2013 IEEE International Conference on Computer Vision Workshops

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

(a)

(b)

(c)

Figure 1. (a) Three kinds of mixed paints computed by the proposed method, (b) those illuminated by blue light, (c) those illuminated byyellow light.

Abstract

mon sense, and fully brings out the value, disregarded in thepast, of metamerism. Metamerism color charts are available commercially for conﬁrming metamerism, but obtaining paints that cause metamerism under the user’s desired
light source is difﬁcult for the average person. The development of automatic calculating software for the blending ratios of paints would allow production of metamerism works
by even the average person in the apparel and advertisingindustries (without specialized knowledge in optics, such as
spectra). In this paper, we show an artistic illusion, whose
mixing ratio of oil paints are computed by our method, withthree kinds of mixed paints (Fig. 1 (a)): Two of them becomes the same appearance under a certain colored light(Fig. 1 (b)), while another two paints becomes the same under different light (Fig. 1 (c)).

Metamerism is a phenomenon where two objects recognized as having different colors under one light are also
recognized as having the same color under another light.
This research proposes technology for actualizing artistic
illusion that exploits metamerism. Speciﬁcally, the purposeof the research relates to automatic calculation of blending
ratios of oil paints that cause metamerism to occur under
speciﬁc light sources. We entails metamerism occurring between three types of object colors under two types of lightsources. Also, we utilize plausible reﬂection model for the
mixture of oil paints.

1. Introduction

2. Related work

The phenomenon where two objects recognized as having different colors under one light are also recognized
as having the same color under another light is called
metamerism. This research proposes technology for actualizing artistic illusion that exploits metamerism. Speciﬁcally, the purpose of the research relates to automatic calculation of paint blending ratios that cause metamerism tooccur under speciﬁc light sources.
Metamerism, in which the colors of clothing and printed
materials vary under ﬂuorescent lighting and sunlight, is
known as a source of annoyance among designers and photographers, and among those in the apparel, printing, andadvertising industries. This paper rebels against such com978-1-4799-3022-7/13 $31.00 © 2013 IEEE
978-0-7695-5161-6/13
DOI 10.1109/ICCVW.2013.120

Works of media art have increased in number immensely
over the past decades, in which digital technologies havebeen exploited in the creation of art. In particular, projection mapping onto large-scale architecture with the use ofa projector has gained tremendous interest in the past few
years. As the number of such media art works balloons,however, the problem arises that people grow accustomed
to it. The same is true of analog artistic illusion: people
get used to the existing artistic techniques, even though it
can surprise people. Thus, the computer-assisted creationof analog artistic illusion has recently become the subjectof research efforts to create new art that the human mind874

would ﬁnd difﬁcult to accomplish. Hersch and Chosson [1]developed technology to represent premeditated pictures by
exploiting Moiré patterns. Mitra and Pauly [2] developed
technology for creating solids that generate premeditatedshadow pictures when light is shone from three directions.
Yue et al. [3] developed technology for designing transparent objects that enable expression of premeditated shapes by
the concentration of light. Papas et al. [4] developed technology for designing transparent objects so that premeditated shapes can be represented when the objects are placedon an underlying illustration. These research ﬁelds are referred to as computer-assisted art illusions or computationalart. The research of this paper considers metameric art likethat produced by Valluzzi [5]. Although Valluzzi [5] had
no goal of representing any premeditated shapes, the purpose of this research is the blending of paints to generate
metamerism to thus enable the representation of premeditated shapes.

CIE-XYZ value

Spectral response

Light

ObjectFigure 2. Principle of perceiving visible light.

periment also demonstrates in real world by employing thespectral distributions of actually existing light sources.
Miyazaki et al. [8] proposed a method for calculating the blending ratios of paint that generate the greatest
metamerism in response to light sources designated by theuser. Miyazaki et al. worked on metamerism occurring between two types of object colors under two types of lightsources, but our research entails metamerism occurring between three types of object colors under two types of lightsources. Moreover, they represented object colors by an additive color mixture, but our research employs the reﬂection
model suited to represent object colors.
Finlayson et al. [9, 10] proposed a method for calculating spectral distributions that generate metamerism, as
well as a method for estimating many spectral distributions
observed as the same color as given RGB values or XYZvalues. Spectral distributions observed as the same color
exist inﬁnitely in theory; however, the variation of paints
that cause metamerism is limited in reality. Therefore, they
limit the metamer sets to be a linear sums of the spectral
distributions of each patch of Macbeth ColorChecker, manufactured by X-Rite, Inc. As the purpose of our researchis to reproduce with real paints, the spectral distributions ofoil paints were used from a database rather than from theMacbeth ColorChecker. Unlike light, object colors are represented under a subtractive color mixture rather than linear
sums of spectral distributions. Thus, we calculate object
colors using a reﬂection model suited for object colors.
Morimoto et al. [11] described the importance ofmetamerism and noted that spectral distribution analysis
was indispensable for the digital archiving cultural assets.
Johnson and Fairchild [12] also described the importance ofmetamerism and showed the need to calculate colors fromspectral distributions rather than from RGB values for computer graphics generation. Our research demonstrates theusefulness of metamerism by its use in art.

