Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 334

7.4.3.2 Dot Area Coverages and Neugebauer Weights

For binary printers, multiple colors are achieved by varying dot area coverages of the
primary colors. For the case where the dot locations for the colorants are statistically
independent, Demichel

s equations [56,57] can be used to express the Demichel
weights as the primary dot area coverages. These steps are not always necessary
unless there is a requirement for further tuning of the Neugebauer weights to improve
the prediction accuracy of the model, and a need for reduction in number of training
samples due to cost reasons.
For random mixing, since the separations are printed independently and the
relative position of dots is random, the Demichel weights corresponding to the
primaries can be obtained by a probabilistic model as

'

W 1 ¼ ( 1 c )( 1 m )( 1 y )( 1 k ) W 9 ¼ ( 1 c ) my ( 1 k )

W 2 ¼ c (

m )( y )( k )

W 10 ¼ (

c ) m ( y ) k

1 1 1 1 1

W 3 ¼ (

c ) m ( y )( k )

W 11 ¼ (

c )( m ) yk

1 1 1 1 1

W 4 ¼ ( 1 c )( 1 m ) y ( 1 k ) W 12 ¼ cmy ( 1 k )

( 7 : 54 )

W 5 ¼ ( 1 c )( 1 m )( 1 y ) k W 13 ¼ cm ( 1 y ) k

W 6 ¼ cm ( 1 y )( 1 k ) W 14 ¼ c ( 1 m ) yk

W 7 ¼ c ( 1 m ) y ( 1 k ) W 15 ¼ ( 1 c ) myk

W 8 ¼ c ( 1 m )( 1 y ) k W 16 ¼ cmyk

where c, m, y, and k are the actual fractional areas covered by cyan, magenta, yellow,
and black colorant toner dots, respectively. These areas are functions of the input
digital counts (control values) C, M, Y, and K, which are integers between 0 and 255.
The mappings from the input digital counts C, M, Y, and K to the fractional area
coverage values c, m, y, and k are called dot growth functions or dot area functions
(see Example 7.7). Thus, for a , Equation 7.51 (with Equation 7.54) represents

a fourth order polynomial in c, m, y, and k. Figure 7.19 shows a schematic input

xed l

-
output diagram of the printer model with the weighted Neugebauer Equation 7.51,
the Demichel mixing Equation 7.54, and the dot growth functions C ! c, M ! m,
Y ! y, and K ! k.
Another commonly used halftone con

guration is the dot-on-dot screen, where
the c, m, y, and k dots are placed at the same screen angle and phase as illustrated
in Figure 7.20 for an ideal dot pattern with no noise in a four-colorant system. In
this system, the colorants are drawn with a decreasing area coverage [29,43]. For this
screen design, if pi i

(with i ¼ 1, 2, 3, 4) represent the printer colorants of increasing

dot area coverage, and a i 1, 2, 3, 4) represent the corresponding dot area

coverages, then the Neugebauer Equation 7.51 contains five primaries (i.e., K ¼ 5).
The

(with i ¼

five primaries consist of the corresponding measured re ectance spectra and

. The

are denoted by R i (l) 2 R p 1 p 2 p 3 p 4 (l) , R p 2 p 3 p 4 (l) , R p 3 p 4 (l) , R p 4 (l) , R w (l)

weights corresponding to the primaries are expressed as

W i 2 f a 1 , ( a 2 a 1 ) , ( a 3 a 2 ) , ( a 4 a 3 ) ,1 a 4 g: ( 7 : 55 )