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On robust Monte Carlo algorithms for multi-pass global illumination

On robust Monte Carlo algorithms for multi-pass global illumination. Frank Suykens – De Laet 17 September 2002. Overview. Introduction Realistic image synthesis Global illumination Algorithms for global illumination Contributions Weighted multi-pass methods Path differentials

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On robust Monte Carlo algorithms for multi-pass global illumination

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  1. On robust Monte Carlo algorithms for multi-pass global illumination Frank Suykens – De Laet 17 September 2002

  2. Overview • Introduction • Realistic image synthesis • Global illumination • Algorithms for global illumination • Contributions • Weighted multi-pass methods • Path differentials • Density control for photon maps • Conclusion

  3. Overview • Introduction • Realistic image synthesis • Global illumination • Algorithms for global illumination • Contributions • Weighted multi-pass methods • Path differentials • Density control for photon maps • Conclusion

  4. Realistic image synthesis • Goal: Compute images that appear to an observer as real photographs Which one is real?

  5. Realistic image synthesis • Applications • Architecture • Movie industry • Lighting design • Computer games • Archeology • Product design • …

  6. Light Transport Simulation Compute illumination Realistic image synthesis Scene description Image

  7. Scene description • Geometry • Materials • Light sources • Camera / Eye Position, size, … (e.g., CAD)

  8. Scene description • Geometry • Materials • Light sources • Camera / Eye Diffuse paint, glass, metal, …  BSDF

  9. Materials: BSDF • Bidirectional scattering distribution function (reflection & transmission)   Fraction of incoming radiance L(x  ) that is scattered into the direction θ x

  10. BSDF Components Diffuse (D) Glossy (G) Specular (S) Diffuse, glossy and specular: (D|G|S) = X

  11. Scene description • Geometry • Materials • Light sources • Camera / Eye Position, brightness, spotlight, …

  12. Scene description • Geometry • Materials • Light sources • Camera / Eye Position, viewing angle, …

  13. Light Transport Simulation • Geometry • Materials • Light sources • Camera/Eye Realistic image synthesis Compute illumination Scene description Image

  14. Light Transport Simulation Compute illumination • For every pixel: how much light passes through? Account for all possible paths from light to eye!  Global illumination

  15. Light Transport Simulation Global illumination • Mathematical basis for light transport  L x Outgoing radianceL in x in direction θ ?  Rendering equation

  16. Light Transport Simulation  Lr Le   L x x Self emitted radiance Reflected (& refracted) radiance x Recursive Radiance Unknown incoming radiance BSDF Integration over all directions Rendering equation = +

  17. Light Transport Simulation Compute illumination • Geometry • Materials • Light sources • Camera/Eye Realistic image synthesis Scene description Image • Global illumination • Rendering equation

  18. Overview • Introduction • Realistic image synthesis • Global illumination • Algorithms for global illumination • Contributions • Weighted multi-pass methods • Path differentials • Density control for photon maps • Conclusion

  19. Example scene Many different illumination features: Indirect illumination Specular refraction Indirect caustics Caustics We want a full global illumination solution!

  20. Algorithms for global illumination • Computation: Numerical integration • Monte Carlo integration • Algorithms • Image space algorithms • Stochastic ray tracing • Particle tracing • Bidirectional path tracing • Object space algorithms • Radiosity

  21. Monte Carlo integration • Estimate integrals by random sampling • draw a number of random samples • average their contribution  estimate of integral • Statistical errors  Noise in images • Convergence: More samples, less noise

  22. Monte Carlo integration Stochastic ray tracing • Trace paths starting from the eye E L 9 paths/pixel

  23. Particle tracing • Trace paths starting from the light E L 9 paths/pixel Pattanaik ’92, Dutré ’93

  24. Bidirectional path tracing • Trace paths starting from the light AND the eye E L Lafortune ’93, Veach ’94

  25. Comparison Stochastic ray tracing (9 samples per pixel) Particle tracing (9 samples per pixel) Bidirectional path tracing (4 samples per pixel) Same computation time (± 5 min.)

