玉木 徹 : 「CG・CVにおける散乱・表面下散乱」, 第5回 広島画像情報学セミナー, 広島大学, 広島 (2011 04).

1. Scattering
in CG and CV
Toru Tamaki
(Hiroshima University)
HIISeminar 2011/4/15

2. Fog

3. Underwater

4. Sunset

5. Drink

6. Jewely

7. Hair

8. Konnyaku
http://photosozai-database.com/modules/photo/photo.php?lid=664

9. Outline
• Reflection, Scattering • Measuring scattering
– Diffuse / specular – Single scattering with
reflection, BRDF liquid
– Subsurface scattering, – Multiple scattering
single/multiple (2D・3D)
scattering – 2 layer model, multi-
• Subsurface scattering layer model
models
– Diffuse approximation
• Dipole/Multipole
– Plane-parallel
approximation
• Semi-analytic solution
• Anisotropic scattering
– Donner’s empirical
BSSRDF

10. Diffuse / specular reflection, BRDF
Subsurface scattering, single/multiple scattering
REFLECTION, SCATTERING
OF LIGHT

11. Diffuse reflection
• Constant radiance
– Independent to
viewpoint
• Many CV assume
– Stereo, multi-view
– Shape-from-shading
• Pure diffuse surface
– Lambertian
• Example
– Plaster statues

12. copyright©2010 石膏像ドットコム（堀石膏制作）,All Rights Reserved.
http://sekkouzou.shop-pro.jp/?pid=22649690

13. Copyright © 2009, Shuntaro Yamazaki.
Active range finder
山崎 俊太郎, DLPプロジェクタによる高速度構造化光投影を利用した高速度アクティブビジョン,
http://www.dh.aist.go.jp/~shun/research/dlp/index.html.ja

14. Copyright © by Authors
If not Lambertian:
古瀬達彦, 日浦慎作, 佐藤宏介, スリット光の変調による相互反射と表面下散乱に頑健な三次元形状計
測, MIRU2009, pp. 214-221, 2009.
Tatsuhiko Furuse, Shinsaku Hiura and Kosuke Sato, 3-D Shape Measurement Method with Modulated
Slit Light Robust for Interreflection and Subsurface Scattering, PROCAMS2009, pp. 1-2, 2009.

15. Specular reflection
• Angle of reflection
– is angle of
incidence 𝜃
• Highlights
– More reflection
near to the angle
of reflection
– Phong model
• Proportional to
cos 𝑛 𝜃

16. BRDF
• Any refection
• Bidirectional
Reflectance 𝜔𝑜
𝜔𝑖
Distribution Function
– 双方向反射分布関数
• 6 parameters
– Point 𝑥, angles of 𝑥
incidence 𝜔 𝑖 and
reflection 𝜔 𝑜
• If isotropic and
homogeneous
– 3 parameters

17. 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.

18. Eurographics Association Aire-la-Ville, Switzerland, Switzerland ©2003
Rendering with measured BRDF
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.

19. 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 .

20. Scattering
• Media • Number of
– Volumetric scattering
– Subsurface – Single scattering
– Multiple scattering
• Double scattering
• Wavelengths
• Triple scattering
– Rayleigh scattering • …
– Mie scattering

21. 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

22. 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

23. Subsurface scattering
• Transmitted light
– Non-metal
• Scattering
– Inside medium
– Some come the
surface
– Some absorbed
• Outgoing light
– From a point
different from the
incident point

24. 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.

25. 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.

26. 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.

27. 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.

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).
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.

30. Single scattering

31. Double scattering

32. Multiple scattering

33. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Multiple 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.

34. 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.

35. 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.

36. 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

37. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Single 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

38. BSSRDF
• Bidirectional
Scattering Surface
Reflectance 𝜔𝑖
Distribution Function
– 双方向深層散乱反射 𝜔𝑜
分布関数
• 9 parameters 𝑥𝑖 𝑥𝑜
– Points of incidence 𝑥 𝑖
and outgoing 𝑥 𝑜 ,
angles of incidence 𝜔 𝑖
and outgoing 𝜔 𝑜
• If isometric and
homogeneous
– 5 parameters

39. Diffuse approximation: Dipole/Multipole
Plane-parallel approximation: Semi-analytic solution,
Anisotropic scattering,
Donner’s empirical BSSRDF
SUBSURFACE SCATTERING
MODELS

40. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Dipole model
• Homogeneous and
semi-infinite medium
• Single + multiple
scattering (isometric
and diffusion)
• Sum of two terms
– Each represents a
virtual point light source
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.

