1. Jiaping Wang 1 Peiran Ren 1,3 Minmin Gong 1 John Snyder 2 Baining Guo 1,3 1 Microsoft Research Asia 2 Microsoft Research 3 Tsinghua University

2. Complex, detailed reflectance  Spatial/temporal variation  All BRDF types: parametric ↔ measured isotropic ↔ anisotropic glossy ↔ mirror-like

3. Previous work Temporal Variation Spatial Variation static single BRDF SVBRDF dynamic

4. Previous work [Wang04] [Ng03] [Wang04] [Liu04] [Wang06] [Tsai06] [Krivanek08] Temporal Variation Spatial Variation static single BRDF SVBRDF dynamic

5. Previous work [Wang04] [Green06] [Green07] [Green06] Temporal Variation Spatial Variation static single BRDF SVBRDF dynamic

6. Previous work [Wang04] [Ben-Artzi06] [Sun07] [Ben-Artzi08] [Green06] [Ben-Artzi06] Temporal Variation Spatial Variation static single BRDF SVBRDF dynamic

7. Previous work [Wang04] [Green06] [Ben-Artzi06] Our method: - per-pixel SVBRDF - dynamic SVBRDF - all BRDF types - all-frequency Our method: - per-pixel SVBRDF - dynamic SVBRDF - all BRDF types - all-frequency [Wang09] Temporal Variation Spatial Variation static single BRDF SVBRDF dynamic

8. Rendering Equation  2D lighting  4D visibility  6D reflectance (SVBRDF) SVBRDF lightvisibility cosine o i n x

9. Precomputed Radiance Transfer  Dot product [Sloan et al. 2002] light transfer light

10. Precomputed Radiance Transfer  Dot product [Sloan et al. 2002]  Triple product [Ng et al. 2004 ] light transfer light Light Transport & Precomputed BRDF × cosine light visibility

11. Precomputed Radiance Transfer  Dot product [Sloan et al. 2002]  Triple product [Ng et al. 2004 ]  Ours method light transfer light BRDF × cosine light visibility light BRDFvisibilitycosine LT & P

12. Precomputed Radiance Transfer  Dot product [Sloan et al. 2002]  Triple product [Ng et al. 2004 ]  Ours method light transfer light BRDF × cosine light visibility light BRDFvisibilitycosine LT & P

13. Algorithm Overview Spherical Gaussians o

15. Algorithm Overview Spherical Gaussians SSDF o Environment

16. Dynamic, spatial varying BRDF

17. o Outline  Reflectance Representation Microfacet Model with SGs  Visibility Representation Signed Spherical Distance Function  Lighting & Rendering

18. o Outline  Reflectance Representation Microfacet Model with SGs  Visibility Representation Signed Spherical Distance Function  Lighting & Rendering

19. trivial rotation all-frequency signals intensity sharpness center Spherical Gaussian (SG)

20. trivial rotation all-frequency signals intensity sharpness center Spherical Gaussian (SG) inner product: vector product:

21. SG Mixtures Sum of Multiple SGs : Origina l SG, N = 7SG, N = 3SG, N = 1

22. Microfacet BRDF Model [Cook 82]  surface modeled by tiny mirror facets

23. Microfacet BRDF Model [Cook 82]  surface modeled by tiny mirror facets shadow term fresnel term normal distribution Represented by SG

24.  single-lobe, analytic approximation Cook-Torrance [Cook et al. 1981] Ward [Ward 1992] Blinn-Phong [Blinn 1977] Parametric Models

25. Parametric BRDFs

26. n u =8, n v =128 n u =25, n v =400 n u = 75, n v = 1200 7-lobe SGM ground truth Anisotropic Parametric Models

27. Measured BRDFs BRDF from [Matusik03] svBRDF from [Wang08] & [Lawance06]

28. Representation Efficiency  Parametric BRDF Texturing of original BRDF parameters isotropic : 7 float/texel: diffuse, specular, shininess Anisotropic: 8 float/texel: diffuse, specular, shininess u/v  Measured BRDF Texturing of SGs number of SGs Floats per SG floats per texel isotropic1-344~12 + 3 anisotropic2-7612~42 + 3

29. Normal Distribution in Half-vector Domain BRDF Slice in light-vector o BRDF Slices Half-vector Domain

30. SG Warping  SG not closed under  -1  approx. by per-SG warp of D *

31. SG Warping  SG not closed under  -1  approx. by per-SG warp of D *

32. Parametric svBRDF Painting

33. o Outline  Reflectance Representation Microfacet Model with SGs  Visibility Representation Signed Spherical Distance Function  Lighting & Rendering

34. Visibility at one point scene binary visibility function x V(x,i)

35. Visibility Prerequisite  Preserve sharp visibility boundary  inner product for Diffuse Term  vector product for Specular Term SGs ? ?

