Cryptography Reference
In-Depth Information
Definition 2
A Difference Value
h
is changeable under the integer average
value
l
if
h
2
2
+ b
≤min (2(255−l), 2l−1)
for both
b =0
and
1
.
From Definitions 1 and 2, it can be proved that:
1) A changeable difference value h remains changeable even after modifying
its LSB.
2) An expandable difference value h is changeable.
3) After the DE, the expanded difference value h
′
is changeable.
4) If h =0or−1, the conditions for expandable and changeable are equiva-
lent.
At the receiving end, to extract embedding data and restore the original
image, the expandable, changeable, and non-changeable sets must be iden-
tified. Since an expanded difference value via the DE h
′
and a changeable
difference value with its modified LSB are both changeable after embedding ,
which is mentioned above. All difference values in NC (not changeable) can be
unambiguously identified during extraction using the condition in Eq. (13.15).
It is necessary to know which difference value has been selected for the DE.
That is, some additional information needs to be used to further identify all
the expanded difference values via the DE from all the changeable values.
The authors create a binary location map, which contains the location infor-
mation of all selected expandable difference values, as an overhead for later
reconstruction of the original image.
To achieve the payload capacity limit, they select all expandable differ-
ences that are in the range of [−255, 255] for the DE, but the peak signal to
noise ratio (PSNR) value is generally very low and the visual quality degra-
dation of the watermarked image is almost perceptible. To build a balance
between the PSNR value and payload size, they present two selection meth-
ods to reduce payload size which is less than the payload capacity limit, and
consequently improve the PSNR value. The first method is described as fol-
lows. They select h with small magnitudes for the DE. That is, they choose
a threshold value T , h∈[−T,T], partition
EN
into
EN
1
and
EN
2
.Using
EN
1
=h∈
EN
:h≤T,
EN
2
=h∈
EN
:h>T. For a payload whose
size is equal to the payload capacity limit
EN
1
=
EN
,and
EN
2
=∅. For an
h in
EZ
∪
EN
1
, a value of 1 is assigned in the location map; for a value of h
in
EN
2
∪
CN
∪
NC
, a value of 0 is assigned. Hence a value of 1 indicates
the selected expandable difference values.
The embedding process is generalized as follows. After creating the location
map, it is compressed without loss using a JBIG2 compression or an arithmetic
compression coding to form a bitstream L. For every h in
EN
2
∪
CN
,LSB
(h) is stored in a bitstream C. The payload P , including an authentication
hash of the original image (for example, MD5), bitstream L and bitstream C
are concatenated to form final binary bitstream B. They then embed B into
LSBs of one bit left-shifted versions of difference values in
EZ
∪
EN
1
and also
into LSBs of difference values in
EN
2
∪
CN
. In the embedding process, the
difference values in
NC
is kept intact.
