玉木 徹 : 「CG・CVにおける散乱」,第5回名古屋CV・PRML勉強会, 中部大学, 名古屋 (2011 03).

1. CG・CVにおける散乱
玉木徹（広島大学）
2011年3月26日第5回 名古屋CV・PRML勉強会

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. アウトライン
• 光の反射・散乱 • 散乱の計測
– 拡散反射・鏡面反 – 単散乱計測（液体）
射・BRDF – 多重散乱解析（2D・
– 表面下散乱・単散 3D）
乱・多重散乱 – 2層モデル・多層モデ
• 表面下散乱モデル ル
– 拡散近似
• Dipole/Multipole
– Plane-parallel近似
• 準解析解
• 異方性拡張
– Donner’s empirical
BSSRDF

10. 拡散反射・鏡面反射・BRDF
表面下散乱・単散乱・多重散乱
光の反射・散乱

11. 拡散反射
• 反射輝度一定
– 視点に依存しない
• 多くのCVが仮定
– ステレオ，多視点
– Shape-from-shading
• 拡散反射のみ
– 完全拡散面
– ランバート面
• 石膏など

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
完全拡散面でないと困る．．．
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. 鏡面反射
• 正反射方向
– 輝度最大
𝜃
• ハイライト
– 正反射方向付近の
輝度が強い
– Phongモデル
• cos 𝑛 𝜃 に比例

16. BRDF
• 任意の反射
• Bidirectional
𝜔𝑜
Reflectance 𝜔𝑖
Distribution
Function
– 双方向反射分布関
𝑥
数
• 5パラメータ
– 点𝑥，入射方向𝜔 𝑖 ，
出射方向𝜔 𝑜
• 等方・均等を仮定
– 3パラメータ

17. Eurographics Association Aire-la-Ville, Switzerland, Switzerland ©2003
等方BRDF計測
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
計測されたBRDFを使用
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
異方性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. 散乱
• 散乱媒質 • 散乱回数
– ボリューム散乱 – 単散乱
– 表面下散乱 – 多重散乱
• 二重散乱
• 波長
• 三重散乱
– Rayleigh散乱
• …
– Mie散乱

21. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
CGにおける散乱の表現
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).
CGにおける散乱の表現
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. 表面下散乱
• 透過光
– 非金属物質
• 散乱光
– 物体内部での散乱
– 一部は表面に
– 一部は吸収される
• 出射光
– 入射点とは異なる
出射点から

24. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
表面反射
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).
表面下散乱
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).
表面反射
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).
表面下散乱
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).
表面反射
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).
表面下散乱
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. 単散乱

31. 二重散乱

32. 多重散乱

33. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
多重散乱
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).
単散乱
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).
単散乱＋多重散乱＋フレネル反射
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).
多重散乱
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).
単散乱
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 𝜔𝑜
– 双方向深層散乱反
射分布関数 𝑥𝑖 𝑥𝑜
• 8パラメータ
– 入射点𝑥 𝑖 ，出射点𝑥 𝑜 ，
入射方向𝜔 𝑖 ，出射方
向𝜔 𝑜
• 等方・均等を仮定
– 5パラメータ

39. 拡散近似：Dipole/Multipole
Plane-parallel近似：準解析解，異方性拡張
Donner’s empirical BSSRDF
表面下散乱モデル

40. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Dipole（双極子点光源）モデル
• 均質媒体，半無限
• 単散乱＋多重散乱
（等方・拡散近似）
• 二項の和
– それぞれ仮想点光
源
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近似
• 厚さが有限
– Dipoleの無限和
– Multipoleモデル
• 有限厚の層が重
なった場合
– Multipoleモデルを
複数利用
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近似
均質媒体 均質媒体
＋
塗料塗布
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近似
後ろから光を当てた場合
均質媒体 均質媒体
＋
塗料塗布
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近似
有限厚の媒質（紙）
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近似
有限厚の媒質（紙）
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).
複数皮膚層のMultipole近似
後ろから光を当てた場合 右から光を当てた場合
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近似
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近似
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近似
• Dipole
単層半無限平面
• Multipole
有限厚複数層
• 半無限平面媒体
– 密度が表面からの
深さ𝑧にのみ依存
層状均質
– Plane-parallel

51. Copyright © 画像電子学会および(社)情報処理学会
準解析解（固有解）
偏微積分方程式
常微積分方程式
離散化
固有解 固有関数
固有値
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
準解析解と単散乱の比較
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
異方性Plane-parallelモデル
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
• 5Dパラメータの • 半無限均質平面媒
BSSRDFをシミュ 𝜔 𝑖 体を仮定
レーション
– 6パラメータ 𝜔𝑜
– 85万通り
𝑥𝑖 𝑥𝑜
• 関数近似
– 各入射角度，各出
射点，各出射方向
– 36GBデータ
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).
モンテカルロ法
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).
単散乱のみ
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).
単散乱＋dipoleモデル
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).
単散乱＋このモデル
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).
モンテカルロ法
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. 単散乱計測（液体）
多重散乱解析（2D・3D）
2層モデル・多層モデル
散乱の計測

63. Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
液体を薄めて単散乱で計測
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).
散乱パラメータの変更
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
散乱パラメータの補間
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
単散乱，二重散乱，三重散乱．．．
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.

69. Copyright © by Authors
散乱回数毎に分離
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.

70. Copyright © by Authors
固体の散乱計測（Dipoleモデル）
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.

71. Copyright © by Authors
PP（ポリプロピレン）
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.

72. Copyright © by Authors
PE（ポリエチレン）
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.

73. Copyright © by Authors
POM（ポリオキシメチレン）
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.

74. Copyright © by Authors
2層モデル：化粧＋肌の解析
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.

75. Copyright © by Authors
化粧の乗り具合
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.

76. Copyright © by Authors
年齢・性別による肌の変化
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.

77. Copyright © by Authors
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.

78. Copyright © by (社)情報処理学会
2層モデル：液体透過＋固体反射
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.

79. Copyright © by Authors
2層モデル：半透明媒体×２
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.

80. Copyright © by Authors
多層モデル：混合正規分布によ
る異方性BSSRDFの表現
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
計測機器・反射成分分離
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
直接反射成分
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
多層表面下散乱
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.

84. Copyright © by Authors
直接反射＋多層表面下散乱
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.

85. Copyright © by Authors
直接反射＋均質表面下散乱
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.

86. Copyright © by Authors
実画像
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.

87. Copyright © by Authors
直接反射＋多層表面下散乱
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.

88. アウトライン
• 光の反射・散乱 • 散乱の計測
– 拡散反射・鏡面反 – 単散乱計測（液体）
射・BRDF – 多重散乱解析（2D・
– 表面下散乱・単散 3D）
乱・多重散乱 – 2層モデル・多層モデ
• 表面下散乱モデル ル
– 拡散近似
• Dipole/Multipole
– Plane-parallel近似
• 準解析解
• 異方性拡張
– Donner’s empirical
BSSRDF

89. CG・CVにおける散乱
玉木徹（広島大学）
2011年3月26日第5回 名古屋CV・PRML勉強会