Neural Poisson Surface Reconstruction: Resolution-Agnostic Shape Reconstruction via Fourier Neural Operators

Reconstructing high-quality 3D shapes from sparse or noisy point clouds is a long-standing challenge. Traditional methods struggle with low-quality inputs, while modern learning-based approaches can be computationally demanding or fail to generalize. To bridge this gap, we propose Neural Poisson Surface Reconstruction (nPSR), a novel hybrid method that combines traditional model-based Poisson Surface Reconstruction and learned neural operators for accurate 3D shape reconstruction from oriented point clouds. We solve the classical Poisson reconstruction formulation with Fourier Neural Operators, leveraging their efficiency while learning a robust data-driven prior, significantly enhancing reconstruction quality, especially under sparse or noisy sampling conditions. Importantly, nPSR achieves resolution-agnostic performance, training on low-resolution grids and generalizing effectively to higher resolutions without retraining. Experimental results demonstrate that nPSR outperforms state-of-the-art reconstruction methods when reconstructing from sparse samples and generalizes to unseen datasets. The reconstruction occurs in a single forward pass, allowing for integration into larger differentiable vision pipelines for end-to-end optimization.