A DWT-DFT composite watermarking scheme robust to both affine transform and JPEG compression

Abstract

Robustness is a crucially important issue in watermarking. Robustness against geometric distortion and JPEG compression at the same time with blind extraction remains especially challenging. A blind discrete wavelet transform-discrete Fourier transform (DWT-DFT) composite image watermarking algorithm that is robust against both affine transformation and JPEG compression is proposed. The algorithm improves robustness by using a new embedding strategy, watermark structure, 2D interleaving, and synchronization technique. A spread-spectrum-based informative watermark with a training sequence is embedded in the coefficients of the LL subband in the DWT domain while a template is embedded in the middle frequency components in the DFT domain. In watermark extraction, we first detect the template in a possibly corrupted watermarked image to obtain the parameters of an affine transform and convert the image back to its original shape. Then, we perform translation registration using the training sequence embedded in the DWT domain, and, finally, extract the informative watermark. Experimental work demonstrates that the proposed algorithm generates a more robust watermark than other reported watermarking algorithms. Specifically it is robust simultaneously against almost all affine transform related testing functions in StirMark 3.1 and JPEG compression with quality factor as low as 10. While the approach is presented for gray-level images, it can also be applied to color images and video sequences.

Full text

Page 1

776IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003
A DWT-DFT Composite Watermarking
Scheme Robust to Both Affine Transform
and JPEG Compression
Xiangui Kang, Jiwu Huang, Senior Member, IEEE, Yun Q. Shi, Senior Member, IEEE, and Yan Lin
Abstract—Robustness is one of the crucial important issues
in watermarking. Robustness against geometric distortion and
JPEG compression at the same time with blind extraction remains
especially challenging. In this paper, a blind discrete wavelet
transform-discrete Fourier transform (DWT-DFT) composite
image watermarking algorithm that is robust against both affine
transformation and JPEG compression is proposed. This algo-
rithm improves the robustness via using new embedding strategy,
watermark structure, 2-D interleaving, and synchronization
technique. A spread-spectrum-based informative watermark
with a training sequence are embedded in the coefficients of the
LL subband in the DWT domain while a template is embedded
in the middle frequency components in the DFT domain. In
watermark extraction, we first detect the template in a possibly
corrupted watermarked image to obtain the parameters of affine
transform and convert the image back to its original shape. Then
we perform translation registration by using the training sequence
embedded in the DWT domain and finally extract the informative
watermark. Experimental works have demonstrated that the
watermark generated by the proposed algorithm is more robust
than other watermarking algorithms reported in the literature.
Specifically it is robust against almost all affine transform related
testing functions in StirMark 3.1 and JPEG compression with
quality factor as low as 10 simultaneously. While the approach
is presented for gray-level images, it can also be applied to color
images and video sequences.
Index Terms—Affine transformation, geometric attacks, image
watermarking, robustness, template matching.
I. INTRODUCTION
D
tion and tamper proofing [1]. Robustness of watermarking is
one of the key issues for some applications. A serious problem
constrainingsomepracticalexploitationsofwatermarkingtech-
nology is the insufficient robustness of existing watermarking
algorithms against geometrical distortions such as translation,
IGITAL watermarking has emerged as a potentially effec-
tive tool for multimedia copyright protection, authentica-
Manuscript received December 16, 2002; revised March 20, 2003. This
work was supported by the National Science Foundation (NSF) of China
(69975011, 60172067, 60133020), the “863” Program (2002AA144060), the
NSFGD (013164), Funding of China National Education Ministry, the New
Jersey Commission of Science and Technology via NJWINS, the New Jersey
Commission of High Education via NJ-ITOWER, and the NSF via IUCRC.
X. Kang, J. Huang, and Y. Lin are with the Department of Electronics and
Communication Engineering, Sun Yat-Sen University, Guangzhou 510275,
China (e-mail: isskxg@zsu.edu.cn; isshjw@zsu.edu.cn; ly.king@263.net).
Y. Q. Shi is with the Department of Electrical and Computer Engineering,
New Jersey Institute of Technology, Newark, NJ 07102 USA (e-mail:
shi@njit.edu).
Digital Object Identifier 10.1109/TCSVT.2003.815957
rotation, scaling, cropping, change of aspect ratio and shearing.
These geometrical distortions cause the loss of geometric syn-
chronization that is necessary in watermark detection and de-
coding [2]. Vulnerable to geometric distortion is a major weak-
ness of many watermarking methods [3].
Although some significant progresses have been made re-
cently,thesenewschemesarenormallynotrobusttoJPEGcom-
pression at the same time as shown below. There are two dif-
ferent types of solutions to resisting geometrical attacks: non-
blind and blind methods [4]. With the nonblind approach, due
toavailabilityoftheoriginalimage,theproblemcanberesolved
with a good solution by effective search between the geometri-
cally attacked and unattacked image [5], [6].The blindsolution,
which does not use the original image in watermark extraction,
has wider application but is obviously more challenging. Three
major approaches to the blind solution have been reported in
the literature. The first approach hides a watermark signal in
the invariants of a host signal (invariant with respect to scaling,
rotation, shifting and etc.), and is somewhat awkward due to
the theoretical and practical difficulties in constructing invari-
ants with respect to combinations of the above-mentioned op-
erations. Specifically, Ruanaidh et al. [7] first proposed a wa-
termarking scheme based on transform invariants via applying
Fourier-Mellin transform to the magnitude spectrum of an orig-
inal image. However, the resulting stego-image quality is poor
due to interpolation errors [2]. In [3], instead of a “strong in-
variant” domain, the watermark is embedded into the magni-
tudes of the DFT coefficients resampled by the LPM. The de-
tection process involves a comparison of the watermark with all
cyclic shifts of the extracted watermark to cope with rotation.
To deal with scaling, the correlation coefficient is selected as
the detection metric. Only one bit information is hidden in the
image, and the watermark cannot resist the general transforma-
tions.
The second approach exploits the self-reference principle
based on an auto-correlation function (ACF) or the Fourier
magnitude spectrum of a periodical watermark [8], [9]. In [8],
the watermark is replicated in the image in order to create four
repetitions of the same watermark such that the experienced
geometrical transformation can be detected by applying au-
tocorrelation to the investigated image. Experimental results
showed that the algorithm could resist generalized geometrical
transformations. However, the watermarking is vulnerable to
the lossy coding scheme such as JPEG compression. In [9], the
usage of a periodical block allocation of a watermark pattern
for recovering from geometrical distortions is proposed. It is
1051-8215/03$17.00 © 2003 IEEE

Page 2

KANG et al.: A DWT-DFT COMPOSITE WATERMARKING SCHEME ROBUST TO BOTH AFFINE TRANSFORM AND JPEG COMPRESSION 777
noticed that, however, the watermark estimation is key-inde-
pendent, the periodical watermark results in an underlying
regular grid. Hence, the watermark may be detected and may
be destroyed [10], [11]. It has been proposed recently that
the resulting watermark can be slightly pre-distorted in such
a way that this problem may be resolved [12]. In [12], it is
reported that the watermark is robust against local or nonlinear
geometrical distortions, such as random bending attack.
Thethirdapproachutilizesanadditionaltemplate(e.g.asinu-
soid or a cross [13], [14]). In [15], Pereira and Pun proposed an
affine resistant image watermark in DFT domain. The informa-
tive watermark (the message to be conveyed to the detector/re-
ceiver) together with a template is embedded in the middle fre-
quency components in DFT domain. The template consists of
intentionally embedded peaks in the Fourier spectrum. That is,
the watermark embedder casts extra peaks in some locations of
the Fourier spectrum. The locations of the peaks are predefined
orselectedbyasecretkey.Thestrengthisadaptivelydetermined
by using local statistics of the Fourier spectrum. In watermark
detection, all local maxima are extracted by using small win-
dows. While resistant to affine transform, the watermark gener-
ated with the scheme is not robust enough. In particular, it is not
robust to JPEG compression with the quality factor below 75.
In this paper, a new blind image watermarking algorithm ro-
bust against both affine transformations and JPEG compression
is proposed. The proposed DWT-DFT composite watermarking
scheme embeds a message and a training sequence in
subband in the DWT domain, and embeds a template in magni-
tude spectrum in DFT domain. The watermarking incorporates
DWT/DFT, concatenated coding of direct sequence spread
spectrum (DSSS) and BCH, 2-D interleaving, resynchroniza-
tion based on the template and training sequence. Experimental
results have demonstrated that the watermark is robust against
both affine transformations and JPEG compression when the
quality factor is as low as 10.
The rest of this paper is organized as follows. In Section II,
we introduce the watermark embedding. Section III describes
the watermark extraction based on resynchronization. The ex-
perimental results are presented in Section IV. A conclusion is
drawn in the last section.
II. WATERMARK EMBEDDING
This algorithm achieves enhanced robustness via improving
embedding strategy and watermark structure, and using a
new effective synchronization technique. DWT is playing an
increasingly important role in watermarking, due to its good
spatial-frequency characteristics and its wide applications in
the image/video coding standards. According to Cox et al.
[16] and Huang et al. [17], watermark should be embedded
in the DC and low frequency AC coefficients in DCT domain
due to their large perceptual capacity. The strategy can be
extended to DWT domain. We embed informative watermark
into
subband in the DWT domain to make it more robust
while keeping the watermark invisible. When the marked
image undergoes affine transformation
the matrix can be determined by using a template as ref-
erence. The template is embedded into the middle frequency
,
Fig. 1.Watermark embedding process.
components in the magnitude spectrum to avoid interfering
with the informative watermark. To determine the translation
parameter, we embed a training sequence in the DWT domain.
To survive all kinds of attacks, we use the concatenated
coding of BCH and DSSS method to encode the message
(in our work).
To cope with bursts of errors which possibly occurred with
watermark, a newly developed 2-D interleaving [18], [19]
is exploited. The watermark embedding process is shown in
Fig. 1.
A. Message Encoding and Training Sequence Embedding in
the DWT Domain
The watermark embedding in the DWT domain is imple-
mented through the following procedures.
1) By using the Daubechies 9/7 bi-orthogonal wavelet fil-
ters,weapplyafour-levelDWTtoaninputimage
( ,in ourwork), generating12subbands
of high frequency (
,
low-frequency subband
2) The message
is first encoded using BCH (72, 60) to
obtain the message
of length
bit
ofis DSSS encoded using an
-sequence
coded spreadly as
,,) and one
.
. Then each
-bit bipolar
, where “1” is
, “0” as
, thus obtaining a binary string
3) The training sequence,
, which is a key-based sequence, should
be distributed all over the image in order to survive all
kinds of attacks, especially cropping. To this purpose, in
our work, the training sequence
in row 16 and column 16 of the
noted that a different combination of row and column
corresponding to the important image portion can also be
chosen. The informative watermark
and embedded in the leftover portion of the
(Fig. 2).
In implementation, we allocate the 63 bits of the
training sequence
into row 16 and column 16 of a 32
32 2-D array, we then de-interleave [18] it, resulting in
a new 32
32 array. The binary string
into the remaining portion of the above-mentioned array.
(63 bits) is embedded
subband. It is
is 2-D interleaved
subband
is embedded

