Cryptography Reference
In-Depth Information
(2) Because of the error concealment capability for index assignment in
MDSQ, when only one description is received, the block can be partly
reconstructed. The watermark bit needs to be determined from several
possible indices assigned in MDSQ row or column matrix [27].
a) If Channel 1 breaks down, then i 2 will be received. By visualizing
Fig. 12.7, we choose the column containing i 2 and infer that the trans-
mitted description should be one of the several possible indices on the
column. We use a majority vote to estimate the watermark bit W
2,k
by checking whether the subscripts of the possible indices are odd or
even. If there are more odd indices, we set W
2,k = 1. Otherwise, we
set W
2,k = 0 with the modulus operation in Eq. (12.9). After check-
ing, if there are equal numbers of 0s and 1s in the MDSQ matrix in
Fig. 12.7, we randomly assign the watermark bit. On the other hand,
we calculate the conditional expectation from the possible indices, and
produce the reconstructed block X
k .
b) If Channel 2 breaks down, then i 1 will be received. By visualizing
Fig. 12.7, we choose the row containing i 2 and infer that the trans-
mitted description should be one of the several possible indices on the
row. With the same procedures in the previous case, we can obtain
the extracted watermark bit W
2,k
k .
and the reconstructed block X
(3) If no description is received, the value of watermark bit W
2,k
is randomly
k cannot be recon-
structed, and the luminance of that block is set to 128 for the 8-bit per
pixel grey level images.
By gathering all the extracted watermark bits W
assigned. With no received information, the block X
2,k , we obtain the ex-
2 . By gathering all the reconstructed blocks X
k ,we
tracted watermark W
obtain the reconstructed image X
which contains the first watermark. We
proceed with watermark extraction as shown in Sec. 12.5.2 in order to extract
the first watermark embedded from the received descriptions.
Extracting the First Watermark
After obtaining the codeword i
S in Sec. 12.5.2, we are prepared to extract
W 1 .Assumingthati
S
=c i . We examine whether the codeword c i belongs to
′′
, and the extract watermark bit W
the sub-codebook C
1,k .Thiscan
be estimated with Eq. (12.10), which is an inverse operation of Eq. (12.6):
or C
0, if c i
∈C
;
1,k
W
=
i∈[0,L−1] ,k∈[0,M W
N W
−1] . (12.10)
′′
1, if c i
∈C
;
By gathering all the extracted watermark bits W
1,k , we obtain an estimate of
the first embedded watermark W
1 .
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