The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
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k=n-1
Then C = Z g{k)*w{k)
k=0
c = w W + Z s\k)*w(k)
k=0 k=0
X#)«0 => c=Y u g’(k)*w(k)
k=0 ¿=0
c = X £ W * ~ wcr2 ) ( 6 )
k=0
From (6) we can get that the random noise with mean jl and
variance u 1 is equal to the random noise with mean 0 and
variance cr 2 . So, the bad influence of mean ( [d ) to the
watermark detection is eliminated by adding some restrictions
to the process of watermark generation.
5. THE PROBABILITY OF MULTIPLE WATERMARK
EMBEDDING
Some time, many watermarks are embedded into a same copy
of data (ZHANG Fan,2007; Li Boya,2007). The problem is
how to eliminate mutual influence of different watermark.
Simple watermark extraction can not solve this problem; the
autocorrelation detection can solve this problem, so watermark
detection should be executed.
Suppose n watermark w k (k = 0,1, • • • n -1) are embedded into a
same copy of data. When detecting with w , the other
watermarks can be treated as the overlap of n-1 random noises
with mean 0 and variance;^ = 0,1,•••/-!,•••,z' + l,«-l) •
There is an example of embedded 10 watermarks into the same
data, 100 random noises are used to perform autocorrelation
detection, in which the 45 th ~ 54 th are the embedded
watermarks and the others are pseudo random sequence. The
figure 4 is autocorrelation detection result.
Figure 4. The detection result of multiple watermarks
6. CONCLUSIONS
Based on the Mahalanobis distance discriminant analysis in the
statistics theory and he self-characteristic of watermarking
techniques, this paper solve the problem of the setting of
detection threshold and the calculating of false alarm and flow
detection probability, get the relationship between the length of
watermark > the watermark embedding strength and the attack
strength , prove the probability of multiple watermark
embedding, at the same time, a pseudo random sequence
watermark generation way with restriction is proposed. Theory
and experimentation testify that the research of this paper is
very useful to the watermark generation and watermark
detection.
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ACKNOWLEDGMENTS
This work was funded by 863 project (2006AA12Z223).