A Content-based Watermarking Scheme based on Clifford
Fourier Transform
Maroua Affes
1, 2
, Malek Sellami Meziou
1
, Yassine Lehiani
2
, Marius Preda
2
and Faouzi Ghorbel
1
1
CRISTAL, National School of Computer Sciences, Mannouba campus, Mannouba, Tunisia
2
ARTEMIS, Institute TELECOM/TELECOM SudParis, 9, Charles Fourier, Evry, France
Keywords: Image Watermarking, Clifford Fourier Transform, Harris Detector, JPEG Compression, Robustness.
Abstract: In this paper, we propose a new watermarking method based on Harris interest points and Fourier Clifford
Transform. We employed Harris detector to select robust interest points and to generate some non-overlapped
circular interest regions. Each region was transformed into Clifford Fourier domain and the watermark was
embedded into the Clifford transform coefficients magnitude. Experimental results show the robustness of the
proposed method against JPEG compression.
1 INTRODUCTION
Due to the open environment of the internet,
download and distribution of digital media have
facilitated the wide use and sharing of digital
multimedia content. However, these advantages
come with challenging problems for copyright
protection of digital property. In order to protect and
preserve digital content, many regulatory measures,
such as copyright protection, are provided. In this
context, watermarking is one of the most prominent
protection techniques. Often, watermarking methods
are categorized by casting/processing domain, the
watermark signal type, and hiding position. In any
case, good visual fidelity and robustness of the
watermark against common image processing and
geometric attacks are essential. Many watermarking
approaches have been proposed in the literature. A
survey of watermarking techniques can be found in
(Potdar et al., 2005). In general, watermarking
methods can be classified into two generations
(Xiaojun and Ji, 2007), (Potdaret al.,2005): traditional
watermarking schemes and host-content based
methods.
The first generation can be divided into three kinds:
Template-based watermarking methods: the
template is a repeated structure and it embeds
into the image to estimate the geometric
distortions and to extract the watermark after
reversing the geometric transformation.
Invariance domain based watermarking
methods which embed the watermark in a
geometrically invariant domain, such as the
Fourier-Mellin domain or log- polar domain.
These methods provide rotation, scaling and
translation (RST) invariance.
Moment-based watermarking methods which
modify the geometric invariants of the image
including ordinary moments, such as Zernike
moments.
The second generation is based on host contents (Bas
et al., 2002). For example, Kutter, Bhattacharjee and
Ebrahimi (1999) claimed that the watermark
information can be associated with the image content.
The basic idea is to use interest points as Harris
corners or Scale-Invariant Feature Transform (SIFT),
etc, to determine the interest areas. Same areas may
be identified in embedding and extraction processes
even after geometric distortions. Lee , Kim and Lee
HK. (2006) extracted the image feature points by
using SIFT and generated a number of circular patch,
the mark is embedded into each patch additively in
spatial domain. This method can resist general
geometric attacks, but their experimental results show
that the watermark similarities are lower than 0.7.
Lei-da, Bao-long and Lei (2008) proposed a RST
invariant image watermarking scheme using Harris
feature points. They extracted Harris feature points to
generate circular regions. Then these regions was
rotation normalized. This method is robust against
374
Affes, M., Meziou, M., Lehiani, Y., Preda, M. and Ghorbel, F.
A Content-based Watermarking Scheme based on Clifford Fourier Transform.
DOI: 10.5220/0005748403720378
In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 3: VISAPP, pages 374-380
ISBN: 978-989-758-175-5
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
RST attacks, but it needs inverse normalization,
which introduces error to weaken the robustness
against common signal operation.
In this paper, we propose a content-based
watermarking scheme that uses a Harris feature point
detector. The watermark is embedded into frequency
domain of interest regions. We will give in section 2
an overview of some frequency watermarking
methods. In section 3, Clifford Fourier Transform
will be recalled and we will describe the embedding
and the extraction process of the watermarking
algorithm. Experimental results will be presented in
section 4. We will eventually conclude and give some
possible perspectives for future work.
