CT-SVD and Arnold Transform for Secure Color Image Watermarking

International Journal of Innovative Research in Information Security (IJIRIS) ISSN: 2349-7017(O)
Volume 1 Issue 2 (August 2014) ISSN: 2349-7009 (P)
http://www.ijiris.com
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© 2014, IJIRIS- All Rights Reserved Page - 59
CT-SVD and Arnold Transform for Secure Color Image
Watermarking
Jeril George Satishkumar Varma Madhumita Chatterjee
Department of IT, Mumbai Department of IT, Mumbai Department of IT, Mumbai
Abstract— Watermarking is used for protecting copyright of digital images. In this paper, we propose a novel technique for
watermarking using Contourlet Transform (CT) and Singular Value Decomposition (SVD). CT ensures imperceptibility of
the watermark and SVD ensures its robustness against attacks. Arnold transform is used for scrambling watermark pixels to
ensure watermark security. Watermark extraction is semi-blind, which avoids the need for original image for extraction.
Both watermark and cover image are color images. Performance of the system is judged by using PSNR and Correlation
Coefficient (CC) values. System shows good robustness against noise, JPEG compression, filtering and cropping.
Keywords— Watermarking; CT; SVD; Arnold transform; Semi-blind
I. INTRODUCTION
Copyright protection of digital images is an issue due to advancement in software for image processing and ever increasing
reach of internet technologies. Thus, it is very difficult, today, to prove the ownership of a digital product-image, audio or video
created. Watermarking is a technique introduced to solve this problem. It involves embedding information called watermark in
the digital product in such a way that the watermark is both invisible as well as robust when subjected to intentional or accidental
image processing operations. This watermark is extracted later on from the digital product to prove its ownership.
Apart from robustness and imperceptibility, issue of watermark security is to be considered. We have to ensure that even
after extraction, watermark is available only to a legitimate user in possession of a secret key.
A. Literature Survey
Digital watermarking techniques can be classified based on the domain used. Spatial domain watermarking involves direct
manipulation of pixel values to embed the watermark. This method gives good imperceptibility but cannot withstand even
common image processing operations. Frequency domain method involves modifying the cover image by applying frequency
transform like Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) etc.
and embedding watermark in transform coefficients. This method gives good imperceptibility as well as robustness. Thus,
frequency domain methods are commonly used today for watermarking.
Early watermarking techniques involve use of DCT [1][2] and DFT [3]. DFT gives only frequency information; hence, it is
not preferred. DCT is widely used for watermarking and gives good robustness against JPEG compression but DCT does not
give good imperceptibility as it does not consider Human Visual System (HVS). More recently, DWT is being preferred for
watermarking as it gives very good imperceptibility because it models HVS. Scheme in [4] makes use of DWT for
watermarking. Embedding watermark in the middle frequency coefficients i.e. LH and HL subbands protects the watermark
from being perceptible and also from being lost due to image compression which happens when embedding in LL and HH
subband respectively. As an efficient geometric representation of natural images, CT has gained many researchers’ attention
introduced by M. N. Do and Vetterli [5]. It overcomes limitations of DWT as DWT cannot capture efficiently geometry of image
edges and can give only limited directional information. CT gives more efficient decomposition of images by capturing smooth
contours. In [6], low frequency subband of CT decomposed image is selected for watermarking and watermark pixels are
scrambled by chaotic encryption. Singular Value Decomposition (SVD) is a linear algebra technique which has applications in
the field of digital watermarking. Singular values generated using SVD show good stability during changes. These also show
proportion and rotation invariance. This feature of SVD makes it suitable for watermarking to ensure maximum robustness
during image processing attacks. Scheme in [7] makes use of SVD for watermarking. Watermarking using two different
transforms is another method to ensure dual benefits obtained from the two and even out the weaknesses of the other. In [8],
SVD is used in combination with DWT to give a better watermarking system. DWT ensures imperceptibility and SVD
guarantees robustness. A very important requirement of watermarking in today’s insecure internet environment is security of the
watermark. It has to be guaranteed that after extraction, watermark is accessible only to an authorized user. This requires a secret
key of some kind which is in possession of the owner and the authorized users. Chaotic encryption is a popular form of
encryption. Arnold Cat Map is a form of chaotic encryption which can give watermark security.
Majority of the watermarking schemes involve grayscale image as a cover image and binary watermark as logo. For
application in real world, we need to consider watermarking of color images. Color image can be also used as watermark for
increased watermark capacity.

