[Paper Review] GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimation

Keqiang Li, Mingyang Zhao+5 more|arXiv (Cornell University)|Jul 23, 2022

3D Shape Modeling and Analysis4 citations

TL;DR

GraphFit proposes a novel graph-convolutional neural network for robust and accurate 3D point cloud normal estimation by modeling local neighborhood geometry through learnable graph structures. It integrates multi-scale features and an attention-based adaptive module to enhance robustness against noise, outliers, and varying point density, achieving state-of-the-art performance on benchmark datasets including PCPNet and NYU Depth V2.

ABSTRACT

We propose a precise and efficient normal estimation method that can deal with noise and nonuniform density for unstructured 3D point clouds. Unlike existing approaches that directly take patches and ignore the local neighborhood relationships, which make them susceptible to challenging regions such as sharp edges, we propose to learn graph convolutional feature representation for normal estimation, which emphasizes more local neighborhood geometry and effectively encodes intrinsic relationships. Additionally, we design a novel adaptive module based on the attention mechanism to integrate point features with their neighboring features, hence further enhancing the robustness of the proposed normal estimator against point density variations. To make it more distinguishable, we introduce a multi-scale architecture in the graph block to learn richer geometric features. Our method outperforms competitors with the state-of-the-art accuracy on various benchmark datasets, and is quite robust against noise, outliers, as well as the density variations.

Motivation & Objective

• To address the limitations of existing normal estimation methods that ignore local neighborhood relationships in point cloud patches.
• To improve robustness against noise, outliers, and non-uniform point density in 3D point clouds.
• To enhance feature representation by explicitly modeling geometric relationships between neighboring points using graph convolution.
• To achieve state-of-the-art accuracy and stability on both synthetic and real-world point cloud datasets.

Proposed method

• The method constructs a local graph for each point using k-nearest neighbors to encode geometric relationships in the neighborhood.
• It employs a graph convolutional block that learns multi-scale features by fusing representations from different receptive fields.
• An attention-based adaptive module dynamically fuses point features with their neighboring features to improve robustness to density variations.
• The model uses a multi-scale representation module that aggregates local features from two different scales in the feature space, enhancing geometric expressiveness.
• The network is trained end-to-end to regress point normals using a loss function that minimizes the angular difference between predicted and ground-truth normals.
• The architecture is designed to be efficient and generalizable, with ablation studies validating each component’s contribution.

Experimental results

Research questions

• RQ1 Can modeling local neighborhood relationships in 3D point clouds significantly improve normal estimation accuracy compared to patch-based methods that ignore such relationships?
• RQ2 How does an attention-based adaptive module enhance robustness to non-uniform point density in normal estimation?
• RQ3 To what extent does a multi-scale graph convolutional architecture improve feature representation and generalization on noisy or sparse point clouds?
• RQ4 How does the proposed method compare to state-of-the-art approaches in terms of accuracy and robustness across diverse benchmarks?
• RQ5 Does the method maintain high performance on real-world scanned data, such as NYU Depth V2, where noise and density variations are prevalent?

Key findings

• GraphFit achieves the state-of-the-art mean RMSE of 10.34 on the PCPNet dataset under varying noise levels and point density, outperforming competitors like AdaFit and DeepFit.
• The method shows high robustness to neighborhood size variations, with average RMSE remaining stable around 10.50 across k=256, 500, and 700.
• The ablation study confirms that the multi-scale module reduces RMSE by up to 0.24 points compared to single-scale baselines, demonstrating its effectiveness in feature enrichment.
• The attention-based adaptive module reduces error by up to 0.35 points on challenging striped and gradient point clouds, proving its value in handling density variations.
• The model maintains strong performance on real-world NYU Depth V2 data, indicating its practical utility beyond synthetic benchmarks.
• Increasing the Jet order from 1 to 4 improves RMSE from 10.92 to 10.44 on PCPNet, showing enhanced geometric modeling capability with higher-order surface fitting.