Post on 13-Apr-2017
On the Scattering of light�
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Scattering
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
Volumetric scattering in CG
1996
2010
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Outline
• Reflection – Diffuse reflection – Specular reflection – BRDF
• Transmission – Diffuse transmission – Specular transmission – BTDF
• Scattering – BSSRDF
• Dipole/Multipole • Plane-parallel
approximation • 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
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
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
REFLECTION, TRANSMISSION, AND
SCATTERING OF LIGHT
Diffuse reflection 拡散反射
• Constant irradiance
– Independent to viewpoint
• Pure diffuse surface
– Lambertian
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
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
Specular reflection 鏡面反射
𝜃
• Angle of reflection – is the angle of
incidence
• Highlights – More reflection near
to the angle of reflection
• Model – Phong
– Blinn
– Cook-Trrance
– Trrance-Sparrow Highlights
Mirror
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
Diffuse + Specular ?
𝑥
𝜔 𝜔
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
BRDF
𝑥
𝜔 𝜔
• Bidirectional Reflectance Distribution Function – 双方向反射率分布
関数
• 6 parameters – Point 𝑥
– angles of incidence 𝜔 and reflection 𝜔
• If isotropic and homogeneous – 3 parameters
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
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.
Isotropic BRDF measurement
Eurographics Association Aire-la-Ville, Switzerland, Switzerland ©2003
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 .
Anisotropic BRDF
Copyright © by Authors
Refraction 回折 Transmission 透過
• Transmitted light
– Translucent materials
– All non-metals
• Refraction
– Snell’s low
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
Specular Transmission 鏡面透過
• Angle of refraction
– depends on • the angle of
incidence
• the indexes of refraction of two materials
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
Diffuse transmission 拡散透過
• Constant irradiance
– Independent to viewpoint inside the material
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
Diffuse + Specular transmission
frosted glass
a light bulb
BTDF
• Bidirectional Transmittance Distribution Function
– 双方向透過率分布関数
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
Reflection + Transmission
• Reflection
– BRDF
• Transmission
– BTDF
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
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
Subsurface scattering
• Scattering
– Inside medium
– Some come the surface
– Some absorbed
• Outgoing light
– From a point different from the incident point
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
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.
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.
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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.
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.
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.
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Surface
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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.
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.
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.
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Surface reflection 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.
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
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
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
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
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.
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.
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.
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Single scattering + Multiple scattering + Fresnel reflection
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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.
Single scattering
only
Multiple scattering
only
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
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Single scattering +
Multiple scattering
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
BSSRDF
𝑥
𝜔
𝜔
𝑥
• Bidirectional Scattering Surface Reflectance Distribution Function – 双方向散乱面(深層散
乱)反射率分布関数
• 8 parameters – Points of incidence 𝑥
and outgoing 𝑥 , angles of incidence 𝜔 and outgoing 𝜔
• If isotropic and homogeneous – 5 parameters
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
SSSID
𝑥
𝜔
𝑥
• Sub-Surface Scattering Irradiance Distribution – 表面下放射照度分布
• Outgoing light – Diffuse transmission
– Independent to viewpoint
• 3 parameters – Isotropic and
homogeneous
– Point of outgoing 𝑥 , angle of incidence 𝜔
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・メディア理解研究会 PRMU2009-77, Vol.109, No.249, pp.37-42, 広島大学, 広島(2009 10).
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
SUBSURFACE SCATTERING MODELS
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
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
Dipole model
• Homogeneous and semi-infinite medium
• Single scattering + multiple scattering (isometric and diffusion)
• Sum of two terms – Each represents a
virtual point light source
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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.
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.
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.
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
Multipole model
• Finite thickness
– Infinite sum of Dipoles
– A multipole model
• Finite-thick layers
– The use of some Multipole models
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
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
Backlight Sidelight
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Multipole approximation of human skin layers
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
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Dipole approximation
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
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
Finite-thick medium (paper)
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Finite-thick medium (paper)
Dipole approximation
Finite-thick medium (paper)
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
Plane-parallel approximation
• Dipole – Plane, semi-infinite,
homogeneous
• Multipole – Finite homogeneous
layers
• Plane-parallel – Layered
homogeneous
– Depends on the depth 𝑧 from the surface
Single layer, semi-infinite
Finite-thick layers
Layered homogeneous
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
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
Analytic solution to plane-parallel
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", Visual Computing / グラフィクスと CAD 合同シンポジウム 2008, 2008. http://nis-lab.is.s.u-tokyo.ac.jp/nis/abs_cgi.html#ipsj09-2
Integro-differential equation
Integro-ordinary differential equation
Discretization
Eigensolution Eigenfunction
Eigenvalue
Copyright © 画像電子学会および(社)情報処理学会
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
Anisotropic Plane-parallel model
Nelson Max, Suguru Saito, Kazuya Watanabe, Masayuki Nakajima, "Rendering Grass Blowing in The Wind with Global Illumination", Pacific Graphics 2009, 2009. 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 2009, 2009.
