Computing Light Transport Gradients using the Adjoint Method

TL;DR

This paper introduces a continuous adjoint theory-based method to compute light transport gradients, simplifying the process by relating it to importance, and aims to improve gradient calculations in path tracing.

Contribution

It formulates a novel continuous adjoint approach for light transport gradients, linking importance and adjoint equations to streamline gradient computations.

Findings

Derives a new adjoint equation for light transport gradients.

Shows that importance functions can be used to compute gradients efficiently.

Facilitates easier implementation of gradients in path tracers.

Abstract

This paper proposes a new equation from continuous adjoint theory to compute the gradient of quantities governed by the Transport Theory of light. Unlike discrete gradients ala autograd, which work at the code level, we first formulate the continuous theory and then discretize it. The key insight of this paper is that computing gradients in Transport Theory is akin to computing the importance, a quantity adjoint to radiance that satisfies an adjoint equation. Importance tells us where to look for light that matters. This is one of the key insights of this paper. In fact, this mathematical journey started from a whimsical thought that these adjoints might be related. Computing gradients is therefore no more complicated than computing the importance field. This insight and the following paper hopefully will shed some light on this complicated problem and ease the implementations of gradient computations in existing path tracers.