Learning Signed Hyper Surfaces for Oriented Point Cloud Normal Estimation

TL;DR

The paper addresses robust oriented normal estimation from 3D point clouds under challenging conditions such as noise and density variations. It introduces SHS-Net, which learns signed hyper surfaces $f_S$ in a high-dimensional feature space, conditioned on two latent codes $z_1, z_2$ derived from local patches and global samples. An attention-weighted normal predictor decodes the fused embedding to output an oriented normal $ _q$ and its sign, enabling end-to-end orientation. Experiments on PCPNet and FamousShape demonstrate state-of-the-art performance for both unoriented and oriented normals and show improvements in downstream tasks like surface reconstruction and point cloud filtering.

Abstract

We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks.

Figures (19)

• Figure 1: We propose SHS-Net to estimate oriented normals directly from point clouds. In contrast, previous studies usually achieve this process through a two-stage paradigm using different algorithms, i.e., (1) unoriented normal estimation (e.g., PCA hoppe1992surface, AdaFit zhu2021adafit and HSurf-Net li2022hsurf) and (2) normal orientation (e.g., MST hoppe1992surface, SNO schertler2017towards and ODP metzer2021orienting).
• Figure 2: The learning pipeline of the signed hyper surfaces for oriented normal estimation. It consists of two parallel branches, i.e., patch encoding and shape encoding, which have similar network architectures (see Fig. \ref{['fig:feat']}), to extract local and global latent codes, respectively. In both branches, the number of point clouds is downsampled relative to the query point $q$. Finally, an embedding of the signed hyper surface is used to regress the oriented normal of the query point, which points to the outside of the shape surface.
• Figure 3: Feature encoding network in patch and shape encoding. $\mathcal{F}$ is the latent code extraction layer. Black dots indicate the repetition of blocks (dashed box).
• Figure 4: Attention-weighted normal prediction module $\mathcal{H}(\cdot)$. After we obtain the surface embedding $z_{q}$ from the fused local and global latent code $[z^{\mathbf{n}}_q : z^s_q]$, we can predict the normal $\mathbf{n}_q$ of the query point $q$ and the sign $s$ to determine its orientation.
• Figure 5: Visual comparison of unoriented normal errors on a point cloud with complex geometry. The normal RMSE is mapped to a heatmap ($0^{\circ}-40^{\circ}$). We provide the average RMSE over shape for each method.