2 FREQUENCY
WATERMARKING METHODS
The watermark can be embedded directly on pixels or
in the image frequency transform coefficients. The
most used transforms are Discrete Fourier Transform
(DFT), Discrete Wavelet Transform (DWT) and the
well-known Discrete Cosine Transform (DCT).
DCT-based watermarking techniques use the
middle-frequency coefficients because the
modification of low frequencies affects the visual
quality of the image and the modification of high
frequencies causes local distortion along the edges
(Neeta et al., 2010).
The watermarking in DCT domain was first
introduced by Koch and Zhao (1994) by modifying
the magnitude of the middle-frequency coefficients.
This method shows good robustness to JPEG
compression. The image is divided into blocks of size
8x8. After that, some blocs are selected by a specific
function and they are transformed to DCT domain.
Before the embedding process, for each block, a
condition tests two selected mi-frequency
coefficients to study the validation of bloc to embed
the watermark bit. The criterion for valid blocks is
specified by the relationships between the two
selected coefficients. This criterion is used in the
extraction process to know if the block contains a bit
of watermark or not. This method is based on
modifying the magnitude of the selected coefficients.
To create the watermarked image, for each block, it is
required to perform the inverse DCT. The extraction
process is very simple and it is a blind procedure. It
has the same steps of the embedding process. To
estimate the inserted bit, it suffices to read the sign of
the difference between the modules of the two
selected mi-frequency. Using these constraints, the
experimental results indicate that the watermark can,
with sufficient noise margins, survive common
processing, such as lossy compression.
Discrete wavelet transform find a great popularity
in watermarking technique. It supports multi-
channels and gives excellent spatial localization. In
general, the DWT watermarking scheme consists first
in partitioning the cover image into high and low
frequency quadrants. The low frequency quadrant is
again split too into more parts of high and low
frequencies and this process is repeated until the
signal has been entirely decomposed. For the first
decomposition the DWT gives four resolution levels:
LL1, LH1, HL1, and HH1. It is well known that the
maximum energy is located in LL sub-band. So, the
mark is embedded in some selected coefficients from
HL, LH and HH via additive modification. In the
detection process, the same steps as the embedding
process are repeated. Typically, it consists of a
process of correlation estimation (Vaishali and
Sachin, 2011). DWT watermarking method is robust
against JPEG compression, cropping, median
filtering, adding noise and scaling. Unfortunately, this
approach has some disadvantages. Computing DWT
is more time consuming than computing DCT. Also,
it embeds the watermark in an additive way. So, to
detect the watermark, it is necessary to correlate the
watermarked image coefficients with the initial
watermark. Therefore, the image itself must be
treated as noise, which makes the detection extremely
difficult (Potdar et al., 2005), (Seema et al., 2012).
The DFT domain is also used in watermarking
technique because it offers robustness against
geometric distortions like cropping translation,
rotation, scaling, etc. DFT based watermark
embedding techniques can be divided into two kinds.
In the first one, the watermark is directly embedded
by modifying the DFT amplitude and phase
coefficients. In the second case, a template is used to
estimate the transformation and resynchronize the
image. For example, O'Runaidh, Dowling and Boland
(1996) proposed a DFT watermarking algorithm
modifying the DFT phase information. Its
experimental results show that this technique is robust
against image contrast operation and rotation. In
(O'Runaidh and Pun, 1998) authors proposed another
DFT watermarking technique using log-polar
coordinates system. Results show that this scheme is
robust against RST attacks. This technique is
basically used for greyscale images watermarking. To
extend the method, a marginal treatment proposes to
perform watermarking for each colour canal
independently. On other side, a lot of interest to find
another Fourier transform applicable directly on
A Content-based Watermarking Scheme based on Clifford Fourier Transform
375
colour images was reported. As example, the Clifford
Fourier Transform has been proposed in 2010 as a
rigorous solution to overcome the limits of the
classical Fourier transform.
