Cryptography Reference
In-Depth Information
g(c; β, µ, σ
2
)=βφ(c; µ, σ
2
)+(1−β)φ(c;−µ, σ
2
).
(7.35)
Step 4: Update β
(f,r)
[t], µ
(f,r)
[t], and σ
2(f,r)
[t] by the following formulas:
1
K
w
(f,r)
k
β
(f,r)
[t +1]=
[t],
(7.36)
k
1
Kβ
(f,r)
[t +1]
w
(f,r)
k
[t]c
(f,r)
k
µ
(f,r)
[t +1]=
,
(7.37)
k
k
w
(f,r
k
[t]c
(f,r)2
σ
2(f,r)
[t +1]=
k
Kβ
(f,r)
[t +1]
−µ
(f,r)
[t]
2
.
(7.38)
Step 5: Stop the process and set
µ
(f,r)
= µ
(f,r)
[t +1],
(7.39)
σ
2(f,r)
= σ
2(f,r)
[t +1],
(7.40)
if the parameters satisfy the following conditions:
β
(f,r)
[t +1]−β
(f,r)
[t]<δ,
(7.41)
µ
(f,r)
[t +1]−µ
(f,r)
[t]<δ,
(7.42)
σ
2(f,r)
[t +1]−σ
2(f,r)
[t]<δ.
(7.43)
The BER of the region, y
′
(f,r)
, p
(f,r)
, is calculated from µ
(f,r)
and σ
2(f,r)
by using formula (7.29).
7.4.4 Experimental Evaluation
We experimentally compared the ability of the statistically adaptive detection
technique to detect watermarks after MPEG-2 encoding for three different
bit rates (3, 4, and 5 Mbps) with that of Kalkers method by using the Walk
standard motion picture (450 frames of 720480 pixels) used in the evaluation
of the motion-adaptive embedding technique (Sect. 7.3.4).
Procedure
A WM pattern representing 256-bit information (K = 256) was generated
using a pseudo-random generator [26] and embedded in each of four 360240-
pixel regions (R = 4) of every frame by using the multiple-bit-WM scheme
described in Sect. 7.4.1.
After MPEG-2 encoding and decoding for three different bit rates (3, 4,
5 Mbps), the 256-bit information was sequentially detected in 30-frame seg-
ments of the 450 frames of the watermarked pictures (F = 30; the number
