Visual Cryptography for Color Images - Visual Cryptography and Secret Image Sharing - page 37

FIGURE 2.7
Lattice for the RGB and CMY color models.
In the additive model the superposition of two colored pixels corresponds to
the greatest lower bound while in the subtractive color model the superposition
corresponds to the least upper bound. The choice of a particular lattice is
equivalent to the choice of a color model. For example, the lattice in Figure 2.7
is equivalent to the color model that uses the following 8 colors: black, white,
R , G , B , C , M , and Y . Notice that this particular set of colors is closed under
the superposition operation. It is worth emphasizing that this lattice is not
equivalent to the RGB and CMY models: it only considers the 8 colors with
zero or full intensity while the RGB and CMY models have many more colors.
2.2.3 The Darkening Problem
When we superpose pixels having the same color, unless we have zero or full
intensity components, the resulting pixel is a darker version of the original
color. This is because each transparency is a filter that absorbs some light,
except when the transparency is white, and thus the resulting pixel is darker.
Figure 2.8 shows examples of superposition of pixels with the same color, a
light grey. As can be noticed in the figure, as we add more pixels the resulting
color becomes darker, with the limit being a full black.
We will refer to this problem as the darkening problem. Some of the schemes
that we will describe later superpose pixels with the same color, but ignore
the darkening problem.