Neuralangelo

High-Fidelity Neural Surface Reconstruction

Motivation

• Muti-resolution 3D hash grid
• numerical gradients for computing higher-order derivatives as a smoothing operation

Background

• Volume rendering of SDF opacity value \(\alpha_i\) introduced by Neus

\(\Phi_s\) is sigmoid function

# Background - Multi-resolution hash encoding. Input position \(x_i\) Resolution \(l\)

# Numerical Gradient Computation - Eikonal loss 需要求二阶导 - 解析梯度只能优化相邻的 vertex

Numerical Gradient Computation

step size 作为对解析导数平滑度的指标 - \(\epsilon\) 越大，重建越平滑的区域 - 反之，则重建细节 - 根据 hash grid 调整 \(\epsilon\)

Progressive Levels of Details

• 先激活 coarse grid
• 降低 \(\epsilon\) 的同时，激活 fine grid
• weight decay 避免单一分辨率主导

curvature loss

Encourage smoothness