Simple Note on NeRF Deduction

• Simple Note on NeRF Deduction
  • Formulation
  • Definitions and Relation
  • Deduction
  • Approximation
  • Volume Rendering

Simple Note on NeRF Deduction

This blog serves as a minimum note on the recent ECCV tutorial on NeRF fundamentals.

Formulation

We have a view direction, or a ray. We intend to return the RGB value at a specific location along that vector.

Definitions and Relation

and are related by the following equation, which is intuitive:

Deduction

The expected color along the ray:

Approximation

Note the nested integration (another inside ). Approximate the outside integration assuming local consistency ( and remains constant).

Let

can be rewritten as:

Volume Rendering

In the previous section, we are basically saying that

By replacing , we can render other quantities of interest.