基于信息熵与法向一致性的自适应邻域法向量估计

Adaptive Neighborhood Normal Vector Estimation Based on Information Entropy and Normal Consistency

摘要: 法向量估计是三维点云处理的基础，其精度依赖于邻域尺度的选择。然而，固定邻域尺度方法存在局限：小尺度邻域在尖锐特征处表现优越但抗噪能力弱，而大尺度邻域虽能有效抑制噪声却会平滑细节。针对这一问题，本文提出一种基于信息熵与法向一致性的自适应邻域选择算法。该算法通过信息熵量化邻域的几何复杂度，并融合法向一致性构建综合评分函数，为每个点动态选择最优邻域尺度。实验结果表明，该自适应框架可与PCA等经典固定尺度方法有效结合，在显著提升噪声抑制能力的同时，尖锐特征区域的法向量估计精度得到明显改善，整体展现出更优的综合性能与鲁棒性。

Abstract: Normal vector estimation is the foundation of 3D point cloud processing, and its accuracy depends on the selection of neighborhood scale. However, fixed neighborhood scale methods have inherent limitations: small-scale neighborhoods perform well at sharp features but exhibit poor noise robustness, while large-scale neighborhoods can effectively suppress noise but tend to smooth out fine details. To address this issue, this paper proposes an adaptive neighborhood selection algorithm based on information entropy and normal consistency. This algorithm quantifies the geometric complexity of neighborhoods using information entropy, incorporates normal consistency to construct a comprehensive scoring function, and dynamically selects the optimal neighborhood scale for each point. Experimental results demonstrate that this adaptive framework can be effectively integrated with classical fixed-scale methods such as PCA, it significantly enhances noise suppression capability, while the accuracy of normal vector estimation in regions with sharp features is also significantly improved, thereby exhibiting better overall comprehensive performance and robustness.