A robust block-based image watermarking scheme using
fast Hadamard transform and singular value decomposition
Emad E. Abdallah, A. Ben Hamza, and Prabir Bhattacharya
Concordia Institute for Information Systems Engineering
Concordia University, Montréal, QC, H3G 1T7, Canada
Abstract
sine transform (DCT) [4, 5], the discrete Fourier transform
(DFT) and the discrete wavelet transform (DWT) [6, 7].
We present a new approach for transparent and high
rate embedding of watermarks into digital images using fast
Hadamard transform (FHT) and singular value decomposition (SVD). The proposed algorithm consists of three main
steps: dividing the cover image into small blocks, applying the FHT to each block, and distributing the singular
values of the visual watermark image over the transformed
cover blocks. The main attractive features of this approach
are simplicity, flexibility in data embedding capacity, and
real-time implementation. The experimental results show
the much improved performance of the proposed method in
comparison with existing techniques, and also its robustness against the most common attacks.
1. Introduction
The rapid development of computer networks and the increased use of multimedia on the Internet has prompted in
recent years a flurry of research activity in multimedia watermarking including digital images, audio, video, and 3D
graphics. Digital watermarking refers to the process of embedding a watermark into a cover multimedia object so that
the watermark may be detected or extracted later to make
an assertion about the object.
A variety of watermarking techniques have been proposed for multimedia protection, and in particular for digital images [1–3]. These techniques can be divided into two
main categories according to the embedding domain of the
cover image: spatial domain methods and transform domain
methods (see [3] for a survey). The spatial domain methods
are the earliest and simplest watermarking techniques but
have a low information hiding capacity, and also the watermark can be easily erased by lossy image compression.
On the other hand, the transform domain approaches insert
the watermark into the transform coefficients of the image
cover, yielding more information embedding and more robustness against watermarking attacks. This second category of watermarking techniques includes the discrete co-
Recently, an SVD-based watermarking technique and its
variants have been proposed [5, 6, 8, 9]. The main idea of
these approaches is to find the SVD of a cover image, and
then modify its singular values to embed the watermark.
In [5, 6], a hybrid non-blind watermarking scheme based on
the DWT, the DCT and the SVD was proposed. The method
proposed in [6] consists of decomposing the cover image
into four transformed sub-bands (LL, LH, HL, and HH),
then the SVD is applied to each band, followed by modifying the singular values of the transformed sub-bands with
the singular values of the visual watermark. This modification in all frequencies provides more robustness to different attacks [5, 6]. Another SVD-block based watermarking
scheme was proposed in [9], and it embeds the watermark in
two layers. In the first layer, the cover image is divided into
small blocks and the singular values of the watermark are
embedded in those blocks. In the second layer, the cover
image is used as a single block to embed the whole watermark. The main limitation of these watermarking techniques is that they are not robust against the different types
of attacks, and require substantial computational time.
Motivated by the computational simplicity of the FHT,
we propose in this paper a new watermarking technique that
has three main attractive features: high rate of watermark
embedding into the cover image, robustness to the most
common attacks, and possible implementation in real time.
The remainder of this paper is organized as follows. In
the next section, we briefly review the FHT. In Section 3, we
introduce the proposed approach and we describe in more
details the fundamental steps of the watermark embedding
and extraction algorithms. In Section 4, we present some
experimental results to demonstrate the much improved performance of the proposed method in comparison with existing techniques, and also to show its robustness against the
most common attacks. Finally, we conclude in Section 5.
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2. Fast Hadamard transform (FHT)
The 2D Hadamard transform has been used with a great
success in image compression and image watermarking [9].
Unlike the other well-known transforms, such as the DFT
and the DCT [4, 5], the elements of the basis vectors of the
Hadamard transform take only the binary values +1 and -1.
Hence, the FHT is well suited for digital image processing
applications where computational simplicity is required.
Let Y be the original image of size N × N . The 2D
Hadamard transform of Y is given by Z = (HY H)/N ,
where H is a Hadamard matrix of order N = 2n (n is an
integer), and with entries {−1, +1}. The Hadamard matrix
H has mutually orthogonal rows or columns, and satisfies
HH T = N IN , where IN is the identity matrix. Hence, the
original image may be recovered using Y = (HZH)/N .