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.
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
Empirical BSSRDF model
• Semi-infinite homogeneous plane medium
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
𝑥
𝜔
𝜔
𝑥
• Simulating 5D parameters of BSSRDF
– 6 parameters
– 0.85 million patterns
• Function fitting
– Each incident / outgoing angles / points
– 36GB data
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
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
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
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
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Monte Carlo simulation
Single scattering
+ Empirical BSSRDF
BSSRDF, A WRONG 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 Airlight approximation Born series Neumann series M’s series
BRDF
𝑥
𝜔 𝜔
• 6 parameters – Point 𝑥
– angles of incidence 𝜔 and reflection 𝜔
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
BRDF, OK!
𝑥
𝜔 𝜔
• BRDF
– Works for a point on a curved surface
– Angles relative to the normal of the point
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
BSSRDF
𝑥
𝜔
𝜔
𝑥
• 8 parameters
– Points of incidence 𝑥 and outgoing 𝑥 , angles of incidence 𝜔 and outgoing 𝜔
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
BSSRDF ?
𝑥
𝜔
𝜔
𝑥
• 8 parameters
– Points of incidence 𝑥 and , angles of incidence 𝜔 and outgoing 𝜔
NG : curved surface 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
BSSRDF ?
𝑥
𝜔
𝜔
𝑥
• 8 parameters
– Points of incidence 𝑥 and , angles of incidence 𝜔 and outgoing 𝜔
NG : curved surface
NG : transmission
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
Single scattering vs BSSRDF
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.
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Single scattering only Multiple scattering only with dipole model
Transmitted light
No light transmission
Blurred by BSSRDF
Curvature dependent BRDF
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.
• Light is reflected
– Even when 𝜃 > 180°
𝜃 < 180°
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Curvature dependent BRDF
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.
• Light is reflected
– Even when 𝜃 > 180°
𝜃 = 180°
Curvature dependent BRDF
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.
• Light is reflected
– Even when 𝜃 > 180°
𝜃 > 180°
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
SCATTERING, A CORRECT WAY
BSSRDF
• Subsurface scattering
𝑥
𝜔
𝜔
𝑥
Translucent material 半透明物質
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
Scattering model
• Volumetric scattering
Participating medium 関与媒質
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
Scattering model
• Volumetric scattering
Participating medium 関与媒質
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
Scattering model
Forward scattering
Backward scattering
Phase function
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
Scattering model
Phase function
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
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
Rendering by ray marching
the line of sight
Numerical integration along
Light in participating medium
Attenuation 減衰
Absorption 吸収
Out-scattering
In-scattering
Multiple scattering
Emission 発光
Usually ignored
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
Absorption
𝐿 𝐿
(Macroscopic) Beer-Lambert Law
モル吸光係数 Molar absorption coefficient
モル濃度 molarity
path length (thickness) 光路長,厚さ
光路長補正項
透明溶液 𝛽 = 1 混濁溶液 𝛽 ≠ 1
𝑑
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.
log𝐿𝐿
= 𝜀𝐶𝛽𝑑
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
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
Absorption
𝐿 𝐿
(Macroscopic) Beer-Lambert Law
モル吸光係数 Molar absorption coefficient
モル濃度 molarity
path length (thickness) 光路長,厚さ
光路長補正項
透明溶液 𝛽 = 1 混濁溶液 𝛽 ≠ 1
𝑑
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.
𝐿
𝐿
𝐿
𝐿
Light pulse
log𝐿𝐿
= 𝜀𝐶𝛽𝑑
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
Absorption
𝐿 𝐿
(Macroscopic) Beer-Lambert Law
モル吸光係数 Molar absorption coefficient
モル濃度 molarity
path length (thickness) 光路長,厚さ
光路長補正項
透明溶液 𝛽 = 1 混濁溶液 𝛽 ≠ 1
𝑑
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.
