Interpolation of Multidimensional Functions - Control of Color Imaging Systems: Analysis and Design - page 276

6.5 COMPRESSION OF LOOKUP TABLES

6.5.1 I NTRODUCTION
In general, as indicated above, the inverse map is a LUT that associates
points in the printer output color space to points in the printer input color space
(L*a*b*

! CMYK).
An important performance measure of the inverse LUT is the accuracy of
inversion. To achieve an improved accuracy for colors inside the printer gamut,
often the manufacturers increase the LUT size greatly (e.g., for an N N N LUT, N
may be chosen equal to 33 when compared to 17). To compensate for the printer
drift, it is highly desirable to update the inverse printer LUT on a regular basis. If we
have to update each node in the inverse LUT through measurements, then this
requires printing and measuring a large number of color patches. Hence, a better
way to do this is by downsampling the input color space from N N N to M
M M (M < N) by selecting the critical colors for measurement such that, when we
upsample the downsampled LUT to the original size, the average

D E a * between the
original L*a*b* and the upsampled L*a*b* is minimized. The process is shown
schematically in a block diagram in Figure 6.16.
The average

D E a * between the original L*a*b* and L*a*b 1 * (the upsampled
value from the downsampled LUT corresponding to the patch represented by
L*a*b*) is de ned as

X

K
i ¼ 1 k L*a*b*

1
K

D E a *

¼ L*a*b 1 * ( i )k ( 6 : 59 )

D E a * . Once these critical colors are

These critical colors are selected by minimizing

identi ed, the updating of the three-to-three inverse printer map is straightforward. It

is obtained simply by first printing and measuring these selected critical colors, and

then upsampling the measured L*a*b* values, which are now in the form of a

N × N × N

CMY

P Lab (out1)

ˆ

Downsample
N 1 × N 1 × N 1
LUT

+

Compute
Δ E * b

Upsample to
N × N × N
LUT

Δ E * b

_

Lab (out2)

FIGURE 6.16 Optimum color selection method illustrated for obtaining minimal colors for
measurement of a three-to-three printer forward map.