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Adjoint-Driven Russian Roulette and Splitting in Light Transport Simulation
J. Vorba, J. Krivanek [SIGGRAPH 2016]
Presenter: Eunhyouk Shin
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Last presentation: Interactive Sound Propagation with Bidirectional Path Tracing
- Acoustic transport equation
- Solution in Neumann series form
- Estimate terms using BDPT & multiple importance sampling
- Caching for interactive performance
- SNR metric for evaluating stochastic sound propagation
- Compared to visual rendering, temporal dimension quality is important
rather than spatial resolution
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Direction sampling Russian roulette / splitting
Recall: Probabilistic Aspects of MCRT
orω? or
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To reduce variance (noise),
we must make more path that contributes more.
But how do we know beforehand how much it will contribute?
Recall: Importance Sampling
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Direction sampling Russian roulette / splitting
Estimating global information
Recent Techniques using Global Estimation
Path Guiding [Vorba et al. 14]
ADRRS [Vorba et al. 16]PIS [Herholtz et al. 16]
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Contents
- Particle tracing
- Russian roulette & splitting
- Determining the RR/splitting factor
- Weight window
- Results
*Figures in the slides is from the authors [Vorba et al. 16]
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Particle Tracing
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Particle Tracing
- Trace weighted particles to get an unbiased estimate of the pixel value
Particle weight
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Particle Tracing
- When a particle collides to a light source, it contributes to the estimation according to the weight.
+Weight Emission
+
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Particle Tracing
- Contribution must be different for before/after a bounce
previous weight?
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Weight Update: Bounce
- Incremental weight update by BRDF, geometric term, sampling distribution
x
particle weight update
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Particle Tracing
We have an unbiased estimator,But when do we terminate?
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Russian Roulette & Splitting
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Russian Roulette
- Upon collision, the particle survives with probability q
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Weight Update: Russian Roulette
0E[ ] = E[ ]
- Key: Expected contribution must remain unchanged
no RR
: Weight of survived particle gets ‘boosted’
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Splitting
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Weight Update: Splitting
split to q particles
- Key: Expected contribution must remain unchanged
E[ ] = E[ ]
no splitting
: Splitted particles share the weight evenly
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Unified RR/Splitting
RR: Split:
or
- RR and splitting has same weight update formula:
- Make q particles in expectation sense- Extends to non-integer splitting
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Determining the RR/Splitting factor
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Issues
- If q is too low, only a small fraction of the particles reach the light source
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Issues
- If q is too high, we are wasting too much resource for particles with low contribution
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Issues
- Existing approaches set q according to the local properties (e.g. reflectance) of the surface, but it’s still far from optimal
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Adjoint Driven Russian Roulette and Splitting
- New approach uses global information of radiance
means “radiance” in this context
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Adjoint Driven Russian Roulette and Splitting
ADRRS
- Set q as expected contribution of outgoing particles
- How to estimate pixel value and reflected radiance?
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Path Guiding [Vorba et al. 2014]
…- Precomputed cache of estimated radiance distribution
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Estimated Radiance
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- Want lower variance in rendered image- Should make more particles for high-contribution paths- We query the precomputed radiance cache to compute the
adjoint-driven RR/splitting factor
Summary: Determining the RR/splitting Factor
radiance cache
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Weight Window
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Weight Invariance
Desired weight after RR/splitting
RR/Splitting factor
Weight after RR/split
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Weight Invariance
split
share weight
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Weight Invariance
roulette
boost weight
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Weight Window
split
pass through
roulette
- More robust by loosening the RR/splitting
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ADRRS Summary
Contribute to pixel estimate
make 0+ new particles
Apply weight window (RR/splitting)
Query radiance cache to compute desired weight
+
Collision
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Results
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Path tracingPlain
+ our ADRRS
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Path tracing
Plain + our ADRRS + our ADRRS Path guiding
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Conclusion
- Use precomputed radiance (adjoint) estimation to compute
expected path contribution
- Set RR/splitting factor as the expected contribution
- Able to make more particles for high-contribution path
- Reduced variance in rendered image