Neural Surface Reconstruction learns a Signed Distance Field~(SDF) to reconstruct the 3D model from multi-view images. Previous works adopt voxel-based explicit representation to improve efficiency. However, they ignored the gradient instability of interpolation in the voxel grid, leading to degradation on convergence and smoothness. Besides, previous works entangled the optimization of geometry and radiance, which leads to the deformation of geometry to explain radiance, causing artifacts when reconstructing textured planes. In this work, we reveal that the instability of gradient comes from its discontinuity during trilinear interpolation, and propose to use the interpolated gradient instead of the original analytical gradient to eliminate the discontinuity. Based on gradient interpolation, we propose VoxNeuS, a lightweight surface reconstruction method for computational and memory efficient neural surface reconstruction. Thanks to the explicit representation, the gradient of regularization terms, i.e. Eikonal and curvature loss, are directly solved, avoiding computation and memory-access overhead. Further, VoxNeuS adopts a geometry-radiance disentangled architecture to handle the geometry deformation from radiance optimization. The experimental results show that VoxNeuS achieves better reconstruction quality than previous works. The entire training process takes 15 minutes and less than 3 GB of memory on a single 2080ti GPU.

翻译：神经表面重建通过学习符号距离场（SDF）从多视角图像重建三维模型。先前的研究采用基于体素的显式表示以提高效率。然而，它们忽视了体素网格中插值梯度的不稳定性，导致收敛性与平滑性下降。此外，先前工作将几何与辐射度的优化过程耦合，导致几何结构为解释辐射度而发生形变，在重建纹理平面时产生伪影。本工作中，我们揭示了梯度不稳定性源于三线性插值过程中梯度的不连续性，并提出使用插值梯度替代原始解析梯度以消除该不连续性。基于梯度插值，我们提出了VoxNeuS——一种轻量级表面重建方法，用于实现计算与内存高效的神经表面重建。得益于显式表示，正则化项（即Eikonal损失与曲率损失）的梯度可直接求解，避免了计算与内存访问开销。此外，VoxNeuS采用几何-辐射度解耦架构以处理辐射度优化引发的几何形变。实验结果表明，VoxNeuS取得了优于先前工作的重建质量。完整训练过程在单块2080ti GPU上仅需15分钟且内存占用低于3 GB。