International Journal of Automation and Computing
04(4), October 2007, 428-432
DOI: 10.1007/s11633-007-0428-2
A Feature-based Robust Digital Image Watermarking
Against Desynchronization Attacks
Xiang-Yang Wang1,2,∗
1
2
Jun Wu1
School of Computer and Information Technique, Liaoning Normal University, Dalian 116029, PRC
State Key Laboratory of Vision and Auditory Information Processing, Peking University, Beijing 100871, PRC
Abstract:
In this paper, a new content-based image watermarking scheme is proposed. The Harris-Laplace detector is adopted to
extract feature points, which can survive a variety of attacks. The local characteristic regions (LCRs) are adaptively constructed based
on scale-space theory. Then, the LCRs are mapped to geometrically invariant space by using image normalization technique. Finally,
several copies of the digital watermark are embedded into the nonoverlapped LCRs by quantizing the magnitude vectors of discrete
Fourier transform (DFT) coefficients. By binding a watermark with LCR, resilience against desynchronization attacks can be readily
obtained. Simulation results show that the proposed scheme is invisible and robust against various attacks which includes common
signals processing and desynchronization attacks.
Keywords:
1
Image watermarking, desynchronization attacks, feature points, discrete Fourier transform.
Introduction
Digital watermarking, as a kind of efficient supplemental method of a traditional cryptographic system, has been
widely used for intellectual property protection of multimedia in the Internet. However, the attacks against the watermarking system have become more sophisticated with the
development of image watermarking in recent years. Desynchronization attacks, which induce synchronization errors
between the original and the extracted watermark during
the detection process, are very difficult to tackle. Most of
the previous schemes show severe problems to desynchronization attacks[1,2] .
Fortunately, several approaches to count the desynchronization attacks have been developed. These schemes
can be roughly classified into three categories: invariant transform[3,4] , template insertion[5] , and content-based
synchronization[6−8] . The approach in this paper belongs
to the third category. However, the recent schemes against
desynchronization attacks remain immature. The first and
second categories can only be robust against global affine
transformation, such as rotation, scaling and translation
(RST), but vulnerable to shearing and random bending attack (RBA). The last category is robust to shearing and
RBA, but hardly survive scaling.
In this paper, a robust content-based watermarking scheme is developed. The Harris-Laplace detector is
adopted to extract scale-space feature points and the characteristic scale is used to adaptively determine the size of
local characteristic region (LCR), which is helpful to reManuscript received May 29, 2006; revised December 17, 2006.
This work was supported by Natural Science Foundation of Liaoning
Province of China (No. 20032100), Open Foundation of State Key
Laboratory of Vision and Auditory Information Processing (Peking
University) (No. 0503), Natural Science Foundation of Dalian City of
China (No. 2006J23JH020), Open Foundation of Jiangsu Province
Key Laboratory for Computer Information Processing Technology
(Soochow University)(No. KJS0602), Open Foundation of Key Laboratory of Image Processing and Image Communication (Nanjing University of Posts and Communications) (No. ZK205014).
*Corresponding author. E-mail address: [email protected]
duce the watermark synchronization problem between the
watermark embedding and detection. In experiments, we
will compare the performance of the proposed scheme with
that of another content-based scheme by applying the various attacks. The results show the appropriateness of the
proposed method for robust watermarking.
2
LCR construction based on scalespace feature points
In content-based synchronization approaches, feature
points, as marks for location resynchronization between
the watermark embedding and detection, must be robust
against various types of common signal processing and geometric distortions. The Harris-Laplace detector was proposed by Mikolajczyk[9] and proved to be invariant to image
rotation, scaling, translation, partical illumination changes,
projective transform, etc. Therefore, we adopt and modify
this method for the watermarking purpose. The details of
the Harris-Laplace detector and the construction of LCR
are described in the next subsections.
