Visual Cryptography and Random Grids - Visual Cryptography and Secret Image Sharing - page 192

(a) (b)

FIGURE 7.2
Reconstructed results by Naor and Shamir's approach for binary image B in
Figure 7.1(a): (a) m = 2, (b) m = 4.

We summarize the reconstructed light contrasts by these three algorithms
in Table 7.3.

TABLE 7.3
Light contrasts by Algorithms 1{3 in producing
VCRG-2.
E T (S[B(0)]) T (S[B(1)]) c( E )

1
2

1
2

Algorithm 1 0

1
2

1
4

1
5

Algorithm 2

1
4

1
4

Algorithm 3 0

It is noticed that various definitions of contrast in [9, 14, 1] all depend on
pixel expansion so that they are not suitable any more to measure the effective-
ness of our schemes. On the contrary, since we consider the light transmissions
through different areas of the transparency, the measurement of light contrast
is more generalized and can be applied to all kinds of schemes.
We discuss how to generate (n;n)-VCRG in the next subsection.

7.3.5 Algorithms of (n;n)-VCRG for Binary Images
Consider an hw binary image B and n random grids R 1 ;R 2 ;:::;R n with
the same dimension. We call r 1 ;r 2 ;:::;r n the corresponding pixels of b 2 B
if all r k 's in R k 's for 1 6 k 6 n have the same coordinates as b (if b = B[i;j],
then r k = R k [i;j] where 1 6 i 6 h and 1 6 j 6 w).
By extending the idea of Algorithm 2 directly, we may obtain a set of two
out of n visual cryptograms of random grids where any pair of two out of the
n shares can reveal the secret when superimposed. Given a binary image B,