Information Technology Reference
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different group sizes
N
. In general, groups with a larger size have a smaller
embedding rate. We looked at the influence of group size, and our experi-
ments showed that groups of one pixel gave us the same embedding rate as
with ternary embedding. We discovered there is a close relationship between
group sizes and disk size. The influence of group sizes
N
and disk sizes
ND
is clear with the DM allocation function. The embedding rate rapidly
decreases with group size, as can be seen in Figure 10.4. The next step is to
outline a methodology for building a theoretical upper bound on the embed-
ding efficiency for the proposed method.
We now state a theoretically achievable bound on embedding efficiency.
Since there are
3
q
ways for making one or fewer changes in
N
pixels; that is
D
max
≤ 1, the proposed scheme has the capacity in bits
Cap
= log
2
|ND| ≤ log
2
3
q
, for
q
∈ Z.
It can be rewritten as a theoretically asymptotic upper bound on embed-
ding efficiency for a given embedding rate
R
=
Cap
/N
:
≤
log
2
3
q
E
.
ND
exp
To determine the maximum average distortion, we consider the expected
distortion of the upper bound. Here, we embed a
3
q
-ary message symbol in
each pixel group of size (
3
q
- 1)/2 by performing, at most, one embedding
change; that is,
D
max
= 1. Thus, we have the expected distortion
2
2
3
D
=
=
,
exp
31
2
−
q
+
q
( )
2
1
and an embedding rate of
log
3
31
2
q
2
log
3
31
q
2
2
R
=
=
.
−
q
q
−
Using the resulting rate-distortion pair (
R
,
D
exp
) = (2 1og
2
3
q
/(3
q
- 1), 2/3
q
),
we obtain an upper bound on the embedding efficiency
R
D
3
q
3
31
log
q
2
E
=
=
,
for
q
∈
Z
,
q
−
exp
which is defined as the average number of embedded bits that can be embed-
ded per change.