2.1
Scale adapted Harris detector
The Harris detector is based on a specific image descriptor called second moment matrix, which reflects the local
distribution of gradient directions in the image. This matrix
must be adapted to scale changes to make it independent
of the image resolution. The scale-adapted second moment
matrix is defined by
µ(x, y, δI , δD") =
2
δD
· G(δI ) ∗
L2x (x, y, δD )
Lx Ly (x, y, δD )
#
Lx Ly (x, y, δD )
L2y (x, y, δD )
(1)
where δI and δD are the integration scale and differentiation
scale, respectively, and La is the derivative computed in the
a direction, and “∗” denotes the linear convolution. The
scale-space representation is a set of images represented at
X. Y. Wang and J. Wu/ A Feature-based Robust Digital Image Watermarking Against Desynchronization Attacks
different levels of resolutions. Given δD , the uniform Gaussian scale space representation L is defined by
L(x, y, δD ) = G(x, y, δD ) ∗ f
(2)
where G is the associated uniform Gaussian kernel with
standard deviation δD and mean zero, f is an image, and
“∗” denotes the linear convolution.
Given δI and δD , the multi-scale Harris corner strength
(MSCS) can be computed by using the determinant and the
trace of the second moment matrix, i.e.,
R(x, y, δI , δD ) =
det (M (x, y, δI , δD )) − k · tr2 (M (x, y, δI , δD ))
(3)
where det(·) and tr(·) denote the determinant and the trace
of matrix, respectively. At each level of the scale-space, the
feature points are extracted as the local maxima in the image plane as follows:
R(x, y, δI , δD ) > R(x̂, ŷ, δI , δD ),
R(x, y, δI , δD ) ≥ tu
∀(x̂, ŷ) ∈ A
(4)
where A and tu are the neighborhood of point (x, y) and
the threshold, respectively.
2.2
Automatic scale selection and scaleinvariant feature points
The idea of automatic scale selection is to select the characteristic scale of the local structure, for which a given
function attains an extremum over scales. The characteristic scale reflects the maximum similarity between the
feature extraction operator and the local image structures.
This scale estimate will obey perfect scale invariance under
rescaling of the image pattern. In this paper, Laplacian of
Gaussians (LOG) is used to find the characteristic scale.
The LOG is defined by
˛ 2
˛
˛ ∂ G(x, y, δI )
∂ 2 G(x, y, δI ) ˛˛
LOG(x, y, δI ) = δI2 ˛˛
+
˛ . (5)
∂x2
∂y 2
Given a point in the image and a set of scales, the characteristic scale is the scale at which the LOG attains a local
maximum over scales.
The extraction of the feature points by using HarrisLaplace detector consists of two steps:
Step 1. Build a scale-space representation with the Harris function for pre-selected scales δn = 1.4 ξ n , where ξ is
the scale factor between successive levels (set to 1.4). At
each level of the representation, the scale adapted Harris
corner strength (SHCS) is computed with the integration
scale δI = δn and the local scale δD = sδn , where s is
a constant (set to 0.7). We then extract the candidate
points which are the maxima in the 8-neighborhood and
their SHCS are higher than the threshold tu = 1 000.
Step 2. For each candidate point, we use an iterative
method to determine the final location and the characteristic scale of the feature points. The extrema over scale of the
LOG are used to select the scale of feature points. Given an
initial point p with the scale δI , the iteration steps include:
Step 2.1 Find the local extremum over the scale of the
LOG for the point pk , otherwise reject the point. The investigated range of scales is limited to
(k+1)
δI
(k)
= t · δI
429
with t ∈ [0.7, 0.8, · · · , 1.4] .
(k+1)
Step 2.2 For the selected δI
, detect the spatial point
pk+1 of the maximum MSCS nearest to pk .
(k+1)
(k)
Step 2.3 Go to Step 1 if δI
6= δI or pk+1 6= pk .
2.3
Scale adapted LCRs
LCRs are the subsets of the host image and used for watermark embedding and detection regions. Therefore, the
problem of geometric synchronization must be considered
by the LCR construction method. In this section, a new
construction method based on characteristic scale is proposed.