Furthermore, the Hadamard matrix of order N may be generated from the Hadamard matrix of order N/2 using the
Kronecker product property HN = H2 ⊗ HN/2 , where H2
is the Hadamard matrix of order N = 2.
3. Proposed watermarking method
In this section, we provide the main steps of the watermark embedding and extraction algorithms which are also
illustrated in the block diagrams shown in Figures 1 and 2.
Denote by A the cover image of size K × K, and W the
watermark image of size M × M .
For all the blocks apply FHT
Divide into
blocks
Cover
Image
DC component
Apply SVD
Watermark
Image
Use one of the SVs to
modify the DC component
IFHT
Modified
component
Figure 1. Watermark embedding algorithm.
respectively, and β = αb/M , where α is a constant
and b is the block number. Note that the di0 are saved
in the secret key during the embedding stage.
=
4) Construct the watermark images using W
T
, where UW and VW are the left and
UW ΣW VW
right singular vectors of W respectively, and ΣW is
the extracted matrix of SVs.
For all the blocks apply FHT
Divide into blocks
Watermarked
Watermark embedding algorithm:
1) Divide the cover image into blocks of size N × N .
2) To each block B, apply the FHT: B = (HBH)/N ,
where H is the Hadamard matrix of order N .
Use the DC component of the original transformed blocks to extract the SVs
Saved in the secret key
T
3) Apply SVD to the watermark: W = UW ΣW VW
, where
ΣW is a diagonal matrix of singular values (SVs).
4) Modify the DC components of the first M transformed
blocks B using diw = di0 +βλiW , where di0 and diw are
the original and the modified DC components respectively, λiW are the SVs of W , and β = αb/M , where α
is a constant and b is the block number. Add the original DC components to the secret key if the original
cover is not available during the extraction phase.
5) Apply the inverse fast Hadamard transform (IFHT) to all
the blocks to produce the watermarked image.
Watermark extraction algorithm:
1) Divide the watermarked image into blocks of size N ×N
2) To each block C, apply the FHT: C = (HCH)/N .
3) Extract the singular values from the first M transformed
blocks using λiw = (diw − di0 )/(β), where di0 and diw
are the original and the watermarked DC components
UW
Watermark
Σ
W
T
VW
Apply SVD
Figure 2. Watermark extraction algorithm.
4. Experimental Results
We conducted a number of experiments to test the performance of the proposed watermarking algorithm in comparison with existing techniques, and in particular with the SVD
watermarking technique [8] and the block-based method
[9]. We performed our simulations on cover images and
visual watermarks of size 512 × 512, and we set the scaling factor α to 0.7. First we divide the cover images into
blocks of different sizes 2i × 2i , i = 2, 3, 4, 5. For i = 4 the
resulting number of blocks is 1024, hence we may embed
the watermark in two sub-bands of 512 blocks each. Figures 3(a) and 3(b) depict the cover image (peppers) and the
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watermark (letter G) respectively. The watermarked peppers image and the extracted watermarks from the two subbands are shown in Figures 3(c), 3(d), and 3(e) respectively.
We tested our proposed scheme against a wide range of at-
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(e)
Figure 3. (a) original image, (b) visual watermark,
(c) watermarked image, and (d)-(e) are extracted watermarks from the two sub-bands.
tacks. Figures 4 and 5 show the watermarked peppers images with different kinds of attacks, and their corresponding
best extracted watermarks respectively. For each attack, we
select the extracted watermark that has the highest correlation coefficient with the original watermark. For the cropping attack the missing part is replaced by the same part
of the cover image. The correlation coefficient results are
depicted in Figure 6, where the performance of our proposed approach over SVD [8] and Block-based SVD [9]
techniques is clearly demonstrated.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
Figure 5. Best extracted watermarks under different
attacks: (a) JPEG 30-1, (b) Gaussian noise 0.3, (c)
Gaussian blurred 5 × 5, (d) Gamma correction 0.6 ,
(e) histogram equalization, (f) cropping 50%, (g) resize 512-256-512, (h) sharpen 80, (i) contrast−20, (j)
mosaic 2, (k) rotation 1800 , (l) rotation 200 + scaling.
using different block sizes as illustrated in Figure 7 which
shows that we achieve more robustness against most of the
attacks by using 8 × 8 block size. However, the best results
for contrast, cropping and histogram equalization attacks
achieved using block size of 4 × 4. Note that for a block
of size 32 × 32, we can only embed watermark images of
size 256 × 256. Figure 8 (resp. Figure 9) displays the correlation coefficient results with the same cover image Peppers
(resp. with the same watermark Letter G) but with different
watermarks (resp. with different cover images). Note that
the correlation coefficient is higher than 0.9 for most of the
attacks. These results are consistent with various images
and watermarks used for experimentation.
