Theory, analysis and applications of 2D global illumination

Abstract

We investigate global illumination in 2D and show how this simplified problem domain leads to practical insights for 3D rendering.We first derive a full theory of 2D light transport by introducing 2D analogues to radiometric quantities such as flux and radiance, and deriving a 2D rendering equation. We use our theory to show how to implement algorithms such as Monte Carlo ray tracing, path tracing, irradiance caching, and photon mapping in 2D, and demonstrate that these algorithms can be analyzed more easily in this domain while still providing insights for 3D rendering.We apply our theory to develop several practical improvements to the irradiance caching algorithm. We perform a full second-order analysis of diffuse indirect illumination, first in 2D, and then in 3D by deriving the irradiance Hessian, and show how this leads to increased accuracy and performance for irradiance caching. We propose second-order Taylor expansion from cache points, which results in more accurate irradiance reconstruction. We also introduce a novel error metric to guide cache point placement by analyzing the error produced by irradiance caching. Our error metric naturally supports anisotropic reconstruction and, in our preliminary study, resulted in an order of magnitude less error than the "split-sphere" heuristic when using the same number of cache points.

Recent Advances in Adaptive Sampling and Reconstruction for Monte Carlo Rendering

“…As a proof-of-concept, they also describe an adaptive sampling algorithm based on gradient magnitudes. Jarosz et al [JSKJ12] recently extended Ramamoorthi et al's work by performing a second-order analysis of indirect illumination. Interestingly, there is a close connection between second order derivatives and Gaussian approximations of local frequency spectra as discussed by Belcour et al [BBS14].…”

A Light Transport Framework for Lenslet Light Field Cameras

“…Light transport analysis formulates these transformations and exploits the structure of the transformed light field for various applications, including synthetic image or light field rendering [Chai et al 2000;Durand et al 2005;Egan et al 2009;Egan et al 2011;Lehtinen et al 2011;Jarosz et al 2012;Belcour et al 2012], processing for light field cameras and displays [Ng 2005;Zwicker et al 2006;Levin and Durand 2010;Wetzstein et al 2012], image formation modeling [Levin et al 2009;Liang et al 2011], and inverse transport analysis [Ramamoorthi and Hanrahan 2001;Seitz et al 2005]. Our approach leverages these foundational analyses, and focuses on analyzing the resolution of lenslet-based light field cameras.…”

Practical Hessian-based error control for irradiance caching

“…Holzschuch and Sillion [1995; derived gradients and Hessians of the point-toarea form factor which we utilize in our approach. Jarosz et al [2012] presented a 2D theory of light transport, derived occlusion-unaware Hessians of irradiance, and proposed to use these for error control in irradiance caching. They also showed that the irradiance Hessian provides enough information to simultaneously obtain both the orientation and eccentricity of elliptical cache records to optimally adapt to the local anisotropic irradiance curvature.…”

“…In this paper, we follow the same basic recipe as suggested by Jarosz et al [2012], but propose a number of fundamental improvements that turn it into a practical, welltested error control for irradiance caching in complex scenes:…”

“…Instead of modifying the original heuristic, Jarosz et al [2012] recently proposed an alternative. While analyzing global illumination in 2D, they derived second order derivatives of irradiance for scenes with no occlusions, and showed how this could potentially be applied to obtain an improved error metric for irradiance caching.…”