# Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation

arXiv: https://arxiv.org/abs/2209.15619 · HTML: https://mlsanity.com/paper/2209.15619/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 50 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 16 of 16)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python](https://mlsanity.com/paper/1907.10121/) (2019)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [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)
- [Stochastic Poisson Surface Reconstruction](https://mlsanity.com/paper/2206.15236/) (2022)
- [Learning Modified Indicator Functions for Surface Reconstruction](https://mlsanity.com/paper/2111.09526/) (2021)

## Built on by (most cited first, 8 of 8)

- [Neural Gradient Learning and Optimization for Oriented Point Normal Estimation](https://mlsanity.com/paper/2309.09211/) (2023)
- [Learning Signed Hyper Surfaces for Oriented Point Cloud Normal Estimation](https://mlsanity.com/paper/2305.05873/) (2023)
- [NeuralGF: Unsupervised Point Normal Estimation by Learning Neural Gradient Function](https://mlsanity.com/paper/2311.00389/) (2023)
- [PPSURF: Combining Patches and Point Convolutions for Detailed Surface Reconstruction](https://mlsanity.com/paper/2401.08518/) (2024)
- [Learning Normals of Noisy Points by Local Gradient-Aware Surface Filtering](https://mlsanity.com/paper/2507.03394/) (2025)
- [Refining 3D Point Cloud Normal Estimation via Sample Selection](https://mlsanity.com/paper/2406.18541/) (2024)
- [OCMG-Net: Neural Oriented Normal Refinement for Unstructured Point Clouds](https://mlsanity.com/paper/2409.01100/) (2024)
- [Deep Learning Approaches for 3D Medical Scene Completion: From Geometric Modeling to Generative Paradigms](https://mlsanity.com/paper/2606.24180/) (2026)

## Abstract (arXiv)

Oriented normals are common pre-requisites for many geometric algorithms based on point clouds, such as Poisson surface reconstruction. However, it is not trivial to obtain a consistent orientation. In this work, we bridge orientation and reconstruction in the implicit space and propose a novel approach to orient point cloud normals by incorporating isovalue constraints to the Poisson equation. In implicit surface reconstruction, the reconstructed shape is represented as an isosurface of an implicit function defined in the ambient space. Therefore, when such a surface is reconstructed from a set of sample points, the implicit function values at the points should be close to the isovalue corresponding to the surface. Based on this observation and the Poisson equation, we propose an optimization formulation that combines isovalue constraints with local consistency requirements for normals. We optimize normals and implicit functions simultaneously and solve for a globally consistent orientation. Thanks to the sparsity of the linear system, our method can work on an average laptop with reasonable computational time. Experiments show that our method can achieve high performance in non-uniform and noisy data and manage varying sampling densities, artifacts, multiple connected components, and nested surfaces. The source code is available at urlhttps://github.com/Submanifold/IsoConstraints.