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1 2003 : ( ) :
2 Phong Torrance-Sparrow i
3 D-3D ii
4 1 1.1 CG [1, 2] Physics- Based Vision boivin [2] boivin 2D-3D
5 ) [13] [21] PC [14, 20] 2 3 [24] 2 3 2D-3D 3 2D-2D [9, 10] 1 [11, 12] CG 2
6 1.1: 3
7 1.4 2 : 3 : 4 : 5 : 6 : 7 : 4
8 Iterative Closest Point(ICP) [15] ICP (1) (2) (3) 3 2 5
9 3 3 [16] 3 [17, 18] [13] 6
10 E( p) = 1 N(M 1) N i M ρ(z ij ( p)) (2.1) j p = ( t, q) (2.2) z ij ( p) = R( q) x i + t y ij 2 (2.3) ρ(z ij ( p)) = log( z ij( p) 2 ) (2.4) N M x i i y ij j x i 2.2 t q (7 ) M 7 E p = 1 N(M 1) = 1 N(M 1) N i N i M j M j ρ(z ij ) z ij z ij p w(z ij )z ij z ij p (2.5) w(z ij ) = 1 z ij ρ(z ij ) z ij (2.6) z ij / p [19] 7
11 (R(q) x i ) = 2C( x) = 2C( x) T (2.7) q ql C( x) 0 a z a y C( d) = a z 0 a x (2.8) a y a x 0 d = a x a y a z (2.9) a b = C( a) b (2.10) z ij ( p) p = 2(R(q) x i + t y ij ) (R(q) x i + t y ij ) p [ ] 2( x i + t y ij ) = 4C( x i ) T ( x i + t y ij ) [ ] 2( x i + t y ij ) = 4 x i ( t y ij ) qi (2.11) Fletcher-Reeves Polak-Riviere kd-tree [22] 8
12 2.2.2 PC [14] x f(x) f(x) 0 f(x) N x f(x) Wheeler [21] f(x) 9
13 k-d tree [22] 2 SmaeSuface( p 0, n o, p 1, n 1 ) = { True ( p0 p 1 δ d ) (n 0 n 1 cos θ n ) False otherwise δ d θ n octree 0 marching-cubes algorithm [23]
14 marching-cubes algorithm [23] : 11
15 F f I I P (X, Y, Z) I P (X c, Y c, Z c ) P X c Y c Z c 0 X = 0 + α Y, Z = 0 (3.1) f f + Z 12
16 X c = fx/(f + Z) Y c = fy/(f + Z) Z c = 0 (3.2) (X, Y, Z) W h (X h, Y h, Z h, W h ) X = X h /W h Y = Y h /W h (3.3) Z = Z h /W h X ch Y ch X ch W ch X = Y Z 0 0 1/f 1 1 (3.4) 4 4 [X, Y, Z, 1] T [X ch, Y ch, Z ch, W ch ] T P P 13
17 3.1: P P P 3.2 T T 11 T 12 T 13 T 14 T 21 T 22 T 23 T 24 T = T 31 T 32 T 33 T (3.5) P P 14
18 X ch Y ch Z ch W ch T 11 T 12 T 13 T 14 X = T 21 T 22 T 23 T 24 Y T 31 T 32 T 33 T 34 Z 0 0 1/f T 11 T 12 T 13 T 14 X T 21 T 22 T 23 T 24 Y = Z T 31 /f T 32 /f T 33 /f T 34 /f (3.6) Zch 0 (Xc Yc) H c X c C 11 C 12 C 13 C X 14 Y H c Y c = C 21 C 22 C 23 C 24 Z H c C 31 C 32 C 33 C 34 1 (3.7) 3 4 C [24] occluding boundary P P 2. P 2 P 15
19 3.2: 3. C P 4. P z 3 P i z i z z z = z sin θ i (3.8) E (t) (p (t) 1 ) = N i ρ(z (t) i (t) (p (t) )) (3.9) i ρ(z i (t,s) (p (t) )) + 1 N (t) s U(t) 16
20 3.3: z ρ(z) = log(1 + 1 z 2 ) (3.10) 2 σ t p (t) t N i 3.10 M
21 3.4: z 3.3 2D-3D 2D-3D 3.5( ) ( ) 2D-3D 18
22 3.5: 2D-3D ( ) ( ) 19
23 pigment (a) (c) (b) 2 20
24 : 21
![4.2: 4.2 4.2.1 Phong Phong [25] Phong I d = I i K d cos α = I i](/docs-images/92/108072334/images/25-0.jpg "K d (L N) (4.1) I d I i K d α L N Phong S = I i W cos n γ (4.")
