  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.
