Information Technology Reference
In-Depth Information
10.4.4 example of embedding and extraction
Suppose that the
ND
-ary message symbol
m
is embedded into the first pixel
group, where
g
(1, 1) = 121,
g
(1, 2) = 122,
g
(1, 3) = 120,
ND
= 14, and
m
= 11. The
sender uses the symbol assignment function
Q
to generate a 3-ary vector
x
=
{
t
(1, 1),
t
(1, 2),
t
(1, 3)} = {1, 2, 0}. As Table 10.4 shows, vector
x
is assigned to disk
unit 7 by using the DM allocation function; that is, DM(
x
) = 7. Since DM(
x
) ≠
11, the stego-vector
y
= {1, 2, 1} is found so that DM(
y
) = 11 and the Hamming
distance between
x
and
y
is the smallest:
H
(
x
,
y
) = 1. The symbol
t
(1, 3) gives the
change, and
g
(1, 3) = 120 is changed into
g
′(1, 3) = 121 since
Q
(121) = 1 =
t
′(1, 3)
and |121 - 120| is minimal.
Given the first stego pixel group where the pixel values are
g
′(1, 1) = 121,
g
′(1, 2) = 122, and
g
′(1, 3) = 121, the recipient generates a 3-ary vector
y
= {1, 2,
1} and simply calculates the DM allocation function to extract the message
symbol DM(
y
) = 11. In this case, we embed a 14-ary message symbol in three
pixels with a distortion
D
= 1. Since the impact of embedding is limited to
±1 embedding changes, it becomes undetectable. Moreover, the recipient can
read the correct messages but does not need to know the selection channel
because the placement of the embedding changes is not communicated
directly. As a result, the embedding ability is more efficient than with either
LSB embedding or ternary embedding.
10.5 Performance Analysis
One of the goals of this paper is to maximize embedding capacity while
keeping distortion as small as possible. In this section, we show how the
parameters of the DM allocation method influence the proposed scheme.
This section also discusses the more complicated issue of the role of group
sizes and disk units as well as the choice of DM allocation function. Finally,
we briefly discuss the embedding efficiency of the proposed scheme in com-
parison with LSB embedding and ternary embedding.
In the proposed method, an
ND
-ary message symbol is embedded into a
pixel group that contains
N
pixels. Thus, the embedding rate is
=
1
R
log
ND
.
2
We have performed a number of experiments to see how the embedding
rate and distortion change for different group size
N
's and disks size
ND
's. A
surprising result was that we get the upper bound on embedding efficiency
whenever each
3
q
-ary message symbol is embedded into each pixel group of
size (
3
q
- 1)/2, where
q
is an integer. Table 10.5 gives an example of how disk