3 PROPOSED WATERMARKING
SCHEME
In this section, we will first remind the principles of
Clifford Fourier transform, which will be used later
for our robust watermarking algorithm against JPEG
compression.
The classical Fourier transform have been used in
many fields such as harmonic analysis and group
theory to process 1D signal and greyscale images. On
colour images, three Fourier transforms are applied
on each channel. To avoid this marginal processing,
several authors have proposed to embed the colour
space in more pertinent geometric spaces such as
quaternions. Sangwine and Ell (2000) defined the
Quaternion Fourier Transform (QFT). They
considered only two Fourier transforms: for the
luminance and chrominance. In the exponential of
Fourier coefficients, they replaced the complex i by
the quaternion. Recently, Batard, Berthier and Saint-
Jean (2010) defined another Fourier Transform,
called Clifford Fourier transform (CFT), which is
mathematically more rigorous. This one clarifies
relations between the Fourier transform and the action
of the translation group through an action spinor
group.
The CFT generalizes the Color QFT (Batard et al.,
2010) because it is based on group representations
theory and Clifford algebras. A pixel of a colour
image can be extended in
1
4,0
algebra (vectors of
4,0
) as follows:
4321
0)()()()( eexbexvexrxf +++=
(1)
Where x = (x
1
, x
2
) and r, v and b are respectively
the red, green and blue channels pixel with
coordinates (x
1
, x
2
).
The CFT is parameterized by a unit vector B whose
expression is as follows :
dxeexfee
BIxuBxuBIxu
R
Bxu
u
B
f
44
2
,
2
1
,
2
1
,
2
1
,
2
1
)(
)(
><><><><
=
(2)
where I
4
is the scalar pseudo of
4,0
and B is its
unit bi-vector. Within the Clifford algebras, a vector
can be decomposed in a parallel part and an
orthogonal part depending on the choice of the bi-
vector B. Being f an image and B a bi-vector, this
decomposition is
B
B
ffBBfBffBBf
+=+==
11
).(
(3)
where
1
).(
= BBff
B
(resp.
1
)(
= BBff
B
) is the
parallel (resp. the orthogonal) projection of f on a bi-
vector B. The above equation can be rewritten as
follows by this decomposition (Batard et al., 2010):
)()()( ufufu
B
f
BB
+=
(4)
where
22
,,
,
22
() () ()
B
ux ux
BB
ux B
BB
RR
f
ue fxe dxfxe dx
<> <>
−< >
==

and
44
4
22
,,
,
22
() () ()
ux ux
IB IB
ux IB
BB B
RR
f
ue fxe dxfxe dx
<> <>
−< >
⊥⊥
==

We will use decomposition in our proposed
schema in order to define the criteria of validity for
CFT coefficients to embed the mark.
In order to synchronize the embedded regions and
the extracted regions, we used the local Harris
features. They provide a potential solution for
watermarking to improve the robustness (Papakostas
et al., 2011). Also, we chose to embed the watermark
in the frequency domain which assures its invisibility
and its robustness more than in spatial domain. We
used also the CFT to avoid the marginal treatment of
colour image which can cause sometimes a false
detection of the watermark. CFT is applied on
windows of 8x8 around the keypoint. The detailed
embedding steps are illustrated in Figure 1. We first
transform the colour image to greyscale in order to
detect the interest points with Harris detector. We
construct the circular locally regions. To avoid
overlap between regions (Figure 2a), the Euclidean
distance d between the interest points must be upper
than the double of patch radius (Figure 2b).
To choose the embedding plane, we set up a small
experiment and embed the mark W in three
Figure 1: Embedding processes.
