The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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strength ( CT 4- /T ) and inversely proportional to the 
watermark length(n) and embedding strength( A ). 
When A * n is fixed, the noise strength (a 2 + p 1 ) can’t be 
too big, otherwise, the rate of false alarms will be so big that it 
is impracticable to use the discrimination rule to judge whether 
there is watermark or not. 
When n = 1000, /1 = 1.0,under the random noise attack which 
has the statistic characteristic of mean ¡i =0, variance <j = 
2.CK 4.CK 6.CK 8.0, the detection result is as figure 2, here, the 
500th to-be-detected information contain watermark. From 
figure 2 we can get that: the rate of false alarms is small when 
variance <j is 2.04.0 and will increase as the variance <j 
increase. 
1 
0.5 
0 
-0.5 
500 1000 
variance=2.0 
500 1000 
variance=4.0 
500 1000 
variance=6.0 
500 1000 
variance=8.0 
Figure 2. The influence of variance G to detection 
In order to get good attack-resistance capability, the “3cr”rule 
is erected. It means that there will be no probability of false 
alarms when > 3\fnG -This rule request that: 
2 
A*n_ > 
2 
3*jn(jU 2 +G 2 ) 
The 7(y + (j 2 ) can be treated as the random noise strength, 
when the watermark detection need to resist the random noise 
below yj(jU 0 2 + cr Q 2 ) , the right value of A, Tl must be set to 
satisfy the follow inequality 
^- > 3 * yjn(jL¿ 2 +G 2 ) (4) 
(5) 
From the formula (4) and (5), it is known that in order to 
promote the attack-resistance capability of detection, we can 
increase the value 2 and n ,but considering the central 
limit theorem, the value of n can’t be too small, experiment 
testify that n should be no less than 800. 
4. THE INFLUENCE OF MEAN ^ OF RANDOM 
NOISE TO THE WATERMARK DETECTION 
Data’s translation has a bad influence on the watermark 
extraction and detection (YANG Cheng-song, 2007), Data’s 
translation can be treat as the mean (jl) of the random noise. 
In order to display the influence of the mean (jLl) of random 
noise to the watermark detection, 
let g = 10, n — 1000, A — 1.0, change the value of ¡U , the 
variation of false alarms is showed in figure 3. 
Figure 3. The influence of noise mean to the false alarm 
probability 
From figure 3 we can get that the mean {JU) of random noise 
has a big influence on the watermark extraction and detection. 
In order to eliminate the bad influence of mean {JU) to the 
watermark detection, restriction is set in the process of 
watermark generation. According to the probability 
p{w(k) — 1} — —,P{w(k) — —1} — — , a series of 
watermark is created, the watermark which meets the inequality 
k=n-1 
^ w(k) ~ 0 is chosen. 
*=o 
Random noise can be expressed as g(k) — JU + g\k) , here 
g'(k)~N(0,a 2 ) 
At the same time, we can control the false alarms under certain 
threshold p by control A ^ n as the formula: