One-Dimensional, Two-Dimensional, and Spot-Color Management and Control Methods - Control of Color Imaging Systems: Analysis and Design - page 435

control as compared to 1-D channel-wise or 1-D gray-balance TRCs and hence can
provide more accurate color rendition than 1-D TRCs, but are still less accurate than
3-D LUTs [5].

8.5 ONE-DIMENSIONAL AND TWO-DIMENSIONAL PRINTER
CALIBRATION USING PRINTER MODELS
In this section, we show how to construct the 1-D and 2-D printer calibration TRC
LUTs if an updated printer model is given. The model can be in any of the forms
described in Chapters 7 or 10 or even a simple input output LUT obtained experi-

-

mentally while characterizing the printer. We first discuss the algorithms for 1-D

calibration, which involves both 1-D channel-wise linearization and 1-D gray
balance to equivalent neutral targets.

8.5.1 O NE -D IMENSIONAL C HANNEL -W ISE (I NDEPENDENT )C ALIBRATION
In channel-independent calibration, each channel is independently linearized. By
linearization, we would like to make the D E a * obtained by measuring color patches
from paper to be linear so that the channel-linearized printer can emulate an ideal
printer, which has the characteristic of linearized

D E a * from
paper is the Euclidean norm between target color and the paper white in the device-
independent color space (L*a*b*). The

D E a * from paper. The

D E 2000 metric is not normally used for the
paper-based 1-D channel-wise calibration.
As an example, let us assume that we choose the cyan channel for linearization
and printed N cyan patches (M ¼ Y ¼ K ¼

0) that represent the step wedge with the

cyan digital count of d 0 ¼ 255, and measured the L*a*b* values

of each cyan patch using a color sensor. Let the corresponding measured L*a*b*
value of the ith patch be (L*a*b*)i. i . Note the

0, d 1 , d 2 ,...,d N 1 ¼

first patch is the paper white which
means that (L*a*b*) 0 is the L*a*b* of the paper. We now compute the

D E a * from

paper for each patch as follows:

D E i ¼k( Lab ) i ( Lab ) 0 k i ¼ 0, 1, , N 1 ( 8 : 1 )

...

The function f(.) is formed by normalizing the D E values to obtain a value of 255 for

the cyan value of 255. It is de ned as

D E i
max i D E ðÞ

255

d i ! fd ðÞ¼ ( 8 : 2 )

To linearize the printer, we need D E i to be a linear function of di. i . To achieve this, we

find the inverse of the transformation given by Equation 8.2, which is the TRC of the
cyan channel. That TRC can be represented by following equation:

c ¼ f 1 Cyan TRC : ( C ) ( 8 : 3 )