On the scattering of light : various models and methods used in computer graphics and computer vision
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This slide reviews techniques on scattering of light used in computer vision and computer graphics.
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On the scattering of light : various models and methods used in computer graphics and computer vision
- 1. On the Scattering of light
- 2. Scattering http://photosozai-database.com/modules/photo/photo.php?lid=664
- 3. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Volumetric scattering in CG 1987 1993 1994 Tomoyuki Nishita, Yasuhiro Miyawaki, and Eihachiro Nakamae. 1987. A shading model for atmospheric scattering 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. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Volumetric scattering in CG 2010 1996 Tomoyuki Nishita, Yoshinori Dobashi, and Eihachiro Nakamae. 1996. Display of clouds taking into account multiple anisotropic scattering and sky light. In Proceedings of the 23rd annual conference on Computer 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. Outline • Reflection • Why BSSDRF is bad? – Diffuse reflection – Specular reflection • Scattering model Reflection – BRDF – Participating medium Diffuse reflection Specular reflection • Transmission • Absorption BRDF Transmission – Diffuse transmission • Emission Diffuse transmission – Specular transmission • In-scattering Specular transmission • Out-scattering BTDF – BTDF Scattering – Rendering equations BSSRDF Dipole/Multipole • Scattering • Airlight approximation Plane-parallel Empirical BSSRDF – BSSRDF • Born series Why BSSDRF is bad? • Dipole/Multipole • Neumann series Scattering model Participating medium • Plane-parallel • M’s series Absorption approximation Emission • Empirical BSSRDF In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 6. Reflection Diffuse reflection Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering BSSRDF Dipole/Multipole Plane-parallel REFLECTION, Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium TRANSMISSION, AND Absorption Emission In-scattering Out-scattering SCATTERING OF LIGHT Rendering equations Airlight approximation Born series Neumann series M’s series
- 7. Diffuse reflection 拡散反射 • Constant Reflection Diffuse reflection irradiance Specular reflection BRDF Transmission – Independent to Diffuse transmission Specular transmission viewpoint BTDF Scattering BSSRDF • Pure diffuse Dipole/Multipole Plane-parallel Empirical BSSRDF surface Why BSSDRF is bad? Scattering model – Lambertian Participating medium Absorption Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 8. Specular reflection 鏡面反射 • Angle of reflection – is the angle of incidence Reflection 𝜃 Diffuse reflection Specular reflection • Highlights BRDF Transmission – More reflection near Diffuse transmission Specular transmission to the angle of BTDF reflection Scattering BSSRDF Dipole/Multipole • Model Plane-parallel Empirical BSSRDF – Phong Why BSSDRF is bad? Scattering model – Blinn Participating medium Absorption Emission – Cook-Trrance In-scattering Highlights Out-scattering – Trrance-Sparrow Rendering equations Airlight approximation Born series Neumann series Mirror M’s series
- 9. Diffuse + Specular 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 approximation Born series Neumann series M’s series
- 10. Diffuse + Specular ? 𝜔 𝜔 Reflection Diffuse reflection Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF 𝑥 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 approximation Born series Neumann series M’s series
- 11. BRDF • Bidirectional Reflectance Distribution 𝜔 𝜔 Reflection Diffuse reflection Function Specular reflection – 双方向反射率分布 BRDF Transmission 関数 Diffuse transmission Specular transmission • 6 parameters 𝑥 BTDF Scattering – Point 𝑥 BSSRDF Dipole/Multipole – angles of incidence Plane-parallel Empirical BSSRDF 𝜔 and reflection 𝜔 Why BSSDRF is bad? Scattering model • If isotropic and Participating medium Absorption homogeneous Emission In-scattering – 3 parameters Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 12. Eurographics Association Aire-la-Ville, Switzerland, Switzerland ©2003 Isotropic BRDF measurement Wojciech Matusik, Hanspeter Pfister, Matthew Brand, and Leonard McMillan. 2003. Efficient isotropic BRDF measurement. In Proceedings of the 14th Eurographics workshop on Rendering (EGRW '03). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 241-247.
