Visual Cryptography for Color Images - Visual Cryptography and Secret Image Sharing - page 39

2.3 Formal Models for Colored VCS
In this section, we discuss the formal model for color visual cryptography, or
Color-VC for short. We first recall the basic properties of the formal model for
black and white visual cryptography, B&W-VC for short, that will be needed
also for the case of color images and then we dwell upon the problems that
need to be tackled in order to define a formal model for Color-VC.
2.3.1 The Models for B&W-VC
For B&W-VC the formal models used in the literature are all equivalent (with
variations on the metrics used for evaluation, like for example the contrast of
the scheme). The two key properties, that will be needed also for color images,
are:
the safety property, which guarantees that nonqualified sets of participants
are not able to reconstruct the secret image;
the contrast property, which guarantees that qualified sets of participants
are able to reconstruct the secret image.
To evaluate visual cryptography schemes the most important metric is the
pixel expansion, that is the number of subpixels used in the reconstructed
image for each pixel of the secret image.
Another important measure for the evaluation of B&W-VC schemes is the
contrast of the reconstructed image that can be defined as a function of the
contrast property. Several contrast properties and metrics can be found in
literature for B&W-VC. We refer the reader to the relevant papers about the
contrast (see for example [5]).
With the exception of the definition of the contrast, the formal model for
B&W-VC is pretty standard.
2.3.2 The Models for Color-VC
For color images even the model becomes dicult to define. Do we start
with a prespecified palette, perhaps the one used in the secret image, or do
we consider all possible colors? What color model do we consider? Do we
consider the darkening problem? Is the palette closed under the superposition
operation? That is, if we start with a prespecified palette, do we consider the
possibility that the reconstructed image contains colors that are not in the
original palette? How do we define the contrast property for color images and
what is the contrast metric? Do we allow the use of the annihilator color?
How do we account for it in the contrast property?