Establishing a consistent normal orientation for point clouds is a notoriously difficult problem in geometry processing, requiring attention to both local and global shape characteristics. The normal direction of a point is a function of the local surface neighborhood; yet, point clouds do not disclose the full underlying surface structure. Even assuming known geodesic proximity, calculating a consistent normal orientation requires the global context. In this work, we introduce a novel approach for establishing a globally consistent normal orientation for point clouds. Our solution separates the local and global components into two different sub-problems. In the local phase, we train a neural network to learn a coherent normal direction per patch (i.e., consistently oriented normals within a single patch). In the global phase, we propagate the orientation across all coherent patches using a dipole propagation. Our dipole propagation decides to orient each patch using the electric field defined by all previously orientated patches. This gives rise to a global propagation that is stable, as well as being robust to nearby surfaces, holes, sharp features and noise.

中文翻译：

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用偶极子传播定向点云

为点云建立一致的法线方向是几何处理中一个众所周知的难题，需要同时关注局部和全局形状特征。点的法线方向是局部曲面邻域的函数；但是，点云并没有公开完整的底层表面结构。即使假设已知的测地线接近度，要计算一致的法线方向也需要全局上下文。在这项工作中，我们介绍了一种新颖的方法来为点云建立全局一致的法线方向。我们的解决方案将本地和全局组件分为两个不同的子问题。在局部阶段，我们训练神经网络以学习每个面片的相干法线方向（即，单个面片内的方向一致的法线）。在全球阶段，我们使用偶极子传播在所有相干斑片上传播方向。我们的偶极子传播决定使用所有先前定向的面片定义的电场来定向每个面片。这导致稳定的全局传播，并且对附近的表面，孔，尖锐的特征和噪声具有鲁棒性。