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

Bayesian online regression for adaptive direct illumination sampling Petr Vévoda, Ivo Kondapaneni, and Jaroslav Křivánek Render Legion, a.s. Charles University, Prague

2 Direct + indirect illumination

3 Direct + indirect illumination

Non-adaptive sampling 4 [Wang et al. 2009] Direct illumination only

Non-adaptive sampling Adaptive sampling Adaptive sampling 5 [Donikian et al. 2006] [Wang et al. 2009] [Donikian et al. 2006] Direct illumination only Direct illumination only

Non-adaptive sampling Adaptive sampling Adaptive sampling 6 [Donikian et al. 2006] [Wang et al. 2009] [Donikian et al. 2006] Direct illumination only Direct illumination only

Non-adaptive sampling Adaptive sampling Ours 7 [Wang et al. 2009] [Donikian et al. 2006] (Bayesian learning) Direct illumination only

Non-adaptive sampling Adaptive sampling Ours 8 [Wang et al. 2009] [Donikian et al. 2006] (Bayesian learning) 510x faster Direct illumination only

Non-adaptive sampling Adaptive sampling Ours 9 [Wang et al. 2009] [Donikian et al. 2006] (Bayesian learning) 510x faster Robust Direct illumination only

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

11 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

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

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

14 Direct illumination Less important Occluded Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

15 Clustering (Lightcuts) [ Paquette et al. 1998, Walter et al. 2006 ] Cluster contribution bounds Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

16 Cluster sampling [ Wang and Akerlung 2009 ] P Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

17 Adaptive light sampling [ Donikian et al. 2006 ] screen space Ad-hoc combination P P + Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

18 Problem summary Cluster contribution bounds MC estimate Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

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

20 Contributions • Optimal sampling of clusters • Adaptive sampling by Bayesian inference Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

21 Optimal cluster sampling mean 2 + variance 𝑄 𝐷 ∝ 𝑄 𝐷 ∝ mean MC estimates P 𝐷 2 𝐷 3 𝐷 1 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

22 Direct illumination only

23 Mean only (Previous) Mean + Variance (Ours) Direct illumination only

24 Contributions • Optimal sampling of clusters • Adaptive sampling by Bayesian inference Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

25 Naive adaptive cluster sampling outlier MC estimates P 𝐷 2 𝐷 3 𝐷 1 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

26 Bayes cluster adaptive sampling outlier MC estimates P Model x Prior 𝐷 2 𝐷 3 𝐷 1 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

27 Cluster-region pairs Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

28 Cluster-Region data MC estimates 𝑒 𝑆 𝑒 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

29 Regresion Data model Cluster-Region data Parameters: 𝑙, ℎ - normal distr. parameters MC estimates 𝑞 0 - probability of occlusion 𝑂(est. | 𝑙 𝑒 2 , ℎ 𝑒 4 ) 1 − 𝑞 0 × 𝑞 0 × 𝜀 est. 𝑒 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

30 Conjugate prior 𝐪𝐩𝐭𝐮𝐟𝐬𝐣𝐩𝐬 ∝ likelihood × 𝐪𝐬𝐣𝐩𝐬 Same functional form Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

31 Our (conjugate) Priors p 0 ~ Beta 𝑞 0 … k, h ~ Normal inverse gamma 𝑙, ℎ 𝜈 0 , … ) Hyperparameters Cluster contrib. estimate Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

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

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

34 Tests • Performance Direct only Direct + indirect Simple occlusion Complex occlusion • Grid resolution • Temporal coherence Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

35 Direct illumination only

Wang Ours Donikian 36 510x faster Robust Wang RMSE time [min] Direct illumination only

37 Tests • Performance Direct only Direct + indirect ✓ Simple occlusion Complex occlusion • Grid resolution • Temporal coherence Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

38 Direct + indirect illumination

Wang Wang 39 6.7x faster 6.7x faster Ours Ours Direct + indirect illumination

40 Tests • Performance Direct only Direct + indirect ✓ ✓ Simple occlusion Complex occlusion • Grid resolution • Temporal coherence Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

41 Direct illumination only

42 Wang Ours Donikian 9.3x faster Wang RMSE time [min] Direct illumination only

43 Wang Ours Donikian Robust Direct illumination only

44 Tests • Performance Direct only Direct + indirect ✓ ✓ Simple occlusion ✓ Complex occlusion • Grid resolution • Temporal coherence Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

45 Direct + indirect illumination

46 Ours Ours Wang Wang 4.3x faster 4.3x faster Direct + indirect illumination

47 Ours Wang Direct + indirect illumination

48 Tests • Performance ✓ Direct only Direct + indirect ✓ ✓ Simple occlusion ✓ ✓ Complex occlusion • Grid resolution • Temporal coherence Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

49 Direct illumination only

50 Ours (64) No regression Wang 3.6x faster 𝑒 2 , ℎ 𝑙 1 − 𝑞 0 × 𝑂 est. 𝑒 4 𝑞 0 × 𝜀 est. Direct illumination only

51 Tests • Performance ✓ Direct only Direct + indirect ✓ ✓ Simple occlusion ✓ ✓ Complex occlusion • Grid resolution ✓ • Temporal coherence Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

Ours Wang 52 52 Direct illumination only

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

54 Future work • BRDF incorporation • Adaptive scene subdivision • Rigorous hyperparameters derivation • Combination with path guiding [ Vorba et al. 2014, Muller et al. 2017 ] Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

55 Contribution • Bayesian framework for robust adaptivity • Optimal cluster sampling • Algorithm for direct illumination – Unbiased, adaptive, robust – Easy to integrate into a path tracer Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling