20110326 cg・cvにおける散乱
DESCRIPTION
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).TRANSCRIPT
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
Fog
Underwater
Sunset
Drink
Jewely
Hair
Konnyaku
http://photosozai-database.com/modules/photo/photo.php?lid=664
アウトライン
• 光の反射・散乱 – 拡散反射・鏡面反
射・BRDF
– 表面下散乱・単散乱・多重散乱
• 表面下散乱モデル – 拡散近似
• Dipole/Multipole
– Plane-parallel近似 • 準解析解
• 異方性拡張
– Donner’s empirical BSSRDF
• 散乱の計測 – 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
光の反射・散乱
拡散反射・鏡面反射・BRDF
表面下散乱・単散乱・多重散乱
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
http://sekkouzou.shop-pro.jp/?pid=22649690
copyright©2010 石膏像ドットコム（堀石膏制作）,All Rights Reserved.
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
Copyright © 2009, Shuntaro Yamazaki.
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.
Copyright © by Authors
鏡面反射
𝜃
• 正反射方向
– 輝度最大
• ハイライト
– 正反射方向付近の輝度が強い
– Phongモデル
• cos𝑛 𝜃 に比例
BRDF
𝑥
𝜔𝑖 𝜔𝑜
• 任意の反射
• Bidirectional Reflectance Distribution Function – 双方向反射分布関
数
• 5パラメータ – 点𝑥，入射方向𝜔𝑖，
出射方向𝜔𝑜
• 等方・均等を仮定 – 3パラメータ
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.
等方BRDF計測
Eurographics Association Aire-la-Ville, Switzerland, Switzerland ©2003
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.
計測されたBRDFを使用
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 .
異方性BRDF
Copyright © by Authors
散乱
• 散乱媒質
– ボリューム散乱
– 表面下散乱
• 波長
– Rayleigh散乱
– Mie散乱
• 散乱回数
– 単散乱
– 多重散乱 • 二重散乱
• 三重散乱
• …
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
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
CGにおける散乱の表現
1996
2010
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
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.
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.
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.
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.
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.
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.
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
単散乱
二重散乱
多重散乱
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.
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.
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.
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
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
BSSRDF
𝑥𝑖
𝜔𝑖
𝜔𝑜
𝑥𝑜
• Bidirectional Scattering Surface Reflectance Distribution Function – 双方向深層散乱反
射分布関数
• 8パラメータ – 入射点𝑥𝑖，出射点𝑥𝑜，
入射方向𝜔𝑖，出射方向𝜔𝑜
• 等方・均等を仮定 – 5パラメータ
表面下散乱モデル
拡散近似：Dipole/Multipole
Plane-parallel近似：準解析解，異方性拡張
Donner’s empirical BSSRDF
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
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).
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.
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
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
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
均質媒体 均質媒体 ＋
塗料塗布
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
均質媒体 均質媒体 ＋
塗料塗布
後ろから光を当てた場合
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
有限厚の媒質（紙）
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
有限厚の媒質（紙）
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
複数皮膚層の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
後ろから光を当てた場合 右から光を当てた場合
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
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
Plane-parallel近似
• Dipole
• Multipole
• 半無限平面媒体
– 密度が表面からの深さ𝑧にのみ依存
– Plane-parallel
単層半無限平面
有限厚複数層
層状均質
準解析解（固有解）
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
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
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
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.
単散乱
モンテカルロ 準解析解
準解析解 形状補正
単散乱
準解析解
Copyright © 画像電子学会および(社)情報処理学会
異方性Plane-parallelモデル
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
Donner’s empirical BSSRDF
• 半無限均質平面媒体を仮定
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
𝑥𝑖
𝜔𝑖
𝜔𝑜
𝑥𝑜
• 5DパラメータのBSSRDFをシミュレーション
– 6パラメータ
– 85万通り
• 関数近似
– 各入射角度，各出射点，各出射方向
– 36GBデータ
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 © 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
Copyright © by Authors
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
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
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
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
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
散乱の計測
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
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
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
Copyright © by Authors
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
Copyright © 2011 by the Association for Computing Machinery, Inc. (ACM).
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
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.
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.
散乱回数毎に分離
Copyright © by Authors
固体の散乱計測（Dipoleモデル）
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.
PP PE POM
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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アウトライン
• 光の反射・散乱 – 拡散反射・鏡面反
射・BRDF
– 表面下散乱・単散乱・多重散乱
• 表面下散乱モデル – 拡散近似
• Dipole/Multipole
– Plane-parallel近似 • 準解析解
• 異方性拡張
– Donner’s empirical BSSRDF
• 散乱の計測 – 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
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