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1 NAIST-IS-MT
2 ( )
3 (AR) (CG) (GI) AR AR GI PRT(Pre-computed Radiance Transfer) SVBRDF(Spatially Varying Bidirectional Reflectance Distribution Function) AR,,, PRT, SVBRDF, NAIST-IS- MT , i
4 Photo-realistic Rendering of Virtual Objects in Augmented Reality Using Global Illumination Technique and Spatially Varying BRDF Tomoyuki Sonoda Abstract To improve photographic reality in augmented reality (AR), photometric registration is very important. In computer graphics (CG), global illumination (GI) techniques realize rich photographic reality. It is useful to apply GI to AR for photographic reality, i.e. soft shadow effect. Moreover, virtual objects should have spatially varying complex reflectance properties because real objects have such properties. This thesis describes a method for improving photographic reality of virtual objects in AR using precomputed radiance transfer (PRT) as a GI technique and spatially varying bidirectional reflectance distribution function (SVBRDF). The experiment shows the results of applying the real light environment to the virtual objects, which have SVBRDF, and shows the validity of the proposed method. Keywords: Augmented Reality, Photometric Registration, Global Illumination, PRT, SVBRDF Master s Thesis, Department of Information Systems, Graduate School of Information Science, Nara Institute of Science and Technology, NAIST-IS-MT , March 17, ii
5 PRT SVBRDF PRT SSDF SG SVBRDF SG AR AR AR iii
6 A. 47 A.1 SG A.2 SG SSDF A.3 SG SSDF A iv
7 1 [13] [26] [26] PRT [28] PRT [22] Pessoa [29] Knecht [30] Franke [31] Blinn-Phong [39] Cook-Torrance [39] Ward [39] Ashikhmin-Shirley [39] Lafortune [39] SVBRDF [40] V x SSDFV d x [25] SG [25] SVBRDF D AR AR v
8 29 AR AR AR vi
9 PC vii
10 1. (Augmented Reality:AR) [1] AR AR [2] [3, 4, 5] [6, 7] [8] AR AR AR [9, 10] GPS [11, 12] AR [13] 1
![(LI) 1 AR AR (a) (b) AR 1 [13] (CG) (GI)](/docs-images/93/112942003/images/11-0.jpg "PRT(Pre-computed Radiance Transfer)")
11 (LI) 1 AR AR (a) (b) AR 1 [13] (CG) (GI) PRT(Pre-computed Radiance Transfer) SVBRDF(Spatially Varying Bidirectional Reflectance Distribution Function) AR AR AR 2
12 AR 3
13 2. AR AR GI GI AR GI DCG LI GI GI (RS)[14, 15, 16] (RT)[17, 18, 19, 20, 21] PRT [22, 23, 24, 25] 1 2 4
![1 LI RS [14, 15] RS [16] RT PRT](/docs-images/93/112942003/images/14-0.jpg "[22] PRT [23, 24, 25] GI [16] 2")
14 1 LI RS [14, 15] RS [16] RT PRT [22] PRT [23, 24, 25] GI [16] 2 [26] 5
![[20] 3(b) [21] (a) (b) 3](/docs-images/93/112942003/images/15-0.jpg "[26] PRT (Image Based")
![Lighting: IBL[27]) PRT 4 5](/docs-images/93/112942003/images/15-1.jpg "PRT 4(b) 4(a) PRT [23, 24,")
15 [20] 3(b) [21] (a) (b) 3 [26] PRT (Image Based Lighting: IBL[27]) PRT 4 5 PRT 4(b) 4(a) PRT [23, 24, 25] 6
16 GI (a) (b) 4 PRT [28] AR Pessoa [29] IBL 6 7
17 (a) (b) 5 PRT [22] 8
