Blind Watermarking in Contourlet Domain with Improved Detection
Jayalakshmi M., S . N. Merchant and U. B. Desai
SPANN Lab, Electrical Department, Indian Institute of Technology, Bombay
Powai, Mumbai-76, India
email: Glakshmi, merchant, ubdesai) @ ee.iitb.ac. in
Abstract
This paper presents a novel method of blind image watermarking in contourlet domain. We have used spread
spectrum technique for additive watermark embedding. A
correlation detector is used to detect the embedded pseudorandom sequence. The binary logo thus retrieved proves
authenticity of the image. The similarity of the retrieved binary logo with the original embedded logo is veriJied using
correlation technique. Post processing of the retrieved logo
gives better visual effects,further aiding threshold selection
for detection. We have verijied the robustness of the proposed method against dzrerent attacks including StirMark
attack. The proposed method is compared with a wavelet
based blind technique and the results prove that contourlet
based technique gives better robustness, under similar embedding conditions.
1. Introduction
Digital watermarking has been proposed as a solution
to illegal copying or reproduction of digital data. The applications like copyright protection and authentication may
mostly require the content owner or the authorized buyer to
prove the authenticity without reference to the cover work.
This creates a demand on blind watermarking techniques
over non-blind watermarking techniques. There are a few
methods of watermarkingwhich do not use the original data
for detecting or recovering the digital watermark embedded
into the cover work [6], [7], [S].
Wavelet based algorithms have been chosen for watermarking since new image coding standards use wavelet
domain representation and it models human visual systems well. But it has been proved that wavelets are good
at representing discontinuities in one dimension only [3].
So, curvelet transform was defined to represent two dimensional discontinuities more efficiently, with least mean
square error in a fixed term approximation [3]. But, curvelet
transform was proposed in continuous domain and its dis-
cretization was a challenge when critical sampling was desired. Contourlet transform was then proposed as an improvement on curvelet transform using a double filter bank
structure.
Contourlet transform provides a flexible multiresolution
representation for two dimensional signals. It makes use of
the Laplacian Pyramid [2] for the multiresolution decomposition of the image. After this, a directional decomposition
is performed on every bandpass image using directional filter banks [I]. Contourlet transform is unique since the number of directionalbands could be specified by the user at any
resolution. In our simulations, we have used a decomposition where the number of directional bands doubles at every
decomposition level.
In this paper, we propose a blind watermarking method,
which embeds a watermark in the second decomposed level.
We embed a pseudorandom sequence generated using a key,
into the transformed coefficients in this band, with respect
to the presence of 0 or 1 in the binary watermark chosen.
The pseudorandom sequence is modulated, so that there is
no visual distortion on the watermarked image. The robustness of the proposed algorithm is tested against various
attacks including StirMark 3.1. For the purpose of comparison, we have simulated results with a wavelet based
blind watermarking method also. The results of watermark
retrieval prove that contourlet based method outperforms
wavelet based method in case of signal processing operations like Gaussian noise addition, salt-pepper noise addition with median filtering, mean filtering, median filtering
and JPEG compression.
The paper is organized as follows. Section 2 describes
the proposed algorithm. The simulation results of embedding and retrieval are given in Section 3. Conclusions are
drawn in Section 4.
2. Proposed Algorithm
Contourlet transform gives a multiresolution, local and
directional expansion of images using Pyramidal Directional Filter Bank (PDFB)[S]. The PDFB combines Lapla-
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cian Pyramid which captures the point discontinuities,with
a directional filter bank which links these discontinuities
into linear structures. Laplacian Pyramid is a multiscale decomposition of the L2(R2)into series of increasing resolution subspaces which are orthogonal complements of each
other as follows.
An 1-level directional filter bank generates a local directional basis for Z2(Z2)that is composed of the impulse response of the directional filter banks and their shifts. In
contourlet transform, the directional filter is applied to the
detail subspace W j . This results in a decomposition of W j
into 2'j subspaces at scale 29.
2.1. Watermark Embedding
The watermark is embedded using spread spectrum technique using and additive rule [4]. A pseudorandom sequence is generated using a key, which is additively embedded into the transformed coefficients. We have selected
a binary watermark which will be embedded into the second decomposed level using the spread spectrum method
depending on whether a 0 or 1 occurs.
Let Y(x,y)represent a pixel in band Y of the transformed
image and Y i ( x ,g) represent the corresponding watermarked pixel. Let the pseudorandom sequence generated
be P. Then, additive watermarking is performed as per the
following equation.
Y ' ( x , Y )= Y ( x , Y )+ c . ~ w k p ( ~ , <
~ x,Y
) , o < ( N / 2 )- 1
(3)
Here W k represents each watermark bit. The multiplication
factor cu is selected such that the watermarked image looks
visually very similar to the original image. We calculate
the Peak Signal to Noise Ratio (PSNR) of the watermarked
image to assess its visual quality with respect to the original
image.
2.2. Watermark Detection
The embedded watermark is retrieved by a correlation
detector. After receiving a possibly attacked image, we take
the contourlet decomposition of the image. The pseudorandom sequence is generated using the secret key and the
correlation of the watermarked pixel with this generated sequence is found out. Let y represent the watermarked pixels obtained after transformation. Then the correlation for
deciding the ithbit is found out as follows.
