A Robust Normal Estimation Method for Terrestrial Laser Scanning Point Cloud Based on Minimum Covariance Determinant
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摘要: 针对地面激光扫描点云中的粗差与不均匀采样对法向量计算的影响，基于最小广义方差估计与局部平面拟合原理提出了一种抗差法向量求解方法。首先通过快速近似最近邻居搜索算法得到最近k邻居点集，然后由确定型最小广义方差估计方法和多元马氏距离得到邻居点集协方差矩阵的抗差估计，最后根据主成分分析法（principal component analysis，PCA）计算得到抗差法向量。通过构造的模拟地面激光扫描（terrestrial laser scanning，TLS）点云数据将提出的方法分别与基于PCA、鲁棒PCA和随机抽样一致的法向量求解方法进行实验比较。结果表明，所提方法的抗差性能优异，且并行优化改进后可以满足大规模TLS点云的计算需求。将该方法应用于实际野外地形TLS点云数据，由求解的抗差法向量重建的泊松表面更符合实际地形，表明了该方法在实际应用中的有效性。
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关键词:
- 点云 /
- 地面激光扫描 /
- 法向量求解 /
- 主成分分析 /
- 确定型最小广义方差估计
Abstract: A robust normal estimation method based on local plane fitting and minimum covariance determinant (MCD) is proposed for terrestrial laser scanning (TLS) point cloud with gross errors and non-uniform sampling. Firstly, fast library for approximate nearest neighbors algorithm is performed to retrieve k nearest neighbor point set. Then, robust estimation of its covariance is calculated by DetMCD (deterministic MCD) and multivariate Mahalanobis distance. Finally, robust estimation of normal vector is calculated through principal component analysis (PCA) method. Compared with PCA, robust PCA and random sample consensus based normal estimation method, on simulated TLS point cloud, experimental results show that the proposed method can get more accurate normal estimation under the influences of gross errors. And its parallel improvement can meet the requirement of efficiency for large scale TLS point cloud processing. Further experiment on real TLS data from natural terrain shows that the proposed method helps to better Poisson surface reconstruction and prove its effectiveness in practical application. -
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图 1 邻居点的马氏距离与抗差马氏距离对粗差的识别
Figure 1. Gross Error Identification Based on Original Mahalanobis Distance and Robust Mahalanobis Distance of Each Neighbor Point
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图 2 不同方法计算出的模拟TLS点云中一组邻居点的法向量(粗差点比例为30%)
Figure 2. Normals of a Neighbor Point Set in Simulated TLS Point Cloud by Different Methods (with 30% Gross Error)
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图 3 不同粗差比例对不同方法角度计算误差均值的影响
Figure 3. Impact of Different Gross Error Rates on Mean of Normal Angle Errors Calculated by Different Methods
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图 4 不同方法不同点云规模的时间效率比较
Figure 4. Comparison of Running Time with Different Point Cloud Scales by Different Methods
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图 5 本文方法得到的真实TLS点云的抗差法向量
Figure 5. Robust Normal Estimation of Real TLS Point Cloud by the Proposed Method
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