- 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. Refraction 回折 Transmission 透過 • Transmitted light – Translucent Reflection materials Diffuse reflection Specular reflection BRDF – All non-metals Transmission Diffuse transmission Specular transmission • Refraction BTDF Scattering BSSRDF – Snell’s low 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 series M’s series
- 15. Specular Transmission 鏡面透過 • Angle of refraction – depends on Reflection • the angle of Diffuse reflection Specular reflection incidence BRDF Transmission • the indexes of Diffuse transmission Specular transmission refraction of two BTDF Scattering materials 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 series M’s series
- 16. Diffuse transmission 拡散透過 • Constant irradiance Reflection Diffuse reflection – Independent to Specular reflection BRDF viewpoint inside Transmission Diffuse transmission the material 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 approximation Born series Neumann series M’s series
- 17. Diffuse + Specular transmission a light bulb frosted glass
- 18. BTDF • Bidirectional Transmittance Reflection Diffuse reflection Distribution Specular reflection BRDF Function Transmission Diffuse transmission Specular transmission – 双方向透過率分布 BTDF Scattering 関数 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 series M’s series
- 19. Reflection + Transmission • Reflection – BRDF Reflection Diffuse reflection • Transmission Specular reflection BRDF Transmission – BTDF 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 approximation Born series Neumann series M’s series
- 20. Subsurface scattering 表面下散乱 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 approximation Born series Neumann series M’s series
- 21. Subsurface scattering • Scattering – Inside medium Reflection Diffuse reflection – Some come the Specular reflection BRDF surface Transmission Diffuse transmission – Some absorbed Specular transmission BTDF Scattering BSSRDF • Outgoing light Dipole/Multipole Plane-parallel – From a point Empirical BSSRDF Why BSSDRF is bad? different from the Scattering model Participating medium Absorption incident point Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 22. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface reflection Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 23. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Subsurface scattering Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 24. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface Subsurface Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 25. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface reflection Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 26. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Subsurface scattering Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 27. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface Subsurface Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 28. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface reflection Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 29. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Subsurface scattering Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 30. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Surface Subsurface Surface reflection Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 31. Single scattering 単散乱 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 approximation Born series Neumann series M’s series
- 32. Single scattering 単散乱 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 approximation Born series Neumann series M’s series
- 33. Double scattering 二重散乱 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 approximation Born series Neumann series M’s series
- 34. Multiple scattering 多重散乱 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 approximation Born series Neumann series M’s series
