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

TL;DR

Neural Poisson Surface Reconstruction (nPSR) uses Fourier Neural Operators to efficiently reconstruct high-quality 3D shapes from point clouds at various resolutions, enabling super-resolution and outperforming existing methods.

Contribution

nPSR introduces a resolution-agnostic neural architecture leveraging Fourier Neural Operators for efficient, high-quality 3D shape reconstruction from point clouds.

Findings

Achieves comparable high-resolution results with low-resolution training.

Surpasses existing methods in reconstruction quality and speed.

Enables one-shot super-resolution from low-resolution data.

Abstract

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.