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Bossen et al. proposed for the first time in [9], the use of blue channel for watermark embedding as human eye is least
sensitive to blue channel. Scheme proposed in [10] embeds the watermark using DWT-SVD into the blue channel of cover
image in RGB color space.
In this paper, we propose a novel color image watermarking using CT-SVD transform on the cover image and scrambled
watermark. Singular values of the cover image are modified to embed the scrambled logo. Algorithm presented involves semi-
blind watermark extraction which avoids the need for original image during extraction process. Our watermarking system gives
good imperceptibility and robustness against attacks.
B. Paper Organization
The paper is organized as follows: CT, SVD and Arnold transform are explained in Section II. System architecture and
proposed watermark embedding and extraction algorithm are presented in Section III. Experimental results and analysis are
given in Section IV. Finally, the paper is concluded in Section V.
II. PRELIMINARIES
A. Contourlet Transform (CT)
CT is a directional multiresolution analysis framework composed of contour segments. It first uses a wavelet-like transform
for edge detection and then local directional transform for contour segment detection [5]. CT makes use of a combination of
Directional Filter Banks (DFB) and Laplacian Pyramid (LP). LP decomposes input image into low frequency coarse image and
bandpass image. Bandpass images from LP are fed into DFB so that directional information can be captured. LP is applied
iteratively to the coarse image generated at each level, to provide multiscale decomposition. Thus, CT decomposes images into
directional subbands at multiple scales.
Consider CT decomposition of Barbara image of level [2,2,2] as shown in fig.1. There are 3 levels of pyramidal
decomposition that generate a coarse image and bandpass image at each level. Bandpass image is fed to DFB to generate
directional subbands. The number of subbands generated by directional decomposition at each pyramidal level (from coarse to
fine) are: 4, 4, 4 respectively.
Figure 1. CT decomposition level [2,2,2] of Barbara
Watermark is embedded in the directional subband of bandpass image generated by DFB decomposition stage as it gives
optimum imperceptibility. Multi-level decomposition helps to increase robustness.
B. Singular Value Decomposition (SVD)
SVD is a linear algebra technique which can be defined as follows:
Any M x N (M > N) real matrix A, can be written as -
A =USVT
(1)
Where U and V are orthogonal matrices of dimensions M x M and N x N respectively, containing singular vectors and S is
an M x N matrix with the diagonal elements si representing the singular values of A. S has the structure as follows:

_______________________________________________________________________________________________________
S =
S
0
where S =
s 0 … 0
0 s … 0
0 0 … s
(2)
Singular values generated are in increasing order with s1 having highest magnitude. Original matrix can be reconstructed
using u, v and the singular values. This is called SVD reconstruction. Random perturbations in matrix cause very small changes
in singular values. This property is used in the field of watermarking. Singular values are modified to embed the watermark. Any
changes in the form of image processing attacks cause very less distortion to the watermark. Thus, SVD gives good robustness.
C. Arnold Transform
Watermark is scrambled using Arnold transform to ensure its security. It is a simple chaotic method. An image is hit with a
transformation that apparently randomizes the original organization of the pixels. On iterating a number of times, the original
image reappears. Arnold transform is given in (3):
(x',y') → (2x + y, x + y) mod N (3)
Where (x,y) is the original pixel, N is the width or height of the image and (x ', y') is the scrambled pixel.
.......
Logo Logo1 Logo2 Logo3 Logo4 Logo46 Logo47 Logo48
Figure 2. Arnold transform applied to logo
In fig.2, Arnold transform is applied to original logo. Pixels are randomized in subsequent iterations as shown. In 48th
iteration, the original logo reappears. Any one logo can be selected as the secret key. To recover a meaningful logo from the
watermark extracted, this key is required. Thus, watermark security is ensured as secret key is known only to the owner and
legitimate users.
III. SYSTEM ARCHITECTURE
The proposed method embeds a color watermark logo in a color cover image. Watermark embedding process as shown in
fig.3(a), starts by splitting the cover image into red, green and blue channels. CT level-2 is applied to the blue channel, followed
by SVD of the directional subband from level 1 of directional decomposition. For CT, ‘9-7’ filter is used in the LP stage and
‘pkva’ filter is used for directional decomposition. ‘9-7’ biorthogonal filter is chosen as it provides best result for images, partly
because it is linear phase and is close to being orthogonal [5]. We use blue channel for watermarking because human eye is least
sensitive to blue channel. Color logo is split into its respective color channels, followed by Arnold transform applied to the blue
channel. Any one output is selected as secret key. CT-SVD of this is taken to give singular values. Singular values of the cover
image are modified as per that of the logo. This is followed by SVD reconstruction and inverse CT and merging of the color
channels to produce color watermarked image.
(a)