Research into metamerism has existed for a long time,
but little research has exploited metamerism for art. Balaet al. [6] engaged in research to create watermarks using
metamerism. For a CMYK printer, the printing of black
is represented as the ”K” (key) ink or the ”CMY” (cyan,
magenta, yellow) inks. Hence, calculations were made forthe representation of a black object color by using as much
K ink as possible and as little CMY ink as possible, andby using as much CMY ink as possible and as little K ink
as possible for an object’s color. These are observed as
the same color under natural light, but as different colors
when exposed to LEDs of speciﬁc wavelengths. Two typesof LEDs were prepared, and the largest difference in theirwavelengths was based on comparison of their spectral distributions. Contrary to the research of Bala et al. [6], our research blended paints that generated the most metamerism
under light sources designated by the user. To also represent spectral distributions that four colors of ink cannot, theoptimum combination of paints was selected from among
many more types.
Drew and Bala [7] took the two types of object colors
prepared by Bala et al. [6], photographed them with an ordinary camera, and converted the colors by multiplying 3 × 3
matrix for emphasizing metamerism. Using virtual LEDsof 31 colors, they also proposed a method for searchingfor combinations that generated the greatest metamerism
among all combinations attainable by individually turning
on and off each LED. Because the spectral distributions of
the virtual LEDs did not actually exist, the paper of Drew
and Bala [7] described no experiment on actual objects.
Since the purpose of our paper is to be observed by the human eye, the colors after observation cannot be converted by
the 3 × 3 matrix for emphasizing metamerism. Instead, we
propose a method for calculating blending ratios of paints
that produce the most emphasis in metamerism. Our ex-

3. Principles of reﬂection
A typical method of expressing human perception ofcolor concerns the XYZ color system deﬁned by the International Commission on Illumination (CIE). The system875

can represent the color sensed by the brain, based on stimuli obtained from photoreceptor cells. X, Y , and Z, correspond to recognition of red, green, and blue colors, respectively. This research utilizes the wavelength data of lightfrom 400 to 800 nm. Suppose that the color matching functions of X, Y , and Z are x̄(λ), ȳ(λ), and z̄(λ), respectively,
as a function of wavelength λ, the observed value X, Y , andZ of the scene can be represented as follows (Fig. 2).
 800
E(λ)S(λ)x̄(λ)dλ ,(1)
X =Light 1

Light 2
Mix paint 2

Mix paint 1

400
 800

Y

=

Z

=

400
 800
400

Mix paint 3

E(λ)S(λ)ȳ(λ)dλ ,(2)E(λ)S(λ)z̄(λ)dλ ,(3)

Figure 3. Metamerism of three sets of mixed paint illuminated by
two different lights.

Mixed Paint 3 appear as different colors and brightness values; under Light Source 2, Mixed Paint 2 and Mixed Paint 3
appear as the same color and brightness, while Mixed Paint
1 and Mixed Paint 3 appear as different colors and brightness values (Fig. 3).
The database of spectral reﬂectance for Np types of paintnecessary for mixing the paints is represented as the Nb ×
Np matrix D.

where E(λ) represents the spectral distribution of the lightsource and S(λ) represents the spectral reﬂectance of theobject surface. Above equations suppose that spectral distribution is calculated as a continous function; however,
we cannot measure the spectral distribution as a continous
function but can measure them as a discretized value. In
our research, we suppose that the spectral distribution are
represented as Nb number of values, where the wavelength
data of visible light from 400 to 800 nm are discretized withequal intervals. Denoting x = (X, Y, Z) as the observed
value, Eq. (1), Eq. (2), and Eq. (3) are represented as following equation.
x = PEs .
(4)

⎛
⎜
⎜
D=⎜
⎝

d12
d22
..
.

