Cryptography Reference
In-Depth Information
DFT Domain Schemes
Nikolaidis et al. [9, 10] proposed a blind watermarking scheme consisting of
embedding a single bit into a polyline by modifying the discrete Fourier
coe
cients of the polylines coordinate sequence. Taking a polyline with
N vertices as the cover data, a hidden bit can be embedded as follows.
Firstly, given the coordinates(x
k
,y
k
) k =1, 2,,Nof the vertices,
a complex sequence z(k) is obtained by combining x and y coordinates as
z(k)=x
k
+ jy
k
k =1, 2,,N. After DFT is performed on z(k), we get
the coe
cient sequence ofZ(k)k =1, 2,,N. Secondly, by denoting a
N -length Pseudo Noise Sequence asW
0
(k)∈−1, +1k =1, 2,,N,the
generation of the watermark W (k) is a spread spectrum procedure as shown
in Eqn. (6.2). Here
W
0
(k);aN <k<bN, or , (1−b)N<k<(1−a)N,
0
W (k)=
(6.2)
;
otherwise,
where two parameters a, b (0 <a<b<1) are used to select the spec-
trum range for data embedding. Next, the generated watermark W (k)isem-
bed by modifying the amplitude of Z(k) using either an additive operation
(Eqn. (6.3)) or a multiplicative operation (Eqn. (6.4)),
′
Z
(k)=Z(k)+ pW (k),
(6.3)
′
Z
(k)=Z(k)+ pZ(k)W (k).
(6.4)
′
To extract the hidden data, the linear correlation (denoted as c)ofZ
(k)
′
and W (k) is calculated. Then the normalized correlation c
= c/µ
c
is used
for a judgement based on a threshold, where µ
c
is the theoretical mean value
of c. The scheme is inherently robust to many types of attacks such as map
translating, rotating, scaling and the start vertex shifting in the watermarked
polyline. Change of the vertex number such as simplification or interpolation
could disturb the synchronization of the detector.
To improve the reliability of the detector, Nikolaidis et al. [11] also pro-
posed an enhanced algorithm where multiple polylines are used for water-
marking. The hidden bit is embedded in each polyline using the same method
as in their former works [9, 10]. When detecting the hidden bit, each polyline
will get a normalized correlation value c
′
i
(i =1, 2,,M), where M is the
number of polylines. A data fusion function f () is then chosen to calculate
a combined parameter c = f (c
′
1
,c
′
2
,,c
′
M
), which will be used for the final
judgement based on a threshold.
Based on the former works [9, 10], Kitamura et al. proposed a modified
scheme [12] embedding multi-watermark bits in the DFT domain. The wa-
termark is a meaningful bit sequence instead of a single bit represented by
PNS. The embedding procedure is similar to the former works whereas the
extracting procedure is different because the original map would be needed.
Consequently, it is not a blind scheme, and this limits its application.