- 35. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multiple scattering only Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 36. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering only Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 37. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single + Multiple scattering + Fresnel reflection Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 38. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multiple Single Single scattering scattering scattering + Multiple scattering only only + Fresnel reflection Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 39. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single + Multiple scattering Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 40. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering only Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 41. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single Single scattering scattering + only Multiple scattering Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 42. BSSRDF • Bidirectional Scattering Surface Reflectance 𝜔 Reflection Diffuse reflection Distribution Function Specular reflection – 双方向散乱面（深層散 𝜔 BRDF Transmission 乱）反射率分布関数 Diffuse transmission Specular transmission BTDF • 8 parameters 𝑥 𝑥 Scattering BSSRDF – Points of incidence 𝑥 Dipole/Multipole and outgoing 𝑥 , Plane-parallel Empirical BSSRDF angles of incidence 𝜔 Why BSSDRF is bad? Scattering model and outgoing 𝜔 Participating medium Absorption • If isotropic and Emission In-scattering homogeneous Out-scattering Rendering equations – 5 parameters Airlight approximation Born series Neumann series M’s series
- 43. SSSID • Sub-Surface Scattering Irradiance Distribution 𝜔 Reflection Diffuse reflection – 表面下放射照度分布 Specular reflection BRDF • Outgoing light Transmission Diffuse transmission – Diffuse transmission Specular transmission BTDF – Independent to 𝑥 𝑥 Scattering BSSRDF viewpoint Dipole/Multipole Plane-parallel • 3 parameters Empirical BSSRDF Why BSSDRF is bad? – Isotropic and Scattering model Participating medium homogeneous Absorption Emission – Point of outgoing 𝑥 , In-scattering angle of incidence 𝜔 Out-scattering Rendering 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. Reflection Diffuse reflection Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering BSSRDF Dipole/Multipole Plane-parallel SUBSURFACE SCATTERING Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering MODELS Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 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 series Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics M’s series and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 46. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multiple scattering with Dipole model Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 47. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 48. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multipole model • Finite thickness – Infinite sum of Reflection Dipoles Diffuse reflection Specular reflection BRDF – A multipole model Transmission Diffuse transmission Specular transmission • Finite-thick layers BTDF Scattering BSSRDF – The use of some Dipole/Multipole Plane-parallel Multipole models Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering Out-scattering Rendering 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. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multipole approximation of human skin layers Backlight Sidelight 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
- 50. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Dipole approximation 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
- 51. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Multipole approximation 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
- 52. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Dipole approximation Multipole approximation 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
- 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. 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. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Dipole approximation Finite-thick medium (paper) Multipole approximation 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
- 56. Plane-parallel approximation • Dipole – Plane, semi-infinite, homogeneous Single layer, semi-infinite Reflection Diffuse reflection Specular reflection • Multipole BRDF Transmission – Finite homogeneous Diffuse transmission Specular transmission layers BTDF • Plane-parallel Finite-thick layers Scattering BSSRDF Dipole/Multipole – Layered Plane-parallel Empirical BSSRDF homogeneous Why BSSDRF is bad? Scattering model – Depends on the Participating medium Absorption depth 𝑧 from the Layered homogeneous Emission In-scattering surface Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 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 equation Reflection Diffuse reflection Discretization Specular reflection BRDF Eigenfunction Transmission Eigensolution Diffuse transmission Specular transmission BTDF Scattering Eigenvalue 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 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. 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 approximation Nelson Max, Suguru Saito, Kazuya Watanabe, Masayuki Nakajima, "Rendering Grass Blowing in The Born series Wind with Global Illumination", Pacific Graphics 2009, 2009. Neumann series Nelson Max, Kazuya Watanabe, Suguru Saito, Masayuki Nakajima, "Plane-Parallel Radiance Transport for 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 series 2009, 2009.