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(b)
Figure 3. System Architecture (a) Watermark Embedding (b) Watermark Extraction
Watermark extraction process as shown in fig.3(b) involves splitting the color channels of the watermarked image, followed
by applying CT level-2 to blue channel. SVD of selected subband gives modified singular values, from which singular values of
the watermark can be extracted. Then, SVD reconstruction and inverse CT gives an unintelligible logo. To extract a meaningful
logo, secret key is applied, known to authorized user only. All color channels are merged to give the watermark logo.
A. Watermark Embedding Algorithm
Steps are as follows:
1) Apply level-2 CT to blue channel to obtain bandpass subband coefficients. We select one directional subband from
level 1 of directional decomposition for watermark embedding.
2) Apply SVD to the subband coefficients to obtain orthogonal matrices u, v and singular values s.
3) Apply Arnold transform to blue channel of watermark to generate randomized logo and select any one logo as the
secret key.
4) Apply level-2 CT to the selected logo to obtain bandpass subband coefficients. We select one directional subband from
level 2 of directional decomposition for embedding into the cover image.
5) Apply SVD to the above to obtain orthogonal matrices - uw, vw and singular values - sw.
6) Singular values of cover image are modified according to singular values of logo.
s' = α * sw (4)
Where α is Watermark embedding strength.
7) Reconstruct image using modified s', u and v values from step 3. This is SVD Reconstruction.
8) Take inverse CT of the above to obtain watermarked blue channel.
9) Merge all color channels to give the watermarked image.
B. Watermark Extraction Algorithm
Steps are as follows:
1) Apply level-2 CT to blue channel of cover image to obtain bandpass subband coefficients. Consider the selected subband
for watermark extraction.
2) Apply SVD to the subband coefficients to obtain orthogonal matrices u, v and singular values s.
3) Recover singular values of logo as shown in Equation 5:
sw = s' / α (5)
4) Reconstruct logo image using above sw and uw and vw values from step 5 of embedding phase. This is SVD
Reconstruction.
5) Take inverse CT of above.
6) We obtain a random image as output.
7) Apply Arnold transform to generate meaningful logo from random image by applying the secret key. This secret key is
known only to a legitimate user.
8) We obtain meaningful blue channel of watermark logo.
9) Merge all color channels obtained after extraction process to retrieve the embedded watermark.
10) The extracted watermark can be used to prove copyright of the digital image.
IV. RESULT AND ANALYSIS
In this section, experimental results of the proposed method are presented. Our system is implemented using MATLAB
R2010a. Contourlet toolbox is needed for computing Contourlet Transform which can be obtained from MATLAB Central
website.

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Watermarking algorithms are usually evaluated with respect to two metrics: Imperceptibility and Robustness. The parameters
used to judge imperceptibility and robustness are Peak Signal to Noise Ratio (PSNR) and Correlation Coefficient (CC)
respectively.
Imperceptibility: Imperceptibility means that the embedded watermark should not distort the visual quality of the image.
Watermarked image should appear similar to the original image and watermark should be invisible. PSNR is the ratio between
the maximum possible power of signal to the power of distorting noise. PSNR in decibels (dB) is given below in (6):
PSNR(dB) = 10 ∗ log (
∗ ∗
∑ ∑ (| |)
) (6)
Where Iij: Original Image, Wij: Watermarked image, x*y: Image size. PSNR value of above 35db is within acceptable levels,
i.e. quality of image representation is not affected.
Robustness: Robustness is a measure of the ability of the watermark to withstand attacks, both intentional and accidental
image processing attacks. CC measures similarity between the original watermark and the watermark extracted from the attacked
image. . CC may take values between 0 and 1. CC of about 0.7 or above is considered acceptable.
CC =
∑ ∑ ( , )∗ ′( , )
∑ ∑ ( , )
(7)
Where w and w' are original and extracted watermarks respectively.
We test the performance of two watermarking systems - DWT-SVD system and proposed CT-SVD system by using test
images of size 512x512 - Baboon, Peacock, Barbara and Mahal in fig.4 as cover image and 256x256 Lena image in fig.5 as
watermark logo. We embed watermark into each test image successively. Extracted watermark in the absence of attack gives CC
value equal to 1 for CT-SVD system.
Figure 4. Test images (a)Baboon (b)Peacock (c)Barbara (d)Mahal
Figure 5. Lena
Table 1 gives PSNR values of the watermarked image in the absence of attack using four cover images and Lena logo as
watermark.
Table 1. PSNR values of Watermarked Image
Sr.No.
Cover
Image
DWT-
SVD
CT-SVD
1 Baboon 29.05 53.83
2 Peacock 22.58 43.63
3 Barbara 34.75 31.34
4 Mahal 28.9 37.91
Table 2. CC values of Watermark during attacks

