方差膨胀的稳健加权总体最小二乘点云平面拟合

Plane Fitting of Point Cloud Using the Robust Weighted Total Least Squares Algorithm Based on Variance Inflation

为了提高平面拟合精度,本文采用总体最小二乘求解平面拟合参数。同时考虑到点云数据中含有的粗差点可能影响点云平面拟合的精度,提出了方差膨胀的稳健加权总体最小二乘。本文通过选取IGG权函数将点云数据分为3段,并引入中位数对IGG权函数进行改进,可以更准确地探测粗差。考虑到点云数据中x、y、z这3个方向的误差并不是等精度,计算了点位的协方差矩阵,使得x、y、z这3个方向的误差分配更加合理。通过实例表明,本文的方法不仅可以消除粗差点的影响,还能减弱可疑点的影响,得到更为准确的平面拟合参数,提高了平面拟合精度。

In order to improve the accuracy of plane fitting, total least squares is applied to obtain the parameters of plane in this paper, and the points with gross errors in point cloud data, which have a negative effect on the accuracy of plane fitting, are taken into consideration. For this reason, the robust weighted total least squares based on variance inflation is proposed. The IGG weight function is chosen to divide point cloud data into three sections in the method of this paper. Then, the median is introduced to improve the IGG weight function. Thus, the points with gross errors can be detected more accurately. In addition, the covariance matrix of point position error is calculated so that the errors of three component ( x,y,z ) can be assigned more reasonably, because the errors of three component ( x,y,z ) are not equal-accuracy in point cloud data. Through the case studies, it can be found that not only the effect of the gross errors points can be eliminated, but also the effect of the suspicious points can be weaken by using the method of this paper. The more accurate parameters of plane fitting are obtained and the accuracy of plane fitting is thus enhanced.