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
376
a) b)
Figure 2: Generation of interest regions (a) overlappe
d
regions, (b) no overlapped regions with Euclidean distance
= 20.
different locations: the parallel part
B
f
of CFT, in the
orthogonal part
B
f
of CFT and in both of them. The
results are presented in the following table. To
evaluate the three insertion methods, we use the
PSNR (Peak Signal Noise Ratio) to measure the
imperceptibility of the mark. We note that best results
are obtained in the first case.
Table 1: PSNR variation depending on the embedding
plane.
Image
references
\method
B
f
B
f
B
f
and
B
f
189003 52,67dB 49,67 dB 48,09 dB
295087 53,14 dB 48,92 dB 47,52 dB
42049 53,37 dB 49,46 dB 48,04 dB
299086 52,89 dB 49,13 dB 48,09 dB
We generate a binary random watermark W = {w
i
,
i = 0…N}. To know the size of the mark, we construct
a bitmap, denoted ξ, which contains "1" if the region
B(i) of
B
f
is valid i.e. the region can contain a bit of
the mark. The validity of
B
f
is computed as
following:
(1) for each region, CFT is applied.
(2) then, two mi-frequency coefficients are
selected. To know the possible location of these two
coefficients, we study the distribution of coefficients
with bases magnitudes values. In this case, we
calculate the average of magnitudes of frequency
coefficients for multiple windows of 8x8 around the
keypoint detected with Harris detector for 30 images.
Figure 3 shows the distribution of the amplitudes for
both DCT and CFT. We can observe that the lower
values of CFT coefficients are shifted to the mi-
frequency coefficients when compared with DCT.
This observation made us choose the support of
potential coefficients where to embed the mark as
illustrated in Figure 4.
a) b)
c) d)
Figure 3: The magnitude of frequency coefficients for DCT
(a) and for CFT (b). Image (c) (resp. Image (d)) represents
the magnitude of frequency coefficients of DCT (resp.
CFT) with the elimination of the DC component.
Figure 4: Possible locations for embedding in 8x8 region
(shadowed area).
(3) let’s denote |Q(k
i
,l
j
)| and |Q(k
n
,l
m
)|, the two mi-
frequency coefficients selected from the shadowed
area in Figure 4. We apply the following criteria to
choose the coefficients to be permuted:
if |Q(k
i
,l
j
)| > |Q(k
n
,l
m
)|+p, ξ(i) 1 then the
region B(i) is valid
else ξ(i) 0.
where p is a marginal noise, in the experiment p
= 0.5. The size of the watermark equals to the number
of "1" on bitmap ξ.
(4) error correcting codes are incorporated in
watermarking system to overcome the corruption of
the watermark in the communication channels. In our
method, we use the Hamming code as an error
detection system to correct bit error. The watermark
is divided into some words, each word contains 4 bits.
The Hamming code is then applied to each word to
generate (7-4) single bit error correcting code. The
use of error-correction codes ensures a better quality
signal at the receiver and a higher recovery increases
the possibility of the perfect match in embedding
process (MacWilliams and Sloane, 1977).
A Content-based Watermarking Scheme based on Clifford Fourier Transform
377
(5) once the robust circular non-overlapping
region and the watermark are generated, we start to
embed the watermark. Similarly with the Zhao
algorithm (Koch and Zhao, 1994), we embed one bit
of the watermark in each region. However, we
integrate it in the CFT domain. So, for each valid
region B(i) (i.e. ξ(i) =1 ) the following steps are
applied:
CFT is applied
If W(i) =1
permute |Q(k
i
,l
j
)| and |Q(k
n
,l
m
)|:
|Q’(k
i
,l
j
)| = |Q(k
n
,l
m
)| and
|Q’(k
n
,l
m
)|=|Q(k
i
,l
j
)|;
If W(i) =0
|Q’(k
i
,l
j
)| = |Q(k
i
,l
j
)| and
|Q’(k
n
,l
m
)|= |Q(k
n
,l
m
)|;
Inverse CFT is applied
The watermarked image f
w
is then obtained
by combining the watermarked regions.
