Real-time Shading with Filtered Importance Sampling

1. Real-time Shading with Filtered Importance Sampling Jaroslav Křivánek Czech Technical University in Prague Mark Colbert University of Central Florida

2. Motivation • material design interfaces • rendering algorithm to back up the interface • immediate feedback Křivánek, ColbertReal-time shading with Filtered Importance Sampling

3. Goal • image-based lighting (environment maps) • improves material perception [Fleming et al. 2003] images [Fleming et al. 2003] natural light point light Křivánek, ColbertReal-time shading with Filtered Importance Sampling

4. Goal • arbitrary materials • low to high gloss, different BRDF models images by Pat Hanrahan Křivánek, ColbertReal-time shading with Filtered Importance Sampling

5. Goal • dynamic materials, geometry, lighting • no pre-computation • production pipeline friendly • minimal code base / single GPU shader • real-time shadows (env. map) • not necessarily Křivánek, ColbertReal-time shading with Filtered Importance Sampling

6. Desired Results Křivánek, ColbertReal-time shading with Filtered Importance Sampling

7. Related Work • pre-filtered environment maps [ Kautz et al. 2000 ] • frequency-space rendering [ Ramamoorthi et al. 2002 ], [ Ng et al. 2004 ] • Efficient Reflectance and Visibility Approximations for Environment Map Rendering [ Green et al. 2007 ] • Efficient Rendering of Spatial Bi-directional Reflectance Distribution Functions[ McAllister et al. 2002 ] Křivánek, ColbertReal-time shading with Filtered Importance Sampling

8. Overview • Motivation • Goal • Related Work • Shading Algorithm • Theory • Real-time Shadows • Results • Conclusion Křivánek, ColbertReal-time shading with Filtered Importance Sampling

9. BRDF Importance Sampling • standard in MC ray tracing • not used on the GPU Křivánek, ColbertReal-time shading with Filtered Importance Sampling

10. Deterministic Sampling • aliasing 40 samples per pixel Křivánek, ColbertReal-time shading with Filtered Importance Sampling

11. Our Approach filtered importance sampling less filtering where samples are denser more filtering where they are sparser 1 » filter size w w N p ( , ) i o Křivánek, ColbertReal-time shading with Filtered Importance Sampling

12. Filtering • MIP-maps • level proportional to log of filter size • independent of the BRDF Křivánek, ColbertReal-time shading with Filtered Importance Sampling

13. Filtered Importance Sampling 40 samples per pixel Křivánek, ColbertReal-time shading with Filtered Importance Sampling

14. Overview • Motivation • Goal • Related Work • Shading Algorithm • Theory • Real-time Shadows • Results • Conclusion Křivánek, ColbertReal-time shading with Filtered Importance Sampling

15. Underlying Theory • why theory? • identify approximations • suggest improvements • … sampling & filtering • signal processing Křivánek, ColbertReal-time shading with Filtered Importance Sampling

16. Sampling and Reconstruction alias = integration error Ä ´ DC-term = integral sample reconstruct aliased original Křivánek, ColbertReal-time shading with Filtered Importance Sampling 16

17. Application to Importance Sampling • problem: non-uniform samples Křivánek, ColbertReal-time shading with Filtered Importance Sampling

18. warp (inverse BRDF IS) pre-filter (=convolve) warp back (BRDF IS) Conceptual Procedure Křivánek, ColbertReal-time shading with Filtered Importance Sampling

19. Practice • isotropic filter approximation Křivánek, ColbertReal-time shading with Filtered Importance Sampling 19

20. Approximations • isotropic filter shape • constant BRDF / PDF ratio across filter support • tri-linear filtering (MIP-map) Křivánek, ColbertReal-time shading with Filtered Importance Sampling

21. Anisotropic Filtering Experiments • anisotropic filter approximation Křivánek, ColbertReal-time shading with Filtered Importance Sampling 21

22. Anisotropic Filtering Experiments 16x anisotropic filter tex2Dgrad for anisotropic texture look-up worse image quality – still don’t know why Křivánek, ColbertReal-time shading with Filtered Importance Sampling 22

23. Overview • Motivation • Goal • Related Work • Shading Algorithm • Theory • Real-time Shadows • Results • Conclusion Křivánek, ColbertReal-time shading with Filtered Importance Sampling

24. Real-time Shadows environment importance sampling (bright light sources = strongest shadows) Křivánek, ColbertReal-time shading with Filtered Importance Sampling

25. Real-time Shadows shadow map for each sample Křivánek, ColbertReal-time shading with Filtered Importance Sampling

26. Real-time Shadows visibility function convert to spherical harmonics at each texel Křivánek, ColbertReal-time shading with Filtered Importance Sampling

27. Real-time Shadows • spatial filtering no filtering after filtering Křivánek, ColbertReal-time shading with Filtered Importance Sampling

28. Real-time Shadows • use for rendering • diffuse • SH coefficient dot product • glossy • attenuate each sample by the visibility Křivánek, ColbertReal-time shading with Filtered Importance Sampling

29. Overview Motivation Goal Related Work Shading Algorithm Theory Real-time Shadows Results Conclusion Křivánek, ColbertReal-time shading with Filtered Importance Sampling 29

30. FIS Results – RMS Environment Sampling Reference Filtered Sampling n = 3 5 Samples n = 17 100 Samples Křivánek, ColbertReal-time shading with Filtered Importance Sampling

31. FIS Results – Complex Geometry 5 Samples 50 Samples 50 Samples 200 Samples Reference Křivánek, ColbertReal-time shading with Filtered Importance Sampling

32. FIS Results – BRDF Anisotropy limited anisotropy ax = 0.01 ax = 0.01 ax = 0.01 ax = 0.08 ax = 0.01 ax = 0.29 Křivánek, ColbertReal-time shading with Filtered Importance Sampling

33. Shadows Results Reference (30,000 Samples) Our Method (16 Samples) Visual Error SH v. Ref 8 samples 16 samples 64 samples Křivánek, ColbertReal-time shading with Filtered Importance Sampling

34. Shadows Performance • NVIDIA GeForce 8800 GTX, Intel Core2 Duo, 512x512 Křivánek, ColbertReal-time shading with Filtered Importance Sampling

35. NVIDIA GeForce 8800 GTX, Intel Core2 Duo, 512x512 Shadows Performance polygon count Křivánek, ColbertReal-time shading with Filtered Importance Sampling 35

36. Video Křivánek, ColbertReal-time shading with Filtered Importance Sampling

37. Conclusion • glossy surface shading • practical, relatively accurate, no pre-computation • signal processing theory • shadows • fast but very approximate • no pre-computation • implementation details: GPU Gems 3 • Code: graphics.cs.ucf.edu/gpusampling/ Křivánek, ColbertReal-time shading with Filtered Importance Sampling

38. Acknowledgements • Dan Sýkora • Petr Olšák • Czech Ministry of Education • “Center for Computer Graphics” • Aktion grant • US NationalScience Foundation Křivánek, ColbertReal-time shading with Filtered Importance Sampling

39. Additional Slides

40. Numerical Integration as Signal Reconstruction • integral = DC term • integration by sampling • sample the function • reconstruct the DC term • insufficient sampling -> aliasing • alias may affect the DC term -> error • anti-aliasing – pre-filtering Křivánek, ColbertReal-time shading with Filtered Importance Sampling

41. Ä ´ ´ Anti-aliasing by Pre-filtering band-limit sample reconstruct Křivánek, ColbertReal-time shading with Filtered Importance Sampling

42. Stochastic Sampling noise slower on the GPU 40 samples per pixel Křivánek, ColbertReal-time shading with Filtered Importance Sampling 42