﻿ 一种改进的选权迭代算法在点云数据拟合中的应用

# 一种改进的选权迭代算法在点云数据拟合中的应用Application of an Improved Selecting Weight Iterative Algorithm in Point Cloud Data Fitting

Abstract: To fit the point cloud data with massive outliers, an improved selecting weight iterative algorithm is proposed: the robust initial value is obtained by using the least trimmed squares algorithm, and the number of iterations is judged by the mixed total least squares algorithm; the parameters of the plane fitting and spherical surface fitting are calculated by the method. The result shows: the better parameters are achieved even if the percentage of outliers is high.

1. 引言

2. 改进的选权迭代拟合算法

2.1. 基于最小截断二乘的参数初值估计

1) 从点云数据集(总个数为p)中随机抽取n + 1个点(n为确定拟合模型参数所需的最少点个数)，利用最小二乘法估计参数；

2) 计算点云中所有点在到每次抽样估计模型中的残差，对残差平方进行升序排序，计算前h(h = int(p + n + 1)/2)个残差的平方和作为抽样拟合质量的评价指标。

3) 确定抽样次数N，重复N次上述计算，选取残差平方和最小所对应的模型参数作为选权迭代估计的初值。

2.2. 权函数的选取

${\stackrel{¯}{p}}_{i}=\left\{\begin{array}{ll}{p}_{i}\hfill & |{v}_{i}/{m}_{v}|\le {k}_{0}\text{}\hfill \\ \frac{{k}_{0}}{|{v}_{i}/{m}_{v}|}\left(\frac{{k}_{1}-|{v}_{i}/{m}_{v}|}{{k}_{1}-{k}_{0}}\right){p}_{i}\hfill & {k}_{0}<|{v}_{i}/{m}_{v}|\le {k}_{1}\hfill \\ 0\hfill & {k}_{1}<|{v}_{i}/{m}_{v}|\hfill \end{array}$ (1)

2.3. 选权迭代终止条件

2.4. 执行迭代

3. 点云数据空间平面数据拟合算例分析

Figure 1. Flowchart of improved selecting weight iterative algorithm

Figure 2. Simulated plane point cloud data

Figure 3. Simulated sphere point cloud data

Table 1. Plane fitting results of different gross errors under selecting weight iterative algorithm

Table 2. Plane fitting results of different gross errors under improved selecting weight iterative algorithm

Table 3. Sphere fitting results of different gross errors under selecting weight iterative algorithm

Table 4. Sphere fitting results of different gross errors under improved selecting weight iterative algorithm

4. 点云数据球面数据拟合算例分析

5. 结束语

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