1 1, 1 1 1 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, 731 319 Japan 1 Presently with The San-In Godo Bank, Ltd. 2. Hersch Chosson[1] Mitra Pauly[2] Yue [3] Papas [] 1
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] 3 3 31 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 2 3 2 Miyazaki [11] Miyazaki 3. CIE XYZ X Y Z JIS Z8120 360 00nm 760 830nm 00nm 800nm λ X Y Z x(λ) ȳ(λ) z(λ) X Y Z 2. 2
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 = 800 00 800 00 800 00 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) 00 800nm 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 3.1.2.1 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
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 = 0 0 0 =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 = 100000, 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
7 8 5 C 1 6 C5 HSC-1700 0 0 T 2 T 2 T 2 C 1 C 5 C 1 C 5 (11) a*b* L* LED 5. 00nm 800nm HSC-1700 700nm 800nm 5nm 81 N b =81 20 N p =20 9 20 10 V 6500K Ra98 20 8 D LED 9 10 V LED LED LED ND 11 12 LED LED LED LED (CRD) LED 3 13 13 1 LED 0.015 30[cd] 800[cd] LED5 20 5
11 LED 12 LED 13 LED 1 1 2 3 0.000 0.000 0.000 0.092 0.011 0.000 0.163 0.06 0.026 0.000 0.000 0.035 0.006 0.000 0.05 0.000 0.000 0.000 0.000 0.000 0.011 0.08 0.000 0.058 NO. 0.085 0.000 0.000 0.000 0.000 0.017 0.270 0.000 0.16 0.000 0.000 0.087 0.122 0.006 0.000 0.011 0.106 0.000 0.000 0.035 0.000 0.032 0.029 0.000 0.192 0.57 0.000 0.000 0.000 0.055 0.16 0.000 0.000 0.000 0.053 0.27 0.230 0.000 0.000 0.06 0.000 0.000 0.000 0.132 0.000 0.000 0.000 0.103 0.000 0.02 0.286 0.000 0.06 0.000 0.000 0.108 1 LED 1 20 1 2 3 15 LED1( LED). 16 LED2( LED) LED 15 1 2 3 1 2 LED 16 1 2 3 1 RGB 2 17 18 2 1 LED 2 LED 1 3 15 2 LED 16 LED RGB LED LED R G B LED 1 97 18 255 LED 2 105 162 26 LED 3 65 101 163 LED 58 93 152 LED 1 26 72 103 LED 2 11 31 53 LED 3 152 2 60 LED 251 75 103 6. 2 Miyazaki [11] Drew Bala[10] 6
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] 17 0 00 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] 2 3 2 LED 2 2 [23] Morovič [2] 11 Tzeng [25] 6 [26] 7 LED LED *1 2700176 (B) 22135003 [1] R. D. Hersch and S. Chosson, Band moiré images, SIG- GRAPH 200 Papers, pp. 239 27, 200. [2] N. J. Mitra and M. Pauly, Shadow art, ACM Trans. Graph., vol. 28, no. 5, article 156, 7 pages, 2009. [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. 575 582, 2012. [] 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, 2012. [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, 2013. [6] N. Kawai, Bump mapping onto real objects, ACM SIG- GRAPH 2005 Sketches, article no. 12, 2005. [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, 2012. [8] R. Valluzzi, LEDs illuminat metamerism in abstract art - no 2, http://www.youtube.com/watch?v= fyjhlinm730, 2012. [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. 139 12, 2009. [10] M. S. Drew and R. Bala, Sensor transforms to improve metamerism-based watermarking, in Proceedings of 18th Color Imaging Conference, pp. 22 26, 2010. [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. 87 882, 2013. [12] A. Alsam and G. Finlayson, Metamer sets without spectral calibration, J. Opt. Soc. Am. A, vol. 2, no. 9, pp. 2505 2512, 2007. [13] G. D. Finlayson and P. Morovic, Metamer sets, J. Opt. Soc. Am. A, vol. 22, no. 5, pp. 810 189, 2005. [1],, 3 SUPPLEMENT, pp. 108 109, 2010. [15],,, 35 SUPPLEMENT, pp. 10 105, 2011. [16], LED *1 http://www.cg.info.hiroshima-cu.ac.jp/ miyazaki/ 7
, 36 SUPPLEMENT, pp. 128 129, 2012. [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. 123201-1 123201-8, 2012. [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. 226 233, 2008. [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, 1999. [20] S. Tominaga and S. Nishi, Surface reflection properties of oil paints under various conditions, Proc. SPIE 6807, 2008. [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. 173 176, 2010. [22] W. H. Press et al., Numerical recipes in C: the art of scientific computing, Cambridge: Cambride University Press, 99 p., 1997. [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, 2013. [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. 335 30, 2012. [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. 32 37, 2000. [26],,, vol. 30, no. 1, pp. 2 3, 2006. 8