Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering

TL;DR

This work tackles the problem of estimating oriented normals from noisy point clouds by introducing local gradient-aware surface filtering that relies on an implicit surface representation. A neural field $f_{\theta}$ is learned from the raw points together with a supplementary set $\mathbf{Q}$, using a distance operator that combines projection-based distances and a projection path $\mathbf{q}' = \mathbf{q} - f_{\theta}(\mathbf{q}) \cdot \mathbf{n}_{\mathbf{q}}$ to fit a zero-level surface. The method adds local gradient constraints (inter-level consistency, intra-level orientation, and inter-level aggregation) via a composite loss $\mathcal{L} = \mathcal{L}_{sd} + \mathcal{L}_{v} + \lambda_1 \mathcal{L}_{d} + \lambda_2 \mathcal{L}_{n}$ and performs gradient-based normal estimation by aggregating normals across neighboring points in $\mathbf{P}$ and $\mathbf{Q}$. Experiments across normal estimation, surface reconstruction, and denoising demonstrate state-of-the-art performance on both synthetic and real-world data without supervision, highlighting robustness to noise and practical applicability for 3D vision tasks. The approach offers a flexible unsupervised pathway to high-quality geometry from noisy point clouds with potential for generalization through future front-end feature extractors and meta-learning strategies.

Abstract

Estimating normals for noisy point clouds is a persistent challenge in 3D geometry processing, particularly for end-to-end oriented normal estimation. Existing methods generally address relatively clean data and rely on supervised priors to fit local surfaces within specific neighborhoods. In this paper, we propose a novel approach for learning normals from noisy point clouds through local gradient-aware surface filtering. Our method projects noisy points onto the underlying surface by utilizing normals and distances derived from an implicit function constrained by local gradients. We start by introducing a distance measurement operator for global surface fitting on noisy data, which integrates projected distances along normals. Following this, we develop an implicit field-based filtering approach for surface point construction, adding projection constraints on these points during filtering. To address issues of over-smoothing and gradient degradation, we further incorporate local gradient consistency constraints, as well as local gradient orientation and aggregation. Comprehensive experiments on normal estimation, surface reconstruction, and point cloud denoising demonstrate the state-of-the-art performance of our method. The source code and trained models are available at https://github.com/LeoQLi/LGSF.

Figures (14)

• Figure 1: Overview of the proposed method. It can be used for different tasks such as surface reconstruction, point cloud denoising, and normal estimation without the need for training labels.
• Figure 2: We minimize the distances from noisy points $\bm{p}$ to discrete points $\hat{\bm{p}}$ of the underlying surface for implicit surface fitting and filtering. To this end, (a-c) we adopt three distance measures $d$, $d_1$ and $d_2$, and use their sum to handle various cases. (d) Meanwhile, we enforce local gradient consistency between adjacent level sets where the noisy points are located. Red arrows indicate normals (i.e., gradients).
• Figure 3: Left: computation of $f_{\theta}(\bm{q}) \cdot \bar{\bm{n}}_{\bm{q}}$ and $\bar{\bm{n}}_{\bm{q}} \!=\! (\bm{n}_{\bm{q}} + \bm{n}_{\bm{q}'} ) / || \bm{n}_{\bm{q}} + \bm{n}_{\bm{q}'} ||$. Gradients point to the positive side of the signed distance field. Right: computation of $\mathcal{H}(\bm{q})$ for specific noise and density using different neighborhood scales $K$.
• Figure 4: Normal estimation through local gradient aggregation.
• Figure 5: Visual comparison of oriented normals on two point clouds with complex geometry. Colors indicate normal errors.