𝐿
𝐿
𝐿
𝐿
Light pulse
log𝐿𝐿
= 𝜀𝐶𝛽𝑑
100 ps = 3 cm by the speed of light
Absorption
𝐿 𝐿
(Macroscopic) Beer-Lambert Law
吸収係数 Absorption coefficient Absorption cross section
path length (thickness)
𝑑
log𝐿𝐿
= 𝜎 𝑑
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
Absorption
𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠
𝐿 𝐿 + 𝑑𝐿
( scopic) Beer-Lambert Law
吸収係数 Absorption coefficient Absorption cross section
Infinitesimal path length
𝑑𝑠 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
Absorption
𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠
𝐿 𝐿 + 𝑑𝐿
( scopic) Beer-Lambert Law
吸収係数 Absorption coefficient Absorption cross section
Infinitesimal path length
𝑑𝑠
log𝐿𝐿 = 𝜎 𝑑 𝐿 = 𝐿 𝑒
(Macroscopic) Beer-Lambert Law
Integration from 0 to 𝑑
or
Exponential attenuation
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
Absorption
𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠
𝐿 𝐿 + 𝑑𝐿
( scopic) Beer-Lambert Law
吸収係数 Absorption coefficient Absorption cross section
Infinitesimal path length
𝑑𝑠
log𝐿𝐿 = 𝜎 𝑑 𝐿 = 𝐿 𝑒
(Macroscopic) Beer-Lambert Law
Integration from 0 to 𝑑
or
Exponential attenuation
𝐿 = 𝐿 𝑒 ∫
When 𝜎 is
not constant
optical depth
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
Out-scattering
𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠
𝐿 𝐿 + 𝑑𝐿
(Microscopic) Beer-Lambert Law
散乱係数 Scattering coefficient Scattering cross section
Infinitesimal path length
𝑑𝑠
log𝐿𝐿 = 𝜎 𝑑 𝐿 = 𝐿 𝑒
(Macroscopic) Beer-Lambert Law
Integration from 0 to 𝑑
or
Exponential attenuation
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
Attenuation = absorption + out-scattering
𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠
𝐿 𝐿 + 𝑑𝐿
𝑑𝑠
𝐿 = 𝐿 𝑒
𝑑𝐿 = − 𝜎 𝐿 𝑑𝑠 Absorption
Out-scattering
𝑑𝐿 = −(𝜎 + 𝜎 ) 𝐿 𝑑𝑠 Attenuation
𝑑𝐿 = −𝜎 𝐿 𝑑𝑠
消散係数・消滅係数 Extinction coefficient
Exponential attenuation
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
Emission
𝐿 𝐿 + 𝑑𝐿
𝑑𝑠
𝑑𝐿 = 𝜎 𝐿 𝑑𝑠 Emission
Absorption coefficient (Emission of absorbed energy)
Emitted light Usually ignored
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
In-scattering
𝐿 𝐿 + 𝑑𝐿
𝑑𝑠
𝑑𝐿(𝑥, 𝜔) = 𝜎 𝑝 𝑥, 𝜔, 𝜔 𝐿 𝑥, 𝜔 𝑑𝜔 𝑑𝑠
𝜔
𝜔′
Phase function (from 𝜔′ to 𝜔 at 𝑥) (usually ignore 𝑥)
Incident light (from 𝜔′ at 𝑥)
Integrating all incoming lights over the sphere
(𝜔 ⋅ 𝛻)𝐿(𝑥, 𝜔) or
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
Rendering equation
𝐿 𝐿 + 𝑑𝐿
𝑑𝑠
𝑑𝐿 𝑥, 𝜔 = −𝜎 𝑥 𝐿 𝑥, 𝜔 𝑑𝑠 + 𝜎 𝑥 𝑝 𝑥, 𝜔, 𝜔 𝐿 𝑥, 𝜔 𝑑𝜔 𝑑𝑠
𝜔
𝜔′
Light transport equation Volume rendering equation (differential form)
In-scattering term Attenuation term
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
Rendering equation
𝐿 𝐿 + 𝑑𝐿
𝑑𝑠
(𝜔 ⋅ 𝛻) 𝐿 𝑥, 𝜔 = −𝜎 𝑥 𝐿 𝑥, 𝜔 + 𝜎 𝑥 𝑝 𝑥, 𝜔, 𝜔 𝐿 𝑥, 𝜔 𝑑𝜔
𝜔
𝜔′
Light transport equation Volume rendering equation (differential form)
In-scattering term Attenuation term
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
Rendering equation
𝐿 𝑥′, 𝜔 𝐿 𝑥, 𝜔
𝐿 𝑥, 𝜔 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔,𝜔
+ 𝑒 ( , )𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′
𝜔
𝜔′
Light transport equation Volume rendering equation ( form)
In-scattering term
Attenuation term
𝜏(𝑥, 𝑥′) = 𝜎 𝑠 𝑑𝑠 Optical depth
Attenuation of scattered light
𝑥′ 𝑥
𝐿 𝑥 + 𝑠𝜔,𝜔
𝑥 + 𝑠𝜔
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
Airlight approximation to in-scattering
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-536- I-543 Vol.1, 27 June-2 July 2004 doi: 10.1109/CVPR.2004.1315078 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1315078&isnumber=29133