···
···
..
.

d1Np
d2Np
..
.

dNb 1

dNb 2

···

dNb Np

⎞
⎟
⎟
⎟.
⎠

(7)

Mixed paint is prepared by combining the Np paints with
Np mixing proportions. The mix ratios are represented as
the Np × 1 vector w.
Assuming the paint mixing to be additive color mixing,
Miyazaki et al. [8] calculated the spectral reﬂectances of
mixed paint. But real paint is subject to subtractive paintmixing; therefore, a reﬂection model suited to the paintmust be used.
The model by Curtis et al. [13] exists for water-color
paint, but for this type of paint, the base color and watercontent cause the observed color to differ from when it was
blended. The model is therefore not suited for this research.
Tominaga and Nishi [14] measured the spectral reﬂectance of oil paint. After measuring actual oil paint, Tominaga and Nishi [14] concluded that the diffuse reﬂection
components of oil paint depended neither on applied thickness nor the amount of solvent oil. The Kubelka-Munktheory is a method for representing multi-layer reﬂection;
however, the Kubelka-Munk model is not suited to oil paint,
based on ﬁndings by Tominaga and Nishi [14] of the nondependence on applied thickness. No dependence on applied thickness means that transparency is low; therefore,
models of sub-surface scattering such as the dipole model
are also not suited for oil paint. Therefore, oil paint can be

Here, discrete data of the color matching functions are represented by the 3 × Nb matrix P, of which the ﬁrst to thirdrows are color matching functions of X, Y , and Z.
⎞⎛x̄1 · · · x̄Nb
(5)
P = ⎝ ȳ1 · · · ȳNb ⎠ .
z̄1 · · · z̄Nb
The spectral reﬂectance of the object surface is represented
as the Nb ×1 vector s. Nb ×Nb diagonal matrix E represents
the spectral distributions of light source.
E = diag (E1 , E2 , · · · , ENb ) .

d11
d21
..
.

(6)

4. Proposed method
This section describes the method for automatic calculation of oil paint blending ratios that cause metamerism
to occur. Two different light sources are labeled as Light
Source 1 and Light Source 2. Three different types of paintmixed from multiple oil paints are labeled Mixed Paint 1,
Mixed Paint 2, and Mixed Paint 3. The purpose of thisresearch is to reproduce the following phenomena: Under
Light Source 1, Mixed Paint 1 and Mixed Paint 3 appear
as the same color and brightness, while Mixed Paint 2 and
876

140

Diffusely reflected light

Spectral radiance [arb. unit][W/sr/m2/nm with unknown scale]

Incident light

B5:M0
B4:M1
B3:M2
B2:M3
B1:M4
B0:M5

0
400

800

Wavelength [nm]Figure 5. Difference of spectral distribution with different mixing
ratio of two paints, HORIZON BLUE and LIGHT MAGENTA,
illuminated by artiﬁcial sunlight.

Figure 4. Diffuse reﬂection of mixed paint.

Spectral radiance [arb. unit][W/sr/m2/nm with unknown scale]

120
100
80
Actual data

60

Linear model
Our model

40
20Light magenta 100%

Horizon blue 20%
Light magenta 80%

Horizon blue 40%
Light magenta 60%

Horizon blue 60%
Light magenta 40%

Horizon blue 80%
Light magenta 20%

0

Horizon blue 100%

represented with the Lambert reﬂection model. Tominaga
et al. [15] estimated the surface normals of picture art withthe photometric stereo method, exploiting the fact that diffuse reﬂection components of oil paint could be represented
by the Lambert reﬂection model.
Based on the ﬁndings of Tominaga and Nishi [14], ourresearch also employed the Lambert reﬂection model as themodel for diffuse reﬂection components of oil paint. Specular reﬂection components are not considered in this paper,
since they are unrelated to our purpose. Because ideal diffuse reﬂection is assumed, light incident to the inside of
the object randomly reﬂects off internal particles a sufﬁcientnumber of times before exiting. Because it is an ideal diffuse reﬂection, no effect is sustained from particle size orparticle density. In such a case, the spectral reﬂectance of
mixed paint can be calculated with the following equation.
⎛
⎞
wNp
w2
1
dw
11 × d12 × · · · × d1Np
⎜ dw1 × dw2 × · · · × dwNp ⎟
⎜
⎟
21
22
2Np
w
⎟.
(8)
s=D ≡⎜
..
⎜
⎟
⎝
⎠
.
wNp
w2
1
dw
Nb 1 × dNb 2 × · · · × dNb Np

Mixture of two paints

Figure 6. Intensity plot with different mixture ratio of two paints(λ = 625nm).

