Visual Cryptography for Color Images - Visual Cryptography and Secret Image Sharing - page 31

2.1 Introduction
The key property used to construct visual cryptography schemes for black
and white images is the following: if we superpose transparencies with black
and white pixels, the resulting pixel that our eyes see is black if at least one
of the superposed pixels is black and is white if all the superposed pixels are
white. Such a property can be rephrased as follows: the possible "state" for
the pixels can be represented with a bit, using 0 for white and 1 for black,
and the human visual systems performs an OR of the input pixels in order to
reconstruct the secret pixels.
This key property does not easily extend to colored pixels. With colored
pixels the state of each pixel cannot be represented anymore with a single
bit and the "reconstruction" operation performed by our eyes is much more
complicated than a simple OR.
In this chapter we will first describe the diculties that arise from the
superposition of colored pixels and then we review the work on visual cryp-
tography for colored images.
We assume that the reader is familiar with (at least the basics of) black
and white visual cryptography.
2.2 Color Superposition
What happens when we stack together two transparencies so that two pixels
get superposed? What is the color that the human eyes see as the result of
this superposition? Figure 2.1 illustrates the superposition operation with two
examples. In the first one we are using black and white pixels: the superpo-
sition of a black pixel with a white pixel yields a black pixel. In the second
example, we are using colored pixels: the superposition of a yellow pixel with
a magenta pixel yields a red pixels.
Using only black and white images the result of the superposition of pixels
printed on transparencies is straightforward: it is black if and only if at least
one of the pixels is black.
The answer to the same question gets much more complicated when we use
colors. In order to understand what happens when we superpose transparen-
cies with colored pixels we have to talk a bit about light and color theory.
2.2.1 Color Vision and Color Models
Modern understanding of light and color vision is based upon the advances
of several great scientists, such as the ones due to Newton. Thanks to them