Visual Cryptography and Random Grids - Visual Cryptography and Secret Image Sharing - page 182

while the others are purely random. When the two grids are superimposed
together, the correlated areas will be resolved from the random background
due to the difference in light transmission so that the secret picture or shape
can be seen visually. Just like conventional schemes in visual cryptography, the
decoding process is done by the human visual system where no computation
is needed; however, no extra pixel expansion is required using random grids.
Observing the interesting features of random grids in image encryption,
which were discussed right before Naor and Shamir's visual cryptographic
scheme (VCS) [9], Shyu [12, 13] generalized the random grids-based ap-
proaches into visual cryptograms of random grids (VCRG) for achieving visual
secret sharing recently. The most appealing benifits using random grids lie in
that the pixel expansion needed is merely one and no basis matrix is needed.
With the same contrast in the reconstructed results, the optimal pixel expna-
sion in (n, n)-VCS is 2 n1 ; while that in (n, n)-VCRG is still 1.
We study the random grids-based schemes, analyze the performances, and
demonstrate their feasibilities in this chapter. The rest of the chapter is or-
ganized as follows. The fundamental characteristics of random grids are dis-
cussed in Section 7.2. Section 7.3 discusses how to apply visual cryptograms
of random grids in visual cryptography where the formal definition of VCRG
is given, and the designs, analyses, and implementations of (2, 2)-VCRGs and
(n;n)-VCRGs for binary, gray-level and color images are examined. Section
7.4 exhibits some concluding remarks.

7.2 Random Grids

7.2.1 Random Pixel, Random Grid, and Average Light

Transmission
We refer to a binary pixel r as a random pixel if the choice for r to be trans-
parent or opaque in R is totally random; or equivalently, the probability for
r to be transparent is equal to that for r to be opaque,

1
2 ;

P rob (r = 0) =P rob (r = 1) = (7.1)

where 0 (1) denotes a transparent (opaque) pixel. Since a transparent pixel lets
through the light while an opaque one stops it, the average light transmission
of random pixel r is

1

2 , denoted as
t (r) =

1
2 :

(7.2)

Definition 1 R is a binary random grid if each pixel r in R is a binary
random pixel.