Generally speaking, the LCRs can be formed with any
shape such as triangle, rectangle and circle. However, it
is necessary to assure that the LCRs are invariant to rotation, so the circle can be available. Moreover, the size of
the LCR should vary with the image scale in order to resist
the scaling distortion, so the characteristic scale is helpful
to determine the size of the LCRs. The radius R of the
LCRs is defined as
R = τ · [δ]
(6)
where δ is the characteristic scale of the feature points and
τ is a positive integer which is used to adjust the size of the
LCRs. A large value of τ would increase the capacity of the
watermarking system. The robustness of the watermarking system, however, would decrease for a large τ . Hence,
there is a trade off between capacity and robustness. When
there is interference between any two LCRs because the selected LCR is perceptually highly textured, we select the
LCR with a large number of feature points since the LCRs
should not interfere with each other.
3
Watermark embedding
We view all LCRs as independent communication channels. To improve the robustness of transmitted information
(watermark), all channels carry the same copy of the chosen
watermark. The transmitted information passing through
each channel may be disturbed by different types of the intentional and unintentional attacks. During the detection
process, we claim the existence of watermark if at least two
copies of the embedded watermark are correctly detected.
Let0 s decompose the embedding scheme into the following
different steps.
First, the Harris-Laplace detector is adopted to generate
feature points (reference centers) and a set of LCRs is constructed by using these centers. Second, perform the zeropadding operation on every LCR to map the circles (LCR)
to the blocks of size 2R × 2R (R is the radius of the LCR).
Then, perform the image normalization technique[4] on all
blocks. As a result, the blocks are mapped to a geometrically invariant space. Next, a 2-dimensional discrete Fourier
transform (DFT) is applied to these normalized blocks. The
watermark is embedded in the transform domain. Finally,
convert the watermarked blocks0 2-dimensional inverse discrete Fourier transform (IDFT) back to the spatial domain
and apply the inverse of the normalization procedure to
them. The watermarked LCRs are gained by using zero-
430
International Journal of Automation and Computing 04(4), October 2007
removing operation and the original LCRs are replaced by
them.
The procedure of selecting and modifying the magnitude of the DFT coefficients for watermark embedding
is illustrated as follows. First, radius R1 = dR/8e and
R2 = R1 + L ≤ b7R/8c are selected and the annular area
between R1 and R2 covers the mid-frequency components
in the DFT domain, where L denotes the length of the watermark, d·e and b·c denote the upper integer and the lower
integer respectively. Let C(ri ) (i = 1, 2, · · · , L) be the homocentric circles around the zero frequency term, where
R1 ≤ ri ≤ R2 . Then, several middle DFT coefficients are
selected according to the secret key K and we should submit it to the watermark detector. Finally, within C(ri ),
the selected pairs ((xi , yi ), (yi , −xi )), 90◦ apart as shown in
Fig. 1, are modified by using vector quantization:
If wi = 1 then
(M ∗ (xi , yi ), M ∗ (yi , −xi )) =
–
8 „»
M (xi , yi )
>
>
· M (yi , −xi ) · Q,
>
>
M (yi , −x
>
«i ) · Q»
–
>
>
>
M (xi , yi )
>
>
M
(y
,
−x
)
,
%2 = 1
>
i
i
<
M (yi , −xi ) · Q
„»
–
>
M (xi , yi )
>
>
>
+
1
· M (yi , −xi ) · Q,
>
>
M (yi , −x
i ) · Q»
>
«
–
>
>
>
M (xi , yi )
>
: M (yi , −xi ) ,
%2 = 0
M (yi , −xi ) · Q
.
