Cryptography Reference
In-Depth Information
watermarked image quality, measured by Peak Signal-to-Noise Ratio (PSNR)
between the watermarked image X
′
and the original X can be calculated
′
using Eq. (12.14). X
is reconstructed from the received descriptions which
are transmitted over two mutually independent, erasure channels. The sec-
ond metric, the Bit Correct Rates (BCR), of the one extracted watermark
in Sec. 12.4.2, or the two extracted watermarks in Sec. 12.5.2, are employed
to evaluate the robustness of the algorithm. They can be calculated using
Eq. (12.15). Generally speaking, the desirable results are to obtain both the
higher PSNR value in the watermarked image quality, and the higher BCR
values in the extracted watermarks. We also make comparisons with other
existing VQ-based watermarking schemes [10, 11] described in Sec. 12.8. Sim-
ulations show the practicality and usefulness of our method.
As shown in Figs. 12.5 and 12.6, only the watermarked VQ codewords
are transmitted over the noisy channels. Therefore, attacking schemes such
as low-pass filtering, or those employed in the Stirmark benchmark [21], are
not suitable when applied into our scheme. Therefore, we only use the situ-
ations where the descriptions can be transmitted over mutually independent
channels.
12.9.1 Results with Single Watermarking
For the single watermarking algorithm in Sec. 12.4.1, simulations with dif-
ferent channel erasure probabilities are now presented. The two memoryless
and mutually independent channels for transmitting bitstreams in Fig. 12.5
have different erasure probabilities, p
1
for Channel 1, and p
2
for Channel 2. In
Table 12.1, we perform a series of simulations by varying p
1
and p
2
for each
transmitted index. Under the no loss condition, p
1
= p
2
= 0, and we obtain
the watermarked image with PSNR = 32.53 dB, and have an extracted wa-
termark with BCR = 100%. This is identical with that embedded. When p
1
and p
2
increase, both channels deteriorate, the PSNR values of watermarked
images become lower, and the BCR values also decrease. This is as shown
in Fig. 12.9. The PSNR and the BCR values are presented in detail in Ta-
ble 12.1. Even under severely erased channel conditions, where p
1
= p
2
=0.5,
the subjective quality of reconstructed, watermarked image is acceptable. This
is because MDC offers good error resilient abilities. In addition, the extracted
watermark is still recognizable. As illustrated in Fig. 12.9(d), it shows that
the capability for copyright protection is still retained using our scheme.
In addition, MDC is suitable for coping with severe channel conditions. We
simulate the instances where one of the channels is totally broken down. The
results are in Fig. 12.10 and Table 12.1. In Fig. 12.10(a), where Channel 1 is
broken down, only the bitstreams transmitted over Channel 2 can be received.
The extracted watermark is recognizable with a BCR value of 80.55%. The
resulting watermarked reconstruction is 26.09 dB with the ability of MDC.
In Fig. 12.10(b), Channel 2 is broken down, and the extracted watermark is
