Bayesian Learning for Guided Direct Illumination Sampling Vvoda , - - PowerPoint PPT Presentation

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Bayesian Learning for Guided Direct Illumination Sampling Vvoda , - - PowerPoint PPT Presentation

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1 Bayesian Learning for Guided Direct Illumination Sampling Vvoda , Kondapaneni, Kivnek - Bayesian online regression for adaptive illumination sampling 2 Guiding needs radiance approximations How to learn them reliably ? Our

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Bayesian Learning for Guided Direct Illumination Sampling

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

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  • Guiding needs radiance approximations
  • How to learn them reliably?
  • Our proposition:

(Online, Bayesian) Machine learning

[Vorba et al. 2014, Vévoda et al. 2018]

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling 2

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Take home message

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling 3

Machine Learning | Bayesian modeling = Excellent framework for guided/adaptive Monte Carlo

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Bayesian online regression for adaptive direct illumination sampling

Petr Vévoda, Ivo Kondapaneni, and Jaroslav Křivánek Chaos Czech 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

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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

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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

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

Direct illumination only

(Bayesian learning)

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

Direct illumination only 510x faster

Ours (Bayesian learning)

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

Direct illumination only 510x faster Robust

Ours (Bayesian learning)

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Previous work

13 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 14

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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 15

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Background

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

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Direct illumination problem

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Less important Occluded

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Non-adaptive, un-occluded light sampling

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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

Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling 20

MC estimates Light contribution bounds

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Our approach

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Contributions

  • What distribution should we learn?
  • Learning the distribution through Bayesian inference

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𝑄 𝑀 ∝ mean2 + variance 𝑄(𝑀) ∝ mean

Optimal light sampling distribution

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MC estimates

𝑀1 𝑀2 𝑀3

Prob

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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 distribution
  • Learning the distribution through Bayesian inference

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Naive adaptive light sampling

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MC estimates

𝑀1 𝑀2 𝑀3

  • utlier

P

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Bayesian adaptive light sampling

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  • utlier

MC estimates

𝑀1 𝑀2 𝑀3

P

Model x Prior

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Scene subdivided in regions

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Light-region statistics

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𝑒 region 𝑆 𝑒

MC estimates

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Regression 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 Light-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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𝑞0 ~ Beta 𝑞0 … 𝑙, ℎ ~ Normal inverse gamma 𝑙, ℎ 𝜈0, … ) Hyperparameters Light contrib. estimate

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Algorithmic summary

  • During each Next event estimation (in a region)

– Compute data distributions for each light (mean, variance). – Build sampling PMF over lights – Choose lights form the PMF & samples on lights at random – Update light-region stats

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Scalability – Light clustering

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MC estimate Cluster contribution bounds Technical detail – not essential for our take-home message

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Results

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Tests

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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

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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

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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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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

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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

  • Grid resolution

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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

  • Grid resolution
  • Temporal coherence

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    

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Ours Wang

Direct illumination only

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Contribution

  • Bayesian framework for robust adaptivity/guiding
  • Optimal sampling distribution
  • Algorithm for direct illumination

– Unbiased, adaptive, robust – Easy to integrate

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Acknowledgments

  • Ludvík Koutný (a.k.a. rawalanche)
  • Funding

– Charles University: GAUK 1172416, SVV-2017-260452 – Czech Science Foundation: 16-18964S, 19-07626S.

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Take home message

Machine Learning | Bayesian modeling = Excellent framework for guided/adaptive Monte Carlo