基于联合邻域质量指标的多尺度邻域漂移法向估计算法

Robust Normal Estimation for Point Clouds via Multi-Scale Shifted Neighborhood Based on a Joint Neighborhood Quality Indicator

摘要: 法向估计是三维点云处理中的一项基础核心任务，其精度直接影响三维重建、曲面拟合等后续应用的质量。基于邻域漂移的法向估计方法通过将邻域中心从当前点偏移至近邻点，能够在一定程度上缓解尖锐特征附近邻域跨曲面的问题。然而，现有方法通常仅依赖协方差矩阵的单一特征值构造平坦性指标，未能充分利用特征值的整体分布信息，导致在强噪声和复杂几何结构下会影响最优邻域选择的稳定性。针对上述问题，本文提出一种基于联合邻域质量指标的多尺度邻域漂移法向估计算法。该方法的核心在于引入特征值信息熵H与法向一致性D构造联合邻域质量指标Q，综合评价候选邻域的平坦性，弥补单一特征值比对噪声敏感的不足；在此基础上，对几何距离项与邻域质量项分别进行归一化后再加权融合，消除不同评价项间数值尺度差异的影响。实验结果表明，相比现有对比方法，所提方法在强噪声与复杂几何场景下表现出更高的估计精度与噪声鲁棒性。

Abstract: Normal estimation is a fundamental task in 3D point cloud processing, whose accuracy directly affects the quality of downstream applications such as 3D reconstruction and surface fitting. Neighborhood-shift-based normal estimation methods mitigate the cross-surface sampling problem near sharp features by shifting the neighborhood center from the current point to its neighboring points. However, existing methods typically rely on a single eigenvalue of the covariance matrix to construct a planarity indicator, which fails to fully exploit the distributional information of all eigenvalues. This limitation compromises the stability of optimal neighborhood selection under strong noise and complex geometric structures. To address this issue, we propose a multi-scale neighborhood-shift normal estimation algorithm based on a joint neighborhood quality indicator. The core idea is to introduce eigenvalue information entropy H and normal consistency D to form a joint quality indicator Q for comprehensively evaluating the planarity of candidate neighborhoods, thereby compensating for the noise sensitivity of single-eigenvalue-based metrics. Furthermore, the geometric distance term and the neighborhood quality term are independently normalized before weighted fusion, eliminating the influence of numerical scale discrepancies between different evaluation terms. Experimental results demonstrate that, compared with existing methods, the proposed approach achieves higher estimation accuracy and noise robustness under strong noise and complex geometric scenarios.