PFF-Net: Patch Feature Fitting for Point Cloud Normal Estimation

TL;DR

This work tackles the problem of robust point cloud normal estimation when data geometries and sampling vary, by introducing Patch Feature Fitting (PFF) implemented as PFF-Net. The approach fuses multi-scale patch features through a two-stage architecture (F1 for low-order structure and F2 for high-order refinement) and an attention-based cross-scale compensation mechanism, underpinned by a Taylor-expansion interpretation of local geometry. It achieves state-of-the-art results on PCPNet and scene datasets with fewer parameters and reduced runtime, while demonstrating strong cross-domain generalization and compatibility with other methods. The results suggest that adaptively aggregating and compensating multi-scale features yields more accurate normals, enhancing downstream tasks such as surface reconstruction and denoising.

Abstract

Estimating the normal of a point requires constructing a local patch to provide center-surrounding context, but determining the appropriate neighborhood size is difficult when dealing with different data or geometries. Existing methods commonly employ various parameter-heavy strategies to extract a full feature description from the input patch. However, they still have difficulties in accurately and efficiently predicting normals for various point clouds. In this work, we present a new idea of feature extraction for robust normal estimation of point clouds. We use the fusion of multi-scale features from different neighborhood sizes to address the issue of selecting reasonable patch sizes for various data or geometries. We seek to model a patch feature fitting (PFF) based on multi-scale features to approximate the optimal geometric description for normal estimation and implement the approximation process via multi-scale feature aggregation and cross-scale feature compensation. The feature aggregation module progressively aggregates the patch features of different scales to the center of the patch and shrinks the patch size by removing points far from the center. It not only enables the network to precisely capture the structure characteristic in a wide range, but also describes highly detailed geometries. The feature compensation module ensures the reusability of features from earlier layers of large scales and reveals associated information in different patch sizes. Our approximation strategy based on aggregating the features of multiple scales enables the model to achieve scale adaptation of varying local patches and deliver the optimal feature description. Extensive experiments demonstrate that our method achieves state-of-the-art performance on both synthetic and real-world datasets with fewer network parameters and running time.

Figures (22)

• Figure 1: Normal estimation for point cloud patches. Top row: on a 3D surface, the normals estimated by different neighborhood sizes $N$ have different directions. Bottom row: the number of neighboring points that can be used to accurately estimate the query point normal varies in different structures. The red points contribute more for normal estimation, and the blue points contribute less.
• Figure 2: Previous methods use (a) fixed-scale patches (DeepFit ben2020deepfit, GraphFit li2022graphfit), (b) pre-computed features (Refine-Net zhou2022refine, Zhang et al. zhang2022geometry), (c) multi-scale networks (AdaFit zhu2021adafit, NeAF li2023NeAF, HSurf-Net li2022hsurf) or (d) multi-branch networks (PCPNet guerrero2018pcpnet, Nesti-Net ben2019nesti, SHS-Net li2023shsnetli2024shsnet-pami). (e) Our patch feature fitting method for normal estimation.
• Figure 3: Normal estimation results of PCA on different point clouds using two different neighbor sizes $N$. The execution time and average normal angle RMSE are provided under each point cloud. The point color is the normal angle RMSE mapped to a heatmap ranging from $0^{\circ}$ to $50^{\circ}$.
• Figure 4: The architecture of our per-point feature extraction module.
• Figure 5: An overview of our normal estimation method. The blocks $\mathcal{F}_1$ and $\mathcal{F}_2$ are built by using different layers $\mathcal{P}_1$ and $\mathcal{P}_2$. Two blocks are stacked recursively to form the normal estimation pipeline. The color of the shape point cloud indicates the predicted normals.