Cryptography Reference
In-Depth Information
1
m
(k)
i
y
(f,r,k)
i
c
k
=
µ.
(7.18)
N
(RK)
FR
f,r,i
In the same way as in one-bit WM detection, each c
k
follows a
normal distribution. That is,
N (µ, σ
2
), if b
k
=1;
N (−µ, σ
2
), if b
k
=0.
c
k
∼
(7.19)
Step D5: Determine K embedded bits b
k
s by comparing c
k
with a threshold
value of T (> 0), where
⎧
⎨
1,
if c
k
≥T ;
b
k
=
0,
if c
k
≤−T ;
(7.20)
⎩
not detected,
if−T<c
k
<T.
Problem with Kalkers Method
WMs on pictures must be able to survive several kinds of video processing
procedures. Kalkers accumulation operation (7.16) is not always effective be-
cause the WM signal µ in formula (7.18) could be attenuated. This is due
to an attempted accumulation from regions from which the WMs had been
removed during video processing. If accumulation or averaging is done on two
regions with the same noise level and WM signal level, the noise level for re-
gion σ is reduced to 1/
√
2σ. WM signal µ is reduced to 1/2µ if the WMs for
one of the two regions is removed. The S/N ratio is worsened by the accumu-
lation. Kalkers accumulation operation could cause the signal of the WMs,
µ, to decrease so much that the embedded bits could not be reliably detected.
The statistically adaptive detection technique solves this problem by iden-
tifying the accumulated regions remaining in WMs and detecting the WMs
from the accumulated region.
7.4.2 Statistically-Adaptive Detection
Principle
The statistically adaptive detection technique identifies the accumulated re-
gions with a minimal degree of WM removal. It detects the WMs from the
accumulated regions. We use the Bit-Error Rate (BER) as the measure of
the degree of WM removal. The BER is estimated for each watermarked re-
gion, and the estimated BERs are used to control the accumulation operation
so that the BER of the accumulated region is minimized. This prevents a
decrease in the S/N ratio.
Fig. 7.10 shows the structure of the process of the statistically adaptive
technique, which comprises a correlation-value calculation, a BER estimation,
a sorting operation, an accumulation control, and a bit-value determination:
