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).

## Possion Reconstruction

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.

[1] Kazhdan M, Bolitho M, Hoppe H. Poisson surface reconstruction[C]//Proceedings of the fourth Eurographics symposium on Geometry processing. 2006, 7: 0.

## SIREN

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

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.