Page 3

778IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003
Fig. 2. Training data set.
By applying 2-D interleaving technique [19] to this array,
we obtain another 2-D array. Scanning this 2-D array,
say, row by row, we convert it into a 1-D array
Coefficients of the
subband are scanned in the
same way as in the embedding, resulting in a 1-D array,
denoted by
. Similar to our nonblind watermarking
technique [6], we embed the binary data
obtain
according to (1), where
related to the watermark embedding strength,
anddenote the amplitude of the
and, respectively. Note that the difference be-
tween
and is between
If
,
. So in the extraction, if the ex-
tracted coefficient
has
the recovered binary bit
In order to extract an embedded bit correctly, the absolute
error (introducedbyimagedistortion)between
, as in (1), shown at the bottom of the page, must
be less than
. The parameter
as to make a good compromise between the contending
requirements of imperceptibility and robustness. We
choose
to be 90 in our work.
This training sequence helps to achieve synchroniza-
tionagainsttranslationpossiblyappliedtostego-image.If
the correlation coefficient between the training sequence
and the test sequenceobtained from a test image sat-
isfies the following condition
, we regard
sider synchronization is achieved. Here, we can calcu-
late the corresponding probability of false positive (false
synchronization) as
where
means taking the nearest integer. In our work, we choose
(empirically value), thus have
.
intoto
is a parameter
element in
and.
, . If
, then
. Otherwise,.
and
can be chosen so
as matched toand con-
,
, and
Fig. 3.Template embedding.
, which may be sufficient low for many ap-
plications.
4) Performing IDWT on the modified DWT coefficients, we
produce the watermarked image
thusgeneratedmarkedimages
image is higher than 42.7 dB.
. The PSNR of
versustheoriginal
B. Template Embedding in DFT Domain
Sincethe DWT coefficients are not invariant under geometric
transformation, to resist affine transform, we embed a template
in DFT domain of the watermarked image inspired by [15]. The
template embedding is as follows.
1) In order to have a required high resolution, the image
is padded with zeros to a size of 1024
the fast Fourier transform (FFT) is then applied.
2) 14 template points uniformly distributed along two lines
(refer to Fig. 3) are embedded, seven points each line
in the upper half plane in the DFT domain at angles
andwith radii varying between
gles
and radii, where
be chosen pseudo-randomly as determined by a key. We
require at least two lines in order to resolve ambiguities
arising from the symmetry of the magnitude of the DFT,
and we choose to use only two lines because adding more
lines increases the computational cost of template detec-
tion dramatically. We empirically find that seven points
per line are enough to lower false positives probability to
asatisfactoryextentduringdetection.Buttoachievemore
robustness against JPEG compression than the technique
reported in [15], a lower frequency band, say
and , is used for embedding the template. This
corresponds to 0.2 and 0.3 in the normalized frequency,
which is lower than the band of 0.35 0.37 used in [15].
Since we do not embed the informative watermark in the
magnitude spectrum of DFT domain, to be more robust
to JPEG compression, a larger strength of the template
points is chosen than in [15]. Concretely, instead of the
local average value plus two times of standard deviation
[15], we use the local average value of DFT points plus
1024,
and. The an-
, may, 2,
(1)

