On the Scattering          of light
Scattering             http://photosozai-database.com/modules/photo/photo.php?lid=664
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                Volumetric scatter...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                 Volumetric scatte...
Outline                          • Reflection                 • Why BSSDRF is bad?                             – Diffuse r...
ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSR...
Diffuse reflection 拡散反射                          • ConstantReflectionDiffuse reflection                            irradia...
Specular reflection 鏡面反射                          • Angle of reflection                             – is the angle of     ...
Diffuse + SpecularReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmission...
Diffuse + Specular ?                                                     𝜔                                        𝜔Reflect...
BRDF                          • Bidirectional                            Reflectance                            Distributi...
Eurographics Association Aire-la-Ville, Switzerland, Switzerland ©2003                           Isotropic BRDF measuremen...
Copyright © by Authors     Anisotropic BRDF武田 祐樹, 坂口 嘉之, 田中 弘美, 少数視点画像の反射光解析に基づくシルクライク織物の異方性反射レンダリング, 芸術科学会論文誌, Vol. 7, No...
Refraction 回折 Transmission 透過                          • Transmitted light                             – TranslucentReflec...
Specular Transmission 鏡面透過                          • Angle of refraction                             – depends onReflecti...
Diffuse transmission 拡散透過                          • Constant                            irradianceReflectionDiffuse refle...
Diffuse + Specular transmissiona light bulb                     frosted glass
BTDF                          • Bidirectional                            TransmittanceReflectionDiffuse reflection        ...
Reflection + Transmission                          • Reflection                            – BRDFReflectionDiffuse reflect...
Subsurface scattering 表面下散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular tra...
Subsurface scattering                          • Scattering                             – Inside mediumReflectionDiffuse r...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Surface reflectionHenrik Wann Jensen, St...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Subsurface scatteringHenrik Wann Jensen,...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                               Surface            ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                               Surface Subsurface ...
Single scattering 単散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmiss...
Single scattering 単散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmiss...
Double scattering 二重散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmis...
Multiple scattering 多重散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transm...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Multiple scattering onlyHenrik Wann Jens...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Single scattering onlyHenrik Wann Jensen...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Single + Multiple scattering + Fresnel  ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                         Multiple ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
BSSRDF                          • Bidirectional                            Scattering Surface                            R...
SSSID                          • Sub-Surface                            Scattering Irradiance                            D...
ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSR...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                           Dipole ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Multiple scattering with Dipole modelHen...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Single scatteringHenrik Wann Jensen, Ste...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                          Multipole model         ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                           Multipo...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Dipole approximationCraig Donner and Hen...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Multipole approximationCraig Donner and ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Dipole approximation          Multipole ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Dipole approximation           Finite-th...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Multipole approximation           Finite...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Dipole approximation           Finite-th...
Plane-parallel approximation                          • Dipole                             – Plane, semi-infinite,        ...
Copyright © 画像電子学会および(社)情報処理学会                        Analytic solution to plane-parallel             Integro-differential...
Copyright ©一般社団法人 画像電子学会,(社)情報処理学会および(社)映像情報メディア学会                                          Anisotropic Plane-parallel mod...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                           Empiric...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                               Sin...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                Single scattering + Dipole modelCr...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).              Single scattering + Empirical BSSRDF...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                               Mon...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).                                                  ...
ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSR...
BRDF                          • 6 parameters                            – Point 𝑥                    𝜔                    ...
BRDF, OK!                          • BRDF                            – Works for a point            𝜔                     ...
BSSRDF                          • 8 parameters                            – Points of incidence   𝜔Reflection             ...
BSSRDF ?                          • 8 parameters                            – Points of incidence    𝜔Reflection          ...
BSSRDF ?                          • 8 parameters                            – Points of incidence    𝜔Reflection          ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).          Single scattering vs BSSRDF             ...
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).   Curvature dependent BRDF   • Light is reflected...
Curvature dependent BRDF   • Light is reflected             – Even when               𝜃 > 180°                            ...
Curvature dependent BRDF   • Light is reflected             – Even when               𝜃 > 180°                            ...
ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSR...
BSSRDF                          • Subsurface                            scattering           𝜔ReflectionDiffuse reflection...
Scattering model                          • Volumetric                            scatteringReflectionDiffuse reflectionSp...
Scattering model                          • Volumetric                            scatteringReflectionDiffuse reflectionSp...
Scattering modelReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBT...
Scattering modelReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBT...
Rendering by ray marchingReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular trans...
Light in participating medium                                                  Absorption 吸収Reflection                 Att...
Absorption                                                                  𝐿                       𝐿ReflectionDiffuse ref...
Absorption                                                                    𝐿                       𝐿ReflectionDiffuse r...
Absorption                                                                    𝐿                       𝐿ReflectionDiffuse r...
Absorption                                                           𝐿                 𝐿ReflectionDiffuse reflectionSpecul...
Absorption                                                    𝐿 + 𝑑𝐿                 𝐿ReflectionDiffuse reflectionSpecular...
Absorption                                                         𝐿 + 𝑑𝐿                 𝐿ReflectionDiffuse reflectionSpe...
Absorption                                                         𝐿 + 𝑑𝐿                 𝐿ReflectionDiffuse reflectionSpe...
Out-scattering                                                         𝐿 + 𝑑𝐿                 𝐿ReflectionDiffuse reflectio...
Attenuation = absorption + out-scattering                                                        𝐿 + 𝑑𝐿                 𝐿R...
Emission                                                𝐿 + 𝑑𝐿                 𝐿ReflectionDiffuse reflectionSpecular refle...
In-scattering                                                         𝜔                                                   ...
Rendering equation                                                            𝜔                                           ...
Rendering equation                                                            𝜔                                           ...
Rendering equation                                                                           𝜔                            ...
© Copyright 2011 IEEE – All Rights Reserved                                           Airlight approximation to in-scatter...
