IPSJ SIG Technical Report Vol.2014-CG-157 No.15 Vol.2014-CVIM-194 No /11/21 1 1, (a) (b) (c) (a) 4 (b) (c) 1(a) 1(b) 1(c) 1. 1 Hiro

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1 1 1, (a) (b) (c) (a) (b) (c) 1(a) 1(b) 1(c) 1. 1 Hiroshima City University, Ozukahigashi 3 1, Asaminami-ku, Hiroshima city, Japan 1 Presently with The San-In Godo Bank, Ltd. 2. Hersch Chosson[1] Mitra Pauly[2] Yue [3] Papas [] 1

2 Nonoyama [5] Kawai[6] Amano[7] Valluzzi[8] Valluzzi[8] Kawai[6] Amano[7] Kawai[6] Amano[7] Bala [9] CMYK K CMY K CMY LED LED LED Bala [9] Drew Bala[10] Bala [9] LED LED LED Drew Bala[10] 3 3 Finlayson [12], [13] RGB XYZ [1], [15], [16] LED Kobayashi [17] 2 LED Morimoto [18] Johnson Fairchild[19] CG RGB Miyazaki [11] Miyazaki Miyazaki [11] Miyazaki 3. CIE XYZ X Y Z JIS Z nm nm 00nm 800nm λ X Y Z x(λ) ȳ(λ) z(λ) X Y Z 2. 2

3 x a.k.a. X Y Z P E s a.k.a. D w Light 1 E 1 Light 2 E 2 Mixed paint 1 E 1 D w1 E 2 D w1 Mixed Mixed paint 2 paint Mixed paint 3 E 1 D w2 E 1 D w3 E 1 D w E 2 D w2 E 2 D w3 E 2 D w CIE-XYZ value Spectral response Light 2 Object 3 2 X = Y = Z = E(λ)S(λ) x(λ)dλ, (1) E(λ)S(λ)ȳ(λ)dλ, (2) E(λ)S(λ) z(λ)dλ. (3) E(λ) S(λ) nm N b x =(X, Y, Z) (1) (2) (3) x = PEs. () 3 N b P 1 3 X Y Z x 1 x Nb P = ȳ 1 ȳ Nb. (5) z 1 z Nb N b 1 s N b N b E. E =diag(e 1,E 2,,E Nb ). (6) Oil paint database D Emitted light E d 11 d 21 d Nb1 Mixing weight w d 12 d 22 d Nb2 d 13 d 23 d Nb3 w 1 w 2 w 3 w Np d 1Np d 2Np d NbNp Lightness L* f L : XYZ L* Photoreceptor P N p N b N p D d 11 d 12 d 1Np d 21 d 22 d 2Np D = (7) d Nb 1 d Nb 2 d Nb N p N p N p N p 1 w Tominaga [20] Tominaga [20] Kubelka-Munk Tominaga Kubelka-Munk Lambert Tominaga [21] Lambert 3

4 Tominaga [20] Lambert Miyazaki [11] Miyazaki exponential color mixing model d w1 11 dw2 12 dwnp 1N p s = D w d w1 21 dw2 22 dwnp 2N p. (8). d w1 N b 1 dw2 N b 2 dwnp N b N p (8) 1 (9) (10) s i =exp ( w 1 log d i1 + w 2 log d i2 + w 3 log d i3 + + w Np log d inp ) (9) = d w1 i1 dw2 i2 dw3 i3 dwnp in p. (10) (9) (10) log 0 (10) 0log0 = =1 (9) Lambert.2 3 F ( ) where, {w 1, w 2, w 3, w } = argmin F (P, E 1, E 2, D, w 1, w 2, w 3, w ), (11) w 1,w 2,w 3,w F (P, E 1, E 2, D, w 1, w 2, w 3, w )= C 1 + C 2 + C 3 + C + C 5 + C 6, (12) { C 1 = { C 3 = C 5 = { c 1 (c 2 1 >T 1 ) c 1 (c 2 1 T 1 ), C 2 = { c 3 (c 3 2 >T 1 ) c 3 (c 3 2 T 1 ), C = I 1 (c 5 0) I 2 (T 2 <c 5 < 0) 1 I 3 c 5 (otherwise) I 1 (c 6 0) C 6 = I 2 (T 2 <c 6 < 0), 1 I 3 c 6 (otherwise) T 1 = 100, T 2 = 1, I 2 I 1 = , I 2 = 1000, I 3 = ( T 2 ) 1, c 1 = (100 f L (PE 1 D w1 ) f L (PE 1 D w2 ) ), c 2 = (100 f L (PE 1 D w3 ) f L (PE 1 D w ) ), c 3 = (100 f L (PE 2 D w1 ) f L (PE 2 D w ) ), c = (100 f L (PE 2 D w2 ) f L (PE 2 D w3 ) ),, c 2 (c 2 2 >T 1 ) c 2 (c 2 2 T 1 ), c (c 2 >T 1 ) c (c 2 T 1 ), c 5 = (100f L (PE 1 D w3 )) 2 + (100f L (PE 1 D w )) 2 (100f L (PE 1 D w1 )) 2 (100f L (PE 1 D w2 )) 2, c 6 = (100f L (PE 2 D w2 )) 2 + (100f L (PE 2 D w3 )) 2 (100f L (PE 2 D w1 )) 2 (100f L (PE 2 D w )) 2, N p w 1n =1, w 2n =1, w 3n =1, w n =1, n=1 N p n=1 N p n=1 N p n=1 0 w 1n, 0 w 2n, 0 w 3n, 0 w n, {n =1,,N p }. f L (X, Y, Z) (X, Y, Z) L*a*b* L* (11) Nelder-Mead [22] 5 C 1 C 1 (12) c 1 5 c 2 1 T 1 6 C 5 C 5 (12) c 5 6 c 5 0