18 IBL HDRI Knecht [30] [16] 7 Franke [31] PRT 9 AR GI 2.2 Bi-directional Reflectance Distribution Function: BRDF BRDF BRDF f r (ω i, ω o ) = dl r(ω o ) de i (ω i ) ω i ω o L r E i 9 (1)
19 6 Pessoa [29] 10
20 7 Knecht [30] 11
21 8 Franke [31] 12
![9 BRDF Lambert [32] Phong [33]](/docs-images/93/112942003/images/22-0.jpg "Blinn-Phong [34] 10 Phong Cook-Torrance")
22 9 BRDF Lambert [32] Phong [33] Blinn-Phong [34] 10 Phong Cook-Torrance [35] 11 13
23 Phong Ward [36] 12, Ashikhmin-Shirley [37] 13 Lafortune [38] 14 BRDF f r (x, ω i, ω o ) SVBRDF x SVBRDF SVBRDF BRDF SVBRDF 2.3 AR GI GI AR AR AR 14
![(a) Blinn-Phong(acrylic-blue) (b) Blinn-Phong(black-oxidized-steel) 10 Blinn-Phong [39] (a)](/docs-images/93/112942003/images/24-1.jpg "Cook-Torrance(acrylic-blue) (b) Cook-Torrance(black-oxidized-steel) 11 Cook-Torrance [39]")
24 (a) Blinn-Phong(acrylic-blue) (b) Blinn-Phong(black-oxidized-steel) 10 Blinn-Phong [39] (a) Cook-Torrance(acrylic-blue) (b) Cook-Torrance(black-oxidized-steel) 11 Cook-Torrance [39] 15
25 (a) Ward(acrylic-blue) (b) Ward(black-oxidized-steel) 12 Ward [39] (a) Ashikhmin-Shirley(acrylic-blue) (b) Ashikhmin-Shirley(black-oxidizedsteel) 13 Ashikhmin-Shirley [39] 16
26 (a) Lafortune(acrylic-blue) (b) Lafortune(black-oxidized-steel) 14 Lafortune [39] (a) (b) 15 SVBRDF [40] 17
27 PRT GI AR PRT PRT SVBRDF Wang PRT[25] 18
28 3. PRT SVBRDF 3.1 AR
29 AR AR PRT Wang PRT[25]. PRT PRT Wang Spherical Signed Distance Function(SSDF) Wang Spherical Gaussian(SG) Wang SVBRDF CG SG Wang 20
30 3.2.2 SSDF V x (i) x i 0 1 SSDF + min Arccos(t i), if V x (i) = 1; Vx d V (i) = x (t)=0 min Arccos(t i), if V x (i) = 0; V x(t)=1 V x (i) t i 17 V x (i) SSDF SSDF SSDF PCA PCA 48 (2) 17 V x SSDFV d x [25] 21
![3.2.3 SG SVBRDF SG G(v) Spherical Radial Basis Function G(v;p, λ, µ) = µe λ(v p 1) (3) p S 2 SG λ (0, + ) SG µ R SG v S 2 SG SG 18 Gaussian 18 SG [25]](/docs-images/93/112942003/images/31-0.jpg "ρ o (i) ρ o (i) = ρ(o, i) = k d + k s ρ s (o, i) (4) i o k d K s ρ s ρ s Torrance Microfacet theory[41] ρ s (o, i) = M o (i)d(h) h = o + i o + i 22")
31 3.2.3 SG SVBRDF SG G(v) Spherical Radial Basis Function G(v;p, λ, µ) = µe λ(v p 1) (3) p S 2 SG λ (0, + ) SG µ R SG v S 2 SG SG 18 Gaussian 18 SG [25] ρ o (i) ρ o (i) = ρ(o, i) = k d + k s ρ s (o, i) (4) i o k d K s ρ s ρ s Torrance Microfacet theory[41] ρ s (o, i) = M o (i)d(h) h = o + i o + i 22 (5)
32 Microfacet theory Cook-Torrance ρ s (o, i) = F CT (o, i)s CT (o, i) e (θ/m)2 (6) π(n i)(n o) M o (i) = F CT (o, i)s CT (o, i), D(h) = e (arccos(h n)/m)2 (7) π(n i)(n o) n F CT S CT m Microfacet theory SG M o (i)d(h) = e (arccos(h n)/m)2 M o (i)g(h;n, 2/m 2, 1) (8) Cook-Torrance SG SG SG mixture Cook-Torrance [35] Blinn-Phong [34] Ward [36] Ashikhmin-Shirley [37] BRDF Lafortune [38] SG PRT L (i) 23
33 SG mixture SG 10 L-BFGS-B[42] SG mixture SG SG L(i) G(v;p, λ, µ) L(i) = µ G(v;p, λ, 1)L(i)di S 2 (9) = µγ L (p, λ) (10) R(o) = k d R d + k s R s (o) (11) R(o) R d R s (o) R d = L(i)V (i)max(0, i n)di S 2 (12) R d (G(i;n x, 2.133, 1.170) L (i)) V d x (i) (13) R s (o) = L(i)ρ s (o, i)v (i)max(0, i n)di S 2 (14) R s (o) (G(i;n x, 2.133, 1.170) ρ s,x(i;o) V d x (i)) L(i) (15) n x ρ s,x(i;o) A 24
34 3.3 AR Kato [9] ARToolkit 19 PnP (Perspective n-point problem)[43, 44, 45] M cm M lw M wm M fm V v ARToolkit M p 3D R d R s (o) R d (G(i;n x, 2.133, 1.170) L (i)) V d x (i) π/2 (16) Rs(o) (G(i;n x, 2.133, 1.170) ρ s,x(i;o) V x d (i) ) L(i) (17) π/2 25
35 19 26
36 4. Wang PRT AR PC, 20 2, 3, 4 OpenGL Nvidia Cg AR ARToolkit 2 PC CPU Quad-Core AMD Opteron 2.81GHz GB Quadro FX GB 3 The Imaging Source DFx 31BU fps
37 (a) PC (b) (c) 20 28
38 4 Logicool Qcam Orbit/Sphere AF fps 4.1 AR 21,
39 AR 25 3D 26, 3D AR 27 26(a) (b) 5734 Blinn-Phong M o (i) = n + 2 (18) 2π D(h) = e n(1 (h n)) (19) n n = 0.5 AR 30
40 4.3 AR AR 28, 29, 30, 31 Blinn-Phong 23 Blinn-Phong n AR 23 SVBRDF (a) 3D 2,694 26(b) 3D 20,522 SG SG λ = 21000, 5250, 1312, 328, 82, 20, 5 1,931 31
41 AR 30fps GPU AR 32
42 25 33
43 (a) (b) 26 3D 34
44 (a) (b) 27 AR 35
45 (a) (b) 28 AR 1 36
46 (a) (b) 29 AR 2 37
47 (a) (b) 30 AR 3 38
48 (a) (b) 31 AR 4 39
49 5. AR AR AR Blinn-Phong SVBRDF AR λ SG GPU 40
50 41
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56 A. R(o) = k d R d + k s R s (o) (20) R d = (G(i;n x, 2.133, 1.170) L (i)) V d x (i) (21) R s (o) = (G(i;n x, 2.133, 1.170) ρ s,x(i;o) V d x (i)) L(i) (22) L (i) ρ s,x(i;o) SG A.1 SG (G 1 G 2 )(v) = G(v; p m p m, λ p m, µ 1 µ 2 e λ m( p m 1) ) (23) p m = fracλ 1 p 1 + λ 2 p 2 )λ 1 + λ 2 (24) λ m = λ 1 + λ 2 (25) A.2 SG SSDF G(i;p, λ, µ) V (i) = µf h (θ d, λ) (26) θ d = V d (p) (27) 1.05 f h (θ d, λ) ( ) 2π 1 + k λ e θ d 2 λ (1 e λ ) (28) k λ 0.204λ λ λ (29) 47
57 A.3 SG SSDF G(i;p, λ, µ) V (i) G(i;p, λ, f h(θ d, λ) f h ( π µ) (30), λ) 2 f h ( π 2, λ) = 2π λ (1 eλ ) (31) A.4 SG mixture h i ρ s (i;o) = M o (i) D (h) (32) n D (h) = G(h;p D i, λ D i, µ D i ) (33) i=1 D (h) SG mixture W (i) = n G(h;p W i, λ W i, µ W i ) D (h) (34) i=1 i = 2(o h)h o (35) p W i = 2(o p D i )p D i o (36) λ W i = fracλ D i 4 p D i o (37) µ W i = µ D i (38) SG ρ s(i;o) = M o (i) W (i) n G(i;p W i, λ W i, M o (p W i )µ W i ) (39) i=1 48
3 3 3 Knecht (2-3fps) AR [3] 2. 2 Debevec High Dynamic Range( HDR) [4] HDR Derek [5] 2. 3 [6] 3. [6] x E(x) E(x) = 2π π 2 V (x, θ i, ϕ i )L(θ
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M. D. Wheler Cyra Technologies, Inc. 3 3 CAD albedo Mapping textures on 3D geometric model using reflectance image Ryo Kurazume M. D. Wheler Katsushi Ikeuchi The University oftokyo Cyra Technologies, Inc.
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UV 1,a) 1,b) 1,c) 1,d) 1,e) UV UV UV UV UV 1. 3D 3D 3D [1] 3D UV 1 UV UV UV: Ultraviolet 1 a) takatani.tsuyoshi.to2@is.naist.jp b) fujita.koki.fg9@is.naist.jp c) ktanaka@is.naist.jp d) funatomi@is.naist.jp
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