(a) Existing surface fitting-based normal estimation methods can only produce unoriented normals (arrows) with inconsistent orientations. (b) Our method can estimate oriented normals (arrows) from unevenly sampled point clouds (black dots) with varying noise levels. The color of the arrow indicates the angle error compared to the ground truth.
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.
Overview of our method. The optimization is formulated as an iterative moving operation of the positions of point set {Q, G}, which is sampled from the raw data P, while the normal estimation is a single forward differentiation of the learned function f(x; θ) using P as input. We move the input set {Q, G} through multiple steps using signed distance fi and gradient ∇fi learned from f(x; θ) to obtain the output set {Q', G'}. The gradient is initialized to point outside the surface.
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@inproceedings{li2023neuralgf,
title={{NeuralGF}: Unsupervised Point Normal Estimation by Learning Neural Gradient Function},
author={Li, Qing and Feng, Huifang and Shi, Kanle and Gao, Yue and Fang, Yi and Liu, Yu-Shen and Han, Zhizhong},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems (NeurIPS)},
year={2023}
}