In this section, we delve into the methods employed for surface reconstruction. The process involves two key steps: firstly, we trained a differentiable implicit signed distance function (SDF) using the oriented point cloud, and secondly, we utilized the Marching Cubes algorithm to extract a smoothed mesh from the SDF.
In this section, we provide a brief overview of the methods we utilized to obtain the signed distance function (SDF).
Poisson surface reconstruction is a well known technique for creating watertight surfaces from oriented point samples acquired with 3D range scanners. In this project, we employed Possion reconstruction as the baseline method.
 Kazhdan M, Bolitho M, Hoppe H. Poisson surface reconstruction[C]//Proceedings of the fourth Eurographics symposium on Geometry processing. 2006, 7: 0.
SIREN utilizes sinusoidal activation functions, allowing the network to produce smooth and continuous outputs. We fit a SIREN to our oriented point cloud using the following contraints:
- Surface constraint: for points on surface, SDF should be 0
- Normal contraint: for points on surface, gradient of SDF should be point’s normal
- Empty space constraint: for points not on surface, SDF should be far from 0
- Eikonal constraint: from differential geometry, SDF gradient’s norm should be 1 everywhere
SHINE learns and store implicit features through an octree-based, hierarchical structure, which is sparse and extensible. The learned implicit features are then transformed into signed distance values using a shallow neural network that follows constraints similar to those employed in SIREN.