- 59. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Empirical BSSRDF model • Simulating 5D • Semi-infinite parameters of 𝜔 homogeneous Reflection Diffuse reflection BSSRDF plane medium Specular reflection – 6 parameters 𝜔 BRDF Transmission Diffuse transmission – 0.85 million Specular transmission 𝑥 𝑥 BTDF Scattering patterns BSSRDF Dipole/Multipole Plane-parallel • Function fitting Empirical BSSRDF Why 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 series Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 M’s series pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 60. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering only Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 61. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering ＋ Dipole model Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 62. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single scattering ＋ Empirical BSSRDF Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 63. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Monte Carlo Method Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 64. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM). Single Monte Carlo scattering simulation + Empirical BSSRDF Craig Donner, Jason Lawrence, Ravi Ramamoorthi, Toshiya Hachisuka, Henrik Wann Jensen, and Shree Nayar. 2009. An empirical BSSRDF model. ACM Trans. Graph. 28, 3, Article 30 (July 2009), 10 pages. In ACM SIGGRAPH 2009 papers (SIGGRAPH '09). DOI=10.1145/1531326.1531336
- 65. Reflection Diffuse reflection Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering BSSRDF Dipole/Multipole Plane-parallel BSSRDF, Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering A WRONG MODEL Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 66. BRDF • 6 parameters – Point 𝑥 𝜔 𝜔 Reflection Diffuse reflection – angles of incidence Specular reflection BRDF 𝜔 and reflection Transmission Diffuse transmission 𝜔 Specular transmission BTDF 𝑥 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 approximation Born series Neumann series M’s series
- 67. BRDF, OK! • BRDF – Works for a point 𝜔 on a curved 𝜔 Reflection Diffuse reflection Specular reflection surface BRDF Transmission Diffuse transmission – Angles relative to Specular transmission BTDF the normal of the 𝑥 Scattering BSSRDF point 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 series M’s series
- 68. BSSRDF • 8 parameters – Points of incidence 𝜔 Reflection 𝑥 and outgoing 𝑥 , Diffuse reflection Specular reflection angles of incidence 𝜔 BRDF Transmission Diffuse transmission 𝜔 and outgoing Specular transmission BTDF 𝜔 𝑥 𝑥 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 approximation Born series Neumann series M’s series
- 69. BSSRDF ? • 8 parameters – Points of incidence 𝜔 Reflection 𝑥 and , NG : curved surface Diffuse reflection Specular reflection angles of incidence 𝜔 BRDF Transmission Diffuse transmission 𝜔 and outgoing Specular transmission BTDF 𝜔 𝑥 𝑥 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 approximation Born series Neumann series M’s series
- 70. BSSRDF ? • 8 parameters – Points of incidence 𝜔 Reflection 𝑥 and , NG : curved surface Diffuse reflection Specular reflection angles of incidence 𝜔 BRDF Transmission Diffuse transmission 𝜔 and outgoing Specular transmission BTDF 𝜔 𝑥 𝑥 Scattering BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering Out-scattering Rendering equations NG : transmission Airlight approximation Born series Neumann series M’s series
- 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 only Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proceedings of the 28th annual conference on Computer graphics with dipole model and interactive techniques (SIGGRAPH '01). ACM, New York, NY, USA, 511-518.
