Cryptography Reference
In-Depth Information
Step D6: Estimate the BERs p(c
(s)
)(s =1,,FR)fromtheFR accumu-
lated sets c
(s)
s
Step D7: Select the set of the correlation values having the smallest BER
c
(s
opt
)
, where s
opt
represents the optimal number of accumulations:
1≤s≤FR
p(c
(s)
).
s
opt
= arg
min
(7.24)
Step D8: Determine K embedded bits b
k
s by comparing c
(s
opt
k
with a thresh-
old value T (> 0) as is the case with formula (7.20) of Kalkers WM
detection:
⎧
⎨
if c
(s
opt
)
k
1,
≥T ;
if c
(s
opt
)
k
b
k
=
(7.25)
0,
≤−T ;
⎩
if−T<c
(s
opt
)
k
not detected,
<T.
Note that the set c
(FR)
of Step D5 is equal to the set c in formula (7.17)
of Kalkers WM detection, meaning that the difference between p(c
(s
opt
)
)and
p(c
(FR)
) represents the rate of BER improvement with the statistically adap-
tive technique.
7.4.3 BER Estimation
To estimate the BERs of the regions, we use inferential statistics because the
correlation values of the regions follow a normal distribution dependant on
the WM signal and the image noise. The basic method of the BER estima-
tion described in Sect. 7.4.2 was previously presented [5]. This method can
be used to estimate the BER from a watermarked still picture after video
processing by using inferential statistics. We expanded this method to han-
dle BER estimation for the regions and implemented it in our statistically
adaptive detection technique.
fr fr
N
σ
(,)
2(,)
:
Distribution of
correlation value of
watermarked region
,
c
b
=
)
Probability of detecting
erroneously
b
=
0
T
0
Fig. 7.12.
Calculation of BER.
