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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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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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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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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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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Vol. 9, No. 6, 2011
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[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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