Ω + θr θi H α N β = + φ φ r x φ i 2 diffuse component specular component (a) 1 (b) BRDF (R) (G) (B) BRDF f BRDF (x, θ i, φ i, θ r, φ r ). (1) 1(b) N φ
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1 1 Measurement and Modeling of Reflection and Scattering Yasuhiro Mukaigawa 1 When an object is illuminated, part of the light reflects on the surface and some scatter underneath the surface. The appearance of the object observed by a camera or human eyes depends on a material and micro-structure of the surface. To analyze a change of the surface intensity due to lighting and viewing directions, a variety of models and measuring methods have been proposed in the past. This paper focuses on optical phenomena of the reflection and scattering and outlines their methods of the measurement and models Osaka University CG CG CG C CG C CG CG C CG CG C (BRDF: Bi-directional Reflectance Distribution Function) x BRDF 1(a) (θ i, φ i ) (θ r, φ r) 1 c 2010 Information Processing Society of Japan
2 Ω + θr θi H α N β = + φ φ r x φ i 2 diffuse component specular component (a) 1 (b) BRDF (R) (G) (B) BRDF f BRDF (x, θ i, φ i, θ r, φ r ). (1) 1(b) N φ = φ r φ i f isotropic BRDF (x, θ i, θ r, φ). (2) BRDF -1: f BRDF (x,, ) = f BRDF (x,, ). (3) -2: Ω + f BRDF (x,, )(N )d 1. (4) Ω + BRDF BRDF (4) cos θ r (= N ) BRDF ambert i = ρ d max(0, N ). (5) ρ d ambert Oren-Nayar 1) c 2010 Information Processing Society of Japan
3 Phong 2) β i = ρ s cos n β. (6) ρ s n CG Torrance-Sparrow 3) Torrance-Sparrow Torrance-Sparrow Blinn 4) Blinn i = ρ s DGF N. (7) D G F D D H N α D 1 α Phong Phong D 1 = cos n 1 α. (8) D 2 Torrance-Sparrow D 2 = e (αn 2) 2. (9) D 3 Trowbridge-Reitz ( ) (n 3 ) 2 2 D 3 =. (10) cos 2 α((n 3 ) 2 1) + 1 G ( G = min 1, 2(N H)(N ), ( H) ) 2(N H)(N ). (11) ( H) F 1 ( ) F = 1 (g c) 2 2 (g + c). (c(g + c) 1)2 1 +, (12) 2 (c(g c) + 1) 2 c = H, g = η 2 + c 2 1. (13) η Cook-Torrance 5) Torrance-Sparrow D D 4 = 1 (n 4 ) 2 cos 4 α e ( ) tan 2 α (n 4 ) 2. (14) Cook-Torrance 1 3 c 2010 Information Processing Society of Japan
4 Ward 6) BRDF Torrance-Sparrow D afortune 7) BRDF BRDF BTF (Bi-directional Texture Function) (a) (c) Ellipsoidal mirror Object (b) Plate mirror (d) 3. CG 2.1 BRDF BRDF 3.1 BRDF BRDF (a) BRDF Projector Beam splitter Camera (e) BRDF (RCG-2) 18) 3 BRDF 8) BRDF BRDF BRDF 3(b) BRDF 9) 4 c 2010 Information Processing Society of Japan
5 BRDF 10) BRDF 11) BRDF (c) BRDF ) ED 13) BRDF BRDF 14) 15) 16) 17) 3(d) 3(e) BRDF 18) BRDF 3.2 BRDF BRDF CG 5-1 RGB BRDF BRDF c 2010 Information Processing Society of Japan
6 (x,ω) absorption (x,ω)+d(x,ω) out-scattering in-scattering ds 4 19) 4 x ω (x, ω) x ds d(x, ω) x (x, ω) + d(x, ω) σ a(x) d(x, ω) = σ a (x)(x, ω)ds. (15) [m 1 ] σ s(x) d(x, ω) = σ s (x)(x, ω)ds. (16) [m 1 ] σ t = σ a + σ s d(x, ω) = σ t (x)(x, ω)ds, (17) 5 x ω (x, ω ) ω x ω p(x, ω, ω) ( ) d(x, ω) = σ s (x) p(x, ω, ω)(x, ω )dω ds. (18) Ω Ω x p ω ω θ p(θ) = 1 4π 1 g 2. (19) (1 + g 2 2g cos θ) 2 3 g 5 g x ω (x, ω) d(x, ω) ( d(x, ω) = σ t(x)(x, ω)ds + σ s(x) 4.2 ) p(x, ω, ω)(x, ω )dω ds. (20) Ω 6(a) x 6(b) x i x o 6 c 2010 Information Processing Society of Japan
