Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 323

0.4

1st
2nd
3rd
4th

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

400 450 500 550 600 650 700

Wavelength (nm)

FIGURE 7.13 First four basis vectors as a function of wavelength.

the D E numbers are plotted as a function of the number of basis vectors to decide

how many basis vectors, K, required for modeling the parameters, W j , using Equa-
tion 7.43 for j ¼

1, 2, . . . , N colors. For conveni-
ence, the color subscript i is not shown in zero-mean re

1, 2, . . . , K basis vectors and for i ¼

ectance r and W j in the
above equations. As shown in Table 7.1, for this printer, over 99% of the spectral
energy is captured in the first six basis vectors.

Once the basis vectors are selected, the weights W j are modeled in terms of input
variables, CMYK, using the training samples, preferably by spanning a large portion
of the operating space of the device. An adaptation estimation algorithm is some-
times more valuable for modeling the parameters.

W j ¼ f j ( C, M, Y, K ) ( 7 : 44 )

The function f j (C, M, Y, K) is modeled as

f j ( C, M, Y, K ) ¼ b j þ a 1j C þ a 2j M þ a 3j Y þ a 4j K þ a 5j CM þ a 6j CY
þ a 7j CK þ a 8j MY þ a 9j MK þ a 10j YK þ a 11j C 2
þ a 12j M 2 þ a 13j Y 2 þ a 14j K 2

þ ( 7 : 45 )

For simplicity, Equation 7.45 is written in matrix form for a simple linear af ne

model containing five parameters for each weight, and K number of such set