Fourier Analysis of Correlated Monte Carlo Importance Sampling

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dc.contributor.authorSingh, Gurpriten_US
dc.contributor.authorSubr, Karticen_US
dc.contributor.authorCoeurjolly, Daviden_US
dc.contributor.authorOstromoukhov, Victoren_US
dc.contributor.authorJarosz, Wojciechen_US
dc.contributor.editorBenes, Bedrich and Hauser, Helwigen_US
dc.date.accessioned2020-05-22T12:24:38Z
dc.date.available2020-05-22T12:24:38Z
dc.date.issued2020
dc.description.abstractFourier analysis is gaining popularity in image synthesis as a tool for the analysis of error in Monte Carlo (MC) integration. Still, existing tools are only able to analyse convergence under simplifying assumptions (such as randomized shifts) which are not applied in practice during rendering. We reformulate the expressions for bias and variance of sampling‐based integrators to unify non‐uniform sample distributions [importance sampling (IS)] as well as correlations between samples while respecting finite sampling domains. Our unified formulation hints at fundamental limitations of Fourier‐based tools in performing variance analysis for MC integration. At the same time, it reveals that, when combined with correlated sampling, IS can impact convergence rate by introducing or inhibiting discontinuities in the integrand. We demonstrate that the convergence of multiple importance sampling (MIS) is determined by the strategy which converges slowest and propose several simple approaches to overcome this limitation. We show that smoothing light boundaries (as commonly done in production to reduce variance) can improve (M)IS convergence (at a cost of introducing a small amount of bias) since it removes discontinuities within the integration domain. We also propose practical integrand‐ and sample‐mirroring approaches which cancel the impact of boundary discontinuities on the convergence rate of estimators.en_US
dc.description.number1
dc.description.sectionheadersArticles
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume39
dc.identifier.doi10.1111/cgf.13613
dc.identifier.issn1467-8659
dc.identifier.pages7-19
dc.identifier.urihttps://doi.org/10.1111/cgf.13613
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13613
dc.publisher© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltden_US
dc.subjectglobal illumination
dc.subjectrendering
dc.subjectsignal processing
dc.subjectmethods and applications
dc.subjectMonte Carlo techniques
dc.subjectmethods and applications
dc.subject•Mathematics of computing → Computation of transforms; Stochastic processes; •Computing methodologies → Ray tracing
dc.titleFourier Analysis of Correlated Monte Carlo Importance Samplingen_US
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