Information Technology Reference
In-Depth Information
[
]
N
(
)
P
ρ
−
ρ
>
0
=
Φ
α
.
(16)
0
,
W
(
0
)
0
,
other
M
2
2
2
σ
+
σ
)
I
N
In extraction,
W
(0) will be judged correctly if
0
,W
(0)
is greater than all
0,other
. Because
the probability given by Equation (16) is very close to 1 and the effect of embedding
W
(
R
) on
ρ
0
,W
(0)
can be neglected, the probability of
0,
W
(0)
being greater than all
0,other
approximately equals
N
.
P
=
1
−
M
1
−
Φ
α
(17)
0
M
2
2
2
(
σ
+
σ
)
I
N
Here the situation
W
(0)=
W
(
R
) has been ignored as the probability of its happening
is rather small. If the decision made for
W
(0) is in error, the average number of bits in
error is
m
/2 as
W
(0) contains
m
mark bits. Therefore, the bit error rate in extraction of
W(
0) is
M
N
BER
=
1
−
Φ
α
.
(18)
M
M
2
2
2
2
σ
+
σ
)
I
N
This is a general expression for the BER in extraction of any
W
(
i
) and
W
(
i
+
R
).
Similar to the method based on addition of ordinary PN sequences, the energy in
the embedded watermark is
1
2
2
.
E
=
2
R
N
α
=
L
N
α
(19)
M,
mark
M
M
M
m
5
Experimental Results and Performance Studies
As a multi-bit embedding scheme, the technique introduced in this paper can be used
in conjunction with various public watermarking frameworks, irrespective of the
types of digital media such as image, audio, and video. Also, it is not restricted to any
specific operating domain (whether time/space or transform domain), transform used
and embedding locations chosen. In our performance study, nonetheless, experiments
were carried out on still images using a DCT technique to embed watermark into a
middle band in the transform domain.
5.1
Description of the Experiment
A 256
8.
Two-dimensional DCT was then performed on the blocks resulting in a total of 64
data groups, each sized 32
×
256 test image Lena was segmented into 32
×
32=1024 blocks, each sized 8
×
32 and composed of coefficients taken from one of 64
positions in all 1024 blocks. The coefficients in these groups were shuffled pseudo-
×
