Estimating normals with globally consistent orientations for a raw point cloud has many downstream geometry processing applications. Despite tremendous efforts in the past decades, it remains challenging to deal with an unoriented point cloud with various imperfections, particularly in the presence of data sparsity coupled with nearby gaps or thin-walled structures. In this paper, we propose a smooth objective function to characterize the requirements of an acceptable winding-number field, which allows one to find the globally consistent normal orientations starting from a set of completely random normals. By taking the vertices of the Voronoi diagram of the point cloud as examination points, we consider the following three requirements: (1) the winding number is either 0 or 1, (2) the occurrences of 1 and the occurrences of 0 are balanced around the point cloud, and (3) the normals align with the outside Voronoi poles as much as possible. Extensive experimental results show that our method outperforms the existing approaches, especially in handling sparse and noisy point clouds, as well as shapes with complex geometry/topology.

翻译：原始点云中具有全局一致性朝向的法向估计在许多下游几何处理应用中至关重要。尽管过去几十年已付出巨大努力，但处理存在各种缺陷的无朝向点云仍具挑战性，尤其是在数据稀疏性伴随邻近间隙或薄壁结构的情况下。本文提出一种平滑目标函数来表征可接受绕数场的需求，该函数能够从一组完全随机的法向出发，找到全局一致的法向朝向。通过将点云Voronoi图的顶点作为检查点，我们考虑以下三个要求：（1）绕数为0或1；（2）绕数值1与0的出现次数在点云周围保持平衡；（3）法向尽可能与外向Voronoi极对齐。大量实验结果表明，我们的方法在现有方法中表现优异，尤其在处理稀疏噪声点云以及具有复杂几何/拓扑结构的形状时优势显著。