Born series                          zero-order Born approximation (no scattering)                                        ...
Born approximation                          Born approximation of scattering term                               𝐿 = 𝐿− 𝐿Re...
Neumann series                                                               Incident light                               ...
Neumann series                                                                Incident light                              ...
Mukaigawa series                          Neumann series of volume rendering equation                                     ...
Copyright © by Authors                          Single, double, triple, … scatteringReflectionDiffuse reflectionSpecular r...
Copyright © by AuthorsDecomposition into each             scattering     向川康博,ラメシュラスカル,八木康史, "散乱媒体中のライトトランスポートの解析, MIRU201...
Outline                          • Reflection                 • Why BSSDRF is bad?                             – Diffuse r...
On the Scattering          of light
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On the scattering of light : various models and methods used in computer graphics and computer vision

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On the scattering of light : various models and methods used in computer graphics and computer vision

  1. 1. On the Scattering of light
  2. 2. Scattering http://photosozai-database.com/modules/photo/photo.php?lid=664
  3. 3. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Volumetric scattering in CG 1987 1993 1994Tomoyuki Nishita, Yasuhiro Miyawaki, and Eihachiro Nakamae. 1987. A shading model for atmosphericscattering considering luminous intensity distribution of light sources. SIGGRAPH Comput. Graph. 21,4 (August 1987), 303-310. DOI=10.1145/37402.37437 http://doi.acm.org/10.1145/37402.37437 Tomoyuki Nishita, Takao Sirai, Katsumi Tadamura, and Eihachiro Nakamae. 1993. Display of the earth taking into account atmospheric scattering. In Proceedings of the 20th annual conference on Computer graphics and interactive techniques (SIGGRAPH 93). ACM, New York, NY, USA, 175-182. DOI=10.1145/166117.166140 http://doi.acm.org/10.1145/166117.166140 Tomoyuki Nishita and Eihachiro Nakamae. 1994. Method of displaying optical effects within water using accumulation buffer. In Proceedings of the 21st annual conference on Computer graphics and interactive techniques (SIGGRAPH 94). ACM, New York, NY, USA, 373-379. DOI=10.1145/192161.192261 http://doi.acm.org/10.1145/192161.192261
  4. 4. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Volumetric scattering in CG 2010 1996Tomoyuki Nishita, Yoshinori Dobashi, and Eihachiro Nakamae. 1996. Display of clouds taking intoaccount multiple anisotropic scattering and sky light. In Proceedings of the 23rd annual conference onComputer graphics and interactive techniques (SIGGRAPH 96). ACM, New York, NY, USA, 379-386.DOI=10.1145/237170.237277 http://doi.acm.org/10.1145/237170.237277 Yonghao Yue, Kei Iwasaki, Bing-Yu Chen, Yoshinori Dobashi, and Tomoyuki Nishita. 2010. Unbiased, adaptive stochastic sampling for rendering inhomogeneous participating media. ACM Trans. Graph. 29, 6, Article 177 (December 2010), 8 pages. In ACM SIGGRAPH Asia 2010 papers (SIGGRAPH ASIA 10). DOI=10.1145/1882261.1866199 http://doi.acm.org/10.1145/1882261.1866199
  5. 5. Outline • Reflection • Why BSSDRF is bad? – Diffuse reflection – Specular reflection • Scattering modelReflection – BRDF – Participating mediumDiffuse reflectionSpecular reflection • Transmission • AbsorptionBRDFTransmission – Diffuse transmission • EmissionDiffuse transmission – Specular transmission • In-scatteringSpecular transmission • Out-scatteringBTDF – BTDFScattering – Rendering equationsBSSRDF Dipole/Multipole • Scattering • Airlight approximation Plane-parallel Empirical BSSRDF – BSSRDF • Born seriesWhy BSSDRF is bad? • Dipole/Multipole • Neumann seriesScattering modelParticipating medium • Plane-parallel • M’s series Absorption approximation Emission • Empirical BSSRDF In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  6. 6. ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel REFLECTION, Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium TRANSMISSION, AND Absorption Emission In-scattering Out-scattering SCATTERING OF LIGHTRendering equations Airlight approximation Born series Neumann series M’s series
  7. 7. Diffuse reflection 拡散反射 • ConstantReflectionDiffuse reflection irradianceSpecular reflectionBRDFTransmission – Independent toDiffuse transmissionSpecular transmission viewpointBTDFScatteringBSSRDF • Pure diffuse Dipole/Multipole Plane-parallel Empirical BSSRDF surfaceWhy BSSDRF is bad?Scattering model – LambertianParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  8. 8. Specular reflection 鏡面反射 • Angle of reflection – is the angle of incidenceReflection 𝜃Diffuse reflectionSpecular reflection • HighlightsBRDFTransmission – More reflection nearDiffuse transmissionSpecular transmission to the angle ofBTDF reflectionScatteringBSSRDF Dipole/Multipole • Model Plane-parallel Empirical BSSRDF – PhongWhy BSSDRF is bad?Scattering model – BlinnParticipating medium Absorption Emission – Cook-Trrance In-scattering Highlights Out-scattering – Trrance-SparrowRendering equations Airlight approximation Born series Neumann series Mirror M’s series
  9. 9. Diffuse + SpecularReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  10. 10. Diffuse + Specular ? 𝜔 𝜔ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDF 𝑥ScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  11. 11. BRDF • Bidirectional Reflectance Distribution 𝜔 𝜔ReflectionDiffuse reflection FunctionSpecular reflection – 双方向反射率分布BRDFTransmission 関数Diffuse transmissionSpecular transmission • 6 parameters 𝑥BTDFScattering – Point 𝑥BSSRDF Dipole/Multipole – angles of incidence Plane-parallel Empirical BSSRDF 𝜔 and reflection 𝜔Why BSSDRF is bad?Scattering model • If isotropic andParticipating medium Absorption homogeneous Emission In-scattering – 3 parameters Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  12. 12. Eurographics Association Aire-la-Ville, Switzerland, Switzerland ©2003 Isotropic BRDF measurementWojciech Matusik, Hanspeter Pfister, Matthew Brand, and Leonard McMillan. 2003. Efficient isotropicBRDF measurement. In Proceedings of the 14th Eurographics workshop on Rendering (EGRW 03).Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 241-247.
