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Local and global illumination in the volume rendering integral
Nelson Max and Min Chen · 2005
Earlier work this paper cites.
Local and global illumination in the volume rendering integral
Nelson Max and Min Chen · 2010
Earlier work this paper cites.

Similar

Physically based rendering: From theory to implementation
Original
Matt Pharr, Wenzel Jakob, and Greg Humphreys · 2018
Cited alongside, same era.

Then

NeRF: Representing scenes as neural radiance fields for view synthesis
Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng · 2020
Later among the works it cites.

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2022

Volume Rendering Digest (for NeRF)

Tagliasacchi, Andrea, Mildenhall, Ben

Understand

Neural Radiance Fields employ simple volume rendering as a way to overcome the challenges of differentiating through ray-triangle intersections by leveraging a probabilistic notion of visibility.

This is achieved by assuming the scene is composed by a cloud of light-emitting particles whose density changes in space.
This technical report summarizes the derivations for differentiable volume rendering.
It is a condensed version of previous reports, but rewritten in the context of NeRF, and adopting its commonly used notation.