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Steganography based on Contourlet Transform

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					                                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                        Vol. 9, No. 6, 2011

                    Steganography based on Contourlet Transform

                  Sushil Kumar1                                                               S.K.Muttoo2
           Department of Mathematics,                                               Department of Computer Science,
       Rajdhani college,University of Delhi,                                              University of Delhi,
                New Delhi, India                                                              Delhi, India
        e-mail- skazad@rajdhani.du.ac.in                                             e-mail- skmuttoo@cs.du.ac.in

Abstract— In this paper we present a steganographic technique              The image steganography in the frequency domain is one of
based on Contourlet transform (CTT). The proposed technique                the growing research areas in recent years because of its
uses a self-synchronizing variable length code to encode the               capability of providing robustness to attacks and posing a real
original message which has been proved better than Huffman                 challenge to anybody trying to discover and decode hidden
code in terms of power energy. The secret data then is embedded
in the high frequency sub-bands obtained by applying CTT to the
                                                                           messages.. Wavelet transforms are most widely-used tool in
cover-image using variable LSB method and Thresholding                     signal processing due to its inherent multi-resolution
method. The Contourlet transform is more suitable for data                 representation akin to the operation of the human visual
hiding applications as Contourlet gives more edges. Moreover               system. However, the research on applying the wavelets to
more data can be hidden in the high frequency regions without              data hiding techniques is still too weak, only a few
perceptibility distorting the original image. Experimental results         publications deal with this topic at present. This paper focuses
show that the original message and original image both can be              on this challenging research topic.
recovered form stego-image accurately. The results are compared            In medical profession and law enforcement fields, it is not
with existing steganographic techniques [10-12] based on Discrete          only the hiding and recovery of message required perfectly but
Wavelet Transform (DWT) and Discrete Slantlet Transform
(SLT). It is known that SLT is a better candidate for signal
                                                                           also the recovery of original image is important for the
compression compared to the DWT based scheme and it can                    examination. Various distortionless (or invertible or lossless)
provide better time localization. Experimental results have                data hiding methods have been proposed and analyzed, e.g.,
confirmed CTT based method gives better imperceptibility and               [3, 5, 6, 13-16]. Xuan et al.[14] have presented distortionless
better embedding rate than the DWT.                                        data hiding based integer wavelet transform. Celik et al. [3]
                                                                           have proposed a reversible data hiding method based on the
Keywords- Steganography, DWT, SLT, CTT, LSB, PSNR                          idea of first compressing portion of the signal that are
                                                                           susceptible to embedding distortion and then transmitting it as
    I. INTRODUCTION                                                        part of embedded payload. Hsiag-Cheh Huang et al. [5] have
                                                                           proposed scheme for protecting and recovering sensitive
In the era of new generation technology, the Internet and                  information by mosaikking the region with confidential
multimedia applications have reached places where other                    information and then delivering the modified image to the
communication or transport means are still at its infancy. It is           public. The person who has the secret key can only to view the
now convenient for people to transmit mass data in the form of             confidential information. In this paper, we propose a
text, images, audio and video through internet. However,                   steganographic technique based on Discrete Contourlet
there is always a threat from the hackers of stealing the                  Transform (CTT). It is well known that SLT offers superior
valuable information. The organizations such as banking,                   compression performance compared to the conventional DCT
commerce, diplomacy and medicine, private communications                   and the DWT based approaches [7]. It has been observed that
are essential. Security is an important issue in the information           SLT can be implemented employing filters of shorter supports
technology now-a-days. Modern cryptography provides a                      and maintaining the orthogonality and an octave-band
variety of mathematical tools for protecting privacy and                   characteristic, with two zero moments.
security that extend far beyond the ancient art of encrypting
messages. However, for carrying out confidential                           The rest of the paper is organized as follows: Section 2
communication over public networks, simply concealing the                  presents a review of Contourlet transform. Section 3 presents
contents of a message using cryptography is found to be                    the proposed algorithms. Performance evaluation is presented
inadequate as it can still raise suspicion to eavesdroppers.               in Section 4. Conclusions and future scope are presented in
People have found the solution to this problem in                          Section 5.
Steganography. Steganography deals with a host of techniques
that conceal the existence of a hidden communication. The
secret message to be transmitted is camouflaged in a carrier
media so that its detection becomes difficult.