25 4.2: Phong Phong [25] Phong I d = I i K d cos α = I i K d (L N) (4.1) I d I i K d α L N Phong S = I i W cos n γ (4.2) 22
26 S i n =0 γ I a K a I = K d cos α + I i W cos n γ + I a K a (4.3) k d α I a k a LIGHT SOURCE DIRECTION SARFACE NORMAL REFLECTION DIRECTION VIEWING DIRECTION L N α α γ OBJECT 4.3: Phong Model Torrance-Sparrow Phong Torrance-Sparrow Torrance-Sparrow Blinn Torrance Sparrow Phong [26] 23
27 Torrance-Sparrow α = cos 1 (N H) b sigma P (α) = bexp( α 2 /2 σ 2 ) (4.4) α = cos 1 (N H) b g V L H L V 2 G = min{1, 2(N H)(N V ), (V H) 2(N H)(N L) } (4.5) (V H) F (θ, η, λ) θ = cos 1 (N V ) λ η Torrance-Sparrow R(N, V, L, g, η, λ) = F (N, L, η, λ)p (N, V, L, g)g(n, V, L) (N V ) (4.6) F G 1 Torrance-Sparrow exp( α2 ) 2σ I = I d + K 2 s (4.7) cos θ
28 LIGHT SOURCE DIRECTION L SARFACE NORMAL N A BISECTOR H VIEWING DIRECTION V α θ OBJECT 4.4: Torrance-Sparrow Model
29 ( 4.5(a)) ( ) ( ) ( 4.5(b)) 2. ( 4.5(c)) 3. (2) ( 4.5(d)) 4. ( 4.5(e)) ( 4.5(f)) 26
30 4.5: 27
31 4.3.3 Torrance-Sparrow [3] [ i c = k d,c cos θ i + k ] s,c exp[ α2 cos θ r 2σ ] Lc (4.8) 2 R 2 [4] c RGB i c L c R 2 k d,c k s,c σ θ i θ r α 2 ( 4.6) surface normal incident light bisector view object surface 4.6: (4.8) k d,c k s,c L c (4.8) K d,c = k d,c L c (4.9) K s,c = k s,c L c (4.10) I c = K d,c cos θ i + K s,c cos θ r exp[ α2 2σ 2 ] (4.11) 28
32 I c = i c R 2 (4.12) (4.11) K d = [K d,r, K d,g, K d,b ] T K s = [K s,r, K s,g, K s,b ] T σ K d K s σ (4.9) (4.10) K d K s RGB RGB c RGB N p L p V p L p N p V p L p = N p + (N p, V p )N p V p (4.13) N p V p 3 2 L p L 3 P L p t L = P + tl p (4.14) L t ( (4.11) 1 ) t f N j ( f(x 1 (t),, x Nj (t)) = x j (t) 1 N j j=1 29 N j l=1 ) 2 x l (t) (4.15)
33 N j x j (t) x j (t) = I (j) cos(θ (j) i (t)) (4.16) I (j) θ (j) i (t) j f (4.15) t f t t 1 = t t t 2 = t t 3 = t+ t 3 f(x 1 (t n ),, x Nj (t n )) (n = 1, 2, 3) f t n t (4.14) L t K d 2 N j ( 2 E 1 (K d ) = I (j) K d cos(θ (j) i (t ))) (4.17) j=1 K d N j / N j Kd = I (j) cos(θ (j) i (t )) (4.18) j=1 j=1 ( ) N k k I (k) s = I (k) K d cos(θ (k) i (t )) (4.19) ( (4.11) 2 ) 30
34 I s = K ] s exp [ α2 cos θ r 2σ 2 (4.20) [4] Y = 1 σ 2 X + ln K s (4.21) X = α2 2 (4.22) Y = ln I s + ln cos θ r (4.23) N k (4.22) (4.23) X Y (4.21) 2 (4.21) K s + σ+ K s + σ+ 2 N k ( E 2 (K s, σ) = I s (k) K s [ k=1 cos(θ r (k) ) exp (α(k) (t )) 2 ]) 2 2σ 2 (4.24) (4.24) 1) 2) 1) σ K s N k K s = k=1 I (k) s / Nk k=1 1 cos(θ r (k) ) exp [ α(k) (t ) 2 2σ 2 ] (4.25) 31
35 2) K s κ (n) = 1 (4.26) σ (n) N k ( κ (n+1) = κ (n) γ I s (k) K s k=1 cos(θ r (k) ) exp [ (α(k) (t )) 2 (κ (n) ) 2 ] )2 K s (α (k) (t )) 2 κ (n) 2 cos(θ r (k) ) exp [ (α(k) (t )) 2 (κ (n) ) 2 ] (4.27) 2 σ (n+1) = 1 (4.28) κ (n+1) 3 σ n γ K s σ [8] N k I (k) d = I (k) K s [ cos(θ (k) ) exp (α(k) (t )) 2 ] 2(σ ) 2 r (4.29) 2 (4.24) (4.21) 32
36 5 5.1 ( 5.1) CYRAX ( 5.3) 5.1: 33
37 5.2: CYRAX : CYRAX2500 Device name CYRAX2500 Supplier Cyla Inc.(USA) Scanning length m Resolution of range 4mm Resolution of derection 60 µ radians Sampling rate maximum 1,000 pixel/sec 34
38 5.3: 35
39 : 36
40 : 37
41 ( ) ( ) : 5.2: K d (R, G, B) ( , , ) K s (R, G, B) ( , , ) σ
42 5.3: K d (R, G, B) ( , , ) K s (R, G, B) ( , , ) σ : 39
43 ( 5.9,5.10,5.11) ( 5.12) 5.8: 40
44 5.9: 5.10: 5.11: 41
45 5.12: 42
46 D-3D 2D-3D 2D-3D 2 3 [24]. 2D-3D D-3D 6 20 ( (a), (b), (c) ) 6.1 (a) (b) (b) (c)
47 3 6.1: 2D-3D : 6 (a) : (b) : 20 (c) 44
48 (A-B) RGB A-B RGB 256 CG 45
49 6.2: : :R 46
50 6.3: :G :B 47
51 6.4: 6.1: (RGB) R G B
52 ,6.6 1 RGB RGB 49
53 6.5: : :R 50
54 6.6: :G :B 51
55 6.7: 6.2: (RGB) R G B ,6.9 1 RGB RGB 52
56 CG 6.8: : :R 53
57 6.9: :G :B 54
58 6.10: 6.3: (RGB) R G B
