Cryptography Reference
In-Depth Information
and that of the image as µ, then the relationship between α
n
and µ
n
can be
taken to be truncated Gaussian. The variation of β
n
with respect to µ
n
is the
reverse of that of α
n
.Soα
n
and β
n
can be computed as:
−(µ
)
2
′
n
exp
′
n
′
α
n
= σ
−µ
,
(11.15)
)
2
1−exp
−(µ
′
n
−µ
′
β
n
=
,
(11.16)
σ
′
n
where µ
′
n
, µ
′
are the normalized values of µ
n
and µ, respectively, and σ
′
n
is
normalized logarithm of σ
n
. This is the variance of the AC DCT coe
cients.
Lastly, α
n
and β
n
are scaled to the ranges (α
min
,α
max
) and (β
min
,β
max
)
respectively. Here α
min
and α
max
are the minimum and maximum values of the
scaling factor, and β
min
and β
max
are the minimum and maximum values of
the embedding factor. In this chapter, four mid-frequency AC DCT coe
cients
are chosen to embed the invisible watermark. Thus in Equation (11.14), the
resultant α
n
and β
n
affect the DCT coe
cients except for the four chosen
coe
cients.
When embedding the visible watermark, the invisible watermark should
be embedded in the blocks where α
n
have smaller values. This is in order to
improve the robustness of the invisible watermark. The embedding process is
based on quantization index modulation (QIM) techniques [15, 29, 30]. Each
selected AC DCT coe
cient is used to embed one watermark bit, so if a
512512 host image is decomposed into nonoverlapping 88 blocks. Only a
quarter of the blocks are required to embed a 6464 binary watermark. We
distinguish those blocks having a smaller α
n
and randomly select a quarter of
all of the blocks from them.
To determine the selected coe
cient c
ij
(n), first compute the integer quo-
tient q
ij
(n) and the remainder r
ij
(n) as follows:
q
ij
(n)=Int[c
ij
(n)/L] ,
(11.17)
r
ij
(n)=c
ij
(n)−q
ij
(n)L, (11.18)
where L is the quantization step, which in this chapter is equal to 24. Then
modify the coe
cient c
ij
(n) according to the value of invisible watermark bit
W by using the following equations.
If c
ij
≥0, then
⎧
⎨
L
⎩
q
ij
(n)L +
2
,
if (q
ij
(n)%2) = W ;
′
3L
2
L
c
ij
(n)=
q
ij
(n)L +
, if (q
ij
(n)%2) = W ANDr
ij
(n)>
2
;
(11.19)
q
ij
(n)L−
2
,
L
2
;
if (q
ij
(n)%2) = W ANDr
ij
(n)<
else if c
ij
< 0, then
⎧
⎨
q
ij
(n)L−
2
,
if (q
ij
(n)%2) = W ;
′
ij
(n)=
q
ij
(n)L−
3
2
L
c
, if (q
ij
(n)%2) = W ANDr
ij
(n)>
2
;
(11.20)
⎩
L
L
q
ij
(n)L +
2
,
if (q
ij
(n)%2) = W ANDr
ij
(n)<
2
;