(7)
If wi = −1 then
(M ∗ (xi , yi ), M ∗ (yi , −xi )) =
–
8 „»
M (xi , yi )
>
>
· M (yi , −xi ) · Q,
>
>
M (yi , −x
>
«i ) · Q»
–
>
>
>
M (xi , yi )
>
>
M
(y
,
−x
)
,
%2 = 0
>
i
i
<
M (yi , −xi ) · Q
–
„»
>
M (xi , yi )
>
>
>
+
1
· M (yi , −xi ) · Q,
>
>
M (yi , −x
i ) · Q»
>
«
–
>
>
>
M (xi , yi )
>
: M (yi , −xi ) ,
%2 = 1
M (yi , −xi ) · Q
(8)
where (M ∗ (xi , yi ), M ∗ (yi , −xi )) are the magnitudes of the
altered coefficients at locations (xi , yi ) and (yi , −xi ) in the
DFT domain, and Q is the quantization strength. The
phase of the selected DFT coefficients is not modified. In
addition, to produce a real-valued image after DFT spectrum modification, the symmetric points have to be altered
to the exact same values as well.
4
Watermark detection
The detection process uses the result of the feature point
extraction and consequently performs a resynchronization
of the watermark. If the watermarked image undergoes geometric distortion, the feature points mainly follow the transformation and several LCRs are consequently conserved.
We now detail the different steps of the detection scheme
as follows.
The feature (reference) points are first extracted. All the
reference points are candidate centers of the LCRs. Since
image contents are altered slightly by the embedded watermarks and perhaps by the attacks as well, the LCRs may be
different from those used in the watermark embedding process. Zero-padding is applied to all the LCRs. As a result,
LCRs are mapped to blocks and image normalization is then
applied to all the blocks. In each 2R × 2R DFT block, the
watermark bits are extracted from the DFT components
specified by the secret key in the annular area [R1 , R2 ]. For
an extracted pair ((x̃i , ỹi ), (ỹi , −x̃i )), the embedded watermark bit is determined by the following formula:
8
>
>
>
< 1,
w̃i =
»
>
>
>
: −1,
Pf
disk
=
L
X
„
L
(0.5) ·
r=T
«
L!
.
r!(L − r)!
(10)
Furthermore, an image is claimed watermarked if at least
two disks are detected as “success”. Under this criterion,
the false-alarm probability of one image is
image
=
M
X
i=2
The pairs, 90◦ apart on the DFT plane
(9)
where M̃ (x̃i , ỹi ) and M̃ (ỹi , −x̃i ) are the magnitudes of the
selected coefficients at locations (x̃i , ỹi ) and (ỹi , −x̃i ). The
extracted L bits sequence is then compared with the original embedded watermark to determine the success of the
detection.
A kind of error named false-alarm probability (no watermark embedded but detected as having one) is possible in the detector. For an unwatermarked image, the extracted bits are assumed to be independent random variables (Bernoulli trials) with the same success probability
Psuccess (It is called a “success” if the extracted bit matches
the embedded watermark bit). We assume the success probability Psuccess = 0.5. Let r be the number of “success” bits
in each LCR. An LCR is claimed watermarked if the number
of its “success” bits is greater than a threshold. The threshold for an LCR is denoted as T . Therefore, the false-alarm
error probability of an LCR is the cumulative probability
of the cases that r ≥ T .
Pf
Fig. 1
–
M̃ (x̃i , ỹi )
+ 0.5 %2 = 1
M̃ (ỹi , −x̃i ) · Q
»
–
M̃ (x̃i , ỹi )
+ 0.5 %2 = 0
M̃ (ỹi , −x̃i ) · Q
!
(Pf
i
disk )
· (1 − Pf
M −i
disk )
·
M
i
(11)
where M is the total number of disks in an image (based
on our experience, M = 10). Given Pf image , T can be
computed in terms of the value of Pf image .
431
X. Y. Wang and J. Wu/ A Feature-based Robust Digital Image Watermarking Against Desynchronization Attacks
4.1
Simulation results
We test the proposed watermarking scheme on the popular test images 512 × 512 Lena, Mandrill, and Pepper. A
bipolar sequence of size 32-bits is used as the watermark. Q
is set to 0.6, τ is set to 11, and the false-alarm probability
Pf image ≈ 5 E-4 when the detection threshold T is set to
24. Besides, the peak signal-to-noise ratio (PSNR) is used
to measure the visual quality of the watermarked images.
