点云数据平面拟合的加权总体最小二乘方法

Plane fitting of poing clouds using weighted total least squares method

介绍了解算加权总体最小二乘问题的Jazaeri算法,分析了直积形式、Mahboub五条原则以及协因数传播律构造协因数阵的优缺点;分别利用Jazaeri算法、Schaffrin算法、总体最小二乘法和加权最小二乘法对仿真点云数据和实际点云数据进行平面拟合,结果表明加权总体最小二乘法对仿真点云数据和均质性较好的实际点云数据平面拟合效果较好;而对于表面附有杂质的材质,杂质部分的点云数据以经验信息确定协因数阵与实际协因数阵有偏差,影响整体点云数据平面拟合效果,导致加权总体最小二乘与总体最小二乘精度相当;在点云数据平面拟合中Jazaeri算法比Schaffrin算法计算效率更高。

Jazaeri ＇s algorithm which solves the weighted total least-squares problems（ WTLS） is introduced in this paper. Advantages and disadvantages of Kronecker product, five principles and variance-covariance propagation law methods which construct variance-covariance matrix of coefficient matrix are analyzed. Analytical experiments based on simulated data and real data and comparison between the methods including Jazaeri＇s algorithm,Schaffrin＇s algorithm,total least squares method and weighted least squares method are conducted. Experimental results show that weighted total least squares is effective for plane fitting of point clouds with good homogeneous. But plane fitting of fractional inhomogeneous point clouds,the precisions of weighted total least squares and total least squares are comparative. Jazaeri ＇s algorithm is more effective than Schaffrin＇s algorithm on the calculation.