Paint-like Compositing Based on RYB Color Model
Junichi Sugita*
Tokyo Healthcare University

Tokiichiro Takahashi*Tokyo Denki University / UEI Research(a) -compositing (α = 0.6)(b) Modified -compositing (w = 0.25)
Figure 1: Paint-like compositing based on RYB color model.

1 Introduction
Many people have been familiar with subtractive color model basedon pigment color compositing since their early childhood. However,the RGB color space is not comprehensible for children due toadditive color compositing. In the RGB color space, the resulting
mixture color is often different from colors viewer expected.
CMYK is a well-known subtractive color space, but its three primalcolors are not familiar. Kubelka-Munk model (KM model in short)
simulates pigment compositing as well as paint-like appearance byphysically-based simulation. However, it is difficult to use KM
model because of many simulation parameters.
In order to realize easy to use for paint-like compositing, we
present two color compositing methods based on an RYB color
model. The RYB color model proposed by Johannes Itten [1973] iswidely used in art education, where red, yellow and blue aredefined as subtractive primaries. Gossett and Chen [2004] proposed
a conversion method from RGB color space to RYB color space
based on tri-linear interpolation among three primaries. However,these conversion method is irreversible, i.e., conversion equations
between RGB and RYB color models have not been proposed yet.
In this paper, we formulate mathematical and bi-directional
conversion equations between RGB and RYB color spaces. We
also propose simple color compositing methods to represent
lower and highly scattering pigments compositing.

2 RYB Color Model and Compositing
We derive conversion equations between RGB, (RRGB, GRGB, BRGB),
and RYB, (RRYB, YRYB, BRYB), color spaces. Note that 0 ≤ RRGB,GRGB, BRGB, RRYB, YRYB, BRYB ≤ 1.

2.1 RGB to RYB Conversion
We introduce two sets of variables, (,,), and (,,) , which are calculated by the following equations.
()=()−( , , ),,,,(1))=− min(,)) /2=(+ min(,(2)=(+− min(,))/2) is a white component in RGB
Here,= min(,,color space. These variables are normalized as(,,)=(/ ,/ ,/ )(3)) /max(
where = max(,,,,).
Finally, by adding a black component, = min(1 −,1 −,1 −) , (RRYB, YRYB, BRYB) in RYB color space areobtained by the following equations.
(,,)=(,,)+( , , )(4)*{sugita, toki}@vcl.jp

2.2 RYB to RGB Conversion
A black component = min(,,) is subtracted fromeach component,,in RYB color space:)−( , , )(,,)=(,,(5)Three variables, (,,) are obtained as follows:)=+− min(,)=+ 2 min(,(6)= 2(− min(,))
These variables are normalized as⁄ ,⁄ ,⁄ )(,,)=((7)) /max(
where, = max(,,,,).
Finally, by adding a white component= min(1 −,1 −), (RRGB, GRGB, BRGB) are obtained as:,1 −(,,)=(,,)+( , , )(8)

2.3 RYB Color Compositing Methods
According to our experiments (see detailed supplemental
documents), we propose two simple RYB compositing methods torepresent lower and highly scattering pigments respectively.
We adopt -compositing for lower scattering pigments (e.g.
water color) with a parameter α. Compositing color Ca is calculated
from given foreground color Cfore and background color Cback in theRYB color space as follows:=+ (1 − )(0 ≤ ≤ 1)(9)
In order to represent highly scattering pigments (e.g. gouache oracrylic), we modify -compositing with a parameter w:=+(0 ≤ ≤ 1)
(10)

3 Results and Conclusion

Figure 1 shows stroke rendering results by our compositing
methods in the RYB color space. Figure 1 (a) shows a result by the-compositing method to represent lower scattering pigments.
Figure 1 (b) shows another result by the modified -compositing
method to represent highly scattering pigments. The modified compositing method enhanced foreground colors more than the compositing method.
We formulated conversion between RGB and RYB, and verified
that paint-like appearance can be realized easily.

References
GOSETT, N., AND CHEN, B. 2004. Paint inspired color mixing andcompositing for visualization. In Proc. INFOVIS 2004, 113-118.
ITTEN, J. 1973. The Art of Color: the subjective experience andobjective rationale of color, New York, Van Nostrand Reinhold.