GradientSurf: Gradient-Domain Neural Surface Reconstruction from RGB Video

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.

Estimating Discrete Total Curvature with Per Triangle Normal Variation

We introduce a novel approach for measuring the total curvature at every triangle of a discrete surface. This method takes advantage of the relationship between per triangle total curvature and the Dirichlet energy of the Gauss map. This new tool can be used on both triangle meshes and point clouds and has numerous applications. In this study, we demonstrate the effectiveness of our technique by using it for feature-aware mesh decimation, and show that it outperforms existing curvature-estimation methods from popular libraries such as Meshlab, Trimesh2, and Libigl. When estimating curvature on point clouds, our method outperforms popular libraries PCL and CGAL.