5 7 8 5 C 1 6 C5 HSC T 2 T 2 T 2 C 1 C 5 C 1 C 5 (11) a*b* L* LED 5. 00nm 800nm HSC nm 800nm 5nm 81 N b =81 20 N p = V 6500K Ra D LED 9 10 V LED LED LED ND LED LED LED LED (CRD) LED LED [cd] 800[cd] LED5 20 5

6 11 LED 12 LED 13 LED NO LED LED1( LED). 16 LED2( LED) LED LED RGB LED 2 LED LED 16 LED RGB LED LED R G B LED LED LED LED LED LED LED LED Miyazaki [11] Drew Bala[10] 6

7 0.5 Mixed paint 1 Spectral reflectivity [no unit] 0 00 Wavelength [nm] 800 Spectral radiance [arb. unit] [W/sr/m 2 /nm with unknown scale] Wavelength [nm] 800 Mixed paint 2 Mixed paint 3 Mixed paint 60 Mixed paint 1 under Light 1 18 Mixed paint 2 under Light 1 Mixed paint 3 under Light 1 Mixed paint under Light 1 Mixed paint 1 under Light 2 Mixed paint 2 under Light 2 Mixed paint 3 under Light 2 Mixed paint under Light 2 2 LED [10], [11] Miyazaki [11] LED 2 2 [23] Morovič [2] 11 Tzeng [25] 6 [26] 7 LED LED * (B) [1] R. D. Hersch and S. Chosson, Band moiré images, SIG- GRAPH 200 Papers, pp , 200. [2] N. J. Mitra and M. Pauly, Shadow art, ACM Trans. Graph., vol. 28, no. 5, article 156, 7 pages, [3] Y. Yue, K. Iwasaki, B. Chen, Y. Dobashi, and T. Nishita, Pixel art with refracted light by rearrangeable sticks, Computer Graphics Forum, vol. 31, no. 2, pp , [] M. Papas, T. Houit, D. Nowrouzezahrai, M. Gross, and W. Jarosz, The magic lens: refractive steganography, ACM Trans. Graph., vol. 31, no. 6, article 186, 10 pages, [5] M. Nonoyama, F. Sakaue, and J. Sato, Multiplex image projection using multi-band projectors, in Proceeddings of the IEEE International Conference on Computer Vision (ICCV) Workshops, [6] N. Kawai, Bump mapping onto real objects, ACM SIG- GRAPH 2005 Sketches, article no. 12, [7] T. Amano, Shading illusion: A novel way for 3-D representation on the paper media, in Proceedings of Procams 2012 Workshop on CVPR2012, W11 01, pp. 1 6, [8] R. Valluzzi, LEDs illuminat metamerism in abstract art - no 2, fyjhlinm730, [9] R. Bala, K. M. Braun, and R. P. Loce, Watermark encoding and detection using narrowband illumination, in Proceedings of Seventeenth Color Imaging Conference, pp , [10] M. S. Drew and R. Bala, Sensor transforms to improve metamerism-based watermarking, in Proceedings of 18th Color Imaging Conference, pp , [11] D. Miyazaki, K. Takahashi, M. Baba, H. Aoki, R. Furukawa, M. Aoyama, and S. Hiura, Mixing paints for generating metamerism art under 2 lights and 3 object colors, in IEEE International Conference on Computer Vision Workshops, pp , [12] A. Alsam and G. Finlayson, Metamer sets without spectral calibration, J. Opt. Soc. Am. A, vol. 2, no. 9, pp , [13] G. D. Finlayson and P. Morovic, Metamer sets, J. Opt. Soc. Am. A, vol. 22, no. 5, pp , [1],, 3 SUPPLEMENT, pp , [15],,, 35 SUPPLEMENT, pp , [16], LED *1 miyazaki/ 7

8 , 36 SUPPLEMENT, pp , [17] K. Kobayashi, T. Yamada, A. Hiraishi, S. Nakauchi, Realtime optical monitoring of microbial growth using optimal combination of light-emitting diodes, Optical Engineering, vol. 51, no. 12, pp , [18] T. Morimoto, T. Mihashi, and K. Ikeuchi, Color restoration method based on spectral information using normalized cut, International Journal of Automation and Computing, vol. 5, no. 3, pp , [19] G. Johnson and M. Fairchild, Full-spectral color calculations in realistic image synthesis, IEEE Computer Graphics and Applications, vol. 19, no., pp. 7 53, [20] S. Tominaga and S. Nishi, Surface reflection properties of oil paints under various conditions, Proc. SPIE 6807, [21] S. Tominaga, H. Ujike, and T. Horiuchi, Surface reconstruction of oil paintings for digital archiving, Proc. IEEE Southwest Symposium on Image Analysis & Interpretation, pp , [22] W. H. Press et al., Numerical recipes in C: the art of scientific computing, Cambridge: Cambride University Press, 99 p., [23] Y. Fu, A. Lam, I. Sato, T. Okabe, and Y. Sato, Separating reflective and fluorescent components using high frequency illumination in the spectral domain, in Proceedings of the IEEE International Conference on Computer Vision, pp. 57 6, [2] P. Morovič, J. Morovič, J. Arnabat, and J. M. García-Reyero, Revisting spectral printing: a data driven approach, in Proceedings of 20th Color Imaging Conference, pp , [25] D.-Y. Tzeng and R. S. Berns, Spectral-based six-color separation minimizing metamerism, in Proceedings of IS&T/SID Eighth Color Imaging Conference, pp , [26],,, vol. 30, no. 1, pp. 2 3,

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