  Normal estimation for unstructured point clouds is an important task in 3D
computer vision. Current methods achieve encouraging results by mapping local
patches to normal vectors or learning local surface fitting using neural
networks. However, these methods are not generalized well to unseen scenarios
and are sensitive to parameter settings. To resolve these issues, we propose an
implicit function to learn an angle field around the normal of each point in
the spherical coordinate system, which is dubbed as Neural Angle Fields (NeAF).
Instead of directly predicting the normal of an input point, we predict the
angle offset between the ground truth normal and a randomly sampled query
normal. This strategy pushes the network to observe more diverse samples, which
leads to higher prediction accuracy in a more robust manner. To predict normals
from the learned angle fields at inference time, we randomly sample query
vectors in a unit spherical space and take the vectors with minimal angle
values as the predicted normals. To further leverage the prior learned by NeAF,
we propose to refine the predicted normal vectors by minimizing the angle
offsets. The experimental results with synthetic data and real scans show
significant improvements over the state-of-the-art under widely used
benchmarks.
