# Consistent Point Orientation for Manifold Surfaces via Boundary Integration

arXiv: https://arxiv.org/abs/2407.03165 · HTML: https://mlsanity.com/paper/2407.03165/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 3 Jul 2024.

## Builds on (most cited first, 15 of 15)

- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Pointfilter: Point Cloud Filtering via Encoder-Decoder Modeling](https://mlsanity.com/paper/2002.05968/) (2020)
- [Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling](https://mlsanity.com/paper/2112.04148/) (2021)
- [NeAF: Learning Neural Angle Fields for Point Normal Estimation](https://mlsanity.com/paper/2211.16869/) (2022)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [Orienting Point Clouds with Dipole Propagation](https://mlsanity.com/paper/2105.01604/) (2021)
- [Iterative Poisson Surface Reconstruction (iPSR) for Unoriented Points](https://mlsanity.com/paper/2209.09510/) (2022)
- [AdaFit: Rethinking Learning-based Normal Estimation on Point Clouds](https://mlsanity.com/paper/2108.05836/) (2021)
- [Stochastic Poisson Surface Reconstruction](https://mlsanity.com/paper/2206.15236/) (2022)
- [Neural Gradient Learning and Optimization for Oriented Point Normal Estimation](https://mlsanity.com/paper/2309.09211/) (2023)
- [NeuralGF: Unsupervised Point Normal Estimation by Learning Neural Gradient Function](https://mlsanity.com/paper/2311.00389/) (2023)
- [RFEPS: Reconstructing Feature-line Equipped Polygonal Surface](https://mlsanity.com/paper/2212.03600/) (2022)
- [Neural Stochastic Screened Poisson Reconstruction](https://mlsanity.com/paper/2309.11993/) (2023)
- [Consistently Orienting Facets in Polygon Meshes by Minimizing the Dirichlet Energy of Generalized Winding Numbers](https://mlsanity.com/paper/1406.5431/) (2014)

## Built on by (most cited first, 4 of 4)

- [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)
- [Voronoi-Assisted Optimization for Diffusing Unsigned Distance Fields from Unoriented Points](https://mlsanity.com/paper/2510.12524/) (2025)
- [OCMG-Net: Neural Oriented Normal Refinement for Unstructured Point Clouds](https://mlsanity.com/paper/2409.01100/) (2024)
- [Joint Orientation and Weight Optimization for Robust Watertight Surface Reconstruction via Dirichlet-Regularized Winding Fields](https://mlsanity.com/paper/2602.13801/) (2026)

## Abstract (arXiv)

This paper introduces a new approach for generating globally consistent normals for point clouds sampled from manifold surfaces. Given that the generalized winding number (GWN) field generated by a point cloud with globally consistent normals is a solution to a PDE with jump boundary conditions and possesses harmonic properties, and the Dirichlet energy of the GWN field can be defined as an integral over the boundary surface, we formulate a boundary energy derived from the Dirichlet energy of the GWN. Taking as input a point cloud with randomly oriented normals, we optimize this energy to restore the global harmonicity of the GWN field, thereby recovering the globally consistent normals. Experiments show that our method outperforms state-of-the-art approaches, exhibiting enhanced robustness to noise, outliers, complex topologies, and thin structures. Our code can be found at urlhttps://github.com/liuweizhou319/BIM.