The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
130 
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. 
REFERENCES 
Li Boya,Han Guoqiang,Wo Yan,2007. A Watermarking Based 
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Li Yuanyuan,Xu Luping,2004.Vector Graphical Objects 
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Sun Shenghe, Lu Zheming, et aL 2004. Digital Watermarking 
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Wang Xuemin,1999. The Applications of Multivariate 
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YANG Cheng-song, ZHU Chang-qing,2007. Watermarking 
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Yang Yixian,Niu Xinxin, 2006. Theory and Applications of 
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ZHANG Fan, LIU Ya-li, SU Yu-ting, ZHANG Chun-tian,2007. 
Multiple Watermarking and Capacity Analysis of Digital Image. 
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Zhong Shang-ping, GAO Qing-shi, 2006. The Feasibility 
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ACKNOWLEDGMENTS 
This work was funded by 863 project (2006AA12Z223).