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.

翻译：本文提出GradientSurf，一种从单目RGB视频进行实时表面重建的新算法。受泊松表面重建启发，该方法基于表面、体积和有向点云之间的紧密耦合，在梯度域中求解重建问题。与通过扫描过程结束后求解线性系统来离线求解泊松方程的泊松表面重建不同，本方法利用神经网络从部分扫描中在线地增量求解，其中泊松层被设计用于监督局部和全局重建。现有方法在从RGB信号重建时面临的主要挑战是重建表面缺乏细节。我们假设这是由于神经网络倾向于学习低频几何特征的频谱偏差所致。为解决此问题，将重建问题投射到梯度域中，并最小化零阶和一阶能量。零阶项惩罚表面的位置。一阶项惩罚重建隐函数的梯度与从自适应局部密度采样的有向点云构成的向量场之间的差异。针对室内场景重建任务，视觉和定量实验结果表明，与先前方法相比，本方法在弯曲区域重建出更多细节，且对小物体具有更高的保真度。