(a) (x, y, z) (θ, ϕ) 1(b) (s, t), (, ) 1(c) D R = (θ R, ϕ R ) C R = ( R, R ) D R C R F R(D R, C R) 1(d) D L = (θ L, ϕ L ) C L = ( L, L ) F L(D
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1 Measrement of 8-D Reflectance Field sing Polyhedral Mirror and its Applications for Comptational Photography Seiichi Tagawa, 1 Yashiro Mkaigawa, 1 Yasyki Matsshita 2 and Yasshi Yagi 1 8-D reflectance field expresses a relationship between 4-D light fields of illminations and reflections. In this paper, we show that the 8-D reflectance field can be sed for a ariety of comptational photography techniqes sch as synthetic apertre, relighting, and confocal imaging. The reflectance field expresses intensities of illminated and reflected rays which pass a hemispherical srface, and it can be measred by placing cameras and projectors on the srface. We show that many low-resoltion cameras and projectors can be irtally generated by combining a polyhedral mirror with real cameras and projectors. The irtal cameras and projectors are placed on a hemisphere with nearly niform density by locating planar mirrors along a conical srface. We confirm that seeral comptational photography techniqes can be realized by sing a constrcted polyhedral mirror )2) 3) 8DRF 4)5)6) 7)8) 8DRF 8DRF 8DRF 8DRF 9) 3) 10) 8DRF 8DRF 11) c 2010 Information Processing Society of Japan
2 (a) (x, y, z) (θ, ϕ) 1(b) (s, t), (, ) 1(c) D R = (θ R, ϕ R ) C R = ( R, R ) D R C R F R(D R, C R) 1(d) D L = (θ L, ϕ L ) C L = ( L, L ) F L(D L, C L) F L F R F (D L, C L, D R, C R ) (1) 8DRF 2.2 8DRF 8DRF 8DRF BSSRDF, BTF, BRDF BSSRDF (, ) ( θ, φ) ( x, y, z) ( s, t) (a) (b) CR = ( R, ) C R R = ( R, R ) CL = ( L, L) DR = ( θ R, φr ) D = θ, φ ) D = θ, φ ) R ( R R ( x, y, z) ( x, y, z) (c) (d) L ( L L 1 Bidirectional Scattering Srface Reflectance Distribtion Fnction: BSSRDF S L = (x L, y L, z L ) S R = (x R, y R, z R) S L D L P L C L = P L (D L, S L ) S R D R P R C R = P R (D R, S R ) D L S L D R S L BSSRDF BSSRDF (D L, S L, D R, S R ) = F (D L, P L (D L, S L ), D R, P R (D R, S R )). (2) BSSRDF 8DRF BTF Bidirectional Textre Fnction: 2 c 2010 Information Processing Society of Japan
3 BTF BTF BSSRDF S = (x, y, z) D L S D R BTF BT F (D L, S, D R ) = F (D L, P L (D L, S), D R, P R (D R, S)). (3) BTF 8DRF BRDF Bidirectional Reflectance Distribtion Fnction: BRDF BTF S BRDF (0, 0) D L (0, 0) D R BRDF BRDF (D L, D R) = F (D L, (0, 0), D R, (0, 0)). (4) BRDF 8DRF 2.3 8DRF 8DRF 8DRF DRF 2(a) Ω D R Π Π S = (x, y, z) Ω M R { 1 : if the ray passes S and D R Ω M R (D R, C R ) = (5) 0 : otherwise F R D R Ω C R I I(D R, C R, Ω) = F R (D R, C R )M R (D R, C R )dd R dc R. (6) Ω DRF F L D R C R I I(D R, C R) = F (D L, C L, D R, C R)F L(D L, C L)dD LdC L. (7) 8DRF Ω D Π Π S = (x, y, z) Ω M 3 c 2010 Information Processing Society of Japan
4 D R C R S Ω Π D R C R S Arbitrary light C, D, D R L (a) (b) (c) 2 { 1 : if the ray passes S and D Ω M(D, C) = (8) 0 : otherwise 8DRF D R Ω C R I I(D R, C R, Ω) = S R C L F (D L, C L, D R, C R)M(D L, C L)M(D R, C R)dD RdC RdD LdC L DRF 7) 11) 8DRF 8DRF DRF 8DRF Ω (9) Π 8DRF 3.2 8DRF 8DRF θ, ϕ, XGA ( ) )5)6) 7)8) θ, ϕ θ ϕ c 2010 Information Processing Society of Japan