Page 4

KANG et al.: A DWT-DFT COMPOSITE WATERMARKING SCHEME ROBUST TO BOTH AFFINE TRANSFORM AND JPEG COMPRESSION779
Fig. 4.Original images, Lena, Baboon, and Plane.
five times of standard deviation. According to our exper-
imental results, this larger strength and lower frequency
band have little effect on the invisibility of the embedded
watermark (refer to Figs. 4 and 5).
3) Correspondingly another set of 14 points are embedded
in the lower half plane to fulfill the symmetry constraint.
4) Calculate the inverse FFT, we obtain the DWT-DFT
composite watermarked image
versus the original image is 42.5 dB, which is
reduced by 0.2 dB compared with the PSNR of
versus the original image due to the template embedding.
The experimental results demonstrate that the embedded
data are perceptually invisible.
. The PSNR of
Fig. 5.Watermarked images with ????? ? ???? ??.
III. WATERMARK EXTRACTION WITH PROPOSED
RESYNCHRONIZATION
In order to extract the hidden information, we extract a data
sequence
DWT
subband of the to-be-checked image
is rescaled to the size of the original image at first, in our work,
512
512. (We assume that the size of the original image is
known to the detector.) If,
tract the informative watermark and recover the message from
subband directly. Otherwise, we need to resynchronize the
hidden data before extracting the informative watermark.
In order to resynchronize the hidden data after geometric dis-
tortion, we restore affine transform according to the template
in row 16 and column 16 in the
, which
, we can then ex-

Page 5

780IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003
embedded, and then restore translation using the training se-
quence. Therefore theprocedure of information extractionis di-
vided into three phases: template detection, translation registra-
tion, and decoding.
A. Template Detection
We first detect the template embedded in DFT domain. By
comparing the detected template with the originally embedded
template, we can determine the affine transformation possibly
applied to the test image. To avoid high computational com-
plexity, we propose an effective method to estimate the affine
transformation matrix.
A linear transform applied in spatial domain results in a cor-
responding linear transform in DFT domain. That is, if a linear
transform
is applied to an image in spatial domain as follows:
(2)
then correspondingly the following transform takes place in
DFT domain [15]:
(3)
The template detection is conducted in the following way,
which is basically the same as in [15] except a more efficient
way to estimate the linear transform matrix.
1) Apply a Bartlett window to the to-be-checked image
to produce the filtered image
2) Calculate the FFT of the image padded with zero to the
size of 1024
1024. A higher resolution in the FFT is
expected to result in a more accurate estimation of the
undergone transformations. However, as we increase the
amount of zero-padding, we also increase the volume of
calculations. We find that using a size of 1024
yields a suitable compromise.
3) Extract and record the positions of all the local peaks
(
, ) in the image. Sort the peaks by angle and divide
them into
equally spaced bins in terms of angle.
4) For both lines in the template, perform the following.
For each of the equally spaced bins search for a
where such that at least
having radial coordinate
the peaks in the original template having radial coordi-
nate
along line where
is meant that
points match, we store the set of matched points. (In our
work, we choose
responding scaling factor considered is hence between 2
and 0.5.)
5) From all sets of matched points, choose one set matching
to template line 1 and another to template line 2 such that
the angle between two sets deviates from the difference
between
andas shown in Fig. 3 within a threshold
. Calculate a transformation matrix
.
1024
local peaks
, match, where
, 2. Here, by match it
. If at least
and. The cor-
such that the
mean square error (mse) defined in (4) is minimized as
follows:
......
......
......
......
(4)
where ( , ) with subscripts represent a peak point’s co-
ordinate, ( ,
) with subscripts represent the original
(known)template’s coordinate,
the number of the matching points. We note that
is
is a 2
2 transformation matrixand the matrix inside
is of. The notationdenotes the
sum of allof thesesquared error elementsin theerror ma-
trix. The rows contain the errors in estimating the
from the original (known) template positions
after applying the linear transformation.
In the following, we propose a method to estimate the
transformation matrix
. It is noted that (5) links the set
of matched points (
,
and
and
) and the set of the
............
............
............
............
...
...
...
...
(5)
original template points (
,) with, 2;
or;or.
Equation (5) can be rewritten as the following matrix-
vector format:
(6)
or
(7)
We seek
solution that satisfies the requirement is [20]
thatminimizes. The
(8)
(9)
Since the matrix
2 matrix,
trices, the above two linear equation systems can
is a positive definite
are 2
2
and1 ma-