# Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field

arXiv: https://arxiv.org/abs/2304.11605 · HTML: https://mlsanity.com/paper/2304.11605/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2023.

## Built on by (most cited first, 30 of 37)

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- [Neural Gradient Learning and Optimization for Oriented Point Normal Estimation](https://mlsanity.com/paper/2309.09211/) (2023)
- [MultiPull: Detailing Signed Distance Functions by Pulling Multi-Level Queries at Multi-Step](https://mlsanity.com/paper/2411.01208/) (2024)
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- [Deep3DSketch+: Rapid 3D Modeling from Single Free-hand Sketches](https://mlsanity.com/paper/2309.13006/) (2023)
- [Consistent Point Orientation for Manifold Surfaces via Boundary Integration](https://mlsanity.com/paper/2407.03165/) (2024)
- [PFF-Net: Patch Feature Fitting for Point Cloud Normal Estimation](https://mlsanity.com/paper/2511.21365/) (2025)
- [NumGrad-Pull: Numerical Gradient Guided Tri-plane Representation for Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2411.17392/) (2024)
- [Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering](https://mlsanity.com/paper/2507.03394/) (2025)
- [A Geometric Algorithm for Blood Vessel Reconstruction from Skeletal Representation](https://mlsanity.com/paper/2402.12797/) (2024)
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- [SplatCo: Structure-View Collaborative Gaussian Splatting for Detail-Preserving Rendering of Large-Scale Unbounded Scenes](https://mlsanity.com/paper/2505.17951/) (2025)
- [A Divide-and-Conquer Approach for Global Orientation of Non-Watertight Scene-Level Point Clouds Using 0-1 Integer Optimization](https://mlsanity.com/paper/2505.23469/) (2025)
- [NeuVAS: Neural Implicit Surfaces for Variational Shape Modeling](https://mlsanity.com/paper/2506.13050/) (2025)
- [Voronoi-Assisted Optimization for Diffusing Unsigned Distance Fields from Unoriented Points](https://mlsanity.com/paper/2510.12524/) (2025)
- [E3-Net: Efficient E(3)-Equivariant Normal Estimation Network](https://mlsanity.com/paper/2406.00347/) (2024)

## Abstract (arXiv)

Estimating normals with globally consistent orientations for a raw point cloud has many downstream geometry processing applications. Despite tremendous efforts in the past decades, it remains challenging to deal with an unoriented point cloud with various imperfections, particularly in the presence of data sparsity coupled with nearby gaps or thin-walled structures. In this paper, we propose a smooth objective function to characterize the requirements of an acceptable winding-number field, which allows one to find the globally consistent normal orientations starting from a set of completely random normals. By taking the vertices of the Voronoi diagram of the point cloud as examination points, we consider the following three requirements: (1) the winding number is either 0 or 1, (2) the occurrences of 1 and the occurrences of 0 are balanced around the point cloud, and (3) the normals align with the outside Voronoi poles as much as possible. Extensive experimental results show that our method outperforms the existing approaches, especially in handling sparse and noisy point clouds, as well as shapes with complex geometry/topology.