Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 420

TABLE 7.17 (continued)
RGB ! L*a*b* ! CMYK LUT for Out-of-Gamut Node Colors
(between Color Index 109-216)

Node L * a * b *
(Out-of-Gamut Colors)

Gamut Mapped
L * a * b *

Gamut Mapped
CMYK RGB Values

Color

Index RGB * a * b * L * a * b * CMYK

210 255 204 255 90.07 34.95 17.12 81.67 26.88 8.51 0 83 0 0

211 255 255 0 100.00 5.47 172.41 81.48 0.22 97.54 14 27 255 20

212 255 255 51 100.00 5.16 123.85 90.93 2.45 98.38 0 16 231 0

213 255 255 102 100.00 4.41 84.58 91.72 2.09 69.57 0 22 171 0

214 255 255 153 100.00 3.27 52.79 93.50 1.64 46.24 0 20 111 0

215 255 255 204 100.00 1.79 25.06 96.26 0.99 23.93 0 13 64 0

216 255 255 255 100.00 0.00 0.00 100.00 0.00 0.00 1 1 0 0

PROBLEMS
7.1 Using the RLS algorithm, obtain a global linear model for a CMY gray color
[C ¼ 127 ¼ M ¼ Y, K ¼ 0]. The solution should include some details of the

experimental procedure.
7.2 Using the RLS algorithm, obtain a local linear model for a CMY gray color
[C ¼

¼ M ¼ Y, K ¼

127 0]. The solution should include some details of the

experimental procedure.

7.3 Using the RLS algorithm, obtain a quadratic and cubic model for the printer.
Calculate the modeling errors with respect to the virtual printer model shown in
Chapter 10. Is a quadratic and cubic model a good choice for this virtual printer?

7.4 In a printing system CMYK values are sampled between 0 and 255 in a uniform

grid to obtain up to 10 4 input output characterization data. Patches are printed

and measured by the spectrophotometer. The spectra are measured at 31 wave-
lengths from 400 to 700 nm at 10 nm intervals. Use PCA mathematical
techniques to analyze the set of multivariate input

-

- output characterization

D E a * , data. Show the D E 2000 ) error plot with respect to number of principal

components. Determine the parameter matrix using least squares. Plot the model
accuracy for the test colors as a function of the number of basis vectors. How
many basis vectors are needed to obtain a reasonably accurate model?

D E (

7.5 Use bootstrapping techniques to gain con dence in the PCA-based modeling.

7.6 A clustered PCA-based model is to be constructed for a 10 4 spectral character-
ization data. Use the K-means algorithm to cluster the color data in spectral
space. Obtain PCA vectors for each cluster. Model each cluster with the RLS
algorithm. Plot the performance of your model for test data as a function of the
number of clusters.