FNIN: A Fourier Neural Operator-based Numerical Integration Network for Surface-form-gradients
Journal:
arXiv
Published Date:
Jan 21, 2025
Abstract
Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface
from its gradients. Traditional methods encounter significant challenges in
achieving high accuracy and handling high-resolution inputs, particularly
facing the complex nature of discontinuities and the inefficiencies associated
with large-scale linear solvers. Although recent advances in deep learning,
such as photometric stereo, have enhanced normal estimation accuracy, they do
not fully address the intricacies of gradient-based surface reconstruction. To
overcome these limitations, we propose a Fourier neural operator-based
Numerical Integration Network (FNIN) within a two-stage optimization framework.
In the first stage, our approach employs an iterative architecture for
numerical integration, harnessing an advanced Fourier neural operator to
approximate the solution operator in Fourier space. Additionally, a
self-learning attention mechanism is incorporated to effectively detect and
handle discontinuities. In the second stage, we refine the surface
reconstruction by formulating a weighted least squares problem, addressing the
identified discontinuities rationally. Extensive experiments demonstrate that
our method achieves significant improvements in both accuracy and efficiency
compared to current state-of-the-art solvers. This is particularly evident in
handling high-resolution images with complex data, achieving errors of fewer
than 0.1 mm on tested objects.
