Image Sharing with Steganography and Authentication - Visual Cryptography and Secret Image Sharing - page 435

a set of edge maps EMi, i , an edge-based LUT, called an ELUT,
is generated. Note that in this step, we call the edge map EM.
The order of the edge pattern of the ij-th block is denoted as BE ij .
The index value for ij-th block is I ij for 0 k 2 16 1. Finally, the
mean grayscale value can be derived from ELUT[I ij , BE ij ], where
0 EM ij 38 based on the number of edge patterns reported
by Chung and Wu [11]. In Chung and Wu's scheme, the value of
GI 0 ij (3, 3) is determinate as Equation 16.12.

GI 0 ij (3; 3) = ELUT[I ij ;BE ij ]

(16.12)

Step 4: Input a halftone image HI, which will be converted to the grayscale

image GI 0 . The detailed procedure is shown in Figure 16.16.

FIGURE 16.16
Procedure for generating final grayscale image in Step 4.

16.3.5 Shamir Scheme for Secret Sharing
The proposed scheme for secret image sharing is based on the (k,n)-threshold
secret sharing scheme proposed by Shamir (1979) [20]. In this section we
describe how to use the Shamir scheme to generate secret sharing. In the
following steps we use the (k-1)-degree polynomial shown in Equation 16.16
to generate n shares for a group of n secret sharing participants from a secret
integer value s for the threshold k.

F(x i ) = s + a 1 x i + a 2 x i + ::: + a k1 x k1 (16.13)

i