Visual Cryptography for Color Images - Visual Cryptography and Secret Image Sharing - page 54

pixels. For example, if a given surface is evenly covered with red and green we
should see yellow as a result. Although this is in principle true, in practice it
works only if the pixels are so tiny and evenly distributed that our eyes are
not able to distinguish the single pixels and perceives an average color mixing
the two primary colors. What really happens is that our eyes perceive the
mixture of red and green. However, this does not mean that we cannot use this
model. We have to accept the fact that a secret color (yellow, for example)
is reconstructed as a mixture of other colors (red and green, for example).
This model allows building schemes with a better pixel expansion, namely
m = dlog ce 2 n1 . The contrast properties that we have used throughout
this paper are not applicable to this model.
In [6] Hou proposes a method that first splits the secret image into the
cyan, magenta, and yellow components and then uses ad-hoc (2; 2)-threshold
schemes to share those components. Although the paper claims that this
method is easily extensible to the (k;n)-threshold scheme it is not clear how
to use the ad-hoc (2; 2)-threshold schemes for the general case of the (k;n)-
threshold scheme. A proof of the security property is also missing.
2.8 Conclusions
Stepping from visual cryptography for black and white images to visual cryp-
tography for color images is not immediate. The color model poses some tricky
questions that arise from the complex behavior of colors superposition. Many
visual cryptography schemes for color images avoid the problem by not super-
posing pixels with different colors. Very few known schemes do actually exploit
color superposition. In this chapter we have first emphasized the diculties
that arise from the superposition of colored pixels; then we have provided a
survey of the models of visual cryptography for color images that have been
considered in the literature and a survey of the schemes that have been pro-
posed for such models.
Visual cryptography for black and white images has been thoroughly stud-
ied. The case of color images is still pretty much unexplored. A first direction
of research concerns the definition of a reference model. We believe that the
General model is the one that best represents the real world. All the models
proposed in the literature lack a well-defined notion of contrast, which is a
very important measure for the evaluation of the schemes. A second direction
of research concerns the search for schemes that do use the properties of color
superposition. The construction of schemes for color images seems to be much
more dicult than for black and white images.