  We propose Neural Gradient Learning (NGL), a deep learning approach to learn
gradient vectors with consistent orientation from 3D point clouds for normal
estimation. It has excellent gradient approximation properties for the
underlying geometry of the data. We utilize a simple neural network to
parameterize the objective function to produce gradients at points using a
global implicit representation. However, the derived gradients usually drift
away from the ground-truth oriented normals due to the lack of local detail
descriptions. Therefore, we introduce Gradient Vector Optimization (GVO) to
learn an angular distance field based on local plane geometry to refine the
coarse gradient vectors. Finally, we formulate our method with a two-phase
pipeline of coarse estimation followed by refinement. Moreover, we integrate
two weighting functions, i.e., anisotropic kernel and inlier score, into the
optimization to improve the robust and detail-preserving performance. Our
method efficiently conducts global gradient approximation while achieving
better accuracy and generalization ability of local feature description. This
leads to a state-of-the-art normal estimator that is robust to noise, outliers
and point density variations. Extensive evaluations show that our method
outperforms previous works in both unoriented and oriented normal estimation on
widely used benchmarks. The source code and pre-trained models are available at
https://github.com/LeoQLi/NGLO.