This model is known as the transmission model. The same
phenomenon occurs for transmitted light and diffusely reﬂected light: Light penetrating a substance is reﬂected andabsorbed by internal particles and then exits.
Now, we introduce a speciﬁc example to explain thephysical meaning of the reﬂection model shown as Eq. (8).
The mixed paint obtained from combination of 70% paintwith reﬂectance d1 (λ) and 30% paint with reﬂectance d2 (λ)
has reﬂectance of d1 (λ)7/10 d2 (λ)3/10 , which is evident
from Fig. 4. This is because, as this is an ideal diffuse reﬂection, the internal particles are reﬂected off a sufﬁcientnumber of times inside the object, meaning the particle reﬂections occur under the same probability as the blend ratio.
To determine whether this reﬂection model was appropriate in practice, spectral distributions were analyzed formixes of actual oil paints. Spectra data for pigment mixesof Horizon Blue (B) and Light Magenta (M) in six stages inproportions of 5 : 0, 4 : 1, 3 : 2, 2 : 3, 1 : 4, and 0 : 5 weretaken, as shown in Fig. 5. Data for the wavelength of 625
nm were extracted from Fig. 5 and provided in Fig. 6. In
Fig. 6, the vertical axis represents the photographed spectral
radiance and the horizontal axis represents the mix ratios of
Horizon Blue and Light Magenta. The straight line drawn in
Fig. 6 provides radiance calculations for additive color mixing [8, 9, 10], and the curve drawn in Fig. 6 provides the radiance calculated with the model of Eq. (8). Because paints
embody subtractive color mixing, there is a trend of being
darker than the radiance predicted under additive color mixing. Eq. (8) is suited for the representation of reﬂection for
paints, and is therefore used in this research.
As a result, the cost function F (·) to be minimized in877

order to fulﬁl our purpose (Fig. 3) is as follows.

could not conﬁrm this phenomenon and stability could be
provided with the addition of a positive constant to the denominator; nevertheless, this research opted to use Eq. (9)as a precaution. Note that multiplication and division becomes addition and subtraction if we calculate logarithm;
therefore, there is only a small difference between the costfunction that uses multiplication and division and that uses
addition and subtraction.
The ﬁrst and second terms of Eq. (9) were squared to increase their weighting, and the third and fourth terms weretaken to the 0.5 power to decrease their weighting. Since
human vision recognizes subtle changes in color or brightness with emphasis, weighting of the ﬁrst and second terms
that make color and brightness the same was increased,
while weighting of the third and fourth terms that makecolor and brightness different was decreased. Another reason for this treatment relates to the difﬁculty in discovering
spectral distributions that produce the same color and theinﬁnite existence of spectral distributions that produce different colors. The preliminary experiment empirically conﬁrmed that Eq. (9) could more stably determine a solution,even more so than the case where all terms were squared.

F (P, E1 , E2 , D, w1 , w2 , w3 ) =PE1 Dw1 − PE1 Dw3 2
2+ PE2 Dw2 − PE2 Dw3 

0.5− PE1 Dw2 − PE1 Dw3 

0.5− PE2 Dw1 − PE2 Dw3  ,{w1 , w2 , w3 } =argmin F (P, E1 , E2 , D, w1 , w2 , w3 ),
w1 ,w2 ,w3

Np

Np

w1n = 1,

s.t.
n=1

(9)
(10)

Np

w2n = 1,n=1

0 ≤ w1n , 0 ≤ w2n , 0 ≤ w3n ,w3n = 1,n=1{n = 1, · · · , Np } .

