Equal-time renderings (50s on 64 cores).
Top:
We propose a new analytical approach to Markov Chain stratification that improves sample distribution similarly to multi-stage MLT [Hoberock and Hart 2010], but at greatly reduced complexity, as it neither requires multiple rendering stages nor other pre-accumulated information.
Bottom:
We construct an adaptive rendering algorithm based on purely forward path tracing that is competitive with state-of-the-art bi-directional algorithms. Our analytic variance bounding scheme serves as a framework for the design and optimization of adaptive sampling distributions.
(Scene credits:
Kitchen scene by Jay-Artist, prepared by Benedikt Bitterli,
and
Torus scene by Olesya Jakob, based on a scene by Cline et al. (2005).)
Abstract
Markov Chain Monte Carlo (MCMC) rendering is extensively studied, yet it remains largely unused in practice.
We propose solutions to several practicability issues, opening up path space MCMC to become an adaptive sampling framework around established Monte Carlo (MC) techniques.
We address non-uniform image quality by deriving an analytic target function for image-space sample stratification. The function is based on a novel connection between variance and path differentials, allowing analytic variance estimates for MC samples, with potential uses in other adaptive algorithms outside MCMC. We simplify these estimates down to simple expressions using only quantities known in any MC renderer.
We also address the issue that most existing MCMC renderers rely on bi-directional path tracing and reciprocal transport, which can be too costly and/or too complex in practice. Instead, we apply our theoretical framework to optimize an adaptive MCMC algorithm that only uses forward path construction. Notably, we construct our algorithm by adapting (with minimal changes) a full-featured path tracer into a single-path state space Markov Chain, bridging another gap between MCMC and existing MC techniques.
Downloads
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Preprint
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Supplementary Data
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(coming soon)
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Teaser Video
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Talk
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TL;DR Slides
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Supplementary Data
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Comparing Temporal Stability for Various MCMC Techniques
Experiments showing 12 independent frames to evaluate temporal stability / consistency
of results across multiple runs or in motion. Also shows reweighted results using
standard DBOR [DeCoro et al. 2010, Zirr et al. 2018], where the MLT splats were rendered
to a cascade of framebuffers and reweighted in post to bound variance.
-: Unbiased Result
DBOR: Standard DBOR applied to each frame individually
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Comparing Stratification for Various MCMC Techniques
Additional results for Fig. 5 (unstratified and stratified MLT, multi-stage MLT)
p-stratified: Simplified stratification based on solid angle PDFs
dX-stratified: Stratification based on fully computed 4D path differentials
multi-stage: Multi-Stage MLT for stratification
unstratified: Using the classic MLT target function
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Using Path Differentials for Reweighting / Variance Bounding
Additional results for Fig. 3, using our variance bounding ratio instead of the downweighting
ratio derived for DBOR by Zirr et al. [2018]
p-reweighted: Reweighting using the simplified variance bounding ratio
dX-reweighted: Reweighting based on ratio obtained from fully computed 4D path differentials
unweighted: The unbiased result
All images were computed using standard path tracing (no MLT involved)
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Comparison of Large-Step Mutations in Various MCMC Techniques
Additional results for Fig. 4 (comparing our PT mutation, the bi-directional Mutation
in Veach MLT and MMLT large steps, with and w/o the Veach small steps resp. MMLT small steps)
PT + MLT: Our large step, with and w/o lens, caustic and multi-chain perturbations
Veach MLT: Bi-directional mutation, with and w/o lens, caustic and multi-chain perturbations
MMLT: Multiplexed MLT large steps, with and w/o small steps
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Amount of Reweighting per Number of Bounces
Shows reweighting experiments separately per number
of path bounces, for a simple scene with varying glossinesses. Thus, it becomes visible
for which cases the variance bounding is most aggressive.
p-reweighted: Reweighting using the simplified variance bounding ratio
dX-reweighted: Reweighting based on ratio obtained from fully computed 4D path differentials
unweighted: The unbiased result
alpha: Roughness coefficient of a microfacet BRDF Beckmann lobe
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