59 6.3 boivin [2] boivin 6.3 boivin CAD 2D-3D 2D-3D boivin 6.4: boivin 2D-3D boivin 56
60 D-3D 1 57
61 3 2 2 M2 M
62 [1] D. Miyazaki, T. Oishi, T. Nishikawa, R. Sagawa, K. Nishino, T. Tomomatsu, Y. Takase, K. Ikeuchi, The Great Buddha Prohect: Modelling Cultural Heritage through Observation, VSMM2000( 6th international conference on virtual sysytems and multimedia), pp , 2000 [2] S. Boivin, A. Gagalowicz, Image-Based Rendering of Diffuse, Specular and Glossy Surfaces from a Single Image, Computer Graphics Proceedings, SIGGRAPH2001, pp , [3] K. E. Torrance and E. M. Sparrow, Theory of off-specular reflection from roughened surfaces, Journal of the Optical Society of America, Vol.57, pp , [4] K. Ikeuchi and K. Sato, Determining reflectance properties of an object using range and brightness images, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol.13, No.11, pp , [5] R. Ramamoorthi and P. Hanrahan, A signal processing framework for inverse rendering, Computer Graphics Proceedings, SIG- GRAPH2001, pp , [6] S. Tominaga and N. Tanaka, Estimating reflection parameters from a single color image, IEEE Computer Graphics and Applications, Vol.20, No.5, pp.58-66, [7] G. D. Finlayson and G. Schaefer, Solving for color constancy using constrained dichromatic reflection model, Inter. J. Computer Vision, Vol42, No.3, pp ,
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64 [18] P. Neugenbauer, Geometrical cloning of 3D objects via simultaneous registration of multiple range images, Proc. International Conference on Shape Modeling and Application, pp , March, [19] M. Wheeler, Automatic Modeling and Localization for Object Recognition, PhDthesis, School of Computer Science, Carnegie Mellon University, [20] R. Sagawa, K. Nishino, K. Ikeuchi, Robust and Adaptive Integration of Multiple Range Images with Photometrics Attributes, IEEE Computer Society Conference on Computer Visionand Pattern Recognition, vol2, pp ,2001. [21] M. Wheeler, Y. Sato, K. Ikeuchi, Consensus surfaces for modeling 3D objects from multiple range images, Proc. International Conference on Computer Vision (ICCV), pp , Jan, [22] J. H. Friedman, J. Bentley, R. Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Transactions on Mathematical Software, pp , [23] W. E. Lorensen, W. E. and H. E. Cline, Marching Cubes : a high resolution 3D surface reconstruction algorithm, Proc. SIG- GRAPH 96, pp [24], 3,, [25],,, pp37-41,1998 [26] K. Ikeuchi, K. Sato, Determining Reflectance Properties of an Object Using Range and Brightness Images, IEEE TRAMSAC- TIONS ON PATTERN ANALYSIS AND MACHINE INTELLI- GENCE, Vol. 13, No. 11, Nov,
65 142 title: date:
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社団法人人工知能学会 Japanese Society for Artificial Intelligence 人工知能学会研究会資料 JSAI Technical Report SIG-Challenge-B3 (5/5) RoboCup SSL Humanoid A Proposal and its Application of Color Voxel Server for RoboCup SSL
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Partial Copy Detection of Line Drawings from a Large-Scale Database Weihan Sun, Koichi Kise Graduate School of Engineering, Osaka Prefecture University E-mail: sunweihan@m.cs.osakafu-u.ac.jp, kise@cs.osakafu-u.ac.jp
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IP 06 16 / IIS 06 32 3 3-D Environment Modeling from Images Acquired with an Omni-Directional Camera Mounted on a Mobile Robot Atsushi Yamashita, Tomoaki Harada, Ryosuke Kawanishi, Toru Kaneko (Shizuoka
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情報処理学会研究報告 方向の組み合わせを変えながら反射光の強度を計測する この方法は単純であるが入射方向と反射方向の組み合わせ を同時に 1 つしか計測できないため すべての方向を計 測するには膨大な計測回数が必要となる問題がある その ため 計測を効率的に行う方法がこれまでに提案されてい る [3
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