# Neural Poisson Surface Reconstruction: Resolution-Agnostic Shape Reconstruction from Point Clouds

arXiv: https://arxiv.org/abs/2308.01766 · HTML: https://mlsanity.com/paper/2308.01766/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 3 Aug 2023.

## Builds on (most cited first, 11 of 11)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [Iterative Poisson Surface Reconstruction (iPSR) for Unoriented Points](https://mlsanity.com/paper/2209.09510/) (2022)
- [A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2301.13656/) (2023)

## Built on by (most cited first, 2 of 2)

- [EuLearn: A 3D database for learning Euler characteristics](https://mlsanity.com/paper/2505.13539/) (2025)
- [HessianForge: Scalable LiDAR reconstruction with Physics-Informed Neural Representation and Smoothness Energy Constraints](https://mlsanity.com/paper/2503.08929/) (2025)

## Abstract (arXiv)

We introduce Neural Poisson Surface Reconstruction (nPSR), an architecture for shape reconstruction that addresses the challenge of recovering 3D shapes from points. Traditional deep neural networks face challenges with common 3D shape discretization techniques due to their computational complexity at higher resolutions. To overcome this, we leverage Fourier Neural Operators to solve the Poisson equation and reconstruct a mesh from oriented point cloud measurements. nPSR exhibits two main advantages: First, it enables efficient training on low-resolution data while achieving comparable performance at high-resolution evaluation, thanks to the resolution-agnostic nature of FNOs. This feature allows for one-shot super-resolution. Second, our method surpasses existing approaches in reconstruction quality while being differentiable and robust with respect to point sampling rates. Overall, the neural Poisson surface reconstruction not only improves upon the limitations of classical deep neural networks in shape reconstruction but also achieves superior results in terms of reconstruction quality, running time, and resolution agnosticism.