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Attacks
CC
Baboon Peacock Barbara Mahal
DWT-
SVD
CT-
SVD
DWT-
SVD
CT-
SVD
DWT-
SVD
CT-
SVD
DWT-
SVD
CT-
SVD
Salt & Pepper Noise 0.86 0.9998 0.81 0.9975 0.87 0.997 0.88 0.9971
Gaussian Noise 0.83 0.9825 0.88 0.9701 0.89 0.9413 0.88 0.9493
Mean Filter 3*3 0.86 0.9948 0.84 0.9964 0.88 0.9971 0.89 0.9963
Mean Filter 5*5 0.86 0.9843 0.87 0.9859 0.88 0.987 0.89 0.9865
Median Filter 3*3 0.88 0.9972 0.82 0.9979 0.87 0.9992 0.89 0.9981
Median Filter 5*5 0.88 0.9892 0.83 0.9875 0.86 0.9956 0.89 0.992
Gaussian Blur 3*3 0.87 0.9993 0.83 0.9996 0.88 0.9999 0.89 0.9994
Gaussian Blur 5*5 0.86 0.9993 0.84 0.9996 0.88 0.9999 0.89 0.9994
Contrast Stretching 0.86 0.998 0.81 0.9945 0.88 0.9934 0.88 0.9952
Histogram Equalization 0.84 0.9963 0.87 0.9648 0.88 0.9828 0.88 0.9734
JPEG Compression 0.86 0.999 0.84 0.9932 0.87 0.9984 0.88 0.9924
Cropping 0.88 0.9997 0.83 0.9997 0.87 0.999 0.87 0.9994
Table 2 gives CC values of watermark using DWT-SVD and CT-SVD systems. The attacks used are Salt and Pepper noise of
density 0.01, Gaussian noise of variance 0.1, Mean, Median and Gaussian filters of kernel sizes 3x3 and 5x5, Contrast stretching
of 30%, Histogram Equalization, JPEG compression and cropping attack where 1/4th
of the pixels are removed.
After analyzing the PSNR and CC values from tables, we observe the following points:
1) Imperceptibility of watermark is better in our system as we can observe from table 1 than DWT-SVD system for all
three cover images other than for Barbara image. For Barbara image, the observed value is greater than 30 dB.
2) CT-SVD gives better robustness than DWT-SVD during salt and pepper noise and Gaussian noise.
3) During all three types of filtering using kernel sizes 3x3 and 5x5, CC values are higher in CT-SVD system than DWT-
SVD system.
4) During contrast stretching, histogram equalization, JPEG compression and cropping, observed CC values are greater in
CT-SVD system compared to DWT-SVD system.
5) CC values of extracted watermark are closer to 1 in CT-SVD system for each type of attack. Thus, proposed system
gives very high level of robustness against image processing attacks and especially, cropping attack which is considered
to be the most dangerous form of attack.
V. CONCLUSION
A semi-blind color image watermarking algorithm based on CT-SVD and Arnold transform is presented in this paper.
CT-SVD is applied to both the host image as well as the watermark. Watermark is first scrambled using Arnold transform before
being used. Resultant singular values of host image are replaced with modified singular values of watermark. In the extraction
procedure, various image processing attacks are used to test the robustness of the presented algorithms. We compared our
system’s performance individually as well as with a DWT-SVD based system. Following conclusion can be drawn:
(1) Our system provides better watermarked image quality, thereby giving better imperceptibility than DWT-SVD based
system.
(2) System showed high robustness against all attacks and gave good resistance to cropping attack.
(3) Our system is semi-blind. Thus, there is no need for original image during watermark extraction. This feature allows it
to be used in the field of copyright protection.
(4) Arnold transform used for scrambling of watermark pixels gives a randomized image which acts as a secret key. This
key is needed for watermark extraction. Thus, watermark can be obtained only by a legitimate user only.
(5) SVD decomposes image into very few singular values. This makes computation simple and compact.
(6) Both cover image and watermark are color images.

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CT guarantees good imperceptibility of the watermark by giving efficient multi-level decomposition of both cover image
and watermark. Singular values generated by SVD show good stability during changes, thus giving good robustness during
common image processing attacks as well as cropping and JPEG compression. SVD allows for a larger watermark, thereby
increasing watermark capacity. SVD helps to implement a simple system. Arnold transform provides for watermark security.
Semi-blind extraction makes extraction possible using only the watermark information and watermarked image. Color
watermarking allows our system to be used in real-world applications. Thus, our system is simple, efficient and completely
secure.
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[8] Qiang Li, Chun Y., Yu-Zhou Z., “Adaptive DWT-SVD Domain Image Watermarking Using Human Visual Model”, IEEE
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