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Abstract Fourier 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 removesC0discontinuities 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.
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Gaussian Product Sampling for Rendering Layered Materials
Abstract To increase diversity and realism, surface bidirectional scattering distribution functions (BSDFs) are often modelled as consisting of multiple layers, but accurately evaluating layered BSDFs while accounting for all light transport paths is a challenging problem. Recently, Guoet al. [GHZ18] proposed an accurate and general position‐free Monte Carlo method, but this method introduces variance that leads to longer render time compared to non‐stochastic layered models. We improve the previous work by presenting two new sampling strategies,pair‐product samplingandmultiple‐product sampling. Our new methods better take advantage of the layered structure and reduce variance compared to the conventional approach of sequentially sampling one BSDF at a time. Ourpair‐product samplingstrategy importance samples the product of two BSDFs from a pair of adjacent layers. We further generalize this tomultiple‐product sampling, which importance samples the product of a chain of three or more BSDFs. In order to compute these products, we developed a new approximate Gaussian representation of individual layer BSDFs. This representation incorporates spatially varying material properties as parameters so that our techniques can support an arbitrary number of textured layers. Compared to previous Monte Carlo layering approaches, our results demonstrate substantial variance reduction in rendering isotropic layered surfaces.
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- PAR ID:
- 10136771
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Computer Graphics Forum
- Volume:
- 39
- Issue:
- 1
- ISSN:
- 0167-7055
- Page Range / eLocation ID:
- p. 420-435
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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