Finally, experimental results are compared with those of the
scheme in [8].
Fig. 2 (a), (b), (c), and (d) show the host image, watermarked image, the difference image between them and the
detection result, respectively.
The number of the watermarked LCR is 6 as shown in
Fig. 2 (c). The number of the correctly detected watermarked LCRs identified by using “white point” is also 6 as
shown in Fig. 2 (d). Table 1 shows the transparency comparison results of two image watermarking schemes.
Table 1
PSNR between watermarked and original images (dB)
Image
Proposed scheme
Lena
55.66
Scheme in [8]
49.42
Mandrill
50.34
45.70
Pepper
50.03
56.60
Simulation results for the various attacks are given in
Table 2. They are compared with those of the scheme in
[8]. It is clear that the proposed scheme outperforms the
scheme in [8] under the most attacks in terms of the detection rates, which is defined as the ratio between the number
of correctly detected watermarked LCRs and the number of
original embedded watermarked LCRs.
(a)
(b)
(c)
5
(d)
Fig. 2 The host image and the watermarked image: (a) The
host image, (b) The watermarked image, (c) The difference
image between host image and watermarked image, (d) The
detection results from the watermarked image
Table 2
Conclusions
Base on the scale-space theory, a robust image watermarking scheme is designed to resist both common signal
processing and desynchronization attacks. There are several key elements in our scheme. For one thing, based on
scale-space theory, the extracted feature points are reliable
under various attacks. For another, an adaptive method
of the LCR construction based on the characteristic scale
is presented and the robustness against desynchronization
attacks, especially scaling distortion, is improved. The proposed scheme is computationally inexpensive and extracts
the watermark without the help from the original image,
which enlarges its applied scope.
Fraction of correctly detected watermark LCR under various attacks (detection rates)
Lena
Attacks
Mandrill
Pepper
Proposed
[8]
Proposed
[8]
Proposed
[8]
Median filter
3/6
1/8
7/12
2/11
4/8
1/4
Sharpening
3/6
4/8
6/12
4/11
5/8
3/4
Gaussian noise
2/6
5/8
4/12
6/11
4/8
3/4
70
4/6
7/8
9/12
10/11
7/8
3/4
50
4/6
5/8
8/12
7/11
6/8
3/4
30
2/6
2/8
8/12
4/11
4/8
0/4
JPEG compression
15
4/6
1/8
5/12
1/11
5/8
0/4
Rotation
30
3/6
1/8
4/12
2/11
4/8
0/4
50
2/6
0/8
4/12
0/11
2/8
0/4
Scaling
0.8
3/6
1/8
5/12
4/11
3/8
2/4
1.4
1/6
0/8
1/12
1/11
2/8
0/4
Translation −x − 10 and −y − 10
5/6
2/8
10/12
8/11
5/8
1/4
Removed 8 rows and 16 columns
5/6
1/8
7/12
2/22
6/8
0/4
Shearing 55%
4/6
1/8
6/12
2/11
6/8
0/4
RBA
3/6
4/8
7/12
5/11
6/8
1/4
Translation -x-10 and -y-10 + Rotation 5 + Scaling 0.9
2/6
0/8
5/12
2/11
5/8
0/4
432
International Journal of Automation and Computing 04(4), October 2007
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Xiang-Yang Wang is a professor at
Liaoning Normal University, and a senior
member of China Computer Federation.
His research interests include multimedia
information processing and network information security.
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Jun Wu received the B.Sc. degree in
computer science and information engineering from the North University for Minority,
China, in 2000. He is currently pursuing
the M.Sc. degree at the School of Computer
and Information Technique, Liaoning Normal University, Dalian, China. He has published about 10 refereed journal and confer-
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ence papers.
His research interests include digital watermarking technique
and multimedia digital signal processing.