5 8DRF Focal point Cred srface 3 Mirror form Facet Tangent plane 2 4(a) 2 4(b) 4(c) 4(d) 2 2 α 2 5 c 2010 Information Processing Society of Japan
6 Virtal camera Virtal camera Virtal cameras Mirror Beam splitter Real camera Real camera Mirror Mirrors Sphere Ellipsoid Geodesic dome (a) Virtal camera Geodesic dome (b) Virtal camera Camera 5 2 Real camera (telecentric) 3.5 Paraboloid Mirror Geodesic dome (c) 4 Directrix Real camera α Mirror Hyperboloid Geodesic dome (d) Focal point β 11) 4(b) 5 2 x y2 + z 2 = DRF 6 c 2010 Information Processing Society of Japan
7 情報処理学会研究報告 75mm 100mm (a) 前方 (b) 下方 90mm (c) スケール 図 6 亀甲多面鏡の設計 6mm projector target object 図8 trtleback reflector (a) 亀甲多面鏡 er litt sp m a be 撮影画像例 camera (b) 撮影装置全体 図7 半球状共焦点撮影のための光学系11) (a) 通常の開口 ングを我々の設計した多面体鏡を用いて実装した結果について述べる 4.1 合成開口撮影 8DRF の演算によって 被写界深度が極端に狭くなる合成開口撮影を実現できることを (b) z = 0mm にフォーカス (c) z = 1mm にフォーカス した合成開口 した合成開口 図9 合成開口撮影の結果 示す 図 9(a) に示すように ABCD の文字が印刷された紙の上に 1mm の間隔をあけ て EFGH の文字か印刷された透明な OHP シートが重ねられているシーンを対象とす 明を変化させたときの見え方を再現した Deebec らが提供している Light Probe を用い る (b) と (c) は それぞれ z = 0mm と z = 1mm にフォーカスした合成開口の例であり て計測した照明環境下では 図 10 のような見え方となった 左図のように赤みがかった照 被写界深度が極端に狭いために その奥行きに配置されたテクスチャのみがはっきりと視認 明下では 合成画像も同様の傾向がみられ 右図の屋外シーンの照明下では 全体に明るい できる このように 8DRF の演算で合成開口撮影を実現できることがわかる 合成画像を得られていることから 任意の照明下における指輪見え方を再現できることを確 4.2 イメージベーストライティング 認できる 物体に対して照明を変化させたときの見え方の変化は 8DRF の演算によって再現でき る ここでは 強い鏡面反射を生じる指輪を対象として 実際に計測された 8DRF から照 7 c 2010 Information Processing Society of Japan
8 8DRF CORE5 ( ) 10 : ( debeec/probes/) : 5. 8DRF 8DRF 1) M. Leoy and P. Hanrahan, Light field rendering, Proc. SIGGRAPH 96, pp.31 42, ) P. Deebec, Rendering Synthetic Objects into Real Scenes: Bridging Traditional and Image-based Graphics with Global Illmination and High Dynamic Range Photography, Proc. SIGGRAPH 98, pp , ) P. Debeec, T. Hawkins, C. Tcho, H. P. Diker, W. Sarokin, and M. Sagar, Acqiring the Reflectance Field of a Hman Face, Proc. SIGGRAPH2000, pp , ) V. Massels, P. Peers, and P. Dtré, and Y. D. Willems, Relighting with 4D incident light fields, Proc. SIGGRAPH2003, pp , ) W. Matsik, H. Pfister, A. Ngan, P. Beardsley, R. Ziegler, L. McMillan, Image- Based 3D Photography sing Opacity Hlls, Proc. SIGGRAPH2002, pp , ) G. Müller, G. H. Bendels, and R. Klein, Rapid Synchronos Acqisition of Geometry and Appearance of Cltral Heritage Artefacts, Proc. VAST2005, pp.13 20, ) M. Leoy, B. Chen, V. Vaish, M. Horowitz, I. McDowall, and M. Bolas, Synthetic Apertre Confocal Imaging, Proc. SIGGRAPH2004, pp , ) O. Cossairt, S. K. Nayar, and R. Ramamoorthi, Light Field Transfer: Global Illmination Between Real and Synthetic Objects, Proc. SIGGRAPH2008, pp.1 6, ) V. Vaish, B. Wilbrn, N. Joshi, and M. Leoy, Using Plane + Parallax for Calibrate Dense Camera Arrays, Proc. CVPR ) M. Minsky, Microscopy apparats, US Patent , ),,,,,,, 13 (MIRU2010), pp , c 2010 Information Processing Society of Japan
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