Spectral Theory of Light Transport Operators

Light Transport Operators (LTOs) represent a fundamental concept in computer graphics, modeling single bounces of light within a virtual environment as linears operators on infinite dimensional spaces. While the LTOs play a crucial role in rendering, prior studies have primarily focused on spectral analyses of the light field rather than the operators themselves. This article presents a rigorous investigation into the spectral properties of the LTOs. Due to their non-compact nature, traditional spectral analysis techniques face challenges in this setting. However, many practical rendering methods effectively employ compact approximations, suggesting that non-compactness is not an absolute barrier. We show the relevance of such approximations and establish various path integral formulations of their spectrum. These findings enhance the theoretical understanding of light transport and offer new perspectives for improving rendering efficiency and accuracy.