メタメリズムを使ったアート作品を作るための絵の具の調合割合を計算する手法を開発しました．ある光のもとで観測した油絵と別の光のもとで観測した油絵が異なる絵に見えるトリックアート作品を作ることができます． We proposed a method to estimate the mixing ratio of oil paints in order to create artistic illusion caused by metameric paints. You can create artistic illusion that makes different picture seen under different light.

1. Mixing paints for generating
metamerism art under 2 lights and 3
object colors
Daisuke Miyazaki
Masashi Baba
Ryo Furukawa
Shinsaku Hiura
Kanami Takahashi
Hirooki Aoki
Masahito Aoyama
Computer Graphics Laboratory, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/

2. Introduction(1/3)
Perception(3)
Reflection model(5)
Cost function(4)
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Light 1
R: 93
G: 79
B: 94
R: 93
G: 79
B: 93
Light 2
R: 81
G: 77
B: 98
Metamer sets
R: 99
G: 82
B: 101

3. Introduction(2/3)
Perception(3)
Reflection model(5)
Art [Valluzzi 2012]
Cost function(4)
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Watermark [Bala, Braun, Loce 2009]
Microbiology [Kobayashi, Yamada,
Hiraishi, Nakauchi 2012]
[Our work]
Intentionally cause expected metamerism for oil painting art
Related work

4. Introduction(3/3)
Perception(3)
Reflection model(5)
Cost function(4)
Experiment(3)
Light 1
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Light 2
Mix paint 2
Mix paint 1
Mix paint 3
Purpose

5. Introduction(3)
Perception(1/3)
Reflection model(5)
Cost function(4)
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
800nm
400nm
CIE-XYZ value
Spectral response
Light
Human perception
Object

6. Introduction(3)
Perception(2/3)
Reflection model(5)
Cost function(4)
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
X: 0.36
Y: 0.50
Z: 0.14
Color matching func.
(CIE-XYZ)
Light 1
Paint 1
X: 0.36
Y: 0.50
Z: 0.14
Color matching func.
(CIE-XYZ)
Light 1
Paint 2
Spectral distribution: same color

7. Introduction(3)
Perception(3/3)
Reflection model(5)
Cost function(4)
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
X: 0.35
Y: 0.48
Z: 0.17
Color matching func.
(CIE-XYZ)
Light 2
Paint 1
X: 0.38
Y: 0.46
Z: 0.16
Color matching func.
(CIE-XYZ)
Light 2
Paint 2
Spectral distribution: different color

8. Introduction(3)
Perception(3)
Reflection model(1/5)
Cost function(4)
Previous model: linear model
Experiment(3)
Our model: exponential model
[Finlayson, Morovic 2005]
[Alsam, Finlayson 2007]
[Miyazaki, Nakamura, Baba, Furukawa,
Aoyama, Hiura, Asada 2012]
s
w1 d 1
w2 d 2

wN p d N p
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
d: spectral reflectance
w: mixing weight
s
d
w1
1
d
w2
2

wN
dNpp
Elegant relationship
s
d
w1
1
d
w2
2

wN
dNpp
exp w1 log d 1
w 2 log d 2

w N p log d N p
Our model = linear model in logarithmic space
Reflection model of mixing paints

9. Introduction(3)
Perception(3)
Reflection model(2/5)
Cost function(4)
Incident light
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Diffusely reflected light
10
d1 =
Reflectance: Paint 1

10. Introduction(3)
Perception(3)
Reflection model(3/5)
Cost function(4)
Incident light
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Diffusely reflected light
10
d2 =
Reflectance: Paint 2

11. Introduction(3)
Perception(3)
Reflection model(4/5)
Incident light
7
Reflectance =
Cost function(4)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Experiment(3)
Diffusely reflected light
3
d1
1
10
Reflectance: Paint 1 & 2
d2
1
10

12. Introduction(3)
Perception(3)
Reflection model(5/5)
Cost function(4)
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Database D
Recognized color
PEDw
Light E
Mixing weight w
Perception P

13. Introduction(3)
Perception(3)
Reflection model(5)
w1
Cost function(1/4)
Experiment(3)
w3
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
w2
D
D
D
Paint 1
Paint 3
Paint 2
Cost function

14. CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Cost function

15. Introduction(3)
Perception(3)
Reflection model(5)
Cost function(2/4)
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
E1
w1
PE1 D
Paint 1
w3
PE1 D
w2
PE1 D
Paint 3
Paint 2
w3
PE2 Dw2
Paint 3
Paint 2
E2
PE 2 Dw1
Paint 1
PE 2 D
Cost function

16. CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
w1
w
min
PE1 D
3
PE1 Dmax
max
PE 2 Dw1
3
PE 2 Dmin
w
Cost function
w2
PE1 D
PE2 Dw2

17. Introduction(3)
Perception(3)
Reflection model(5)
w1
Cost function(3/4)
w3
min
PE1 D
PE1 D
max
PE 2 Dw1
PE 2 D
w3
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
w3
max
PE1 D
min
PE 2 D
Cost function
w3
w2
PE1 D
PE2 Dw2

18. Introduction(3)
arg min
w 1, w 2, w 3
Perception(3)
Reflection model(5)
w1
PE1 D
w1
PE 2 D
Cost function(4/4)
w3
2
w3
0.5
PE1 D
PE 2 D
Experiment(3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
w3
PE1 D
w3
PE 2 D
Cost function
w2
0.5
w2
2
PE1 D
PE2 D

19. Introduction(3)
Perception(3)
Reflection model(5)
Cost function(4)
Experiment(1/3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Hyper-spectral camera
Oil paints
Artificial sunlight
Diffuse white
reflectance standard
Narrow-band
filter
Experimental equipments

20. Introduction(3)
Perception(3)
Reflection model(5)
Cost function(4)
Experiment(2/3)
CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/
Synthesized paint 2
Synthesized paint 1
Synthesized paint 3
Result

21. CG Lab, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/

22. (c) Daisuke Miyazaki 2013
All rights reserved.
http://www.cg.info.hiroshima-cu.ac.jp/~miyazaki/
Daisuke Miyazaki, Kanami Takahashi, Masashi Baba, Hirooki
Aoki, Ryo Furukawa, Masahito Aoyama, Shinsaku Hiura,
“Mixing paints for generating metamerism art under 2 lights
and 3 object colors,” CPCV, 2013.
Computer Graphics Laboratory, Hiroshima City University
http://www.cg.info.hiroshima-cu.ac.jp/