Cryptography Reference
In-Depth Information
Eq. (12.13), the fitness function, in order to balance the effects from the PSNR,
representing the image quality, and the BCR, representing the watermark
robustness.
12.8 Other Related Watermarking Algorithms
To demonstrate the effectiveness of the proposed algorithm, we compare two
VQ-based watermarking algorithms given in the literature. The two water-
marking algorithms are described as follows.
(1) Review of Watermarking Algorithm in [10].
The algorithm in [10] is one of the pioneering VQ-based watermark-
ing methods proposed in literature. The authors trained the codebook
C with length L in advance. Then, C is partitioned into N groups,
G
0
, G
1
,, G
N−1
, where
N−1
i=0
G
i
;
a) C =
N−1
i=0
G
i
=∅;
c) G
i
=
b)
C
0
, C
1
, i∈[0,N−1].
For a given input vector X
k
, we assume that the codeword C
t
∈G
p
, p∈
[0,N−1], t∈0, 1, is the nearest codeword. To embed the corresponding
watermark bit w∈0, 1in X
k
,thej-th codeword of G
p
is the output
as the watermarked vector X
′
k
:
j =(t + w)modG
p
,
(12.16)
= C
j
,
′
k
X
(12.17)
where j∈[0,G
p
], andG
p
denotes the number of codewords contained
in group G
p
, and mod means the modulus operation. For embedding
only one bit into each vector,
=2.
After all of the watermark bits have been embedded into the corresponding
vectors, the output vectors are pieced together to form the watermarked
image, X
G
p
′
. In addition, due to the embedding strategy employed, this
method requires the original cover image to be presented during extrac-
tion, or otherwise the hidden information cannot be obtained. This is a
fatal disadvantage for the practical application of this algorithm.
(2) Review of Watermarking Algorithm in [11].
The algorithm described in this sub-section is an improvement on some
existing schemes for VQ-based watermarking given in literature [31]. The
trained codebook has a length L which is an even number, then C =
c
0
,c
1
,,c
L−1
is employed for vector quantization. In [11], the authors
propose a method to partition the codebook according to the watermark-
ing bits 0 or 1 to be embedded. They divide C into the odd-indexed and
even-indexed sub-codebooks C
o
and C
e
, with C
o
=c
1
,c
3
,c
5
,,c
L−1
and C
e
=c
0
,c
2
,c
4
,,c
L−2
.Thus,C
o
∪C
e
= C and C
o
∩C
e
=∅.
