# Stochastic Poisson Surface Reconstruction

arXiv: https://arxiv.org/abs/2206.15236 · HTML: https://mlsanity.com/paper/2206.15236/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2022.

## Built on by (most cited first, 13 of 13)

- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (2023)
- [Ghost on the Shell: An Expressive Representation of General 3D Shapes](https://mlsanity.com/paper/2310.15168/) (2023)
- [Objects as volumes: A stochastic geometry view of opaque solids](https://mlsanity.com/paper/2312.15406/) (2023)
- [Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation](https://mlsanity.com/paper/2209.15619/) (2022)
- [Neural Stochastic Screened Poisson Reconstruction](https://mlsanity.com/paper/2309.11993/) (2023)
- [Monge-Ampere Regularization for Learning Arbitrary Shapes from Point Clouds](https://mlsanity.com/paper/2410.18477/) (2024)
- [Consistent Point Orientation for Manifold Surfaces via Boundary Integration](https://mlsanity.com/paper/2407.03165/) (2024)
- [Stochastic Poisson Surface Reconstruction with One Solve using Geometric Gaussian Processes](https://mlsanity.com/paper/2503.19136/) (2025)
- [A Bayesian Approach for Task-Specific Next-Best-View Selection with Uncertain Geometry](https://mlsanity.com/paper/2605.05095/) (2026)
- [Approximating Signed Distance Fields With Sparse Ellipsoidal Radial Basis Function Networks: A Dynamic Multi-Objective Optimization Strategy](https://mlsanity.com/paper/2505.02350/) (2025)
- [Wavelet-based Global Orientation and Surface Reconstruction for Point Clouds](https://mlsanity.com/paper/2506.16299/) (2025)
- [Uncertainty Quantification for Cardiac Shape Reconstruction with Deep Signed Distance Functions via MCMC methods](https://mlsanity.com/paper/2605.07987/) (2026)
- [SplatCtrl: Perception-Action Coupling via Gaussian Scene Representations and Reactive Robot Control](https://mlsanity.com/paper/2607.08948/) (2026)

## Abstract (arXiv)

We introduce a statistical extension of the classic Poisson Surface Reconstruction algorithm for recovering shapes from 3D point clouds. Instead of outputting an implicit function, we represent the reconstructed shape as a modified Gaussian Process, which allows us to conduct statistical queries (e.g., the likelihood of a point in space being on the surface or inside a solid). We show that this perspective: improves PSR's integration into the online scanning process, broadens its application realm, and opens the door to other lines of research such as applying task-specific priors.