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                                                                                                      ISSN 1947-5500
                                                                (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                          Vol. 9, No. 6, 2011
    II. CONTOURLET TRANSFORM                                                We can extract important coefficients and edge directional
                                                                            information by contourlet transform, as shown in the figure
                                                                            2.2.3. The figure 2.2.4 is the level 2 decompositon of image
In image compression, the Wavelet transforms produces much                  ‘aeroplane.tif’.
less blocking artifacts than the DCT. They are adopted in
JPEG2000. They also perform well in image de-noising.
                                                                                            LL                LH1                       LH2


However, 2D wavelet transform is, intrinsically, a tensor-
product implementation of the 1D wavelet transform, and it
provides local frequency representation of image regions over
a range of spatial scales, and it does not represent 2D
singularities effectively. Therefore it does not work well in
retaining the directional edges in the image, and it is not
sufficient in representing the contours not horizontally or                                H1L                H1H1                      H1H2
vertically.
The Contourlet transform (CTT) is a true 2-D geometrical
image based transform, which is recently introduced by M.N.
Do and M. Vetterli [5]. It overcomes the difficulty in
exploring the geometry in digital images due to the discrete
nature of the image data. It possesses the important properties
of directionality and anisotropy which wavelet do not
possesses.. It can represent a smooth contour with fewer                                   H2L                H2H1                      H2H2
coefficients compared with wavelets ( figure 2.2.1).

The CTT is based on a double filter bank structure by
combining the Laplacian Pyramid (LP) with a directional filter
bank (DFB). The Laplacian pyramid (LP) is used to
decompose an image into a number of radial subabnds and the
directional filter bank ( DFB) decompose each LP details
subband into a number of directional subbands. The required
number of directions can be specified by the user.                                Figure 2.2.3: low sub-band and directional sub-bands
Multiresolution flexibility, local and directional image                          Of level 2 decompositon of image ‘zoneplate.png’
expansion in the contourlet image representation, allows for
easy sub-band processing. In all, Contourlet has the properties
Multiresolution ,i.e, representing images from a coarse level to
fine-resolution level, Localization , i.e., basis elements can be
localized in both the spatial and the frequency domains,
Critical sampling ,i.e., representation form a basis, or a frame
with small redundancy, Directionality, i.e., representation of
basis elements oriented at variety of directions and
Anisotropy, i.e., capturing of smooth contours in images. The
first three properties are also provided by separable wavelets.
The analysis part of this type of filter is shown figure 2.2.2.



                                                                                  Figure 2.2.2: Respective frequency plane decompositon

                                                                            Contourlet transform has the advantages of high capacity than
                                                                            the wavelet and wavelet-like transform ( that have 3 high
                                                                            frequency subbands whereas we obtain 4 subbands in
                                                                            contourlet.

                                                                                III. PROPOSED METHOD
        Figure 2.2.1: Wavelet versus Contoulet: illustrating
the successive refinement by the two systems near a smooth contour,             The proposed steganographic technique embeds secret
   which is shown as a thick curve separating two smooth regions                data obtained after encoding by T-codes into the 4
                                                                                subbands for horizontal and vertical directions obtained




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                                                                                                       ISSN 1947-5500
                                                                 (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                           Vol. 9, No. 6, 2011
    from the cover image after applying 2-level of CTT.                      To recover the original image, each high frequency coefficient
    Preprocessing is performed prior to data embedding in                    can be restored to its original value by applying the following
    each scheme, viz., LSB and Thresholding, to ensure that                  formula:
    no overflow/underflow takes place. The stego-image
    carrying hidden message is obtained after inverse CTT.                                       x’ / b if -2T < x’ < 2T
    Figure 4.2 is the flowchart of the proposed embedding                        x=             x ‘- T    if x’ ≥ 2 T
    data hiding. Figure 4.3 is the flowchart for hidden data                                    x’ + T-1 if x’ ≤ -2T +1
    extraction and original cover image recovery.

                              Contourlet coefficients
                                                                             We further note that the best known variable-length codes
                                                                             (VLC) are the huffman codes. They are easy to construct for
                                                                             optimum efficiency if source statistics are known. But, if used
                                                                             in serial communication, a loss of synchronization often
                                                                             results in a complex resynchronization process whose length
                                                                             and outcome are difficult to predict.When corruption occurs in
                                                                             a stream of data which is coded, the decoder can lose track of
                                                                             where codeword boundaries are located in the data stream.
                                                                             Thus, it is required to choose codes which will self-
                                                                             synchronize as a result of the normal decoding process. M.R.
                                                                             Titchner [18] proposed T-codes which are families of VLCs
                                                                             that exhibit extraordinarily strong tendency towards self-
                                                                             synchronization.