41. 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.

42. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Multipole approximation
• Finite thickness
– Infinite sum of
Dipoles
– Multipole model
• Finite-thick layers
– The use of some
Multipole models
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

43. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Multipole approximation
Homogeneous Homogeneous
medium medium
＋
Dye spraying
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

44. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Multipole approximation
Backlight
Homogeneous Homogeneous
medium medium
＋
Dye spraying
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

45. 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

46. 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

47. 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

48. 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

49. 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

50. Plane-parallel approximation
• Dipole
Single layer, semi-infinite
• Multipole
Finite-thick layers
• Semi-infinite plane
medium
– Depends on the Layered homogeneous
depth 𝑧 from the
surface
– Plane-parallel

51. Copyright © 画像電子学会および(社)情報処理学会
Analytic solution
Integro-differential equation
Integro-ordinary differential equation
Discretization
Eigensolution Eigenfunction
Eigenvalue
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

52. Copyright © 画像電子学会および(社)情報処理学会
Comparison between analytic
solution and single scattering
モンテカルロ 準解析解
単散乱
準解析解
形状補正 単散乱
準解析解
新谷 幹夫，土橋 宜典，白石 路雄，岩崎 慶，西田 友是, "多重散乱モデルの効率化と樹木レンダリング
への応用", Visual Computing / グラフィクスと CAD 合同シンポジウム 2009, 2009.

53. 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.
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.

54. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Donner’s empirical BSSRDF
• Simulating 5D • Semi-infinite
parameter 𝜔 𝑖 homogeneous
BSSRDF plane medium
– 6 parameters 𝜔𝑜
– 0.85 million
𝑥𝑖 𝑥𝑜
patterns
• Function fitting
– Each incident /
outgoing angles /
points
– 36GB data
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

55. Copyright © by Authors
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

56. Copyright © by Authors
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

57. 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

58. 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

59. 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

60. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Single scattering ＋ This 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

61. 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

62. Single scattering with liquid
Multiple scattering (2D・3D)
2 layer model, multi-layer model
MEASURING SCATTERING

63. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Measuring single scattering with
diluted liquied
Srinivasa G. Narasimhan, Mohit Gupta, Craig Donner, Ravi Ramamoorthi, Shree K. Nayar, and Henrik
Wann Jensen. 2006. Acquiring scattering properties of participating media by dilution. ACM Trans.
Graph. 25, 3 (July 2006), 1003-1012. In ACM SIGGRAPH 2006 Papers (SIGGRAPH '06).
DOI=10.1145/1141911.1141986

64. Copyright © by Authors
Srinivasa G. Narasimhan, Mohit Gupta, Craig Donner, Ravi Ramamoorthi, Shree K. Nayar, and Henrik
Wann Jensen. 2006. Acquiring scattering properties of participating media by dilution. ACM Trans.
Graph. 25, 3 (July 2006), 1003-1012. In ACM SIGGRAPH 2006 Papers (SIGGRAPH '06).
DOI=10.1145/1141911.1141986

65. Copyright © by Authors
Srinivasa G. Narasimhan, Mohit Gupta, Craig Donner, Ravi Ramamoorthi, Shree K. Nayar, and Henrik
Wann Jensen. 2006. Acquiring scattering properties of participating media by dilution. ACM Trans.
Graph. 25, 3 (July 2006), 1003-1012. In ACM SIGGRAPH 2006 Papers (SIGGRAPH '06).
DOI=10.1145/1141911.1141986

66. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Rendering as
changing scattering parameters
Srinivasa G. Narasimhan, Mohit Gupta, Craig Donner, Ravi Ramamoorthi, Shree K. Nayar, and Henrik
Wann Jensen. 2006. Acquiring scattering properties of participating media by dilution. ACM Trans.
Graph. 25, 3 (July 2006), 1003-1012. In ACM SIGGRAPH 2006 Papers (SIGGRAPH '06).
DOI=10.1145/1141911.1141986

