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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

  1. 1 Bayesian Learning for Guided Direct Illumination Sampling Vévoda , Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  2. 2 • Guiding needs radiance approximations • How to learn them reliably ? • Our proposition: (Online, Bayesian) Machine learning [ Vorba et al. 2014, V évoda et al. 2018 ] Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  3. 3 Take home message Machine Learning | Bayesian modeling = Excellent framework for guided/adaptive Monte Carlo Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  4. Bayesian online regression for adaptive direct illumination sampling Petr V évoda, Ivo Kondapaneni, and Jaroslav Křivánek Chaos Czech a.s. Charles University, Prague

  5. 5 Direct + indirect illumination

  6. 6 Direct + indirect illumination

  7. Non-adaptive sampling 7 Direct illumination only

  8. Non-adaptive sampling Adaptive sampling Adaptive sampling 8 [Donikian et al. 2006] [Donikian et al. 2006] Direct illumination only Direct illumination only

  9. Non-adaptive sampling Adaptive sampling Adaptive sampling 9 [Donikian et al. 2006] [Donikian et al. 2006] Direct illumination only Direct illumination only

  10. Non-adaptive sampling Adaptive sampling Ours 10 [Donikian et al. 2006] (Bayesian learning) Direct illumination only

  11. Non-adaptive sampling Adaptive sampling Ours 11 [Donikian et al. 2006] (Bayesian learning) 510x faster Direct illumination only

  12. Non-adaptive sampling Adaptive sampling Ours 12 [Donikian et al. 2006] (Bayesian learning) 510x faster Robust Direct illumination only

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

  14. 14 Adaptive sampling • General Monte Carlo – Vegas algorithm • [ Lepage 1980 ] – Population MC • [ Capp é 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

  15. 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

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

  17. 17 Direct illumination problem Less important Occluded Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  18. 18 Non-adaptive, un-occluded light sampling P Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  19. 19 Adaptive light sampling [ Donikian et al. 2006 ] screen space Ad-hoc combination P P + Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  20. 20 Problem summary Light contribution bounds MC estimates Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  21. 21 Our approach Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  22. 22 Contributions • What distribution should we learn? • Learning the distribution through Bayesian inference Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  23. 23 Optimal light sampling distribution mean 2 + variance 𝑄 𝑀 ∝ 𝑄(𝑀) ∝ mean MC estimates Prob 𝑀 1 𝑀 2 𝑀 3 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  24. 24 Direct illumination only

  25. 25 Mean only (Previous) Mean + Variance (Ours) Direct illumination only

  26. 26 Contributions • Optimal sampling distribution • Learning the distribution through Bayesian inference Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  27. 27 Naive adaptive light sampling outlier MC estimates P 𝑀 1 𝑀 2 𝑀 3 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  28. 28 Bayesian adaptive light sampling outlier MC estimates P Model x Prior 𝑀 1 𝑀 2 𝑀 3 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  29. 29 Scene subdivided in regions Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  30. 30 Light-region statistics MC estimates 𝑒 region 𝑆 𝑒 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  31. 31 Regression data model Light-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

  32. 32 Conjugate prior 𝐪𝐩𝐭𝐮𝐟𝐬𝐣𝐩𝐬 ∝ likelihood × 𝐪𝐬𝐣𝐩𝐬 Same functional form Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  33. 33 Our (conjugate) priors 𝑞 0 ~ Beta 𝑞 0 … 𝑙, ℎ ~ Normal inverse gamma 𝑙, ℎ 𝜈 0 , … ) Hyperparameters Light contrib. estimate Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  34. 34 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 Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  35. 35 Scalability – Light clustering Technical detail – not essential for our take-home message Cluster contribution bounds MC estimate Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  36. 36 Results Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  37. 37 Tests Direct only Direct + indirect Simple occlusion Complex occlusion Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  38. 38 Direct illumination only

  39. Wang Ours Donikian 39 Robust 510x faster Wang RMSE time [min] Direct illumination only

  40. 40 Tests Direct only Direct + indirect  Simple occlusion Complex occlusion Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  41. 41 Direct + indirect illumination

  42. Wang Wang 42 6.7x faster 6.7x faster Ours Ours Direct + indirect illumination

  43. 43 Tests Direct only Direct + indirect   Simple occlusion Complex occlusion Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  44. 44 Direct illumination only

  45. 45 Wang Ours Donikian 9.3x faster Wang RMSE time [min] Direct illumination only

  46. 46 Wang Ours Donikian Robust Direct illumination only

  47. 47 Tests Direct only Direct + indirect   Simple occlusion  Complex occlusion Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  48. 48 Direct + indirect illumination

  49. 49 Ours Ours Wang Wang 4.3x faster 4.3x faster Direct + indirect illumination

  50. 50 Ours Wang Direct + indirect illumination

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

  52. 52 Direct illumination only

  53. 53 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

  54. 54 Tests Direct only Direct + indirect   Simple occlusion   Complex occlusion • Grid resolution  • Temporal coherence Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  55. Ours Wang 55 55 Direct illumination only

  56. 56 Contribution • Bayesian framework for robust adaptivity/guiding • Optimal sampling distribution • Algorithm for direct illumination – Unbiased, adaptive, robust – Easy to integrate Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

  57. 57 Acknowledgments • Ludvík Koutný (a.k.a. rawalanche) • Funding – Charles University: GAUK 1172416, SVV-2017-260452 – Czech Science Foundation: 16-18964S, 19-07626S. Vévoda, Kondapaneni, Křivánek - Bayesian online regression for adaptive illumination sampling

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