摘要：

受到仪器、周围环境以及被扫描目标本身的特性影响, 点云数据中不可避免会存在一些噪声, 最常见的是高斯噪声。针对点云模型在含有高斯噪声情况下出现的法向量估计误差大的问题, 提出基于统计跳变回归分析的点云法向量估计方法。首先, 根据点云数据建立回归模型, 并基于局部线性核平滑来估计当前点的曲面值; 其次, 为了判断当前点是否在曲面边缘上, 沿垂直于梯度方向将当前点所在的局部邻域分成两部分, 分别用这两部分邻域内的观测值再一次估计该点的曲面值; 最后, 分析计算当前点的带权均方残差(WRMS), 最终确定该点曲面值以及法向量。通过仿真实验、公共数据集实验等大量实验结果表明, 该方法相较于常规的点云法向量估计方法, 在含高斯噪声的情况下法向量估计准确性更高且鲁棒性更好。

关键词: 点云模型, 高斯噪声, 法向量, 统计跳变回归分析, 点云重建

Abstract:

Owing to the characteristics of the instrument, surrounding environment, and scanned target, some noise in the point cloud data is inevitable, the most common being Gaussian noise. To address the problem of a large normal estimation error in the case of Gaussian noise in the point cloud model, this study proposes a point cloud normal estimation method based on statistical jump regression analysis. First, a regression model is established based on point cloud data and the curvature value of the current point is estimated based on local linear kernel smoothing. Second, to determine whether the current point is on the edge of the surface, the local neighborhood of the current point is divided into two parts along the direction perpendicular to the gradient and the surface value of the point is estimated again by observing the two parts of the neighborhood. Finally, the Weighted Root Mean Square residual (WRMS) of the current point is analyzed and calculated to determine the surface value and normal vector of the point. Via numerous experiments, such as simulation and public dataset experiments, the results show that the proposed method is more accurate and robust than the conventional point cloud normal vector estimation methods in the case of Gaussian noise.

Key words: point cloud model, Gaussian noise, normal vector, statistical jump regression analysis, point cloud reconstruction