5. Conclusions
(i)
(j)
(k)
(l)
Figure 4. Watermarked image with different attacks:
(a) JPEG 30-1, (b) Gaussian noise 0.3, (c) Gaussian
blurred 5 × 5, (d) Gamma correction 0.6 , (e) histogram equalization, (f) cropping 50%, (g) resize 512256-512, (h) sharpen 80, (i) contrast−20, (j) mosaic
2, (k) rotation 1800 , (l) rotation 200 + scaling.
To gain further insight into the robustness of the proposed method, we tested the performance of our algorithm
We presented a new watermarking scheme by embedding the singular values of the watermark image in the DC
components of the FHT blocks of the cover image. We
showed through experimentation that our scheme outperforms existing techniques and it is robust against a wide
range of attacks. Furthermore, the proposed algorithm may
be implemented in real time due to the computational simplicity of the FHT. Finally, we note that our experimental
results suggest that significant additional performance gains
of the proposed technique are still possible by using adaptive scaling factors for each block of the cover image.
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Proposed method
Block-based SVD with α = .7
SVD with α = .2
Lena
Cameraman
Letter G
1.1
1
C o rrela tio n C o efficient
Correlation Cofficient
1.1
0.9
0.8
0.7
0.6
1
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0.8
us
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no
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Ga
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s.b
lu
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sto
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op
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pi
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2−
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51
2
Sh
ar
pe
n
8
0
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nt
ra
st
−2
0
M
os
ic
2
0.7
Figure 6. Correlation coefficient comparison results
between the proposed approach and other methods.
4x4
8x8
16x16
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Figure 8. Correlation coefficient results using the
same cover image and three different watermarks.
32x32
1.1
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1.1
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2
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Figure 7. Correlation coefficient results using four
different block sizes.
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0.9
Figure 9. Correlation coefficient results using the
same watermark and three different cover images.
References
[1] I. J. Cox, J. Kilian, T. Leighton and T. Shamoon “Secure spread spectrum satermarking for multimedia,”
IEEE Trans. on Image Processing, vol. 6, no. 12, pp.
1673-1687, 1997.
[6] E. Ganic and A. M. Eskicioglu, “ Robust DWT-SVD
domain image watermarking: embedding data in all
frequencies,“ Proc. ACM Multimedia and Security
Workshop, Germany, 2004.
[2] N. Memon and P. Wong, “Digital watermarks: protecting multimedia content,” Communications of the
ACM, vol. 47, no. 7, pp. 35-43, 1998.
[7] R. Mehul and R. Priti, “Discrete wavelet transform
based multiple watermarking scheme,” Proc. IEEE
Region 10 Technical Conference on Convergent Technologies for the Asia-Pacific, India, 2003.
[3] F. Hartung and M. Kutter, “Multimedia watermarking
techniques,” Proceedings of the IEEE, vol. 87, no. 7,
pp. 1079-1107, 1999.
[4] V. Fotopoulos and A. N. Skodras,“A subband DCT
approach to image watermarking,” Proc. X European
Signal Processing Conference, Finland, 2000.
[5] A. Sverdlov, S. Dexter, and A. M. Eskicioglu, “Robust DCT-SVD domain image watermarking for copyright protection: Embedding data in all frequencies,” Proc. European Signal Processing Conference,
Turkey, 2005.
[8] R. Liu and T. Tan, “A SVD-based watermarking
scheme for protecting rightful ownership,” IEEE
Trans. on Multimedia, vol. 4, no. 1, pp.121-128, 2002.
[9] E. Ganic, N. Zubair and M. Eskicioglu, “An optimal
watermarking scheme based on singular value decomposition,” Proc. Communication, Network, and Information Security, 2003.
[10] S. Gilani and A. Skodras, “ Watermarking by multiresolution Hadamard transform,” Proc. Electronic Imaging and Visual Arts, Italy, 2001.
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