Cryptography Reference
In-Depth Information
BER of Region
We estimate the BER for each watermarked region from the K correlation
values c
(f,r
k
in formula (7.22) of the statistically adaptive detection technique.
As mentioned in Sect. 7.4.1, in Kalkers WM detection, each correlation value,
c
(f,r)
k
, follows a normal distribution with meanµ
(f,r)
and variance σ
2(f,r)
if
the number of m
(k)
i
y
(f,r,k)
i
N
(RK)
s,
is large enough:
N (µ
(f,r)
,σ
2(f,r)
)ifb
k
=1;
N (−µ
(f,r)
,σ
2(f,r)
)ifb
k
=0.
c
(f,r)
k
∼
(7.26)
The calculation of the BER when b
k
= 1 is embedded is illustrated in
Fig. 7.12, where the gray area indicating the probability of erroneously de-
tecting b
k
= 0 is given by
−T
−∞
φ(c; µ
(f,r)
,σ
2(f,r)
) dc,
p(c
(f,r)
)
BEb
k
=1
=
(7.27)
where φ(c; µ
(f,r)
,σ
2(f,r)
) is the probability density function of N (µ
(f,r)
,σ
2(f,r)
).
The probability of detecting b
k
= 1 erroneously (when the embedded bit is 0)
is correspondingly given by
T
∞
φ(c;−µ
(f,r)
,σ
2(f,r)
) dc.
p(c
(f,r)
)
BEb
k
=0
=
(7.28)
From formulas (7.27) and (7.28), p(c
(f,r)
)
BEb
k
=1
= p(c
(f,r)
)
BEb
k
=0
.Thus,
′
(f,r)
the BER of the region y
for an arbitrary embedded bit is
−T
−∞
φ(c; µ
(f,r)
,σ
2(f,r)
) dc.
p(c
(f,r)
)=
(7.29)
As shown in formula (7.29), the mean µ
(f,r)
and variance σ
2(f,r)
of the
normal distribution can be used to obtain the BER. There are, however, two
problems.
• The information we get from watermarked region y
′
(f,r)
is not µ
(f,r)
and
σ
2(f,r)
;itistheK correlation values c
(f,r)
k
.
• As shown in Fig. 7.13, the correlation values are subject to change by
video processing, and the two normal distributions the values follow can
approach each other.
The µ
(f,r)
and σ
2(f,r)
should thus be estimated from correlation values
that follow a mixture normal distribution.