  26. Radiosity methods • Object space method • Diffuse surfaces only • View independent Galerkin radiosity

  27. Overview • Introduction • Realistic image synthesis • Global illumination • Algorithms for global illumination • Contributions • Weighted multi-pass methods • Path differentials • Density control for photon maps • Conclusion

  28. Overview • Introduction • Realistic image synthesis • Global illumination • Algorithms for global illumination • Contributions • Weighted multi-pass methods • Path differentials • Density control for photon maps • Conclusion

  29. Multi-pass methods • Combine different algorithms • Separate light transport • Based on BSDF components • Different algorithms  different illumination • Preserve strengths of individual algorithms • Regular expressions (e.g., LD* , LX*E ) • derive path evaluation from regular expression

  30. E G|S D|G|S LD* Radiosity & stochastic ray tracing 1. Radiosity Use radiosity solution at end points 2. Stochastic ray tracing Full global illuminationbutdrawbacks of stoch. ray tracing LD*(G|S)X*E LX*E  Combine with bidirectional path tracing

  31. Multi-pass configuration Indirect diffuse Self-emitted light LDD+(G|S)X*E + LDD+E L(G|S)X*E LD(G|S)X*E + LDE Direct diffuse + + BPT Use weighting ??? Rad + SR

  32. Weighted multi-pass methods • Weighting instead of separation • allow overlapping transport between different algorithms • weight individual paths  automatic ‘separation’ • Technique • General Monte Carlo variance reduction technique • Constraints, weighting heuristics

  33. Results (unweighted)  Bidirectional path tracing Radiosity + stoch. ray tracing LD(G|S)X*E + LDE LD(G|S)X*E + LDE

  34. Results (weighted) + Bidirectional path tracing Radiosity + stoch. ray tracing LD(G|S)X*E + LDE

  35. Final result BPT only Weighted combination Radiosity + Stoch. RT and Bidirectional path tracing Radiosity + Stoch. RT

  36. Conclusion: WMP • Multi-pass methods • separation: path evaluation from regular expression • weighting: each path is weighted individually  automatic ‘separation’ • General technique • Robust combination of bidirectional path tracing and radiosity

  37. Overview • Introduction • Realistic image synthesis • Global illumination • Algorithms for global illumination • Contributions • Weighted multi-pass methods • Path differentials • Density control for photon maps • Conclusion

  38. Path differentials • Idea • Many algorithms trace paths • A path is infinitely thin: no neighborhood information • Knowledge about ‘region of influence’ or ‘footprint ’ would be useful in many applications: • bias-noise trade-off • Footprint definition • Path differentials

  39. Path footprint • Path = function of random variables • direction sampling, light source sampling, …

  40. Path footprint • Variables change  path perturbation

  41. Path footprint • Set of path perturbations  footprint

  42. Path differentials • Partial derivatives • approximate perturbations • combine into footprint (first order Taylor approx.) • footprint estimate from a single path!

  43. Applications • Path differentials widely applicable • Any Monte Carlo path sampling algorithm • Texture filtering • Hierarchical particle tracing radiosity • Importance maps

  44. Small elements  noise Large elements  blur fixed In which level should the particle contribute? Path differentials: size of footprint  size of element hierarchical Application: hierarchical radiosity • Particle tracing radiosity • Trace light paths • Each hit contributes to the illumination of the element L

  45. Application: hierarchical radiosity Fixed size (small) Fixed size (large) Path differentials

  46. Application: hierarchical radiosity Fixed size (small) Fixed size (large) Path differentials

  47. Conclusion: Path differentials • New, robust technique to compute path footprint • Handles general BSDFs, complex geometry • Many applications in global illumination

  48. Overview • Introduction • Realistic image synthesis • Global illumination • Algorithms for global illumination • Contributions • Weighted multi-pass methods • Path differentials • Density control for photon maps • Conclusion

  49. Photon mapping • Popular 2-pass global illumination algorithm • 1. Particle tracing • trace light paths Jensen ’96, …

  50. Photon mapping • Popular 2-pass global illumination algorithm • 1. Particle tracing • trace light paths • record all hitpoints  Set of photons: ‘Photon map’ Jensen ’96, …

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