Information Technology Reference
In-Depth Information
We use the embedding function Emb to modify the values of selected pixels
so that the stego-image
S
= {
s
1
, s
2
,
…
,
s
n
} conveys the desired message using
the extraction function Ext:
S
= Emb(
C
,
M
,
K
),
M
= Ext(Emb(
C
,
M
,
K
),
K
),
where
K
is the stego key shared between the sender and the recipient.
Note that the embedded message can always be extracted from the stego-
image
S
without error; that is, the message
M
′ can be extracted by a recipient
so that
P(
M
′
≠
M
) = 0.
The stego-image must always be close to the cover image; that is, the
expected distortion
w
∑
=
( )
=
(
(
)
)
×
=
( )
DEdC S
[
,
]
d C
,
Emb
C
,
MK
,
Pr
Mm
i
,
exp
i
=
1
should be as small as possible and
n
1
∑
,
( )
=
−
( )
dC S
Dc
s
i
i
n
i
=
1
is the distortion between
C
and
S
. Here, the distortion measure considered is
the squared error:
D
(
c
i
-
s
i
) = (
c
i
- s
i
)
2
. The value log
2
|
M
| is called the embed-
ding capacity (in bits) and
=
1
R
log
M
2
n
is called the embedding rate (so-called relative payload, in bpp).
We further defined
E
=
R/D
exp
as embedding efficiency. Fridrich and
Soukal [12] gave the following upper bound on embedding efficiency
E
for
the embedding rate
R
for the LSB embedding scheme:
R
HR
E
≤
,
0
≤≤
R
1
,
( )
−1
where
H
(
x
) = -
x
log
2
x
- (1 -
x
) log
2
(1 -
x
) is the binary entropy function, and
H
-1
(
x
) is the inverse function of
H
(
x
).
