Normal estimation for 3D point clouds is a fundamental task in 3D geometry processing. The state-of-the-art methods rely on priors of fitting local surfaces learned from normal supervision. However, normal supervision in benchmarks comes from synthetic shapes and is usually not available from real scans, thereby limiting the learned priors of these methods. In addition, normal orientation consistency across shapes remains difficult to achieve without a separate post-processing procedure. To resolve these issues, we propose a novel method for estimating oriented normals directly from point clouds without using ground truth normals as supervision. We achieve this by introducing a new paradigm for learning neural gradient functions, which encourages the neural network to fit the input point clouds and yield unit-norm gradients at the points. Specifically, we introduce loss functions to facilitate query points to iteratively reach the moving targets and aggregate onto the approximated surface, thereby learning a global surface representation of the data. Meanwhile, we incorporate gradients into the surface approximation to measure the minimum signed deviation of queries, resulting in a consistent gradient field associated with the surface. These techniques lead to our deep unsupervised oriented normal estimator that is robust to noise, outliers and density variations. Our excellent results on widely used benchmarks demonstrate that our method can learn more accurate normals for both unoriented and oriented normal estimation tasks than the latest methods. The source code and pre-trained model are publicly available at https://github.com/LeoQLi/NeuralGF.

翻译：三维点云法向估计是三维几何处理中的基础任务。现有最先进方法依赖通过法向监督学习局部表面拟合的先验知识。然而，基准数据集中的法向监督来自合成形状，通常无法从真实扫描中获取，这限制了这些方法学习到的先验知识。此外，若无独立的后期处理步骤，跨形状的法向方向一致性仍难以实现。为解决上述问题，我们提出一种直接从未标注真实法向的点云中估计有向法向的方法。为此，我们引入一种学习神经梯度函数的新范式，通过激励神经网络拟合输入点云并在各点处生成单位法向梯度。具体而言，我们设计损失函数促使查询点迭代逼近移动目标并聚合至近似表面，从而学习数据的全局表面表示。同时，我们将梯度融入表面近似过程以测量查询点的最小有符号偏差，由此生成与表面关联的一致梯度场。这些技术使得我们的深度无监督有向法向估计器对噪声、离群点和密度变化具有鲁棒性。在广泛使用的基准测试中，我们的优异结果表明：无论对于无向还是有向法向估计任务，该方法均能比最新方法学习到更精确的法向。源代码与预训练模型已在 https://github.com/LeoQLi/NeuralGF 公开。