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