Cryptography Reference
In-Depth Information
duration of T
S
iterations.
Intermediate and long-term learning strategies:
These strategies are
implemented with intermediate and long-term memory functions. Their
operations are to record good features of a selected number of moves gen-
erated during the execution of the algorithm.
Short-term strategy or overall strategy:
This strategy manages the in-
terplay between the different strategies listed above. A candidate list is a
sub-list of the possible moves which are generally problem dependent.
The best-solution strategy:
This strategy selects an admissible solution
from the current solutions if it yields the greatest improvement or the least
distortion in the cost function. This is provided that the tabu restrictions
and aspiration criterion are satisfied.
Termination:
A stopping criterion terminates the tabu search procedure
either after a specified number of iterations has been performed, or the
currently best solution has shown no improvement for a given number of
iterations.
Using the background information presented in this section, we are able to
apply the tabu search algorithm to digital watermarking.
12.7.2 Multiple Watermarking with Tabu Search
When embedding multiple watermarks with MDC in Sec. 12.5.1, the main
problem for embedding the first watermark is how to split the codebook C
into two sub-codebooks C
′
′′
. The result for splitting C will not only
influence the watermark imperceptibility and the robustness of the first wa-
termark, but it will also effect the robustness of the second watermark. All
the problems can be optimized using tabu search [12] by offering the rea-
sonable fitness function. Using the fundamentals of tabu search described in
Sec. 12.7.1, and the watermarking requirements depicted in Sec. 12.1, we can
consider both the imperceptibility of the watermarked image, represented by
Peak Signal-to-Noise Ratio (PSNR), and the robustness of the extracted wa-
termarks, represented by Bit Correct Rates (BCR), for optimization. The
fitness function with this system is:
and C
f
i
= PSNR
i
+ λ
1
BCR
1,i
+ λ
2
BCR
2,i
(12.13)
where f
i
denotes the fitness score in the i-th iteration, PSNR
i
,BCR
1,i
and
BCR
2,i
denote Peak Signal-to-Noise Ratio (PSNR) and Bit Correct Rates
(BCR), respectively. Because the PSNR values are generally many times larger
than the BCR values, we include λ
1
and λ
2
to represent the weighting fac-
tors to balance the effects of PSNR and BCR. The objective is to maximize
