Cryptography Reference
In-Depth Information
add
(
R
;
G
) =
Y
,
add
(
Y
;
M
;
C
) = . Figure 2.5 shows some other examples of
superposition of colored pixels.
FIGURE 2.5
(See color insert.) Examples of pixels superposition.
The
add
operator can be easily extended to any number of pixels. Indeed
since the operation is commutative it is enough to add any two pixels each
time until we get to one pixel. Let
1
= (x
1
;y
1
;z
1
);
2
= (x
2
;y
2
;z
2
);:::;
n
=
(x
n
;y
n
;z
n
) be the colors of the pixels. The color of the pixel that results from
the superposition is:
add
(
1
;
2
;:::;
n
) = (X;Y;Z)
where
x
1
x
2
:::x
n
L
n1
y
1
y
2
:::y
n
L
n1
z
1
z
2
:::z
n
L
n1
X =
int
;Y =
int
;Z =
int
:
Figure 2.6 shows examples of superpositions with 3 pixels.
FIGURE 2.6
(See color insert.) More examples of pixels superposition.
2.2.2 Lattices
Some papers (e.g., [7]) use finite lattices to formalize the properties of the
superposition of colored pixels. A finite lattice is a partially ordered set for
which any two elements of the set have a least upper bound and a greatest
lower bound. We can use a lattice to describe a color model.
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