Nayar, S.K.; Narasimhan, S.G.; , "Vision in bad weather," Computer Vision, 1999. The Proceedings of the Seventh IEEE International Conference on , vol.2, no., pp.820-827 vol.2, 1999 doi: 10.1109/ICCV.1999.790306 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=790306&isnumber=17141
© Copyright 2011 IEEE – All Rights Reserved
Vision in bad weather Clear underwater vision
𝐿 𝑥, 𝜔 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔,𝜔 + 1 − 𝑒 , 𝐿
Airlight 天空光
Opacity 不透明度
Transparency 透明度
Born series
𝐿 𝑥, 𝜔 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔,𝜔
𝐿 𝑥, 𝜔 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔,𝜔
+ 𝑒 ( , )𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′
𝐿 𝑥, 𝜔 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔,𝜔
+ 𝑒 ( , )𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′
first-order Born approximation (single scattering)
second-order Born approximation (double scattering)
zero-order Born approximation (no scattering)
𝐿 , 𝐿 , 𝐿 , … are called Born series.
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
Born approximation
𝐿 = 𝐿 − 𝐿
Born approximation of scattering term
𝐿 = 𝐿 log𝐿𝐿
Rytov approximation of scattering term
Weak Scattering Acoustic Wave Field Analysis Using Backward Propagation Rytov Transform Akira Yamada Jpn. J. Appl. Phys. 36 (1997) 3203 http://jjap.jsap.jp/link?JJAP/36/3203
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
Neumann series
𝐿 𝑥, 𝜔 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔,𝜔
+ 𝑒 ( , )𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′
𝐿 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔, 𝜔
𝑇 = 𝑑𝑥 𝑒 ( , )𝜎 𝑥′ 𝑑𝜔 𝑝 𝑥′, 𝜔, 𝜔
𝐿 = 𝐿 + 𝑇𝐿
= 1 − 𝑇 𝐿 = 𝐿 + 𝑇𝐿 + 𝑇 𝐿 + 𝑇 𝐿 +⋯ = 𝑇 𝐿
Incident light
Linear operator of scattering
Neumann series
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
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
Similar to interreflection cancellation operator (Seitz, ICCV2005)
Neumann series
𝐿 𝑥, 𝜔 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔,𝜔
+ 𝑒 ( , )𝜎 𝑥′ 𝑝 𝑥′, 𝜔, 𝜔 𝐿 𝑥′, 𝜔 𝑑𝜔 𝑑𝑥′
𝐿 = 𝑒 ( , )𝐿 𝑥 + 𝑠𝜔, 𝜔
𝑇 = 𝑑𝑥 𝑒 ( , )𝜎 𝑥′ 𝑑𝜔 𝑝 𝑥′, 𝜔, 𝜔
𝐿 = 𝐿 + 𝑇𝐿
= 1 − 𝑇 𝐿 = 𝐿 + 𝑇𝐿 + 𝑇 𝐿 + 𝑇 𝐿 +⋯ = 𝑇 𝐿
Incident light
Linear operator of scattering
Neumann series
Mukaigawa series
𝐿 = 𝑇 𝐿
𝐿 = 𝑇 𝐿
Neumann series of volume rendering equation
Linear operator (integral)
Continuous light
distribution
Mukaigawa series of light transport (CVPR2010, MIRU2010)
Light transport matrix
Discretized light field
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
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
Single, double, triple, … 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.
Copyright © by Authors
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.
Decomposition into each scattering
Copyright © by Authors
Outline
• Reflection – Diffuse reflection – Specular reflection – BRDF
• Transmission – Diffuse transmission – Specular transmission – BTDF
• Scattering – BSSRDF
• Dipole/Multipole • Plane-parallel
approximation • Empirical BSSRDF
• Why BSSDRF is bad?
• Scattering model – Participating medium
• Absorption • Emission • In-scattering • Out-scattering
– Rendering equations • Airlight approximation • Born approximation • Neumann series • M’s series
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
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