Towards Interactive Global Illumination Effects via Sequential Monte Carlo Adaptation. Carson Brownlee Peter S. Shirley Steven G.

Transcription

1 Towards Interactive Global Illumination Effects via Sequential Monte Carlo Adaptation Vincent Pegoraro Carson Brownlee Peter S. Shirley Steven G. Parker

2 Outline Motivation & Applications Monte Carlo Integration Light Transport Sequential Adaptation Control Variates Importance Sampling Adaptive Refinement Minimizing Variance Estimate Evaluation Results Discussion and Future Work Conclusion

3 Motivation Plausible depiction Efficient rendering : scientific implications Applications Movie and gaming industries Scientific visualization

4 Monte Carlo Integration Estimating multi-dimensional integrals Stochastic nature noise Variance reduction techniques

5 Monte Carlo Integration Control Variates Importance Sampling

6 Monte Carlo Integration Combined Estimator Standard Deviation

7 Light Transport Rendering Equation where

8 Sequential Adaptation Estimates cached in per-pixel structure Correlation of rays efficient integration Dynamic predicate functions without bias

9 Sequential Adaptation Control Variates Low-cost read/write access Efficient integration B-splines Representation Cheap & continuous interpolantsorder 1 Adaptive grids / azimuth period / polar averages Update cell s coefficient + integral + averages

10 Sequential Adaptation Control Variates

11 Sequential Adaptation Importance Sampling Efficiency same resolution CDF inversion low-orders Continuity not crucial order 0 Representation Cell also contains scalar estimate of f g Compute scalar PDF sample from f g channels Tree of partial PDF sums efficient sampling

12 Sequential Adaptation Importance Sampling

13 Sequential Adaptation Adaptive Refinement Representation adapting to records population Initialization : single cell with uniform sampling Update : radiance estimate cached based on target pixel and sample direction Refinement criterion subdivide, set counters Inheritance non-zero PDFs

14 Sequential Adaptation Refinement Criterion Threshold on average of records counters Promote refinement based on density of rays Controls inertia Versatile structure quickly morphing to target Unreliable predicates increased variance Optimal value determined empirically

15 Sequential Adaptation Minimizing Variance Start-up : MCMC BRDF importance sampling Higher population : sequential estimator Variance tracker associated to each cache Evolutive variance of sequential estimator Threshold correlated with refinement criterion

16 Sequential Adaptation Estimate Evaluation

17 Results Root Mean Squared Error

18 Results Efficiency : 1 / (variance cost)

19 Results 1024 spp 1066 spp 1059 spp 1144 spp

20 Results 256 spp 261 spp 258 spp 274 spp

21 Results 1024 spp 1074 spp 1026 spp 1203 spp

22 Results Characteristics Sponza Room David

23 Results 4 sec 15 sec 1 min 4 min

24 Discussion and Future Work Memory requirements Less sensitive to specularity of BRDF Optimal refinement criterion Increase efficiency at low population levels

25 Conclusion Symbiotic control variates / imp. sampling Dynamic predicates and marginal overhead convergence and efficiency increase Inheritance strategy well-behaved PDFs Online estimation and caching without bias no pre-pass + visual imp. & scene driven Scene independent while exploit coherency Simple to implement and to tune Sequential adaptation learning estimator

26 Acknowledgments U.S. Department of Energy Dave Edwards, Thiago Ize and Ingo Wald Thank you!