67. Copyright © by Authors
Interpolation of
scattering parameters
Srinivasa G. Narasimhan, Mohit Gupta, Craig Donner, Ravi Ramamoorthi, Shree K. Nayar, and Henrik
Wann Jensen. 2006. Acquiring scattering properties of participating media by dilution. ACM Trans.
Graph. 25, 3 (July 2006), 1003-1012. In ACM SIGGRAPH 2006 Papers (SIGGRAPH '06).
DOI=10.1145/1141911.1141986

68. Copyright © by Authors
Interpolation of
scattering parameters
Srinivasa G. Narasimhan, Mohit Gupta, Craig Donner, Ravi Ramamoorthi, Shree K. Nayar, and Henrik
Wann Jensen. 2006. Acquiring scattering properties of participating media by dilution. ACM Trans.
Graph. 25, 3 (July 2006), 1003-1012. In ACM SIGGRAPH 2006 Papers (SIGGRAPH '06).
DOI=10.1145/1141911.1141986

69. Copyright © by Authors
2 layer model:
two translucent materials
貴田健介，坂上文彦，佐藤淳, "表面下散乱に基づく半透明物体の厚み推定", MIRU2010, pp. 578-584,
2010.

70. Copyright © by (社)情報処理学会
2 layer mode: scattering in liquid
and metal reflectance
馬場葉子，向川康博，八木康史，"照明光と反射光の散乱を考慮した反射特性の推定"，CVIM, 2011-
CVIM-175(41), 2011.

71. Copyright © by Authors
2 layer model:
makeup and skin layers
馬場葉子，向川康博，八木康史，"化粧と肌の２層構造からなる化粧肌反射特性モデル", MIRU2010,
pp. 1679-1685, 2010.

72. Copyright © by Authors
How heavy (or light) makeup is
馬場葉子，向川康博，八木康史，"化粧と肌の２層構造からなる化粧肌反射特性モデル", MIRU2010,
pp. 1679-1685, 2010.

73. Copyright © by Authors
Analysis of face skin
w.r.t ages and genders
馬場葉子，間下以大，向川康博，八木康史，"大規模データベースを用いた肌の反射・散乱光の統計的
解析", MIRU2009, pp. 1164-1171, 2009.

74. Copyright © by Authors
Blue : men Variance of
Red : women scattering
Senior
Specular
Senior
馬場葉子，間下以大，向川康博，八木康史，"大規模データベースを用いた肌の反射・散乱光の統計的
解析", MIRU2009, pp. 1164-1171, 2009.

75. Copyright © by Authors
Multiple layer model:
Anisotropic BSSRDF with GMM
間下以大，向川康博，八木康史， "多層表面下散乱モデルによる皮膚の異方性散乱と不均一性の表現
"，MIRU2009, pp. 1216-1222, 2009.

76. Copyright © by Authors
Separating direct / indirect
reflections
間下以大，向川康博，八木康史， "多層表面下散乱モデルによる皮膚の異方性散乱と不均一性の表現
"，MIRU2009, pp. 1216-1222, 2009.

77. Copyright © by Authors
Direct reflection
間下以大，向川康博，八木康史， "多層表面下散乱モデルによる皮膚の異方性散乱と不均一性の表現
"，MIRU2009, pp. 1216-1222, 2009.

78. Copyright © by Authors
Multi-layer anisotropic BSSRDF
間下以大，向川康博，八木康史， "多層表面下散乱モデルによる皮膚の異方性散乱と不均一性の表現
"，MIRU2009, pp. 1216-1222, 2009.

79. Copyright © by Authors
Direct reflection +
Multi-layer anisotropic BSSRDF
間下以大，向川康博，八木康史， "多層表面下散乱モデルによる皮膚の異方性散乱と不均一性の表現
"，MIRU2009, pp. 1216-1222, 2009.

80. Copyright © by Authors
Direct reflection +
homogeneous isotropic BSSRDF
間下以大，向川康博，八木康史， "多層表面下散乱モデルによる皮膚の異方性散乱と不均一性の表現
"，MIRU2009, pp. 1216-1222, 2009.

81. Copyright © by Authors
Real image
間下以大，向川康博，八木康史， "多層表面下散乱モデルによる皮膚の異方性散乱と不均一性の表現
"，MIRU2009, pp. 1216-1222, 2009.

82. Copyright © by Authors
Direct reflection +
Multi-layer anisotropic BSSRDF
間下以大，向川康博，八木康史， "多層表面下散乱モデルによる皮膚の異方性散乱と不均一性の表現
"，MIRU2009, pp. 1216-1222, 2009.