Since Eq. (10) is a complicated function with constraint
conditions, simulated annealing based on the NelderMead downhill simplex method [16] was adopted to solve
the equation stably. The Nelder-Mead downhill simplex
method is not the simplex method of linear programming,but a type of algorithm that minimizes the cost function.
The cost function in Eq. (9) is not in quadratic form and may
even take negative values. Thus, neither Newton’s method
nor the Levenberg-Marquardt method can be applied. The
solution therefore requires the steepest descent method, theconjugate gradient method, the genetic algorithm, or the
Nelder-Mead downhill simplex method. The convergency
speed of the genetic algorithm is slow. The steepest descentmethod and conjugate gradient method require C 1 (ﬁrstorder differentiable) smoothness for the cost function, but
the Nelder-Mead downhill simplex method does not require
the function to be differentiable. Eq. (9) is a smooth function, but the spectral distribution of the database is not asmooth distribution. Thus, the Nelder-Mead downhill simplex method was used as a precaution. The Nelder-Meaddownhill simplex method derives solutions in a stable manner and thus is commonly used [17]. This algorithm wasthus used for our research. Eq. (9) is not unimodal and canbe problematic in readily tending to a local solution. To
avoid falling into a local solution, simulated annealing wasused. Since certain papers note that simulated annealing iseffective in the problem of estimating parameters of somekind by exploiting multi-spectral data [18, 19], this researchalso adopted this algorithm. The source code of Press etal. [16] was utilized for implementation of the algorithm
combining the Nelder-Mead downhill simplex method andsimulated annealing.
Eq. (9) employs addition and subtraction; however, multiplication and division may be used instead. A preliminary experiment conﬁrmed that similar results could be obtained in either case. However, the calculations become unstable as the denominator approaches zero when multiplication and division are used. The preliminary experiment

5. Experimental results
A hyper-spectral camera HSC-1700 (Fig. 7) was used tophotograph the spectral data from 400 nm to 800 nm. Radiance could be analyzed for a total of 81 bands (Nb = 81)
from 400 nm to 800 nm in 5 nm intervals. Spectral distributions were analyzed for 29 types (Np = 29) of different
color oil paints (Fig. 9), which were exposed to an artiﬁcial
sunlight. Since brightness as well as chromaticity inﬂuence
the result, the paint database of 29 types included white andblack paints for adjusting brightness. The artiﬁcial sunlight(Fig. 10) is the Probright V manufactured by Nippon Paint
Co., Ltd. with a color temperature of 6500 K and color rendering performance of Ra98. The 29 spectral distributions
were divided by the spectral distribution of a white perfectdiffuser (Fig. 8) exposed to the artiﬁcial sunlight in orderto yield spectral reﬂectances utilized as database D. The
spectral distributions of all 29 types of oil paints are shownin Fig. 11 and represent the distributions exposed to the artiﬁcial sunlight. Subsequent processing utilized spectral reﬂectances that were derived by division of the above by thespectral distribution of the white diffuser.
The mixing proportions were initially calculated for 29
colors (Np = 29) and recalculated for 10 colors of paint(Np = 10) with blending ratios exceeding the thresholdvalue. The reason for this procedure is the fact that, in reality, the operation of mixing paints becomes complicated as
the number of paints to be blended grows large, and not because of any problem arising from the proposed algorithms.
Based on the blending ratios determined, actual paints weremixed and visually conﬁrmed to deliver the results envi878

Figure 7. Hyper-spectral camera HSC-1700 manufactured
by Eba Japan Co., Ltd.

Figure 8. Diffuse white reﬂectance standard.

Figure 12. Blue narrow bandﬁlter (peak = 460 nm, bandwidth = 10 nm).

Figure 9. 29 types of oilpaints included in the
database.

Figure 13. Yellow narrow
band ﬁlter (peak = 577 nm,
bandwidth = 10 nm).

sioned in Fig. 3, and the results are shown in Fig. 1. Moreover, paint was not applied in layers, but after stirring, sothat all paint colors were completely mixed and applied insuch a way that the base was not visible. Interference ﬁlters
shown in Fig. 12 and Fig. 13 were utilized to provide lightsources of two colors. Since the artiﬁcial sunlight was large,
the ﬁlters were not installed in front of the light source, but
in front of the camera for photographs. The same light canbe observed whether the ﬁlter is installed in front of thelight source or in front of the camera, because the subject is
an ideal Lambert object that generates no change to wavelengths, such as interference or dispersion.
Calculations were made for each paint type and not ona pixel-unit basis. In this case, calculations were made forthree types of mixed paints. The calculation time for operating the single-core Intel Xeon 2.50 GHz CPU was 19.16
seconds when utilizing the 29-color database.

Figure 10. Artiﬁcial sunlight
Probright V manufactured by
Nippon Paint Co., Ltd.

6. Discussion
The solution depends on the oil paint database. If thespectral distributions of the database form 81 orthonormalbases, then any spectral distribution can be represented, andthus, a solution necessarily exists (except for ill-posed setting issues, such as identical spectral distributions for thetwo light sources). Spectral distributions of actual oil paints,
however, are not exclusively linearly independent. Paint isformed from pigment (particles) originated from minerals.
This means that the types of pigments used in actual paints
are ﬁnite.
Hence, the principal components were analyzed for all
29 types of paints in the database. The spectral distributions
obtained from the database are shown in Fig. 11. The top
nine eigenvalues along with the contribution ratios and cumulative contribution ratios obtained as a result of the prin-

Figure 11. Whole 29 spectral distributions of oil paintings usedas database. These spectral distributions represent the observed
intensity, and do not represent spectral reﬂectances; namely, thespectral distribution of those are not divided by the spectral distribution of the artiﬁcial sunlight.