- 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 2010 Talks (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. 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 2010 Talks (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. 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 2010 Talks (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. Reflection Diffuse reflection Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering BSSRDF Dipole/Multipole Plane-parallel SCATTERING, Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering A CORRECT WAY Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 76. BSSRDF • Subsurface scattering 𝜔 Reflection Diffuse reflection Specular reflection 𝜔 BRDF Transmission Diffuse transmission Specular transmission BTDF 𝑥 𝑥 Scattering BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Emission Translucent material In-scattering 半透明物質 Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 77. Scattering model • Volumetric scattering 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 Participating medium In-scattering 関与媒質 Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 78. Scattering model • Volumetric scattering 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 Participating medium In-scattering 関与媒質 Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 79. Scattering model Reflection Diffuse reflection Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering BSSRDF Backward scattering Dipole/Multipole Plane-parallel Empirical BSSRDF Forward scattering Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering Out-scattering Rendering equations Phase function Airlight approximation Born series Neumann series M’s series
- 80. Scattering model 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 Phase function Airlight approximation Born series Neumann series M’s series
- 81. Rendering by ray marching Reflection Diffuse reflection Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering BSSRDF Dipole/Multipole Plane-parallel Numerical integration along Empirical BSSRDF the line of sight Why BSSDRF is bad? Scattering model Participating medium Absorption Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 82. Light in participating medium Absorption 吸収 Reflection Attenuation 減衰 Diffuse reflection Out-scattering Specular reflection BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering BSSRDF Dipole/Multipole In-scattering Plane-parallel Empirical BSSRDF Why BSSDRF is bad? Multiple scattering Scattering model Participating medium Absorption Emission In-scattering Out-scattering Emission 発光 Rendering equations Airlight approximation Born series Usually ignored Neumann series M’s series
- 83. Absorption 𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑 BRDF Transmission 𝐿 Diffuse transmission (Macroscopic) Beer-Lambert Law log = 𝜀𝐶𝛽𝑑 Specular transmission BTDF 𝐿 Scattering BSSRDF Dipole/Multipole モル吸光係数 Plane-parallel Molar absorption coefficient path length Empirical BSSRDF Why 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-scattering Rendering 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. Absorption 𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑 BRDF Transmission 𝐿 Diffuse transmission (Macroscopic) Beer-Lambert Law log = 𝜀𝐶𝛽𝑑 Specular transmission BTDF 𝐿 Scattering BSSRDF Dipole/Multipole Light モル吸光係数 Plane-parallel pulse Molar absorption coefficient path length Empirical BSSRDF Why 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-scattering Rendering 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. Absorption 𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑 BRDF 100 ps = 3 cm by the speed of light Transmission 𝐿 Diffuse transmission (Macroscopic) Beer-Lambert Law log = 𝜀𝐶𝛽𝑑 Specular transmission BTDF 𝐿 Scattering BSSRDF Dipole/Multipole Light モル吸光係数 Plane-parallel pulse Molar absorption coefficient path length Empirical BSSRDF Why 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-scattering Rendering 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. Absorption 𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑 BRDF Transmission 𝐿 Diffuse transmission (Macroscopic) Beer-Lambert Law log = 𝜎 𝑑 Specular transmission BTDF 𝐿 Scattering BSSRDF Dipole/Multipole Plane-parallel 吸収係数 path length Empirical BSSRDF Why BSSDRF is bad? Absorption coefficient (thickness) Scattering model Participating medium Absorption cross section Absorption Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 87. Absorption 𝐿 + 𝑑𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Transmission Diffuse transmission Specular transmission ( scopic) Beer-Lambert Law 𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠 BTDF Scattering BSSRDF Dipole/Multipole Plane-parallel 吸収係数 Infinitesimal Empirical BSSRDF Why BSSDRF is bad? Absorption coefficient path length Scattering model Participating medium Absorption cross section Absorption Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 88. Absorption 𝐿 + 𝑑𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Transmission Diffuse transmission Specular transmission ( scopic) Beer-Lambert Law 𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠 BTDF Scattering BSSRDF Dipole/Multipole Integration Plane-parallel 吸収係数 Infinitesimal Empirical BSSRDF from 0 to 𝑑 Why BSSDRF is bad? Absorption coefficient path length Scattering model Participating medium Absorption cross section Absorption Emission (Macroscopic) Beer-Lambert Law In-scattering Out-scattering Rendering equations 𝐿 Airlight approximation log = 𝜎 𝑑 or 𝐿 = 𝐿 𝑒 Born series 𝐿 Neumann series Exponential attenuation M’s series