83. Copyright © by Authors
Measuring a solid object with
Dipole model
PP PE POM
向川康博，鈴木和哉，八木康史， "一般照明下での表面下散乱の解析''，MIRU2008, pp.63-70, 2008.
Y.Mukaigawa, K.Suzuki, Y.Yagi, "Analysis of Subsurface Scattering under Generic Illumination",
Proc. ICPR2008, 2008.
Y.Mukaigawa, K.Suzuki, Y.Yagi, ``Analysis of Subsurface Scattering based on Dipole Approximation'',
IPSJ Transactions on Computer Vision and Applications, Vol.1, pp.128-138, 2009.

84. Copyright © by Authors
PP (Polypropylene)
向川康博，鈴木和哉，八木康史， "一般照明下での表面下散乱の解析''，MIRU2008, pp.63-70, 2008.
Y.Mukaigawa, K.Suzuki, Y.Yagi, "Analysis of Subsurface Scattering under Generic Illumination",
Proc. ICPR2008, 2008.
Y.Mukaigawa, K.Suzuki, Y.Yagi, ``Analysis of Subsurface Scattering based on Dipole Approximation'',
IPSJ Transactions on Computer Vision and Applications, Vol.1, pp.128-138, 2009.

85. Copyright © by Authors
PE (Polyethylene)
向川康博，鈴木和哉，八木康史， "一般照明下での表面下散乱の解析''，MIRU2008, pp.63-70, 2008.
Y.Mukaigawa, K.Suzuki, Y.Yagi, "Analysis of Subsurface Scattering under Generic Illumination",
Proc. ICPR2008, 2008.
Y.Mukaigawa, K.Suzuki, Y.Yagi, ``Analysis of Subsurface Scattering based on Dipole Approximation'',
IPSJ Transactions on Computer Vision and Applications, Vol.1, pp.128-138, 2009.

86. Copyright © by Authors
POM (Polyoxymethylene)
向川康博，鈴木和哉，八木康史， "一般照明下での表面下散乱の解析''，MIRU2008, pp.63-70, 2008.
Y.Mukaigawa, K.Suzuki, Y.Yagi, "Analysis of Subsurface Scattering under Generic Illumination",
Proc. ICPR2008, 2008.
Y.Mukaigawa, K.Suzuki, Y.Yagi, ``Analysis of Subsurface Scattering based on Dipole Approximation'',
IPSJ Transactions on Computer Vision and Applications, Vol.1, pp.128-138, 2009.

87. Copyright © by Authors
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.

88. 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.

89. Outline
• Reflection, Scattering • Measuring scattering
– Diffuse / specular – Single scattering with
reflection, BRDF liquid
– Subsurface scattering, – Multiple scattering
single/multiple (2D・3D)
scattering – 2 layer model, multi-
• Subsurface scattering layer model
models
– Diffuse approximation
• Dipole/Multipole
– Plane-parallel
approximation
• Semi-analytic solution
• Anisotropic scattering
– Donner’s empirical
BSSRDF

90. Scattering
in CG and CV
Toru Tamaki
(Hiroshima University)
HIISeminar 2011/4/15

91. Scattering
not for CG and CV
Toru Tamaki
(Hiroshima University)
HIISeminar 2011/4/15

92. A lot of related research fields
• tissue optics Laser-tissue interaction 光医工学 光医療工学
• 放射光 X線CTR散乱 位相CT 位相Ｘ線イメージングシステム 光
CT 蛍光CT赤外線散乱トモグラフィー 光ヘテロダイン
• 医療での人体可視化 拡散光トモグラフィー 無侵襲計測 生体可
視化 光イメージング 屈折イメージング
• 超音波非破壊検査 超音波検査 アコースティックイメージング 超
音波医学 医用超音波 ティッシュハーモニックイメージング コント
ラストハーモニックイメージング
• interstellar diffusion 宇宙塵 小惑星 惑星間塵 惑星間空間塵
Interplanetary dust cloud Cosmic dust
• 雪の中に埋もれた人を電磁波で探知 # 偏波情報によるターゲット
の識別・分類 レーダポーラリメトリ 地中レーダー 雪中レーダー
レーダーリモートセンシング レーダー光学
• 地質探査 物理探査 地震波トモグラフィー 地震波散乱 地震波
探査 地下構造イメージング
• 中性子散乱 核反応の散乱
• 光散乱