879

Table 1. Cumulative proportion of variance from the ﬁrst eigenvalue to the nineth eigenvalue.

1
2
3
4
5
6
7
8
9

Eigenvalue
46.17
22.36
8.34
2.43
0.71
0.53
0.24
0.13
0.04

Variance (%)
57.00
27.60
10.30
3.00
0.87
0.66
0.29
0.15
0.05

top eight basis functions. Judd et al. [21], Cohen [23],Maloney [24], and Vrhel et al. [25] have performed similar analyses and reached similar conclusions. Especially,
the similar conclusion for oil paints’ database is derived byTominaga and Tanaka [22]. Our experiment conﬁrmed thatthe afﬁrmations of these papers are also valid for our choiceof oil paints.

Cumulative (%)
57.00
84.60
94.90
97.89
98.77
99.43
99.72
99.87
99.92

The experiment showed that representing arbitrary spectral distributions was impossible with actual paint. The proposed method involves calculating with simulated annealing so that metamerism is generated as much as possible,
but the desired solution may not necessarily be obtained, depending on the conditions and light source colors used forgenerating metamerism and the paint database. However,
the results also showed that metamerism could be generated
with just 4 to 9 types of paint. The actual experiment did not
directly use blending ratios of all 29 types of paint. Instead,
10 of them with the largest percentages were selected, andthe paints were mixed after the blending proportions had
been determined again with the selected paints.

7. Conclusion
This research conﬁrmed the occurrence of metamerism
between three object colors and two light sources. The
purpose was to generate metamerism under a light source
designated by the user. Methods to automatically select or
blend light sources from a light source database to generate
optimum metamerism are planned for future work.

Figure 14. Scree plot of the top nine PCs.

Morovič et al. [26] argued that printers that use 11 colors of ink are useful for printing spectral distributions ofvarious object colors. Tzeng and Berns [27] also conducted
research on printers that use four or six colors of ink. A
future task is to join with printer manufacturers to develop
printers capable of printing spectral distributions of various
object colors.
In this research and the research of Miyazaki et al. [8],metamerism was emphasized with the blending of paints.
Drew and Bala [7] emphasized metamerism with combinations of LED light sources. For the future, the automatic selection of optimum light source combinations is being considered, rather than the blending of paints only, to generatestronger metamerism than in this and other existing research[8, 7].

Figure 15. PCs of the largest four eigenvalues.

cipal component analysis are shown in Table 1. The top
nine eigenvalues are plotted in Fig. 14, and the eigenvectorsof the top four principal components are graphed in Fig. 15.
According to Table 1, the cumulative contribution ratios exceed 95% with the fourth eigenvalue, 99% with the sixth
eigenvalue, and 99.9% with the ninth eigenvalue. These results mean that even with a database of 29 types of paint,
the amount of information contained is comparable to just
4 to 9 types.
Parkkinnen et al. [20] analyzed spectral distributions ofvarious kinds of objects and showed that all object colors
within the database could be completely represented by the

As a course of action for the future, a database with thespectral distributions of oil paints and the spectral distributions of widely commercially available lighting and software on the Internet are being considered, so that generalusers who have no instruments for measuring spectral distribution can produce works of metamerism art with Holbeincommercial oil paints.
880

Acknowledgments[13] C. J. Curtis, S. E. Anderson, J. E. Seims, K. W. Fleischer,and D. H. Salesin, “Computer-generated watercolor,” in Proceedings of the 24th annual conference on Computer graphics and interactive techniques (SIGGRAPH ’97), pp. 421–
430, 1997. 3

This research was supported in part by the Grant-in-Aid
for Scientiﬁc Research on Innovative Areas “Shitsukan”(no. 22135003) from MEXT, Japan, and in part by the
Grant-in-Aid for Young Scientists (no. 24700176) from
JSPS, Japan. The authors thank Naoki Asada for useful discussions. They also thank anonymous reviewers for theircareful reviews of the paper.

[14] S. Tominaga and S. Nishi, “Surface reﬂection properties ofoil paints under various conditions,” Proc. SPIE 6807, 2008.
3, 4[15] 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. 4

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