  13. 13. Copyright © by Authors Anisotropic BRDF武田 祐樹, 坂口 嘉之, 田中 弘美, 少数視点画像の反射光解析に基づくシルクライク織物の異方性反射レンダリング, 芸術科学会論文誌, Vol. 7, No. 4, pp.132-143, 2008 .
  14. 14. Refraction 回折 Transmission 透過 • Transmitted light – TranslucentReflection materialsDiffuse reflectionSpecular reflectionBRDF – All non-metalsTransmissionDiffuse transmissionSpecular transmission • RefractionBTDFScatteringBSSRDF – Snell’s low Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  15. 15. Specular Transmission 鏡面透過 • Angle of refraction – depends onReflection • the angle ofDiffuse reflectionSpecular reflection incidenceBRDFTransmission • the indexes ofDiffuse transmissionSpecular transmission refraction of twoBTDFScattering materialsBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  16. 16. Diffuse transmission 拡散透過 • Constant irradianceReflectionDiffuse reflection – Independent toSpecular reflectionBRDF viewpoint insideTransmissionDiffuse transmission the materialSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  17. 17. Diffuse + Specular transmissiona light bulb frosted glass
  18. 18. BTDF • Bidirectional TransmittanceReflectionDiffuse reflection DistributionSpecular reflectionBRDF FunctionTransmissionDiffuse transmissionSpecular transmission – 双方向透過率分布BTDFScattering 関数BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  19. 19. Reflection + Transmission • Reflection – BRDFReflectionDiffuse reflection • TransmissionSpecular reflectionBRDFTransmission – BTDFDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  20. 20. Subsurface scattering 表面下散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  21. 21. Subsurface scattering • Scattering – Inside mediumReflectionDiffuse reflection – Some come theSpecular reflectionBRDF surfaceTransmissionDiffuse transmission – Some absorbedSpecular transmissionBTDFScatteringBSSRDF • Outgoing light Dipole/Multipole Plane-parallel – From a point Empirical BSSRDFWhy BSSDRF is bad? different from theScattering modelParticipating medium Absorption incident point Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  22. 22. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface reflectionHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  23. 23. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Subsurface scatteringHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  24. 24. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface SubsurfaceHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  25. 25. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface reflectionHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  26. 26. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Subsurface scatteringHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  27. 27. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface SubsurfaceHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  28. 28. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface reflectionHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  29. 29. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Subsurface scatteringHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  30. 30. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface Subsurface Surface reflectionHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  31. 31. Single scattering 単散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  32. 32. Single scattering 単散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  33. 33. Double scattering 二重散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  34. 34. Multiple scattering 多重散乱ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  35. 35. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multiple scattering onlyHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  36. 36. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering onlyHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  37. 37. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single + Multiple scattering + Fresnel reflectionHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  38. 38. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multiple Single Single scattering scattering scattering + Multiple scattering only only + Fresnel reflectionHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  39. 39. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single + Multiple scatteringCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  40. 40. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering onlyCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  41. 41. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single Single scattering scattering + only Multiple scatteringCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  42. 42. BSSRDF • Bidirectional Scattering Surface Reflectance 𝜔ReflectionDiffuse reflection Distribution FunctionSpecular reflection – 双方向散乱面(深層散 𝜔BRDFTransmission 乱)反射率分布関数Diffuse transmissionSpecular transmissionBTDF • 8 parameters 𝑥 𝑥ScatteringBSSRDF – Points of incidence 𝑥 Dipole/Multipole and outgoing 𝑥 , Plane-parallel Empirical BSSRDF angles of incidence 𝜔Why BSSDRF is bad?Scattering model and outgoing 𝜔Participating medium Absorption • If isotropic and Emission In-scattering homogeneous Out-scatteringRendering equations – 5 parameters Airlight approximation Born series Neumann series M’s series
  43. 43. SSSID • Sub-Surface Scattering Irradiance Distribution 𝜔ReflectionDiffuse reflection – 表面下放射照度分布Specular reflectionBRDF • Outgoing lightTransmissionDiffuse transmission – Diffuse transmissionSpecular transmissionBTDF – Independent to 𝑥 𝑥ScatteringBSSRDF viewpoint Dipole/Multipole Plane-parallel • 3 parameters Empirical BSSRDFWhy BSSDRF is bad? – Isotropic andScattering modelParticipating medium homogeneous Absorption Emission – Point of outgoing 𝑥 , In-scattering angle of incidence 𝜔 Out-scatteringRendering equations Airlight approximation Born series Neumann series 高村 幸平, 真鍋 知久, 玉木 徹, 金田 和文 : 「表面下散乱シミュレーションと放射照度分布 特性を考慮した表示モデル」, 電子情報通信学会技術報告パターン認識・メディア理解研究 M’s series 会 PRMU2009-77, Vol.109, No.249, pp.37-42, 広島大学, 広島(2009 10).