Figure 2.2.4: Contourlet decomposition of level 2 of image: new3.tif

The basic idea of LSB embedding is to embed the message bit
at the rightmost bits of pixel value so that the embedding
method does not affect the original pixel value greatly. The
formula for the embedding is as follows:
             x’ = x - x mod 2k + b
 where k is the number of LSBs to be substituted.
The extraction of message from the high frequency
coefficients is given as:
          b = x mod 2k

Threshold embedding method for the lossless data hiding is
given by Xuan et al. [11]. We predefine a threshold value. To
embed data into a high frequency coefficient of sub-band HH,
LH or HL, the absolute value of the coefficient is compared
with T. If the absolute value is less than the threshold, the
coefficient is doubles and message bit is added to the LSB. No
message bit is embedded otherwise, however, the coefficients
                                                                             The proposed Embedding algorithm can be summarized into 4
are modified as follows:
                                                                             steps:
                   2*x + b if |x| < T
   x’ =            x+T       if x ≥ T                                        Embedding algorithm :
                   x – (T-1) if x ≤ -T

where T is the threshold value, b is the message bit, x is the
high frequency coefficient and x’ is the corresponding                       Step0. We first obtain the secret data by applying best T-codes
modified frequency coefficients.                                             as a source encoder to the given input text/message.




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                                                                                                        ISSN 1947-5500
                                                            (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                      Vol. 9, No. 6, 2011
Step1: We apply pre-processing to prevent possible                       The imperceptibility is better in case of Slantlet transform than
“overflow” during embedding ( e.g., replacing the grayscale              others, however , acceptable in case of Contourlet transform
values 0 to 255 into 15 to 240).                                         too. The algorithm does not need original image for recovering
Step2. Then we consider 8-bit greyscale image and decompose              the secret data. The use of T-codes provides self-
it into 5 sub-bands: one lowpass subaband and 4 subbands for             synchronization in the decoding stage. Experimental results
horizontal and vertical directions by applying 2-level CTT.              prove that the proposed algorithm is better than the earlier
Step3. We then embed data in the two horizontal and two                  algorithms based on DWT. The SLT results are better than
vertical sub-bands in case of CTT using two methods, LSB                 even CTT, but the embedding capacity is more in CTT.
method and Thresholding method.
Step4. Finally, we obtain stego-image by taking the inverse
slantlet transform/ inverse CTT of the modified image of                 Table 5.3 Comparison of proposed algorithm based on Contourlet
step3.                                                                   with wavelet and Slantlet based method , using PSNR


Extraction algorithm :                                                        Images        Wavelet        Slantlet      Proposed
Step 4. Apply 2-level CTT to the stego image                                               Method (       Method (         Method
                                                                                             secret         secret         (CTT)
Step5. Extract secret data from the four horizontal and vertical
                                                                                           bits=154)      bits=154)       ( secret
sub-bands of CTT, by applying LSB/ thresholding techniques.
                                                                                                                         bits=241)
Step 6. Extract embedded secret data and
                                                                             new1.tif       26.6451        51.9163        43.6949
Step7. Recover the original image by reverse operation of the              (aeroplane)
embedding.                                                                   new2.tif       26.2758        59.4998        47.5772
Step8. Obtain the original message by T-decoding the secret                   (lena)
data, with the help of encoding key.                                         new3.tif       22.1978        47.6719        47.5818
                                                                            (guerilla )
                                                                             new5.tif       26.7111        59.9642        53.7938
                                                                              (boat)
                                                                             new7.tif       26.9762        54.3398        47.2034
                                                                            (peppers)
                                                                             new9.tif       22.8241        59.4137        46.8714
                                                                          (Cameraman)
                                                                            new11.tif       25.3919        54.5226        43.6528
                                                                             (Image)
                                                                           Barbara.png      31.1244        54.0462        50.2019
                                                                             pool.bmp       27.6686        59.4805        50.0180
                                                                           lena256.bmp      28.8096        59.4296        53.1674
                                                                             Tulips.jpg     27.7425        60.2497        47.9466