The extraction process has the same steps as
in embedding process. With Harris detection and
the map ξ, we can specify which regions are
watermarked. The detailed extraction steps are
described in Figure 5. So, for each region if ξ(i)=
1 then W' is computed as follow:
W’ = 1, |Q’(k
n
,l
m
)| > |Q’(k
i
,l
j
)|
0, |Q’(k
n
,l
m
)| < |Q’(k
i
,l
j
)|
(5)
Figure 5: Extraction processes.
4 EXPERIMENTAL RESULTS
Several experiments were performed in order to test
the effectiveness of the proposed watermarking
method. The visual perceptibility and robustness
against compression attacks were tested. Experiments
have been conducted on various colour images from
the data base of BSD300 (Berkeley Segmentation
Dataset 300) as illustrated in Figure 6.
Figure 6: Samples from Berkeley Segmentation Dataset
300.
4.1 Visual perceptibility
The watermarked images were assessed for visual
distortion using PSNR. Images in Figure 7 show no
visible degradation. For Lena image, the PSNR value
is 51.07 dB, for Lion 48.90 dB (ref 108085 in the
BSD300). Similar observations were noted for other
test images. These PSNR values are all greater than
30.00 dB which is the empirical value for the image
without any perceivable degradation (Hsieh and
Tesng, 2004).
a)
b)
c) d)
Figure 7: (a) Original and (b) watermarked images at a
PSNR value of 51.07 dB for Lena image and (c) original
and (d) watermarked image at a PSNR of 48.90 dB for Lion
image.
4.2 Robustness to JPEG
Compression Attack
The first frequency watermarking method was
developed by Koch and Zhao (1994). A modified
version of this method was used as a reference to
evaluate the robustness of our method against
compression attacks. The original Zhao method is
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
378
applicable on greyscale images and based on DCT
domain. We extend it to be applicable on colour
image. In fact, we decomposed the RGB image and
we applied Zhao method on the red component. An
error correction Hamming codes is also used.
To evaluate the robustness of the proposed
algorithm, we calculated the Normalized Hamming
Similarity NHS:
N
WWHD
NSH
)',(
1=
(6)
where W (resp. W’) is the inserted watermark (resp.
the extracted watermark) and N is its size
.
Figure 8: The variation of the NSH depending on the
compression rate for the image “Lena” to CFT
watermarking method and Zhao modified method.
Figure 9: The variation of the NSH depending on the
compression rate the image of ref “295087” to CFT
watermarking method and Zhao modified method.
For all tests, we chose |Q(k
i
=3,l
j
=1)| and
|Q(k
n
=1,l
m
=5)| as two mi-frequency coefficients of
CFT. They have been modified to carry one bit
watermark in each region.
As shown in Figures 8 and 9, our scheme
performs better than the modified Zhao method under
JPEG compression attack. For example, the NSH for
image Lena with quality factor 80% using ECC is
0.94 and 0.61 for Zhao’s method and it is 0,765 with
quality factor 60% using ECC instead of 0.6 for
Zhao’s method.
5 CONCLUSION
In this paper, we introduced a new method for
invisible watermarking based on CFT. The key idea
of the proposed algorithm is the combination of
generation of the Harris interest regions and colour
image watermarking technique. We first used Harris
detector to generate circular patch for watermark
embedding. Then, we transformed these patches to
CFT domain and we selected two mi-frequency
coefficients. After that, we inserted the watermark on
these selected coefficients by a substitution way. The
capacity of the proposed scheme is flexible, since we
can manipulate the number of feature points as we
want. The experimental results showed that the
proposed scheme preserves not only the high
perceptual quality, but also the robustness against
JPEG compression comparing with Zhao’s method.
Future work will be focused on the geometrics
attacks.
