COL 9(6), 063301(2011) CHINESE OPTICS LETTERS June 10, 2011
Spectral-based color separation method for
a multi-ink printer
Binyu Wang (
QQQ
)
1,2
, Haisong Xu (
MMM
°°°
ttt
)
1
∗
, M. Ronnier Luo
2
, and Jinyi Guo (
HHH
AAA
)
1,2
1
State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China
2
Department of Colour Science, University of Leeds, Leeds, LS2 9JT, UK
∗
Corresponding author: chsxu@zju.edu.cn
Received November 12, 2010; accepted December 17, 2010; posted online April 28, 2011
A sp ectral-based 8-ink characterization model is developed to accurately predict the recipe for a multi-ink
printer. The 8-ink color separation method is a union of five 3-ink and six 4-ink combinations based on
the cellular Yule-Nielsen spectral Neugebauer model with a recipe selection strategy. The performance
levels of the forward and backward models are evaluated for individual ink combinations using printed
testing samples. Furthermore, the spectral-based method performs bett er compared with the XYZ-based
approach. On the b asis of the backward model performance, a novel fast recipe selection strategy is
proposed and estimated.
OCIS codes: 330.1690, 300.6550, 330.1710, 330.1715.
doi: 10.3788/COL201109.063301.
In printer systems, two major approaches are used, i.e.,
the analytical and generic methods, to derive a character-
ization model. The analytical metho d is based on mod-
eling physical phenomena, such as Kubelka-Munk the-
ory and Neugebauer equations. The parameters of the
model are usually obtained from a relatively small num-
ber of samples, while the accuracy depends on the e x-
tent to which the model describes the actual behavior of
the device; some of these models are difficult to invert.
The generic method requires a large set o f training data
to build the model, as in three-dimensional (3D) look-
up table with interpolation
[1]
. Because the spectral data
contain all color information compared with tristimulus
values, the spectral-based approach achieves higher ac-
curacy and lower illuminant metamerism than does the
XYZ-based method at the expense of more calculations.
Typical 4-ink color printers have sma ll color gamut and
limited deg rees of freedom; thus, the use o f more inks not
only incre ases color gamut and the number of degrees of
freedom, but also improves accuracy
[2,3]
.
In this letter, the cellular Yule-Nielsen spectral Neuge-
bauer (CYNSN)
[2,4]
model is implemented to character-
ize a HP Desig njet Z3200ps 44 -inch photo printer, which
uses 12 inks
[5]
. For s implicity, 8 inks are used in the
exp eriment, including grey (Gy), photo black (K), light
cyan (C), magenta (M), yellow (Y), chromatic red (R),
green (Gn), and blue (B). The 8-ink color separation al-
gorithm is a union of five 3-ink and six 4-ink sets based
on the CYNSN model
[6]
with a recipe selection strat-
egy, containing the ink combinations of CMY, RMY,
CGnY, CMB, RGnB, CMYK, RMYK, CGnYK, CMBK,
RGnBK, a nd CMYGy. A large number of training and
testing hardcopy samples were prepared and measured,
and then the performa nce levels of the forward and back-
ward models were individually evaluated. In addition,
the spec tral-based method was compared with the XYZ-
based approach in terms of color difference, reflectance
root mean square
[7]
(RRMS) error, and metamerism in-
dex (MI). Finally, a novel fast recipe selection strategy
with high accuracy is proposed for the printer.
In 1937, Neugebauer developed a method for modeling
CMY halftone printing
[4]
. It was based on improving the
Murray-Davies
[2]
model and can be extended to use mor e
inks. Afterward, two main improvements
[2]
were pre -
sented. One is the Yule-Nielsen n-factor describing the
light sca ttering. The classical CMY Neugebauer model
modified by the Yule-Nielsen effect is expressed as
R(λ) =
(
8
X
i=1
w
i
[R
i
(λ)]
1/n
)
n
, (1)
where R
i
(λ) is the reflectance of the ith primaries (i =
1, 2, · · ·, 8) at wavelength λ, w
i
denotes the weighting
coefficient for the ith primary defined by the Demichel
equation
[8]
, n-factor is usually determined by optimiza-
tion, and the typical value of n-factor rang e s from 1 to
4. The other improvement is called the cellular Neuge-
bauer model. Firstly, the entire color space (e.g. CMY,
CMYK) is divided into smaller sub-spaces called ce lls,
and then the classical Neugeba uer model is applied in
the selec ted cell dependent on the input ink amounts.
Combining these two improvements with the classical
Neugebauer model forms the CYNSN model, in which
predicting ac c uracy drama tically increases.
The Yule-Nielsen spectral Neugebauer (YNSN) model
is not analytically invertible; thus, its inversion is usually
solved using iteratio n. A well-known method was pr o-
posed by Urban and Grigat, in which linear regres sion
iteration was used
[9]
, based on which Li et al. introduced
“QR” decomposition, further reducing computational
costs
[10]
. Therefore, Li algorithm was employed in this
letter.
Before conducting the backward YNSN model, deter-
mining the optimal cell is an indispensable step, within
which the most accurate recipe can be predicted by the
backward model. Urban et al. developed a cellular lin-
ear regression iteration algorithm, which dramatically
decreased the number of cells tr ied but did not guaran-
tee that the selected cell was the actual optimal cell
[11]
.
Later, Guo et al. proposed a cell searching method,
which ensured that the optimal cell was found at the
1671-7694/2011/063301(4) 063301-1
c
2011 Chinese Optics Letters
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