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Table 12.3. Comparisons of watermark robustness under different channel erasure
probabilities with codebook length of L = 512 after considering the embedding of
two watermarks in Sec. 12.5.1.
Channel erasure BCR with our method
BCR with [10] BCR with [11]
probability
(in %)
(in %)
(in %)
W 1
W 2
W 1
W 1
p 1
p 2
0
0
100
100
100
100
0.1
0.1
94.12
93.60
90.48
94.90
0.25
0.25
87.50
85.64
78.47
87.19
0.5
0.5
74.30
72.08
62.88
74.69
0
1
81.03
68.23
75.72
79.72
1
0
67.00
69.71
66.38
66.52
Fig. 12.13(b)(d), they represent the results when transmitting over the lightly
to heavily erased channels. The BCR values are high and the extracted wa-
termarks are recognizable even with p 1 = p 2 =0.5. When comparing these
results with Fig. 12.11(b)(d), although the BCR values are a little inferior,
all the extracted watermarks are recognizable. In Fig. 12.14, when one of the
channels fails, both of the first watermarks are recognizable, while the second
watermarks can only be partially distinguished.
In Table 12.4 and Table 12.5, PSNR and BCR values under different era-
sure probabilities are indicated. Comparisons with results from [10] and [11]
are also made. PSNR values in Table 12.4 show the error-resilient capabilities
using MDVQ having severely erased channels. The PSNR values using our al-
gorithm outperform others in most cases, and under the error free condition,
the watermarked PSNR using our algorithm performs best. In comparison
with Table 12.2, with a larger codebook length given in Table 12.4, we obtain
better PSNR values. Also, the BCR values in Table 12.3 are acceptable even
with heavily erased channels. Again, with our algorithm, we can embed twice
as much watermark capacity than those in [10] and [11]. Only one watermark
can be extracted with existing algorithms, and the corresponding BCR values
with our algorithm are better than [10] and [11].
Summing up, under a wide range of channel erasure situations, the results
using the multiple watermarking algorithm with MDC demonstrate both the
effective transmission of watermarked images, and the robustness of the ex-
tracted watermarks. To compare with the results in Sec. 12.4.1, we also double
the amount of watermark capacity embedded with our algorithm.
12.10 Conclusions
In this chapter, we propose an innovative scheme for VQ-based image multi-
watermarking with multiple description coding (MDC), which is suitable for
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