7 x x i x o xi xo (a) (b) 6 d1 xm θ d2 p(θ) 8 (a) 7 (b) BSSRDF: Bidirectional Scattering Surface Reflectance Distribution FunctionBSS- RDF x i x o f BSSRDF (x i,, x o, ). (21) 7 f single BSSRDF f multiple BSSRDF 1 f BSSRDF (x i,, x o, ) = f single BSSRDF (x i,, x o, ) + f multiple BSSRDF (x i,, x o, ). (22) x i x m x o x i x m d 1 e σ td 1 x m θ σ s p(θ) x m x o d 2 e σ td 2 f single BSSRDF (x i,, x o, ) = σ s p(θ)e σ t(d 1 +d 2 ). (23) ) 20) 21) 7 c 2010 Information Processing Society of Japan
8 z v r z r 10 9 Jensen 22) BSSRDF f multiple BSSRDF (x i,, x o, ) = 1 π F t(η, )R d (x i, x o )F t (η, ) (24) η F t R d (x i, x o) x i x o 2 r = x o x i R d (r) = α ( {z r σ tr + 1 ) e σ tr d r ( +z v σ tr + 1 ) } e σ tr d v 4π d r d v d 2 r d r = r 2 + zr, 2 d v = r 2 + zv, 2 z r = 1 σ t, z v = z r (1 + 4 A) (26) 3 d 2 v (25) A = 1 + F dr, F dr = η (27) 1 F dr η 2 η σ tr = 3σ a σ t, σ t = σ s + σ a, σ s = σ s (1 g), α = σ s σ t σ s, σ a, η, g 9 (28) 23) GPU 24) 25) C Narasimhan 26) Narasimhan 27) 8 c 2010 Information Processing Society of Japan
9 (a) (b) (c) 12 PO-Ray (a) 22) (b) 28) (c) 29) 30) 31) 5.3 BSSRDF 3.2 BRDF BSSRDF BSSRDF Peers 32) BSSRDF BSSRDF 6. CG/C 6.1 PO-Ray (a) (b) CG 13 PO-Ray PO-Ray (Persistence of ision Ray-Tracer) CG PO-Ray CG Windows, Mac OS X, inux SunOS UNIX MS-DOS PO-Ray CG C 12 9 c 2010 Information Processing Society of Japan
10 3.1.4 BRDF 13(a) BRDF 1 1 BRDF PO-Ray 13(b) (a) Phong void do_phong() BRDF 6.2 PBRT SIGGRAPH pbrt Matt Pharr and Greg Humphreys, PHYSICAY BASED RENDERING FROM THEORY TO IMPEMENTATION, Elsevier (ISBN ) CG CG pbrt BRDF BRDF pbrt PO-Ray C SIGGRAPH2010 pbrt BRDF 6.3 CG Magic 2007 CG Magic, 1 pbrt CG SIGGRAPH CG/C C C CG C 7. C 1) M. Oren and S. K. Nayar, Generalization of ambert s Reflectance Model, Proc. SIGGRAPH 94, pp , ) B. T. Phong, Illumination for computer generated pictures, Proc. SIG- GRAPH 75. pp , ) K. E. Torrance and E. M. Sparrow, Theory for Off-Specular Reflection From Roughened Surfaces, JOSA, ol. 57, Issue 9, pp , ) J. F. Blinn, Models of light reflection for computer synthesized pictures, Proc. SIGGRAPH 77, pp , ) R.. Cook and K. E. Torrance, A reflectance model for computer graphics, Proc. SIGGRAPH 81, pp , ) G.J.Ward, Measuring and Modeling anisotropic reflection, Proc. SIG- GRAPH 92, pp , ) E. P. F. afortune, S. C. Foo, K. E. Torrance, and D. P. Greenberg, Non-inear 10 c 2010 Information Processing Society of Japan
11 Approximation of Reflectance Functions, Proc. SIGGRAPH 97, pp , ) H. i, S. C. Foo, K. E. Torrance, and S. H. Westin, Automated three-axis gonioreflectometer for computer graphics applications, Proc. SPIE, ol.5878, pp , ) S. R. Marschner, S. H. Westin, E. P. F. afortune, K. E. Torrance, Image-Based Bidirectional Reflectance Distribution Function Measurement, Applied Optics, ol.39, No.16, pp , ) R. u, J. J. Koenderink, and A. M.. Kappers, Optical Properties (Bidirectional Reflection Distribution Functions) of elvet, Applied Optics, ol.37, No.25, pp , ) S. R. Marschner, S. H. Westin, E. P. F. afortune, K. E. Torrance, and D. P. Greenberg, Image-Based BRDF Measurement Including Human Skin, Proc. 10th Eurographics Workshop on Rendering, pp , ) G. Müller, G. H. Bendels, and R. Klein, Rapid Synchronous Acquisition of Geometry and Appearance of Cultural Heritage Artefacts, AST2005, pp13-20, ) M. Ben-Ezra, J. Wang, B. Wilburn, X. i, and. Ma, An ED-only BRDF Measurement