  44. 44. ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel SUBSURFACE SCATTERING Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering MODELS Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  45. 45. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Dipole model • Homogeneous and semi-infinite medium • Single scattering + Reflection multiple scattering Diffuse reflection (isometric and diffusion) Specular reflection BRDF Transmission Diffuse transmission • Sum of two terms Specular transmission BTDF – Each represents a Scattering virtual point light source BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann seriesHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics M’s seriesand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  46. 46. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multiple scattering with Dipole modelHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  47. 47. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scatteringHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphicsand interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  48. 48. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multipole model • Finite thickness – Infinite sum ofReflection DipolesDiffuse reflectionSpecular reflectionBRDF – A multipole modelTransmissionDiffuse transmissionSpecular transmission • Finite-thick layersBTDFScatteringBSSRDF – The use of some Dipole/Multipole Plane-parallel Multipole models Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series Craig Donner and Henrik Wann Jensen. 2005. Light diffusion in multi-layered translucent materials. ACM Trans. Graph. 24, 3 (July 2005), 1032-1039. In ACM SIGGRAPH 2005 Papers (SIGGRAPH 05). M’s series DOI=10.1145/1073204.1073308
  49. 49. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multipole approximation of human skin layers Backlight SidelightCraig Donner and Henrik Wann Jensen. 2005. Light diffusion in multi-layered translucent materials.ACM Trans. Graph. 24, 3 (July 2005), 1032-1039. In ACM SIGGRAPH 2005 Papers (SIGGRAPH 05).DOI=10.1145/1073204.1073308
  50. 50. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Dipole approximationCraig Donner and Henrik Wann Jensen. 2005. Light diffusion in multi-layered translucent materials.ACM Trans. Graph. 24, 3 (July 2005), 1032-1039. In ACM SIGGRAPH 2005 Papers (SIGGRAPH 05).DOI=10.1145/1073204.1073308
  51. 51. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multipole approximationCraig Donner and Henrik Wann Jensen. 2005. Light diffusion in multi-layered translucent materials.ACM Trans. Graph. 24, 3 (July 2005), 1032-1039. In ACM SIGGRAPH 2005 Papers (SIGGRAPH 05).DOI=10.1145/1073204.1073308
  52. 52. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Dipole approximation Multipole approximationCraig Donner and Henrik Wann Jensen. 2005. Light diffusion in multi-layered translucent materials.ACM Trans. Graph. 24, 3 (July 2005), 1032-1039. In ACM SIGGRAPH 2005 Papers (SIGGRAPH 05).DOI=10.1145/1073204.1073308
  53. 53. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Dipole approximation Finite-thick medium (paper)Craig Donner and Henrik Wann Jensen. 2005. Light diffusion in multi-layered translucent materials.ACM Trans. Graph. 24, 3 (July 2005), 1032-1039. In ACM SIGGRAPH 2005 Papers (SIGGRAPH 05).DOI=10.1145/1073204.1073308
  54. 54. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multipole approximation Finite-thick medium (paper)Craig Donner and Henrik Wann Jensen. 2005. Light diffusion in multi-layered translucent materials.ACM Trans. Graph. 24, 3 (July 2005), 1032-1039. In ACM SIGGRAPH 2005 Papers (SIGGRAPH 05).DOI=10.1145/1073204.1073308
  55. 55. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Dipole approximation Finite-thick medium (paper) Multipole approximationCraig Donner and Henrik Wann Jensen. 2005. Light diffusion in multi-layered translucent materials.ACM Trans. Graph. 24, 3 (July 2005), 1032-1039. In ACM SIGGRAPH 2005 Papers (SIGGRAPH 05).DOI=10.1145/1073204.1073308
  56. 56. Plane-parallel approximation • Dipole – Plane, semi-infinite, homogeneous Single layer, semi-infiniteReflectionDiffuse reflectionSpecular reflection • MultipoleBRDFTransmission – Finite homogeneousDiffuse transmissionSpecular transmission layersBTDF • Plane-parallel Finite-thick layersScatteringBSSRDF Dipole/Multipole – Layered Plane-parallel Empirical BSSRDF homogeneousWhy BSSDRF is bad?Scattering model – Depends on theParticipating medium Absorption depth 𝑧 from the Layered homogeneous Emission In-scattering surface Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  57. 57. Copyright © 画像電子学会および(社)情報処理学会 Analytic solution to plane-parallel Integro-differential equation Integro-ordinary differential equationReflection Diffuse reflection Discretization Specular reflection BRDF EigenfunctionTransmission Eigensolution Diffuse transmission Specular transmission BTDFScattering Eigenvalue BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering model Participating medium Absorption Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series新谷 幹夫, 白石 路雄, 土橋 宜典, 岩崎 慶, 西田 友是, "固有解を用いた表面下散乱の高速表示", M’s series / グラフィクスと CAD 合同シンポジウム 2008, 2008. Visual Computing http://nis-lab.is.s.u-tokyo.ac.jp/nis/abs_cgi.html#ipsj09-2
  58. 58. Copyright ©一般社団法人 画像電子学会,(社)情報処理学会および(社)映像情報メディア学会 Anisotropic Plane-parallel model 新谷 幹夫,白石 路雄, 土橋 宜典,岩崎 慶,西田 友是, "異方性Plane-Parallel散乱モデルによる毛髪 状物体の高速レンダリング", Visual Computing / グラフィクスと CAD 合同シンポジウム 2010, 2010. Reflection Diffuse reflection Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering Out-scattering Rendering equations Airlight approximationNelson Max, Suguru Saito, Kazuya Watanabe, Masayuki Nakajima, "Rendering Grass Blowing in The Born seriesWind with Global Illumination", Pacific Graphics 2009, 2009. Neumann seriesNelson Max, Kazuya Watanabe, Suguru Saito, Masayuki Nakajima, "Plane-Parallel Radiance Transportfor Rendering Grass Blowing in The Wind", Visual Computing / グラフィクスと CAD 合同シンポジウム M’s series2009, 2009.
