Image Processing Reference
In-Depth Information
We repeat the above process for all the other three channels to obtain the TRCs
for the remaining magenta, yellow, and black channels by printing and measuring
corresponding color patches. Instead of step wedges, pure sweeps covering 0
255
digital counts can also be used for channel-wise linearization. In such cases, the
measurement aperture of the sensing process becomes more important than the
gradient of the sweep. The following example shows the 1-D channel-independent
linearization process for the cyan channel using patches representing step wedges.
-
Example 8.1
Assume that N¼
11 Cyan patches with digital counts of 0, 25, 50, 75, 100, 125,
150, 175, 200, 225, and 255 are printed on a color digital printer. The measured
L*a*b* values of these 11 patches and their corresponding
DE from paper are
shown in Table 8.2. Note that the
first row, which corresponds to CMYK¼
[0 0 0 0], is the paper white. Therefore, all the
DE values are measured
with respect to this reference. In practice, the L*a*b* of different spots on the
paper can be measured and the average of all these L*a*b* values used as
the reference paper white to avoid errors in the measurement process. The
function f(d) is obtained by dividing the
DE values by its maximum and multiplying
the results by 255. The function is shown in the last column of Table 8.2. The TRC
is obtained by
finding the inverse of the function f(d). The inverse can be simply
obtained by interchanging the dependent and independent variables as shown
in Table 8.3. Also see Section 9.9 for additional information about
finding an
inverse for different conditions. The TRC for the digital counts between the
data points of Table 8.3 is obtained by curve
fitting or interpolation. The function
f(d) and the resulting TRC for the cyan channel are shown in Figure 8.4. In this
figure, the nodes represent the measured points and the solid curve is obtained with
linear interpolation. A higher-order interpolation approach can be adopted based
on the need.
TABLE 8.2
Measured L*a*b* Values of Cyan Patches
d
D
E
a
*
L*
a*
b*
f(d)
0
97.81
0.004
0.22
0
0
25
94.24
6.43
9.78
12.06
42
50
90.13
9.52
14.96
19.15
66.68
75
86.67
13.08
16.07
23.37
81.37
100
82.23
16.71
19.90
30.15
104.97
125
77.87
18.87
21.34
34.64
120.57
150
74.44
20.29
25.32
39.85
138.71
175
70.45
24.03
34.33
49.89
173.68
200
67.34
27.49
39.25
56.63
197.14
225
63.43
31.05
44.05
63.77
221.99
255
57.50
35.59
49.97
73.26
255
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