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of detecting points was 450/30 = 15) and the BERs measured using the sta-
tistically adaptive detection technique described in Sect. 7.4.2 were compared
with those measured using Kalkers detection method described in Sect. 7.4.1.
The above procedure was done using 1000 different random WM patterns. We
did not control watermark strength for each pixel, which would minimize the
degradation in picture quality, because we focused on evaluating the WM
detection method and such control might affect the evaluation. We instead
made the watermark strength, ยต (f,r) in formula (7.15), uniform for all pixels.
The example strength we used were three, and the corresponding PSNR was
38.6. We also set the threshold value for determining the bit value of the for-
mulas (7.20) and (7.25) to zero (T = 0) so that the 256-bit information was
always detectable.
0.08
0.07
0.06
Kalker's 3M
Adaptive 3M
Kalker's 4M
Adaptive 4M
Kalker's 5M
Adaptive 5M
0.05
0.04
0.03
0.02
0.01
0
1 2 3 4 5 6 7 8 9 1 0
1 1
1 2
1 3
1 4
1 5
Detecting point
Fig. 7.15. Evaluation results.
Results
The average values (over 1000 WM patterns) of the measured BERs obtained
using the statistically adaptive and Kalkers methods are shown for each bit
rate in Fig. 7.15, where the horizontal axis represents the detecting points,
from 1 to 15, and the vertical axis represents the average BERs. We can
see that the BERs with the statistically adaptive technique were better than
or equal to those of Kalkers method for each bit rate. For all bit rates, the
average ratios of the statistically adaptive BER to the Kalkers BER are 0.903.
The statistically adaptive technique thus yielded an average improvement of
9.7%.
From the plots of Fig. 7.15, we sampled two cases for each evaluated
sample: effective and non-effective cases of statistically adaptive detection.
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