Cryptography Reference
In-Depth Information
From the reported information in [10], the proposed scheme shows an
advantage in capacity while retaining good quality of watermarked image.
The Reversible Method Based on the Difference Expansion
Method
Tian [11] presented a high-capacity approach based on expanding the pixel
difference value between neighboring pixels. His method allows one bit to be
embedded in every pair of pixels.
The main idea of his technique is given below. For a pair of 8 bits grayscale-
valued x and y, they first compute the integer average l and difference h of x
and y, where
x + y
2
l =
h= x−y.
(13.12)
The inverse transform of Eq. (13.12) is
h +1
2
h
2
x = l +
y:= l−
.
(13.13)
The reversible integer transforms in Eqs. (13.12) and (13.13) is called In-
teger Haar Wavelet Transform, or the S transform. They shift h to the left
one unit and append the watermarking bit b in LSB (Least Significant Bit)
according to Eq. (13.14),
′
=2h + b. (13.14)
This reversible data-embedding operation given in Eq. (13.14) is called the
Difference Expansion (DE).
To prevent overflow and underflow problems, that is to restrict x and y
in the range of [0, 255], h must satisfy the condition in Eq. (13.15). Here the
inverse transform is computed as,
h
h≤min (2(255−l), 2l−1) .
(13.15)
The authors classify Difference Values into four disjoint sets according to
the following definitions.
(1) The first set,
EZ
, contains all the expandable h = 0 and the expandable
h =−1.
(2) The second set,
EN
, contains all the expandable h/∈EZ.
(3) The third set,
CN
, contains all the changeable h which are not in EZ∪EN.
(4) The fourth set,
NC
, contains the rest of h, which are not able to be
changed.
Definition 1
A difference value
h
is expandable under the integer average
value
l
if
2h + b≤min (2(255−l), 2l−1)
for both
b =0
and
1
.
