Image Processing Reference
In-Depth Information
dot area coverages from the digital counts CMYK as well as the Yule
Nielson
correction factor m. Use these values in Equation 7.51 along with the measured
Neugebauer primaries (i.e., re
-
ectance spectra of the primaries, Ri(l),
i
(
l
), i
¼
1, 2, . . . , 16
for four-color CMYK printer) to predict the spectral re
ectance for any CMYK input.
The dot area coverages may be determined from spectral re
ectance samples using a
parameter
fitting or any of the estimation algorithms (least square, RLS, total least
square [43], robust estimation [44], genetic algorithm, neural networks, etc.). As an
example, we show how to model the dot area coverages for a random halftone screen
with the least-squares algorithm and the RLS algorithm.
7.4.3.3 Estimation of Dot Area Coverages Using Least Squares
An approach of relating the dot area coverage to the corresponding digital counts,
CMYK, is shown for one of the separations (e.g., cyan) and the same method is
carried out for other colorants to
find their respective dot area coverages. The
relationship between the dot area coverage and digital counts is called dot growth
function, which can be obtained by solving an optimization problem in (a) spectral
space or (b) L*a*b* space.
7.4.3.3.1 Optimization in Spectral Space
Consider a set of cyan re
ectance measurements R
Ci
(
l
) corresponding to input
digital values C
¼
i, M
¼
Y
¼
K
¼
0. To estimate the dot area coverage for cyan in
a least squared error sense in the spectral re
ectance space, the following metric is
minimized
n
o
2
X
N
1
m
1
m
R
C
i
lðÞ
J
¼
w
(l)
R
C
i
lðÞ
½
(
:
)
7
57
k
¼
1
In Equation 7.57, R
Ci
(
ectance obtained using the Neugebauer
model and is given by the following equation
l
) is the estimated re
R
C
i
(l) ¼
c
i
P
C
(l) þ
ð
1
c
i
Þ
P
W
(l)
(
7
:
58
)
where P
C
(
ectance spectra of cyan primary and paper white,
respectively. To improve themodeling accuracy, a wavelength dependent weight w(
l
)andP
W
(
l
) are the re
)is
often included to emphasize the errors in the regions of the visible spectrum to which the
human visual system is most sensitive. Spectral weights can be selected as w(
l
l
)
¼
max
(
) are tristimulus functions (i.e., color matching
functions: see Appendix A). Other weighting functions are explored in Ref. [31].
To minimize the error metric in Equation 7.57, the derivative of J with respect to
x(
l
),
y(
l
),
z(
l
)), where
x(
l
),
y(
l
),
z(
l
c
i
is set equal to zero. For w(l)¼
l
)
¼
1, this gives
n
o
2
X
N
@
c
i
¼
@
@
J
1
m
1
m
½
R
C
i
lðÞ
c
i
P
C
lðÞþ
½
ð
1
c
i
Þ
P
W
lðÞ
¼
0
(
7
:
59
)
@
c
i
k
¼
1
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