                                                                             V. CONCLUSIONS

                                                                         The present paper proposed a steganographic technique based
                                                                         on Discrete Contourlet Transform. A self-synchronizing
                                                                         variable length code, T-codes are used for encoding the
                                                                         original message. It has two advantages: to compress the
                                                                         original message and to obtain the message correctly at
                                                                         decoding stage. Two different embedding techniques LSB
                                                                         embedding and Threshold embedding have been used for
                                                                         embedding the secret message in the cover object. The results
    IV. EXPERIMENTAL RESULTS
                                                                         are compared with the data hiding techniques based on
    To evaluate the performance of the proposed data hiding              Wavelet and Slantlet transforms. The experimental results
    algorithm, we have used 128 x128 and 256 x256 gray                   show better imperceptibility than the DWT based method.
    scale images . Simulations were done using MATLAB ver                Since there is no artifact in the stego-image, the original image
    7.0 and Window XP. Some of the stego images obtained                 can be distortionlessly recovered from the stego-image after
    from the implementation of proposed algorithm for CTT                the hidden data has been been extracted. The payload in the
    are shown in Fig.5.1 and original and reconstructed                  proposed embedding techniques is also the better than the
    images are shown in Fig. 5.2.                                        DWT technique.




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                                                                                                      ISSN 1947-5500
                                                                      (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                Vol. 9, No. 6, 2011
            stego-image                         stego-image




                                                                                               Original image           Reconstructed image




           stego-image                            stego-image




                                                                                                Original image           Reconstructed image




           stego-image




                                                                                               Original image           Reconstructed image



Figure 5.1 : Stego images of proposed algorithm
              based on CTT.


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                                                                                   Figure 5.2 : original images and reconstructed
                                                                                     images of proposed algorithm based on CTT.

                                                                                   [7] NI Z., Shi Y.Q., Ansari N., Su Wei, Sun Q. and Lin X.( 2004), Robust
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                                                                                                                   ISSN 1947-5500
                                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                 Vol. 9, No. 6, 2011
     Symposium on Intelligence Information Processing and Trusted                   [20] Do M.N. and Vetterli M. (2005), The Contourlet transform: An efficient
     Computing, IPTC 2010, Huanggang, China, Oct. 28-29, 2010                            directional multiresolution image representation , IEEE Trans. On Image
[12] Sushil Kumar, S.K. Mutttoo, Image Steganography based on                            Processing, 14(12), 2091-2106.
     Complex Double Dual Tree Wavelet Transform, MINES 2010, Nanjing,               [21] Navas K.A., Mathew N.M., and Sasikumar M. (2009), Contourlet based
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[13]Tian J. (2003), High capacity reversible data embedding and content
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     Signal Processing, April 6-10, vol. 3, pp. 517-520.                            1
[14] Xuan G., Zhu J., Chen J., Shi Y.Q., Ni Z, and Su W.(2002),
                                                                                     Sushil Kumar is associate professor in the Department of
     Distortionless data hiding based on integer wavelet transform, IEEE            Mathematics, Rajdhani College, University of Delhi, New
     Electronics Letters, Dec., pp. 1646-1648                                       Delhi. He has been teaching graduate and under-graduate
[15] Xuan G.,.Shi Y.Q., Yang C., Zhang Y., Zou D. and Chai P. (2002),               students for last 30 years. He is the author of three text books:
     Lossless Data Hiding using integer wavelet transform, and threshold            ‘Computer fundamental and Software’, ‘Scientific and
     embedding technique, in Proceeding of IEEE International Workshop on
     Mutimedia Signal Processing, Marriott Beach Resort ST. Thomas, US              Statistical computations using Fortran 77’ and ‘Theory of
     Virgin Islands, Dec. 9-11.                                                     Computations’. His areas of research include Harmonic
[16] Xuan G., Yang C., Zhen Y., Shi Y.Q., Ni Z.(2004), Reversible data              analysis, Fuzzy topology, Parallel Computing, Image
     hiding based on wavelet spread spectrum, IEEE 6th Workshop on                  Processing, Information Security.
     Multimedia Signal Processing, 211-214.
[17] Titchener, M.R. (1996), Generalised T-codes: extended construction             2
                                                                                        S.K.Muttoo is associate professor in the Department of
     algorithm for self- synchronization codes, IEE Proc. Commun., Vol.
     143, No.3, pp. 122-128.
                                                                                        Computer Science, University of Delhi, Delhi. His research
[18] Ulrich G. (1998), Robust Source Coding with Generalised T-codes, a
                                                                                        areas include information security, computer graphic and
     thesis submitted in the University of Auckland.                                    image-processing.
[19] Yu L. and Sun S.,(2000), Slantlet transform based image fingerprints,
     Communication, Netwirk and information security, CNIS.




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