ACM Transactions on Graphics 2024 (SIGGRAPH Asia 2024 Journal Track)

Fast and Globally Consistent Normal Orientation based on the Winding Number Normal Consistency

 

Siyou Lin1, Zuoqiang Shi2,3, Yebin Liu1

1Department of Automation, Tsinghua University

2Yau Mathematical Sciences Center, Tsinghua University

3Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA)

 

 

Paper | Code

 

Overview

We derive the Winding Number Normal Consistency (WNNC) property, as well as an iterative algorithm based on the WNNC for estimating globally consistent normals. We implement a highly efficient treecode-based acceleration algorithm, parallelized using CUDA, enabling notably faster execution time than other winding number based methods.

 

 

Algorithm

Our algorithm is extremely simple, involving only three steps in each iteration:
  • a gradient step as in PGR [Lin et al. 2022];
  • a WNNC update that computes new normals from current normals;
  • a per-point rescaling step to ensure numerical stability.

Convergence

We compare the convergence process of our method, iPSR [Hou et al. 2022] and GCNO [Xu et al. 2023].

Results

We compare our method with iterative Poisson Surface Reconstruction (iPSR) [Hou et al. 2022], Dipole [Metzer et al. 2021], Parametric Gauss Reconstruction (PGR) [Lin et al. 2022] and GCNO [Xu et al. 2023].

For comparisons with iPSR and Dipole, each input has 160,000 points.
†Inputs downsampeld to 50,000 points.
‡Inputs downsampeld to 5,000 points.

Normal orientation results

Reconstruction results

Reconstruction results for noisy points

Full Video