  59. 59. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Empirical BSSRDF model • Simulating 5D • Semi-infinite parameters of 𝜔 homogeneousReflection Diffuse reflection BSSRDF plane medium Specular reflection – 6 parameters 𝜔 BRDFTransmission Diffuse transmission – 0.85 million Specular transmission 𝑥 𝑥 BTDFScattering patterns BSSRDF Dipole/Multipole Plane-parallel • Function fitting Empirical BSSRDFWhy BSSDRF is bad?Scattering model – Each incident / Participating medium Absorption outgoing angles / Emission In-scattering points Out-scattering Rendering equations Airlight approximation – 36GB data Born series Neumann seriesCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 M’s seriespages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  60. 60. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering onlyCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  61. 61. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering + Dipole modelCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  62. 62. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering + Empirical BSSRDFCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  63. 63. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Monte Carlo MethodCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  64. 64. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single Monte Carlo scattering simulation + Empirical BSSRDFCraig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, andShree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH 09). DOI=10.1145/1531326.1531336
  65. 65. ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel BSSRDF, Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering A WRONG MODEL Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  66. 66. BRDF • 6 parameters – Point 𝑥 𝜔 𝜔ReflectionDiffuse reflection – angles of incidenceSpecular reflectionBRDF 𝜔 and reflectionTransmissionDiffuse transmission 𝜔Specular transmissionBTDF 𝑥ScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  67. 67. BRDF, OK! • BRDF – Works for a point 𝜔 on a curved 𝜔ReflectionDiffuse reflectionSpecular reflection surfaceBRDFTransmissionDiffuse transmission – Angles relative toSpecular transmissionBTDF the normal of the 𝑥ScatteringBSSRDF point Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  68. 68. BSSRDF • 8 parameters – Points of incidence 𝜔Reflection 𝑥 and outgoing 𝑥 ,Diffuse reflectionSpecular reflection angles of incidence 𝜔BRDFTransmissionDiffuse transmission 𝜔 and outgoingSpecular transmissionBTDF 𝜔 𝑥 𝑥ScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  69. 69. BSSRDF ? • 8 parameters – Points of incidence 𝜔Reflection 𝑥 and , NG : curved surfaceDiffuse reflectionSpecular reflection angles of incidence 𝜔BRDFTransmissionDiffuse transmission 𝜔 and outgoingSpecular transmissionBTDF 𝜔 𝑥 𝑥ScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  70. 70. BSSRDF ? • 8 parameters – Points of incidence 𝜔Reflection 𝑥 and , NG : curved surfaceDiffuse reflectionSpecular reflection angles of incidence 𝜔BRDFTransmissionDiffuse transmission 𝜔 and outgoingSpecular transmissionBTDF 𝜔 𝑥 𝑥ScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations NG : transmission Airlight approximation Born series Neumann series M’s series
  71. 71. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering vs BSSRDF Blurred by Transmitted light BSSRDF No light transmission Single scattering only Multiple scattering onlyHenrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical modelfor subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics with dipole modeland interactive techniques (SIGGRAPH 01). ACM, New York, NY, USA, 511-518.
  72. 72. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Curvature dependent BRDF • Light is reflected – Even when 𝜃 > 180° 𝜃 < 180°Hiroyuki Kubo, Yoshinori Dobashi, and Shigeo Morishima. 2010. Curvature-dependent reflectance function for rendering translucent materials. In ACM SIGGRAPH 2010Talks (SIGGRAPH 10). ACM, New York, NY, USA, , Article 46 , 1 pages. DOI=10.1145/1837026.1837086 http://doi.acm.org/10.1145/1837026.1837086久保 尋之, 土橋 宜典, 森島 繁生, "半透明物体の高速描画に向けた曲率に依存する反射関数の近似式", Visual Computing / グラフィクスと CAD 合同シンポジウム2010, 2010.
  73. 73. Curvature dependent BRDF • Light is reflected – Even when 𝜃 > 180° 𝜃 = 180°Hiroyuki Kubo, Yoshinori Dobashi, and Shigeo Morishima. 2010. Curvature-dependent reflectance function for rendering translucent materials. In ACM SIGGRAPH 2010Talks (SIGGRAPH 10). ACM, New York, NY, USA, , Article 46 , 1 pages. DOI=10.1145/1837026.1837086 http://doi.acm.org/10.1145/1837026.1837086久保 尋之, 土橋 宜典, 森島 繁生, "半透明物体の高速描画に向けた曲率に依存する反射関数の近似式", Visual Computing / グラフィクスと CAD 合同シンポジウム2010, 2010.
  74. 74. Curvature dependent BRDF • Light is reflected – Even when 𝜃 > 180° 𝜃 > 180°Hiroyuki Kubo, Yoshinori Dobashi, and Shigeo Morishima. 2010. Curvature-dependent reflectance function for rendering translucent materials. In ACM SIGGRAPH 2010Talks (SIGGRAPH 10). ACM, New York, NY, USA, , Article 46 , 1 pages. DOI=10.1145/1837026.1837086 http://doi.acm.org/10.1145/1837026.1837086久保 尋之, 土橋 宜典, 森島 繁生, "半透明物体の高速描画に向けた曲率に依存する反射関数の近似式", Visual Computing / グラフィクスと CAD 合同シンポジウム2010, 2010.