- 89. Absorption 𝐿 + 𝑑𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Transmission Diffuse transmission Specular transmission ( scopic) Beer-Lambert Law 𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠 BTDF Scattering BSSRDF Dipole/Multipole Integration Plane-parallel 吸収係数 Infinitesimal Empirical BSSRDF from 0 to 𝑑 Why BSSDRF is bad? Absorption coefficient path length Scattering model Participating medium Absorption cross section Absorption Emission (Macroscopic) Beer-Lambert Law optical depth In-scattering Out-scattering Rendering 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. Out-scattering 𝐿 + 𝑑𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Transmission Diffuse transmission Specular transmission (Microscopic) Beer-Lambert Law 𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠 BTDF Scattering BSSRDF Dipole/Multipole Integration Plane-parallel 散乱係数 Infinitesimal Empirical BSSRDF from 0 to 𝑑 Why BSSDRF is bad? Scattering coefficient path length Scattering model Participating medium Scattering cross section Absorption Emission (Macroscopic) Beer-Lambert Law In-scattering Out-scattering Rendering equations 𝐿 Airlight approximation log = 𝜎 𝑑 or 𝐿 = 𝐿 𝑒 Born series 𝐿 Neumann series Exponential attenuation M’s series
- 91. Attenuation = absorption + out-scattering 𝐿 + 𝑑𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Transmission Diffuse transmission Specular transmission Absorption 𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠 BTDF Scattering Out-scattering 𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠 BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDF Why BSSDRF is bad? Attenuation 𝑑𝐿 = −(𝜎 + 𝜎 ) 𝐿 𝑑𝑠 Scattering model 𝑑𝐿 = −𝜎 𝐿 𝑑𝑠 Participating 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. Emission 𝐿 + 𝑑𝐿 𝐿 Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Transmission Diffuse transmission Specular transmission Emission 𝑑𝐿 = 𝜎 𝐿 𝑑𝑠 BTDF Scattering BSSRDF Usually ignored Dipole/Multipole Emitted light Plane-parallel Empirical BSSRDF Absorption coefficient Why BSSDRF is bad? (Emission of absorbed energy) Scattering model Participating medium Absorption Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 93. In-scattering 𝜔 𝐿 + 𝑑𝐿 𝐿 𝜔′ Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Transmission Diffuse transmission Specular transmission BTDF Integrating all incoming lights over the sphere Scattering BSSRDF Dipole/Multipole Plane-parallel Empirical BSSRDF 𝑑𝐿(𝑥, 𝜔) = 𝜎 𝑝 𝑥, 𝜔, 𝜔 𝐿 𝑥, 𝜔 𝑑𝜔 𝑑𝑠 Why BSSDRF is bad? or Scattering model Participating medium (𝜔 ⋅ 𝛻)𝐿(𝑥, 𝜔) Absorption Emission In-scattering Out-scattering Phase function Incident light Rendering equations Airlight approximation (from 𝜔′ to 𝜔 at 𝑥) (from 𝜔′ at 𝑥) Born series (usually ignore 𝑥) Neumann series M’s series
- 94. Rendering equation 𝜔 𝐿 + 𝑑𝐿 𝐿 𝜔′ Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Light transport equation Transmission Diffuse transmission Volume rendering equation (differential form) Specular transmission BTDF Scattering BSSRDF 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 BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Attenuation term In-scattering term Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 95. Rendering equation 𝜔 𝐿 + 𝑑𝐿 𝐿 𝜔′ Reflection Diffuse reflection Specular reflection 𝑑𝑠 BRDF Light transport equation Transmission Diffuse transmission Volume rendering equation (differential form) Specular transmission BTDF Scattering BSSRDF (𝜔 ⋅ 𝛻) 𝐿 𝑥, 𝜔 = −𝜎 𝑥 𝐿 𝑥, 𝜔 + 𝜎 𝑥 𝑝 𝑥, 𝜔, 𝜔 𝐿 𝑥, 𝜔 𝑑𝜔 Dipole/Multipole Plane-parallel Empirical BSSRDF Why BSSDRF is bad? Scattering model Participating medium Absorption Attenuation term In-scattering term Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 96. Rendering equation 𝜔 𝑥 + 𝑠𝜔 𝑥 𝑥′ 𝐿 𝑥, 𝜔 𝐿 𝑥′, 𝜔 𝐿 𝑥 + 𝑠𝜔, 𝜔 𝜔′ Reflection Diffuse reflection Specular reflection BRDF Light transport equation Transmission Diffuse transmission Volume rendering equation ( form) Specular transmission BTDF ( , ) Scattering 𝐿 𝑥, 𝜔 = 𝑒 𝐿 𝑥 + 𝑠𝜔, 𝜔 BSSRDF 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 term Participating medium Absorption Emission Attenuation of In-scattering scattered light In-scattering term Out-scattering Rendering equations Airlight approximation Born series Optical depth 𝜏(𝑥, 𝑥′) = 𝜎 𝑠 𝑑𝑠 Neumann series M’s series
