Image Processing Reference
In-Depth Information
and
C
(
k
) ¼
B
(
k
)
x
k
b
(
k
) ¼
w
(
k
) þ
x
k
C
(
k
)
B
(
k
þ
(
6
:
33
)
) ¼
B
(
k
)
C
(
k
)
C
T
(
k
)=
b
(
k
)
1
) ¼
D
(
k
)
x
k
y
k
=
w
(
k
)
D
(
k
þ
1
Step 4:
Is k
¼
N
1? If the answer is no, go to Step 2; otherwise, stop and compute
matrix A using the following equation:
A
¼
D
(
N
)
B
(
N
)
(
6
:
34
)
6.4 LOOKUP TABLE INVERSE
6.4.1 I
NTRODUCTION
A color printer can be seen as a device that is mapping a requested color in the image
into a device independent color (or printed color). An approximation to this color
mapping can be obtained by constructing a forward map of the printer using
experimental data in the form of a LUT. To reproduce colors accurately, we need
to build the inverse map of the forward LUT [6,7]. More description about the
inverse LUTs can be found in Chapter 7. One form of this LUT associates the input
colors in L*a*b* space to printer speci
c CMYK space. Each entry in the inverse
LUT is called a node. It is desirable to have an inverse LUT with input nodes regularly
spaced on a sequential plane (i.e., a structured input). While generating the printer
forward table, if we select node colors appropriately in the forward LUT, then, theor-
etically speaking, an inverse LUT is just the reversal of the forward LUT. The reversal
can be easily obtained by swapping the data from the forward LUT. The resulting
inverse LUT will not conform to the structured speci
cations required for the input
nodes. Also, for colors at the gamut boundary, this type of inverse LUT may not be well
de
ned. It may give multivalued outputs. Multidimensional interpolation approaches,
such as tetrahedral, conjugate gradient (CG), and iteratively clustered interpolation
(ICI) algorithms, are often used to restructure the inverse LUT when such LUTs are
constructed with experimental data such that the inverse LUT
finally ends up with a
uniformly sampled, structured input grid. However, it is important to note that the
various other approaches described in Chapter 7 do not always use these methods.
6.4.2 I
NVERSE
P
RINTER
MAP
Let us describe the inversion process using the CMY to L*a*b*, a three-to-three printer
forwardmap, P, as shown inFigure6.14. Let P
1
denote anestimateof the printer inverse
map. The CMY values are converted to CMYK using gray-component replacement or
under-color removal (GCR
UCR) algorithms before printing on a CMYK to L*a*b*
printer (Section 7.5.1). For the purpose of this discussion, the GCR
=
UCR function is
embedded inside the printermap, P, andonly in-gamut colors are considered. The inverse
printer map P
1
is a three-to-three map, de
=
ned mathematically as L*a*b*
!
CMY,
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