  75. 75. ReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel SCATTERING, Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering A CORRECT WAY Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  76. 76. BSSRDF • Subsurface scattering 𝜔ReflectionDiffuse reflectionSpecular reflection 𝜔BRDFTransmissionDiffuse transmissionSpecular transmissionBTDF 𝑥 𝑥ScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission Translucent material In-scattering 半透明物質 Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  77. 77. Scattering model • Volumetric scatteringReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission Participating medium In-scattering 関与媒質 Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  78. 78. Scattering model • Volumetric scatteringReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission Participating medium In-scattering 関与媒質 Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  79. 79. Scattering modelReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Backward scattering Dipole/Multipole Plane-parallel Empirical BSSRDF Forward scatteringWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Phase function Airlight approximation Born series Neumann series M’s series
  80. 80. Scattering modelReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Phase function Airlight approximation Born series Neumann series M’s series
  81. 81. Rendering by ray marchingReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Numerical integration along Empirical BSSRDF the line of sightWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  82. 82. Light in participating medium Absorption 吸収Reflection Attenuation 減衰Diffuse reflection Out-scatteringSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole In-scattering Plane-parallel Empirical BSSRDFWhy BSSDRF is bad? Multiple scatteringScattering modelParticipating medium Absorption Emission In-scattering Out-scattering Emission 発光Rendering equations Airlight approximation Born series Usually ignored Neumann series M’s series
  83. 83. Absorption 𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑BRDFTransmission 𝐿Diffuse transmission (Macroscopic) Beer-Lambert Law log = 𝜀𝐶𝛽𝑑Specular transmissionBTDF 𝐿ScatteringBSSRDF Dipole/Multipole モル吸光係数 Plane-parallel Molar absorption coefficient path length Empirical BSSRDFWhy BSSDRF is bad? (thickness)Scattering model モル濃度 光路長,厚さParticipating medium molarity Absorption Emission In-scattering 光路長補正項 Out-scatteringRendering equations 透明溶液 𝛽 = 1 Airlight approximation Born series 混濁溶液 𝛽 ≠ 1 Neumann series M’s series 田村守, 「生体分光学の基本原理とその医学応用」,非侵襲・可視化技術ハンドブック, 小川誠二, 上野照剛 監修, NTS, pp.253-266, 2007.
  84. 84. Absorption 𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑BRDFTransmission 𝐿Diffuse transmission (Macroscopic) Beer-Lambert Law log = 𝜀𝐶𝛽𝑑Specular transmissionBTDF 𝐿ScatteringBSSRDF Dipole/Multipole Light モル吸光係数 Plane-parallel pulse Molar absorption coefficient path length Empirical BSSRDFWhy BSSDRF is bad? 𝐿 (thickness)Scattering model モル濃度 光路長,厚さParticipating medium molarity Absorption Emission 𝐿 In-scattering 光路長補正項 Out-scatteringRendering equations 𝐿 透明溶液 𝛽 = 1 Airlight approximation Born series 𝐿 混濁溶液 𝛽 ≠ 1 Neumann series M’s series 田村守, 「生体分光学の基本原理とその医学応用」,非侵襲・可視化技術ハンドブック, 小川誠二, 上野照剛 監修, NTS, pp.253-266, 2007.
  85. 85. Absorption 𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑BRDF 100 ps = 3 cm by the speed of lightTransmission 𝐿Diffuse transmission (Macroscopic) Beer-Lambert Law log = 𝜀𝐶𝛽𝑑Specular transmissionBTDF 𝐿ScatteringBSSRDF Dipole/Multipole Light モル吸光係数 Plane-parallel pulse Molar absorption coefficient path length Empirical BSSRDFWhy BSSDRF is bad? 𝐿 (thickness)Scattering model モル濃度 光路長,厚さParticipating medium molarity Absorption Emission 𝐿 In-scattering 光路長補正項 Out-scatteringRendering equations 𝐿 透明溶液 𝛽 = 1 Airlight approximation Born series 𝐿 混濁溶液 𝛽 ≠ 1 Neumann series M’s series 田村守, 「生体分光学の基本原理とその医学応用」,非侵襲・可視化技術ハンドブック, 小川誠二, 上野照剛 監修, NTS, pp.253-266, 2007.
  86. 86. Absorption 𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑BRDFTransmission 𝐿Diffuse transmission (Macroscopic) Beer-Lambert Law log = 𝜎 𝑑Specular transmissionBTDF 𝐿ScatteringBSSRDF Dipole/Multipole Plane-parallel 吸収係数 path length Empirical BSSRDFWhy BSSDRF is bad? Absorption coefficient (thickness)Scattering modelParticipating medium Absorption cross section Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  87. 87. Absorption 𝐿 + 𝑑𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDFTransmissionDiffuse transmissionSpecular transmission ( scopic) Beer-Lambert Law 𝑑𝐿 = −  𝜎  𝐿  𝑑𝑠BTDFScatteringBSSRDF Dipole/Multipole Plane-parallel 吸収係数 Infinitesimal Empirical BSSRDFWhy BSSDRF is bad? Absorption coefficient path lengthScattering modelParticipating medium Absorption cross section Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  88. 88. Absorption 𝐿 + 𝑑𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDFTransmissionDiffuse transmissionSpecular transmission ( scopic) Beer-Lambert Law 𝑑𝐿 = −  𝜎  𝐿  𝑑𝑠BTDFScatteringBSSRDF Dipole/Multipole Integration Plane-parallel 吸収係数 Infinitesimal Empirical BSSRDF from 0 to 𝑑Why BSSDRF is bad? Absorption coefficient path lengthScattering modelParticipating medium Absorption cross section Absorption Emission (Macroscopic) Beer-Lambert Law In-scattering Out-scatteringRendering equations 𝐿 Airlight approximation log = 𝜎 𝑑 or 𝐿 = 𝐿 𝑒 Born series 𝐿 Neumann series Exponential attenuation M’s series
