This paper proposes GradientSurf, a novel algorithm for real time surface
reconstruction from monocular RGB video. Inspired by Poisson Surface
Reconstruction, the proposed method builds on the tight coupling between
surface, volume, and oriented point cloud and solves the reconstruction problem
in gradient-domain. Unlike Poisson Surface Reconstruction which finds an
offline solution to the Poisson equation by solving a linear system after the
scanning process is finished, our method finds online solutions from partial
scans with a neural network incrementally where the Poisson layer is designed
to supervise both local and global reconstruction. The main challenge that
existing methods suffer from when reconstructing from RGB signal is a lack of
details in the reconstructed surface. We hypothesize this is due to the
spectral bias of neural networks towards learning low frequency geometric
features. To address this issue, the reconstruction problem is cast onto
gradient domain, where zeroth-order and first-order energies are minimized. The
zeroth-order term penalizes location of the surface. The first-order term
penalizes the difference between the gradient of reconstructed implicit
function and the vector field formulated from oriented point clouds sampled at
adaptive local densities. For the task of indoor scene reconstruction, visual
and quantitative experimental results show that the proposed method
reconstructs surfaces with more details in curved regions and higher fidelity
for small objects than previous methods.

本文提出了 GradientSurf，这是一种从单目 RGB 视频中实时重建表面的新算法。该方法通过渐变域中的表面、体积和定向点云之间的紧密耦合解决重建问题，利用神经网络增量式地从部分扫描中在线找到 Poisson 层的解，以监督局部和全局重建。与离线求解 Poisson 方程的 Poisson Surface Reconstruction 不同，现有方法在从 RGB 信号重建时缺乏细节，本文通过在梯度域中对零阶和一阶能量进行最小化，解决了这个问题。在室内场景重建的任务中，视觉和定量实验结果表明，该方法在曲线区域重建的细节更多，对小物体的保真度更高。