Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 331

Neugebauer model for a CMYK printer with corrections to the penetration and
scattering of light onto paper [52 - 56] is given by the following equation

" # m

X

K

1
m

R (l) ¼ W i R

i (l)

( 7 : 51 )

i ¼ 1

where
R( l ) is the average output spectral re ectance (estimated)

W i is the Demichel weighting of the ith Neugebauer primary

R i ( ectance spectra of the ith Neugebauer primary which is the ith

basis vector, and a free parameter
m is the Yule

l ) is the re

- Nielson correction factor

The penetration represented by the m factor was expressed as a function of wide band
re ectance. More recently, the m factor has been expressed in terms of narrow-band

spectral curves and is allowed to vary over a wide range to obtain a best fit with

the measurement [47,48]. The Neugebauer model, Equation 7.51, assumes that the
re

ectances of the
primary colors and their overprints. K is equal to the number of Neugebauer
primaries, which is 16 for a four-color CMYK printer. They are the measured
re

ectance of a spatial area is the additive combination of the re

ectance spectra of the corresponding primary samples with 100% area coverage
on paper white:

R i (l) ) Reflectance Spectra of { W, C, M, Y, K, CM, CY, MY, MK, YK, CK, CMY,
CMK, MYK, CYK, CMYK }

Weights, Wi, i , can be tuned from spectral re ectance measurements using standard

least square or RLS algorithms as described in earlier sections. The weights can be
further represented as individual fractional area coverages as in Demichel s equation

'

[56 58] and then these fractional area coverages can be tuned from spectral meas-

urements. Alternatively,

-

fixing the weights, Wi, i , and tuning of Neugebauer primaries
with least squares or weighted least squares using training spectral re ectance

measurements are other basic ideas being attempted for CMYK printers [30].

7.4.3.1 Parameterized Model for Neugebauer Weights

For convenience, let us denote the Yule - Nielson corrected ith re ectance values at a

r i ¼ R 1 = m
i

given wavelength by the vector, 1, 2, . . . , K. With the corre-

sponding new notation for the estimated spectra, r ¼ R 1 = m , the Neugebauer equation
(Equation 7.51) can be represented in vector form as

, where i ¼

r ¼ BW ( 7 : 52 )

The matrix, B ¼ [r 1 r 2 ... r K ], is the matrix of size n K (e.g., n ¼ 31) when there are

[W 1 W 2 ...W K ] T is the Demichel weight vector. 31 re ectance values, and vector W ¼