9 times faster than the Euclidian space method.At the same time,the application example verifies that the proposed method can effectively improve the efficiency of the algorithm on the premise of ensuring the measurement accuracy,and can be applied in engineering practice.

关 键 词：空间圆形物体 共形几何代数 最小二乘 拟合 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]