REFERENCES
Bas P., Chassery J. M. and Macq B., 2002. Toward a
content-based watermarking scheme. Traitement du
signal 2002_volume 19 n°1 2002. p.11-17.
Batard T., Berthier M. and Saint-Jean C., 2010. Clifford
Fourier Transform for Color Image Processing. In E.
Bayro-Corrochano & G. Scheuermann, editeurs,
Geometric Algebra Computing in Engineering and
Computer Science, chapitre 8, pages 135–161. Springer
Verlag, 2010.
Hestenes D. and Sobczyk G., 1987. Clifford Algebra to
Geometric Calculus. A Unified Language for
Mathematics and Physics (Fundamental Theories of
Physics). Broché – 31 août 1987.
Hsieh M. S. and Tseng D. C., 2004. Perceptual digital
watermarking for image authentication. Electronic
commerce Research. Volume 4, Issue 1-2 , p.157-170.
Koch E. and Zhao J., 1994. Embedding robust labels into
images for copyright protection. Technical report,
Fraunhofer Institut For Computer Graphics,
Darmstadh, Germany. p.242-251.
Kutter M., Bhattacharjee S. K and Ebrahimi T., 1999.
Toward second generation watermarking schemes. In
Proceedings of IEEE International Conference Image
Processing, vol. 1, Kobe, Japan. p.320-324
Lee H. Y., Kim H. S. and Lee H. K., 2006. Robust image
watermarking using local invariant features. In Optical
Engineering, 2006. p.037002-037002-11
Lei-da L., Bao-long G. and Lei G., 2008. Rotation, scaling
and translation invariant image watermarking using
feature points. In The Journal of China Universities of
Posts and Telecommunications, 2008. p.82-87.
A Content-based Watermarking Scheme based on Clifford Fourier Transform
379
MacWilliams F. J. and Sloane N. J., 1977. Theory of Error
Correcting Codes. 8, North-Holland, Amsterdam,
Netherlands, 1977.
Neeta D., Archana R. and Manthalkar R., 2010. Review of
Robust Video Watermarking algorithms. In
International Journal of Computer Science and
Information Security. p. 237-246.
O’Ruanaidh J., Dowling W. J. and Boland F. M., 1996.
Phase watermarking of digital images. In Proc. IEEE
Int. Conf. Image Processing. p. 239-242.
O’Ruanaidh J. and Pun T., 1998. Rotation, scale, and
translation invariant digital image watermarking. In
Signal Processing. p.303-317.
Papakostas G. A., Tsougenis E.D., Koulouriotis D.E. and
Tourassis, V. D., 2011. On the robustness of Harris
detector in image watermarking attacks. In Optics
Communications. p.4394-4407.
Potdar, V. M., Song Han and Chang, E., 2005. A survey of
digital image watermarking techniques. Industrial
Informatics, 2005. INDIN '05. 2005 3rd IEEE
International Conference. p.709-716.
Sangwine S. J., and Ell T. A., 2000. The discrete Fourier
transform of a colour image. In J. M. Blackledge & M.
J. Turner, editeurs, Image Processing II : Mathematical
Methods, Algorithms and Applications, (Proceedings
of Second IMA Conference on Image Processing, De
Montfort University, Leicester, UK, September 1998),
pages 430–441. Horwood Publishing for Institute of
Mathematics and its Applications, 2000.
Seema M., Hitesh G. and Saurabh M., 2012. Survey of
Digital Image Watermarking Techniques to achieve
Robustness. In International Journal of Computer
Applications, 2012 by IJCA Volume 45-No 13. p.1-8.
Vaishali J. S. and Sachin R. G., 2011. Literature Review of
Wavelet Based Digital Image Watermarking
Techniques. In International Journal of Computer
Applications. p.28-35.
Xiaojun Q. and Ji Q., 2007, A robust content-based digital
image Watermarking scheme. Signal Processing
Volume 87, Issue 6, June 2007, P.1264–1280.
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
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