direct illumination sampling Petr Vvoda, Ivo Kondapaneni, and - - PowerPoint PPT Presentation

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Bayesian online regression for adaptive direct illumination sampling Petr Vvoda, Ivo Kondapaneni, and Jaroslav Kivnek Render Legion, a.s. Charles University, Prague 2 Direct + indirect illumination 3 Direct + indirect illumination

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Bayesian online regression for adaptive direct illumination sampling

Petr Vévoda, Ivo Kondapaneni, and Jaroslav Křivánek Render Legion, a.s. Charles University, Prague

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Direct + indirect illumination

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Direct + indirect illumination

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Direct illumination only

Non-adaptive sampling [Wang et al. 2009]

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Adaptive sampling [Donikian et al. 2006] Direct illumination only Direct illumination only

Adaptive sampling [Donikian et al. 2006] Non-adaptive sampling [Wang et al. 2009]

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Adaptive sampling [Donikian et al. 2006] Direct illumination only Direct illumination only

Adaptive sampling [Donikian et al. 2006] Non-adaptive sampling [Wang et al. 2009]

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Ours Adaptive sampling [Donikian et al. 2006] Non-adaptive sampling [Wang et al. 2009]

Direct illumination only

(Bayesian learning)

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Adaptive sampling [Donikian et al. 2006] Non-adaptive sampling [Wang et al. 2009]

Direct illumination only 510x faster

Ours (Bayesian learning)

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Adaptive sampling [Donikian et al. 2006] Non-adaptive sampling [Wang et al. 2009]

Direct illumination only 510x faster Robust

Ours (Bayesian learning)

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Previous work

10 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

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Adaptive sampling

  • General Monte Carlo

– Vegas algorithm

  • [Lepage 1980]

– Population MC

  • [Cappé et al. 2004, ...]
  • Rendering

– Image sampling

  • [Mitchell 1987, ...]

– Indirect illumination (path guiding)

  • [Dutre and Willems 1995, Jensen 1995, Lafortune et al. 1995, ...]
  • [Vorba et al. 2014, Muller et al. 2017]

– Direct illumination

  • [Shirley et al. 1996, Donikian et al. 2006, Wang et al. 2009]

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling 11

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Bayesian methods in rendering

  • Filtering

– NonLocal Bayes [Boughida and Boubekeur 2017]

  • Global illumination

– Bayesian Monte Carlo [Brouilat et al. 2009, Marques et al. 2013] – Path guiding [Vorba et al. 2014]

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling 12

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Background

13 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

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Direct illumination

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Less important Occluded

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Clustering (Lightcuts)

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling 15

[Paquette et al. 1998, Walter et al. 2006]

Cluster contribution bounds

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Cluster sampling

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling 16

[Wang and Akerlung 2009]

P

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Adaptive light sampling

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[Donikian et al. 2006]

screen space

P P

Ad-hoc combination

+

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Problem summary

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MC estimate Cluster contribution bounds

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Our approach

19 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

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Contributions

  • Optimal sampling of clusters
  • Adaptive sampling by Bayesian inference

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Optimal cluster sampling

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MC estimates

𝐷1 𝐷2 𝐷3

𝑄 𝐷 ∝ mean P 𝑄 𝐷 ∝ mean2 + variance

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Direct illumination only

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Mean only (Previous)

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Direct illumination only

Mean + Variance (Ours)

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Contributions

  • Optimal sampling of clusters
  • Adaptive sampling by Bayesian inference

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Naive adaptive cluster sampling

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MC estimates

𝐷1 𝐷2 𝐷3

  • utlier

P

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Bayes cluster adaptive sampling

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  • utlier

MC estimates

𝐷1 𝐷2 𝐷3

P

Model x Prior

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Cluster-region pairs

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Cluster-Region data

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𝑒 𝑆 𝑒

MC estimates

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Regresion Data model

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𝑂(est. | 𝑙 𝑒2 , ℎ 𝑒4) 𝑞0 × 𝜀 est.

Parameters: 𝑙, ℎ - normal distr. parameters 𝑞0 - probability of occlusion Cluster-Region data

𝑒

MC estimates

1 − 𝑞0 ×

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Conjugate prior

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𝐪𝐩𝐭𝐮𝐟𝐬𝐣𝐩𝐬 ∝ likelihood × 𝐪𝐬𝐣𝐩𝐬 Same functional form

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Our (conjugate) Priors

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p0 ~ Beta 𝑞0 … k, h ~ Normal inverse gamma 𝑙, ℎ 𝜈0, … ) Hyperparameters Cluster contrib. estimate

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Summary

  • Light preprocess (clustering)
  • During each Next event estimation:

– Obtain clustering (Cut) cached in a region – Compute distributions of estimates for each cluster in Cut

  • > mean, variance

– Build distribution over clusters – Sample direct illumination – Record new data for sampled cluster

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Results

33 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

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Tests

  • Performance
  • Grid resolution
  • Temporal coherence

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Direct only Direct + indirect Simple occlusion Complex occlusion

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Direct illumination only

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Wang Ours Donikian

510x faster Robust Direct illumination only

RMSE time [min]

Wang

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Tests

  • Performance
  • Grid resolution
  • Temporal coherence

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Direct only Direct + indirect Simple occlusion Complex occlusion

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✓

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Direct + indirect illumination

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Direct + indirect illumination

Wang Ours

6.7x faster 6.7x faster

Wang Ours

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Tests

  • Performance
  • Grid resolution
  • Temporal coherence

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

Direct only Direct + indirect Simple occlusion Complex occlusion

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✓ ✓

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Direct illumination only

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Direct illumination only

Ours Donikian Wang

9.3x faster

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RMSE time [min]

Wang

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Ours Donikian Wang

Direct illumination only Robust

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Tests

  • Performance
  • Grid resolution
  • Temporal coherence

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Direct only Direct + indirect Simple occlusion Complex occlusion

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✓ ✓ ✓

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Direct + indirect illumination

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Direct + indirect illumination

Ours Wang Ours Wang

4.3x faster 4.3x faster

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Direct + indirect illumination

Ours Wang

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Tests

  • Performance
  • Grid resolution
  • Temporal coherence

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Direct only Direct + indirect Simple occlusion Complex occlusion

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✓ ✓ ✓ ✓ ✓

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Direct illumination only

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Wang Ours (64) No regression

Direct illumination only 3.6x faster

1 − 𝑞0 × 𝑂 est. 𝑙 𝑒2 , ℎ 𝑒4 𝑞0 × 𝜀 est.

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Tests

  • Performance
  • Grid resolution
  • Temporal coherence

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

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✓ ✓ ✓ ✓ ✓ ✓

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Ours Wang

Direct illumination only

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Conclusion

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Future work

  • BRDF incorporation
  • Adaptive scene subdivision
  • Rigorous hyperparameters derivation
  • Combination with path guiding

[Vorba et al. 2014, Muller et al. 2017]

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Contribution

  • Bayesian framework for robust adaptivity
  • Optimal cluster sampling
  • Algorithm for direct illumination

– Unbiased, adaptive, robust – Easy to integrate into a path tracer

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Acknowledgments

  • Ludvík Koutný (a.k.a. rawalanche)
  • Charles University Grant Agency project GAUK

1172416, by the grant SVV-2017-260452

  • Czech Science Foundation grant 16-18964S

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Thank you!

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