Device, Proc. CPR2008, pp.1-8, ) P. R. Mattison, M. S. Dombrowski, J. M. orenz, K. J. Davis, H. C. Mann, P. Johnson, and B. Foos, Handheld directional reflectometer: an angular imaging device to measure BRDF and HDR in real time, Proc. SPIE ol.3426, pp , ) K. J. Dana and J. Wang, Device for convenient measurement of spatially varying bidirectional reflectance, J. Opt. Soc. Am. A, ol.21, Issue 1, pp.1-12, ) S. Kuthirummal and S. K. Nayar, Multiview Radial Catadioptric Imaging for Scene Capture, Proc. SIGGRAPH2006, pp , ) J. Y. Han and K. Perlin, Measuring Bidirectional Texture Reflectance with a Kaleidoscope, ACM Transactions on Graphics, ol.22, No.3, pp , ) Y.Mukaigawa, K.Sumino, Y.Yagi, Rapid BRDF Measurement using an Ellipsoidal Mirror and a Projector, IPSJ Transactions on Computer ision and Applications, ol.1, pp.21-32, ) J. Stam, Multiple scattering as a diffusion process, Proc. Eurographics Rendering Workshop, ) M. Pharr and P. Hanrahan, Monte Carlo evaluation of non-linear scattering equations for subsurface reflection, Proc. SIGGRAPH2000, pp.75-84, ) H. W. Jensen and P.H. Christensen, Efficient Simulation of ight Transport in Scenes with Participating Media using Photon Maps, Proc. SIGGRAPH 98, pp , ) H. W. Jensen, S. R. Marschner, M. evoy, and P. Hanrahan, A Practical Model for Subsurface ight Transport, Proc. SIGGRAPH2001, pp , ) C. Donner H. W. Jensen, ight Diffusion in Multi-ayered Translucent Materials, Proc. SIGGRAPH2005, pp , ) E.d Eon, D. uebke, and E. Enderton, Efficient Rendering of Human Skin, Eurographics Symposium on Rendering, ) C. Donner,J. awrence, R. Ramamoorthi, T. Hachisuka, H. W. Jensen, and S. K. Nayar, An empirical BSSRDF model, Proc. SIGGRAPH2009, pp.1-10, ) S. G. Narasimhan, S. K. Nayar, B. Sun, and S. J. Koppal, Structured ight in Scattering Media, Proc. ICC 05, ol.1, pp , ) S. G. Narasimhan, M. Gupta, C. Donner, R. Ramamoorthi, S. K. Nayar, and H. W. Jensen, Acquiring Scattering Properties of Participating Media by Dilution, Proc. SIGGRAPH2006, pp , ) M. Goesele, H. P. A. ensch, J. ang, C. Fuchs, and H. P. Seidel, Disco - Acquisition of Translucent Objects, Proc. SIGGRAPH2004, pp , ) A. Ghosh, T. Hawkins, P. Peers, S. Frederiksen, and P. Debevec, Practical Modeling and Acquisition of ayered Facial Reflectance, Proc. SIGGRAPH Asia ) S. Tariq, A. Gardner, I. lamas, A. Jones, P. Debevec, and G. Turk, Efficient Estimation of Spatially arying Subsurface Scattering Parameters, ision, Modeling, and isualization (M2006), ) T. Weyrich, W. Matusik, H. Pfister, B. Bickel, C. Donner, C. Tu, J. McAndless, J. ee, A. Ngan, H. W. Jensen, and M. Gross, Analysis of Human Faces using a Measurement-Based Skin Reflectance Model, Proc. SIGGRAPH2006, pp , ) P. Peers, K. vom Berge,, W. Matusik, R. Ramamoorthi, J. awrence, S. Rusinkiewicz, and P. Dutre, A Compact Factored Representation of Heterogeneous Subsurface Scattering Proc. SIGGRAPH2006, pp , c 2010 Information Processing Society of Japan
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1,a) 1,b) 1,c) 1,d) 1. CG 1 1 630 0192 8916 5 a) kushida.takahiro.kh3@is.naist.jp b) funatomi@is.naist.jp c) hkubo@is.naist.jp d) mukaigawa@is.naist.jp 散乱なし 散乱あり 1 2. c 2017 Information Processing Society
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