36. binary visibility, V(i) i0i0 i1i1 SSDF, V d (i) V d (i 1 ) V d (i 0 ) Spherical Signed Distance Function

37. SSDF-SG Product SSDFVisibility

38. SSDF-SG Product p p p SG centered at p SSDFVisibility p ≈ Approx. Visibility for p p

39. SSDF-SG Product p p p SG centered at p SSDFVisibility p ≈ Approx. Visibility for p =0.329 Inner product vector product

40. Per-pixel Shading & Shadowing

41. o Outline  Reflectance Representation Microfacet Model with SGs  Visibility Representation Signed Spherical Distance Function  Lighting & Rendering

42.  Point light  directional light Local Light Source

43. prefiltered MIPMAP [Kautz et al. 2000] SGs (10 lobes) [Tsai and Shih 2006] for diffuse shading for specular shading Environment Light

44. prefiltered MIPMAP [Kautz et al. 2000] SGs (10 lobes) [Tsai and Shih 2006] for diffuse shading for specular shading Environment Light

45. Environment + Local Lighting

46. Rendering Summary: Diffuse Microfacet Model Environment Light

47. Rendering Summary: Diffuse Microfacet Model Environment Light Visibility in SSDF ● BRDF Slice in SGs Cosine Term in SGs Environment in SGs

48. Rendering Summary: Specular Microfacet Model Environment Light BRDF Slice in SGs Cosine Term in SGs Visibility in SSDF Prefiltered Environment ●

49. Performance Summary SceneBRDF Type svBRDF Resolusion svBRDF Size Env. FPS Pt. FPS Teapot CT (iso. 1 SG) 1024×10247.2MB171250 Dragon Ward (iso. 1 SG) 512×5121.8MB165231 DishBall AS (aniso. 7 SGs) 512×10244.1MB5530 DishCard card(iso. 2 SGs) 512×5124.2MB satin(aniso. 5 SGs) 850×85022.4MB4835 velvet (aniso. 2SGs) 850×8509.4MB168145  Testing Machine Intel Core2 Duo 3.2G CPU, 4GB memory nVidia Geforce 8800 Ultra graphics card

50. Performance Summary SceneBRDF Type svBRDF Resolusion svBRDF Size Env. FPS Pt. FPS Teapot CT (iso. 1 SG) 1024×10247.2MB171250 Dragon Ward (iso. 1 SG) 512×5121.8MB165231 DishBall AS (aniso. 7 SGs) 512×10244.1MB5530 DishCard card(iso. 2 SGs) 512×5124.2MB satin(aniso. 5 SGs) 850×85022.4MB4835 velvet (aniso. 2SGs) 850×8509.4MB168145  Testing Machine Intel Core2 Duo 3.2G CPU, 4GB memory nVidia Geforce 8800 Ultra graphics card

51. bump maps dynamic BRDFs anisotropic BRDFs measured BRDFs All-Frequency Visual Effects

52. parametric BRDFs measured SVBRDFs Reflectance Painting

53. Conclusion  Overall method: glossy to mirror-like, detailed, dynamic reflectance all-frequency shadows real-time per-pixel shading  SG mixtures for microfacet-based reflectance compact yet accurate fast rotation, warping, products  SSDFs for visibility fast products with SG mixtures non-ghosting spatial interpolation

54. Conclusion  Overall method: glossy to mirror-like, detailed, dynamic reflectance all-frequency shadows real-time per-pixel shading  SG mixtures for microfacet-based reflectance compact yet accurate fast rotation, warping, products  SSDFs for visibility fast products with SG mixtures non-ghosting spatial interpolation

55. Future work  dynamic visibility  inter-reflection  anisotropic spherical Gaussian  SSDF compression  simpler SVBRDF acquisition

56. Future work  dynamic visibility  inter-reflection  anisotropic spherical Gaussian  SSDF compression  simpler SVBRDF acquisition

57. Thank you for your attention.

59. Visibility Cuts [Cheslack-Postava et al.2008]  Light-cut framework No highly glossy reflectance Highly tessellation Not real-time

60. SG Scaling  Shadowing and Fresnel terms  Assume low-frequency [Ashkmin01, Ngan05]  approx. by per-SG scale

61. SSDF Compression PCA: binary visibility SSDF compressed SSDF

62. Error sources  BRDF fitting error  diffuse light fitting error  SG warping error  SSDF-SG product error  SSDF compression error

63. SSDF-SG product error visibility function is approximate product is approximate inner product error typically less than 2% vector product error larger, but not visually significant error decreases as λ increases

64. SG mixtures N -lobe approximation violet-acrylic NDF [Ngan et al. 2005] origina l SG, N = 3 L2 = 6.2% SG, N = 2 L2 = 8.2% SG, N = 1 L2 = 25%

65. SG representation of lighting  distant light → environment map (EM) diffuse shading: ○ fit EM with SG mixture (10 lobes) [Tsai and Shih 2006] specular shading: ○ prefilter EM with SGs of various λ [Kautz et al. 2000]

66. EM Prefiltering with SGs … … MIPMAP of prefiltered cubemaps λ reduced by 1/4 per level λ =21000, level 1 λ =329, level 4 λ =5.1, level 7