- 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 of 536- I-543 Vol.1, 27 June-2 July 2004 the Seventh IEEE International Conference on , vol.2, no., pp.820-827 vol.2, 1999 doi: 10.1109/CVPR.2004.1315078 doi: 10.1109/ICCV.1999.790306 URL: 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. Born series zero-order Born approximation (no scattering) ( , ) 𝐿 𝑥, 𝜔 = 𝑒 𝐿 𝑥 + 𝑠𝜔, 𝜔 Reflection Diffuse reflection first-order Born approximation (single scattering) Specular reflection BRDF 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 Transmission Diffuse transmission ( , ) Specular transmission BTDF + 𝑒 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′ Scattering BSSRDF Dipole/Multipole Plane-parallel second-order Born approximation (double scattering) Empirical BSSRDF Why BSSDRF is bad? 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 Scattering model Participating medium ( , ) Absorption + 𝑒 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′ Emission In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series 𝐿 , 𝐿 , 𝐿 , … are called Born series. M’s series
- 99. Born approximation Born approximation of scattering term 𝐿 = 𝐿− 𝐿 Reflection Diffuse reflection Rytov approximation of scattering term Specular reflection BRDF Transmission 𝐿 Diffuse transmission 𝐿 = 𝐿 log Specular transmission 𝐿 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 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. Neumann series Incident light 𝐿 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 Reflection Diffuse reflection ( , ) Specular reflection + 𝑒 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′ BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering 𝑇= 𝑑𝑥 𝑒 ( , ) 𝜎 𝑥′ 𝑑𝜔 𝑝 𝑥′, 𝜔, 𝜔 BSSRDF Dipole/Multipole Plane-parallel Linear operator of scattering Empirical BSSRDF Why 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 𝐿 Born series Neumann series Neumann series M’s series
- 101. Neumann series Incident light 𝐿 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 𝐿 𝑥, 𝜔 = 𝑒 ( , ) 𝐿 𝑥 + 𝑠𝜔, 𝜔 Reflection Diffuse reflection ( , ) Specular reflection + 𝑒 𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′ BRDF Transmission Diffuse transmission Specular transmission BTDF Scattering 𝑇= 𝑑𝑥 𝑒 ( , ) 𝜎 𝑥′ 𝑑𝜔 𝑝 𝑥′, 𝜔, 𝜔 BSSRDF Dipole/Multipole Plane-parallel Linear operator of scattering Empirical BSSRDF Why 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 𝐿 Similar series Born to interreflection cancellation series Neumann operator Neumann series M’s series (Seitz, ICCV2005)
- 102. Mukaigawa series Neumann series of volume rendering equation 𝐿= 𝑇 𝐿 Reflection Diffuse reflection Specular reflection Continuous Linear operator BRDF Transmission light (integral) Diffuse transmission Specular transmission distribution BTDF Scattering BSSRDF Dipole/Multipole Plane-parallel Mukaigawa series of light transport (CVPR2010, MIRU2010) Empirical BSSRDF Why BSSDRF is bad? Scattering model 𝐿= 𝑇 𝐿 Participating medium Absorption Emission In-scattering Out-scattering Discretized Light transport Rendering equations light field matrix Airlight approximation Born series Neumann series M’s series
- 103. Copyright © by Authors Single, double, triple, … scattering 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 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. Copyright © by Authors Decomposition 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. Outline • Reflection • Why BSSDRF is bad? – Diffuse reflection – Specular reflection • Scattering model Reflection – BRDF – Participating medium Diffuse reflection Specular reflection • Transmission • Absorption BRDF Transmission – Diffuse transmission • Emission Diffuse transmission – Specular transmission • In-scattering Specular transmission • Out-scattering BTDF – BTDF Scattering – Rendering equations BSSRDF Dipole/Multipole • Scattering • Airlight approximation Plane-parallel Empirical BSSRDF – BSSRDF • Born approximation Why BSSDRF is bad? • Dipole/Multipole • Neumann series Scattering model Participating medium • Plane-parallel • M’s series Absorption approximation Emission • Empirical BSSRDF In-scattering Out-scattering Rendering equations Airlight approximation Born series Neumann series M’s series
- 106. On the Scattering of light