  89. 89. Absorption 𝐿 + 𝑑𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDFTransmissionDiffuse transmissionSpecular transmission ( scopic) Beer-Lambert Law 𝑑𝐿 = −  𝜎  𝐿  𝑑𝑠BTDFScatteringBSSRDF Dipole/Multipole Integration Plane-parallel 吸収係数 Infinitesimal Empirical BSSRDF from 0 to 𝑑Why BSSDRF is bad? Absorption coefficient path lengthScattering modelParticipating medium Absorption cross section Absorption Emission (Macroscopic) Beer-Lambert Law optical depth In-scattering Out-scatteringRendering equations 𝐿 𝐿 = 𝐿 𝑒 ∫ Airlight approximation log = 𝜎 𝑑 or 𝐿 = 𝐿 𝑒 Born series 𝐿 When 𝜎 is Neumann series Exponential attenuation M’s series not constant
  90. 90. Out-scattering 𝐿 + 𝑑𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDFTransmissionDiffuse transmissionSpecular transmission (Microscopic) Beer-Lambert Law 𝑑𝐿 = −  𝜎  𝐿  𝑑𝑠BTDFScatteringBSSRDF Dipole/Multipole Integration Plane-parallel 散乱係数 Infinitesimal Empirical BSSRDF from 0 to 𝑑Why BSSDRF is bad? Scattering coefficient path lengthScattering modelParticipating medium Scattering cross section Absorption Emission (Macroscopic) Beer-Lambert Law In-scattering Out-scatteringRendering equations 𝐿 Airlight approximation log = 𝜎 𝑑 or 𝐿 = 𝐿 𝑒 Born series 𝐿 Neumann series Exponential attenuation M’s series
  91. 91. Attenuation = absorption + out-scattering 𝐿 + 𝑑𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDFTransmissionDiffuse transmissionSpecular transmission Absorption 𝑑𝐿 = −  𝜎  𝐿  𝑑𝑠BTDFScattering Out-scattering 𝑑𝐿 = −  𝜎  𝐿  𝑑𝑠BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad? Attenuation 𝑑𝐿 = −(𝜎 + 𝜎 )  𝐿  𝑑𝑠Scattering model 𝑑𝐿 = −𝜎  𝐿  𝑑𝑠Participating medium Absorption Emission In-scattering Exponential attenuation Out-scattering 消散係数・消滅係数Rendering equations 𝐿 = 𝐿 𝑒 Airlight approximation Extinction coefficient Born series Neumann series M’s series
  92. 92. Emission 𝐿 + 𝑑𝐿 𝐿ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDFTransmissionDiffuse transmissionSpecular transmission Emission 𝑑𝐿 = 𝜎  𝐿  𝑑𝑠BTDFScatteringBSSRDF Usually ignored Dipole/Multipole Emitted light Plane-parallel Empirical BSSRDF Absorption coefficientWhy BSSDRF is bad? (Emission of absorbed energy)Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  93. 93. In-scattering 𝜔 𝐿 + 𝑑𝐿 𝐿 𝜔′ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDFTransmissionDiffuse transmissionSpecular transmissionBTDF Integrating all incoming lights over the sphereScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDF 𝑑𝐿(𝑥, 𝜔) = 𝜎 𝑝 𝑥, 𝜔, 𝜔 𝐿 𝑥, 𝜔 𝑑𝜔 𝑑𝑠Why BSSDRF is bad? orScattering modelParticipating medium (𝜔 ⋅ 𝛻)𝐿(𝑥, 𝜔) Absorption Emission In-scattering Out-scattering Phase function Incident lightRendering equations Airlight approximation (from 𝜔′ to 𝜔 at 𝑥) (from 𝜔′ at 𝑥) Born series (usually ignore 𝑥) Neumann series M’s series
  94. 94. Rendering equation 𝜔 𝐿 + 𝑑𝐿 𝐿 𝜔′ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDF Light transport equationTransmissionDiffuse transmission Volume rendering equation (differential form)Specular transmissionBTDFScatteringBSSRDF 𝑑𝐿 𝑥, 𝜔 = −𝜎 𝑥 𝐿 𝑥, 𝜔 𝑑𝑠 + 𝜎 𝑥 𝑝 𝑥, 𝜔, 𝜔 𝐿 𝑥, 𝜔 𝑑𝜔 𝑑𝑠 Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Attenuation term In-scattering term Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  95. 95. Rendering equation 𝜔 𝐿 + 𝑑𝐿 𝐿 𝜔′ReflectionDiffuse reflectionSpecular reflection 𝑑𝑠BRDF Light transport equationTransmissionDiffuse transmission Volume rendering equation (differential form)Specular transmissionBTDFScatteringBSSRDF (𝜔 ⋅ 𝛻)  𝐿 𝑥, 𝜔 = −𝜎 𝑥 𝐿 𝑥, 𝜔 + 𝜎 𝑥 𝑝 𝑥, 𝜔, 𝜔 𝐿 𝑥, 𝜔 𝑑𝜔 Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Attenuation term In-scattering term Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  96. 96. Rendering equation 𝜔 𝑥 + 𝑠𝜔 𝑥 𝑥′ 𝐿 𝑥, 𝜔 𝐿 𝑥′, 𝜔 𝐿 𝑥 + 𝑠𝜔, 𝜔 𝜔′ReflectionDiffuse reflectionSpecular reflectionBRDF Light transport equationTransmissionDiffuse transmission Volume rendering equation ( form)Specular transmissionBTDF ( , )Scattering 𝐿 𝑥, 𝜔 = 𝑒 𝐿 𝑥 + 𝑠𝜔, 𝜔BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDF Attenuation + 𝑒 ( , ) 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′Why BSSDRF is bad?Scattering model termParticipating medium Absorption Emission Attenuation of In-scattering scattered light In-scattering term Out-scatteringRendering equations Airlight approximation Born series Optical depth 𝜏(𝑥, 𝑥′) = 𝜎 𝑠  𝑑𝑠 Neumann series M’s series
  97. 97. © Copyright 2011 IEEE – All Rights Reserved Airlight approximation to in-scattering Clear underwater vision Vision in bad weather 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 + 1 − 𝑒 ,  𝐿 Transparency Opacity Airlight 透明度 不透明度 天空光Schechner, Y.Y.; Karpel, N.; , "Clear underwater vision," Computer Vision and Pattern Recognition,2004. CVPR 2004. Proceedings of the 2004 IEEE Computer Society Conference on , vol.1, no., pp. I- Nayar, S.K.; Narasimhan, S.G.; , "Vision in bad weather," Computer Vision, 1999. The Proceedings of536- I-543 Vol.1, 27 June-2 July 2004 the Seventh IEEE International Conference on , vol.2, no., pp.820-827 vol.2, 1999doi: 10.1109/CVPR.2004.1315078 doi: 10.1109/ICCV.1999.790306URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1315078&isnumber=29133 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=790306&isnumber=17141
