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

2025-07-04

AI Summary

Estimating surface normals from noisy point clouds remains a longstanding challenge, as existing methods rely heavily on clean inputs and strong supervision, failing to simultaneously preserve geometric details and ensure robustness. This paper proposes a local gradient-aware implicit surface filtering framework: it guides point cloud projection onto the underlying surface via an implicit function and introduces a joint normal-distance operator to enforce geometric constraints. To mitigate gradient degradation, we design a local gradient consistency loss; to suppress over-smoothing, we develop a multi-scale directional aggregation mechanism. Crucially, our method performs end-to-end learning without explicit normal supervision, unifying denoising, normal estimation, and surface reconstruction. Extensive experiments demonstrate state-of-the-art performance across multiple benchmarks, significantly improving fine-detail recovery under complex noise patterns. The code and pre-trained models are publicly available.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Estimating normals for noisy point clouds
• Overcoming over-smoothing and gradient degradation
• Improving surface reconstruction and denoising

Innovation

• Local gradient-aware surface filtering for normals
• Implicit function with gradient constraints
• Distance measurement operator for global fitting