基于法向集差异的点云法向估计算法

Point Cloud Normal Estimation Algorithm Based on Normal Set Difference

摘要: 法向量作为三维点云必不可少的属性，在基于点云的绘制方法和表面重建算法中起到了重要作用。利用法向差异对邻域点进行筛选赋权是法向估计中一种常用的策略，但是在现有的法向估计方法中，一般使用的是单一的、不准确的初始输入法向来对邻域点的局部结构进行刻画，使得筛选的结果并不精准。对此，本文提出了一种利用法向集之间的差异对邻域点进行筛选赋权的法向估计方法。首先通过对单一的、粗糙的初始法向进行扰动筛选，构造一个更为准确的法向集，然后根据法向集之间的差异对邻域点进行筛选赋权，最后利用加权最小二乘拟合得到估计法向。实验结果表明，该方法在不同噪声水平下均能在尖锐特征处得到更好的法向估计效果。

Abstract: The normal vector, as an essential attribute of three-dimensional point cloud, plays a significant role in point cloud-based rendering methods and surface reconstruction algorithms. Utilizing the differences in normal vectors to filter and weight neighboring points is a commonly used strategy in normal estimation. However, in the existing normal estimation methods, a single and inaccurate initial normal vector is generally used to depict the local structure of neighboring points, resulting in imprecise filtering results. To address this issue, this paper proposes a normal estimation method that uses the differences between normal sets to filter and weight neighboring points. Firstly, a more accurate normal set is constructed by perturbing a single and inaccurate initial normal vector. Then, the neighboring points are filtered and weighted based on the differences between the normal sets. Finally, the estimated normal is obtained through weighted least squares fitting. Experimental results show that this method can achieve better normal estimation effects at sharp features under different noise levels.