NeRF Differentiable Forward Maps

This is part of my journey of learning NeRF.

2.3. Differentiable Forward Maps


Differentiable rendering


Volume rendering can render fogs. Sphere rendering only render the solid surface, and needs ground truth supervision.? Neural renderer combines the two.

Differentiability of the rendering function itself

  • BRDF Shading? details later.

Differentiation itself

Design a neural network with higher order derivatives constraints and therefore directly use its derivative.


For example the Eikonal equation forces the neural network has a derivative as 1. Adding the eikonal loss then promises the neural network valid.

Generally, this kind of problems are: the solutions are constrained by its partial derivatives.

Special: Identity Operator

\[ \text{Reconstruction} \rightarrow \hat 1()\rightarrow \text{Sensor domain}\\ \text{Reconstruction} == \text{Sensor domain} \]


  • Can we obtain a neural network in just one forward, without optimization?
  • Can we design special forward maps for specific downstream tasks, eg., classification? Absolutely yes. We can design it to represent a compact representation as the sensor domain. The key idea is to get a differentiable function to map your specific recon and sensor domain.