Visual Cryptography and Random Grids - Visual Cryptography and Secret Image Sharing - page 202

TABLE 7.6
Light contrasts by Algorithms 4{6 for (n;n)-VCRG.
E T (S[B(0)]) T (S[B(1)]) c( E )

1=2 n1 1=2 n1 Algorithm 4 0

1=2 n1 1=2 n 1=(2 n + 1)

Algorithm 5

1=2 n 1=2 n

Algorithm 6 0

7.3.6 Algorithms of (n;n)-VCRG for Gray-Level and Color
Images
In Shyu [12], the encryption algorithms of (2, 2)-VCRG for gray-level and color
images were generalized from those for a binary image. We apply the same
reasoning and skills adopted by Shyu in [12] to extend the binary (n;n)-VCRG
algorithms to cope with gray-level and color images.
According to Ref. [12], we simply transform a gray-level image G into its bi-
nary version H by some halftone technology and encrypt the binary equivalent
by using the aforementioned algorithms directly. Let Encryption VCRG (B, n)
denote the procedure of applying Algorithms 4, 5, or 6 to obtain (n;n)-VCRG
with respect to binary image B. Algorithm 7 describes the idea formally.

Algorithm 7. Encrypting a gray-level image into a set of (n;n)-VCRG
Input: an hw gray-level image G and an integer n
Output: a set of n random grids

E = fR 1 ;R 2 ;:::;R n g constituting a VCRG-

n of G

1. H =H(G) //H(G) is a halftone function with respect to G

2. (R 1 ;R 2 ;:::;R n ) =Encryption VCRG (H, n)
// Encrypt H by Algorithms 4, 5, or 6 directly

3. output(R 1 ;R 2 ;:::;R n )

Regarding the (n;n)-VCRG for a color image, we follow the experience
from Ref. [12] where the binary (2, 2)-VCRG encryption algorithms were ex-
tended to their color versions by utilizing skills including color decomposition,
halftoning, and color composition. Specifically, we decompose a color image
P into the c, m and y components (which are the primitive colors in the sub-
tractive model ), namely P C ;P m , and P y ; halftone each of them to be P c ;P m ,
and P y such that each pixelp x 2 P x is eitherxor 0 wherex2fc; m; yg and
encrypt the three halftone images into (R c 1 ;R c 2 ;:::;R c n ), (R m 1 ;R m 2 ;:::;R m n ),
and (R y 1 ;R y 2 ;:::;R y n ) by using any of Algorithms 4, 5, or 6 where the cor-
responding sets of binary colors are fc; 0g, fm; 0g, and fy; 0g, respectively
(instead of f1; 0g). LetR i denote the image composed byR c i ,R m i andR y i ,
i.e.,R i = (R c i ;R m i ;R y i ) for 1 6 i 6 n. Then,

= fR 1 ;R 2 ;:::;R n g can be
reported as a set of color (n;n)-VCRG of P. It means that only when all R i 's

E