Cryptography Reference
In-Depth Information
f
i
in our system. The PSNR in the i-th iteration between the original and
watermarked images can be represented by
255
2
PSNR
i
=10log
10
(12.14)
M−1
m=0
N−1
n=0
(X(m, n)−X
i
(m, n))
2
1
MN
′
where X(m, n)andX
′
i
(m, n) denote the pixel values at position (m, n)of
the original image X and watermarked image X
′
i
in the i-th iteration, where
MN denotes the image size. The BCR between the embedded and extracted
watermarks can be defined by
M
W
N
W
−1
1
w
b,i
⊕w
′
BCR
i
=
100%
(12.15)
b,i
M
W
N
W
b=0
′
where w
b,i
and w
b,i
represent the embedded watermark bit and the extracted
oneinthei-th iteration, M
W
N
W
denotes the watermark size,⊕indicates the
exclusive-or operation, and the line above the exclusive-or operation means
the not operation in logic design.
Given the preliminaries in Sec. 12.1, by fixing the watermark capacity, both
the watermark imperceptibility and watermark robustness can be improved
after tabu search optimization. Parameters employed in the tabu search are:
• there are 20 candidate solutions trained for each iteration;
• the tabu list length T
S
is set to 10;
• the weighting factors are set to λ
1
= λ
2
= 10;
• the aspiration value is set to 40, with PSNR
i
≥26, BCR
1,i
≥0.7, and
≥0.7 in Eq. (12.13);
• watermark embedding and extraction are performed in every training it-
eration to obtain the updated PSNR
i+1
,BCR
1,i+1
, and BCR
2,i+1
in the
next iteration;
• the number of total training iterations is set to 100.
The above parameters were chosen carefully. In this chapter, we choose 20
candidates for training with tabu search. After considering the computation
time, the memory consumption, and the convergence rate in tabu search, we
choose 20 candidates for each training iteration based on the fitness function.
If we choose too many candidates, the computation time per iteration will
be increased, and memory allocation might become a problem. In contrast, if
we choose too few candidates, the output result might be a locally optimal
one, which is generally encountered in the optimization problems. Therefore,
in this chapter, we have 20 candidates to be a reasonable number for training
with tabu search.
Moreover, we set the tabu list length T
S
= 10 by considering the tradeoff
between the computation time and the convergence rate in the optimization
process. We can also find that PSNR values are many times larger than the
BCR values, hence, the weighting factors, λ
1
and λ
2
, need to be included in
BCR
2,i