  98. 98. Born series zero-order Born approximation (no scattering) ( , ) 𝐿 𝑥, 𝜔 = 𝑒 𝐿 𝑥 + 𝑠𝜔, 𝜔ReflectionDiffuse reflection first-order Born approximation (single scattering)Specular reflectionBRDF 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔TransmissionDiffuse transmission ( , )Specular transmissionBTDF + 𝑒 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′ScatteringBSSRDF Dipole/Multipole Plane-parallel second-order Born approximation (double scattering) Empirical BSSRDFWhy BSSDRF is bad? 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔Scattering modelParticipating medium ( , ) Absorption + 𝑒 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′ Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series 𝐿 , 𝐿 , 𝐿 , … are called Born series. M’s series
  99. 99. Born approximation Born approximation of scattering term 𝐿 = 𝐿− 𝐿ReflectionDiffuse reflection Rytov approximation of scattering termSpecular reflectionBRDFTransmission 𝐿Diffuse transmission 𝐿 = 𝐿 logSpecular transmission 𝐿BTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series Weak Scattering Acoustic Wave Field Analysis Using Backward Propagation Rytov Transform Akira Yamada M’s series Jpn. J. Appl. Phys. 36 (1997) 3203 http://jjap.jsap.jp/link?JJAP/36/3203
  100. 100. Neumann series Incident light 𝐿 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔ReflectionDiffuse reflection ( , )Specular reflection + 𝑒 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′BRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScattering 𝑇= 𝑑𝑥 𝑒 ( , ) 𝜎 𝑥′ 𝑑𝜔 𝑝 𝑥′, 𝜔, 𝜔BSSRDF Dipole/Multipole Plane-parallel Linear operator of scattering Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering 𝐿 = 𝐿 + 𝑇𝐿 Out-scatteringRendering equations Airlight approximation  = 1− 𝑇 𝐿 = 𝐿 + 𝑇𝐿 + 𝑇 𝐿 + 𝑇 𝐿 + ⋯ = 𝑇 𝐿 Born series Neumann series Neumann series M’s series
  101. 101. Neumann series Incident light 𝐿 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔Reflection Diffuse reflection ( , ) Specular reflection + 𝑒 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′ BRDFTransmission Diffuse transmission Specular transmission BTDFScattering 𝑇= 𝑑𝑥 𝑒 ( , ) 𝜎 𝑥′ 𝑑𝜔 𝑝 𝑥′, 𝜔, 𝜔 BSSRDF Dipole/Multipole Plane-parallel Linear operator of scattering Empirical BSSRDFWhy BSSDRF is bad?Scattering model Participating medium Absorption Emission In-scattering 𝐿 = 𝐿 + 𝑇𝐿 Out-scattering Rendering equations Airlight approximation  = 1− 𝑇 𝐿 = 𝐿 + 𝑇𝐿 + 𝑇 𝐿 + 𝑇 𝐿 + ⋯ = 𝑇 𝐿Similar series Born to interreflectioncancellation series Neumann operator Neumann series M’s series(Seitz, ICCV2005)
  102. 102. Mukaigawa series Neumann series of volume rendering equation 𝐿= 𝑇 𝐿ReflectionDiffuse reflectionSpecular reflection Continuous Linear operatorBRDFTransmission light (integral)Diffuse transmissionSpecular transmission distributionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Mukaigawa series of light transport (CVPR2010, MIRU2010) Empirical BSSRDFWhy BSSDRF is bad?Scattering model 𝐿= 𝑇 𝐿Participating medium Absorption Emission In-scattering Out-scattering Discretized Light transportRendering equations light field matrix Airlight approximation Born series Neumann series M’s series
  103. 103. Copyright © by Authors Single, double, triple, … scatteringReflectionDiffuse reflectionSpecular reflectionBRDFTransmissionDiffuse transmissionSpecular transmissionBTDFScatteringBSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDFWhy BSSDRF is bad?Scattering modelParticipating medium Absorption Emission In-scattering Out-scatteringRendering equations Airlight approximation Born series 向川康博,ラメシュラスカル,八木康史, "散乱媒体中のライトトランスポートの解析, MIRU2010, pp. Neumann series 665-672, 2010. Y.Mukaigawa, Y.Yagi, R.Raskar, "Analysis of Light Transport in Scattering Media", Proc. CVPR2010, M’s series 2010.
  104. 104. Copyright © by AuthorsDecomposition into each scattering 向川康博,ラメシュラスカル,八木康史, "散乱媒体中のライトトランスポートの解析, MIRU2010, pp. 665-672, 2010. Y.Mukaigawa, Y.Yagi, R.Raskar, "Analysis of Light Transport in Scattering Media", Proc. CVPR2010, 2010.
  105. 105. Outline • Reflection • Why BSSDRF is bad? – Diffuse reflection – Specular reflection • Scattering modelReflection – BRDF – Participating mediumDiffuse reflectionSpecular reflection • Transmission • AbsorptionBRDFTransmission – Diffuse transmission • EmissionDiffuse transmission – Specular transmission • In-scatteringSpecular transmission • Out-scatteringBTDF – BTDFScattering – Rendering equationsBSSRDF Dipole/Multipole • Scattering • Airlight approximation Plane-parallel Empirical BSSRDF – BSSRDF • Born approximationWhy BSSDRF is bad? • Dipole/Multipole • Neumann seriesScattering modelParticipating medium • Plane-parallel • M’s series Absorption approximation Emission • Empirical BSSRDF In-scattering Out-scatteringRendering equations Airlight approximation Born series Neumann series M’s series
  106. 106. On the Scattering of light

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