Figure 1. Contourlet decomposition
As seen in Figure 1, we have used a directional decomposition which doubles at every level of multiresolution pyramid. If the original image is of size N x N , the second
decomposed band would be of size ( N / 2 ) x ( N / 2 ) . We
have watermarked all coefficients of band Y and 75% coefficients of band Y with a pseudorandom sequence. The latter was performed since the wavelet decomposed image in
the second decomposed level will be of the same size. The
security of the watermarking scheme could be improved by
selecting any number of decomposition and choosing any
particular band in the selected level for watermark hiding.
The mean of the correlation values pi is calculated and is
selected as a threshold T , for deciding the watermark bit. If
the correlation is above the mean value of the correlation,
i.e., pi > T , then we choose the watermark bit to be 1. Else,
the watermark bit is 0. Thus, entire binary watermark is
generated.
There is no specific threshold defined for retrieving the
logo correctly. We have seen from experiments that the visual quality of the retrieved logo was improved by performing a median filtering operation on it, especially those retrieved after some attacks. After getting this image, we verified the visual resemblance by comparing the correlation
of approximate band or low frequency wavelet coefficient
of this logo with that of the original logo. From experimentation we have observed that if the normalized cross correlation between the approximatebands of these logos is above
0.8, the visual quality of the retrieved mark was very good.
So we have chosen 0.8 as the threshold for correct retrieval.
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3. Simulation Results
Simulation results with 512 x 512 Lena image and 22 x
96 binary watermark are included here. As explained before, we have simulated three different cases of embeddingtwo in contourlet domain and one in wavelet domain. The
(a) Logo
(b) Watermarked image
(c) With authorized key
(d) After median filtering
Figure 2. PSNR variation with a
first method watermarks the entire band Y of size 256 x 256
and the second method watermarks 75% of band Y of size
256 x 384. We have chosen all bands in Y except Y7and Y8
for the second case. In the third method, the vertical, horizontal and diagonal detail bands of wavelet decomposed
image in second decomposed level is chosen for watermark
embedding. The variation of PSNR with multiplication factor a is shown in Figure 2 for all the three cases considered.
The binary watermark selected is shown in Figure 3a.
Watermarked image of Lena with a multiplication factor
0.225 and PSNR 40.84 dB is shown in Figure 3b. The retrieved watermark from this image is also shown in Figure
3c. This retrieved watermark is median filtered to get the
logo given in Figure 3d. Figure 3e shows a retrieved logo
with an unauthorized key.
The variation of watermark retrieval with multiplication
factor is shown in Figure 4 for the three cases considered.
We can see from Figure 4 that contourlet gives better retrieval compared to wavelets under similar conditions of
embedding.
3.1. Resilience to attacks
Watermarking methods should be robust to common signal processing operations which could be intentional or unintentional. This section briefly gives the retrieval results of
the proposed method against various signal processing operations. The results of retrieval from watermarked Lena
image with PSNR of 40.84 corresponding to an embedding strength of 0.225 is included in the second and third
columns of Table 1. The second column gives the correlation coefficient of the retrieved watermark with embedded
(e) With unauthorized key
Figure 3. Original and retrieved logos and watermarked image
Figure 4. Correlation coefficients with a
watermark denoted as 'coeffl'. The third column, denoted
by 'coef%', shows the correlation coefficient between the
low pass bands of the original logo and that of the noise
removed logo. This correlation coefficient is found out to
just decide a threshold for detection. A value above 0.8 in
this column shows that the retrieved logo is visually similar to the original logo embedded. The fourth and fifth
columns show the correlation coefficients from contourlet
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Table 1. Normalized correlation coefficients
after various attacks
Attack
coeffl
coet3-2
Contourlet
Wavelet
(0.225)
(0.225)
(0.275)
(0.275)
(a) Cropped image
(c)
From a
(b) Cropped image
(d) From b
Figure 5. Cropped images and the retrieved
watermarks
based and wavelet based watermarking respectively, under
similar embedding conditions. Both these columns select
98304 (256 x 384) pixels for embedding with multiplications factor 0.275.
The robustness of the proposed method was tested
against different signal processing operations like mean filtering, median filtering (2 x 2 and 3 x 3), Gaussian noise addition (variance 0.I), salt-pepper noise (variance 0.1) with
median filter, JPEG compression, cropping etc. We have
also tested the robustness against StirMark 3.1 and the proposed contourlet based blind method has shown good performance against many of the attacks as shown in Table 1.
Figure 5 shows the cropped images of watermarked Lena
with multiplication factor 0.2 and the retrieved watermarks
from them.
From Table 1 it is obvious that the contourlet algorithm
works better in case of noise addition, mean filtering, median filtering and compression. The results with rotation
and scaling are not included in this paper. Authors are currently working on the directional property of the contourlet
coefficients which could be well exploited to get very good
results of detection in case of attacks like rotation and rotation with scaling.
4. Conclusions
In this paper, we propose contourlet domain blind watermarking for images for better robustness. Different factors like the secret key selected for embedding, the level
of decomposition selected and the number of directional
bands determine the security of the algorithm. The robustness of our algorithm is tested against various attacks and
the results prove that the proposed algorithm is better than
wavelet based method under similar embedding conditions.
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