data hiding using slantlet fusion method and t-codesjicis.org/papers of jicis/volume 3 issue...

ISSN: 2413 – 6999 Journal of Information, Communication, and Intelligence Systems (JICIS)

Volume 3, Issue 1, January 2017

1 All Rights Reserved © 2017 JICIS

Abstract— This paper presents the study of steganography

algorithm based on Slantlet fusion method using a

self-synchronizing variable length encoder, viz., T-codes. The

Slantlet fusion method is the high bit rate data hiding scheme

based on Slantlet Transorm. In this method, the fusion process

takes place between the SLT of the secret data and the SLT of the

cover image. The secret data is obtained by the application of

SSVLC, T-codes to the original data. The proposed algorithm is

compared with the Wavelet fusion method using the metrics

PSNR, PSNRE, PSNRY, CQM, SSIM and KLdiv respectively. It is

found that the proposed scheme is highly secure and efficient in

comparison to the state of the art works.

Index Terms— DWT; SLT; PSNR; PSNRY; CQM; SSIM;

KLDiv

I. INTRODUCTION

Data Hiding is the art and science of hiding information into

a carrier media such as text, image, audio, video, graph etc. so

that the existence of hidden information is concealed and its

detection becomes difficult. Steganography is one of the

disciplines of data hiding. A steganography scheme, which is

an art of covert communication, hides the secret message in

the carrier using an embedding procedure in such a way that it

is imperceptible to a human observer. The Six basic

characteristic of data hiding and their requirements are

represented as follows[5]:

( H= ‘High’ , L= ‘Low’, R=’Reasonable’)

Out of the above, the three major requirements of

steganography are imperceptibility, high embedding capacity,

and robustness.

Dr. Sushil Kumar, Department of Mathematics, Rajdhani College,

University of Delhi, (e-mail:[email protected]).New Delhi, India,

+91-9711234705(m).

Out of the two popular types of embedding schemes: spatial

domain embedding and transform domain embedding, the

latter scheme have been proved more robust against various

attacks.

Amongst many carriers, image file is found to be a most

popular carrier object due to availability of high degree of

redundancy and its confined ability of human visual system.

There are a number of steganography algorithms for digital

images based on different transforms such as DCT, Walsh

transform, Discrete Wavelet transform (DWT), and Complex

Wavelet Transforms (CWTs).

In this paper, we explore the applications of Slantlet

Transform (SLT) in steganography. The SLT, introduced by

Ivan W. Selesnick [4], is based on an orthogonal filterbank for

the discrete wavelet transform with two zero moments, where

the filters, being not the products (as shown in Fig. 1.1(b)), are

of shorter support than those on the iterated D2 filterbank tree.

It possesses improved time-localization and smoothness

properties and can be efficiently implemented like an iterated

DWT filterbank.

(a) (b)

Figure 1.1: (a) Two-scale iterated D2 filterbank, (b) Two-scale Slantlet

filterbank.

Data Hiding using Slantlet Fusion Method and

T-Codes

Dr. Sushil Kumar

Imperceptibility Security Capacity

H H H

Undetectability Robustness Complexity

H R L



2

All Rights Reserved © 2017 JICIS

(a)

(b)

(c)

Figure 1.2: (a) 1-level SLT image of “Tooth1.jpg” and (b) 2-level SLT image of

„lena.bmp‟ (c) 2-level SLT decomposition of image

The Fig. 1.2 (a) shows the 1-level decomposition of image

„Tooth1.jpg‟ by Slantlet transform and the Fig. 1.2 (b) shows

the 2-level decomposition of image „Lena.jpg‟ by Slantlet

transform. The 2-D decomposition of the image by SLT into

low and high subbands are illustrated in the Figure 1.2 (c).

Unlike the Wavelet, HH subband in the SLT has decomposition

into HH1, HH2, HH3 and HH4.

Panda and Meher [3] have observed that signal compression

using SLT scheme has better performance that the DWT

based compression scheme. S. Kumar and Muttoo [6] have

presented adata hiding technique based on SLT using the

LSB and thresholding embedding techniues and compared it

with DWT and Contourlet (CTT) based scheme. They

observed that their SLT based LSB (thresholding) algorithm

is better than the DWT and CTT schemes in terms of PSNR.

They also proposed Varying LSB scheme based on SLT [2]

and observed that their scheme provides better

imperceptibility and better run-time than the Haar based

scheme.

In this paper we present the fusion scheme based on SLT for

color images and compare it with the corresponding DWT

based scheme. In section II, we summarize the embedding and

extraction model of steganography. In section III, the

proposed embedding and extraction schemes are given. The

experimental results of the proposed algorithm are analyzed

in section IV.

II. EMBEDDING AND EXTRACTION METHOD

The process of embedding of the secret data in the frequency

coefficients of middle and high subbands obtained from the

cover image using the 2-D SLT is shown in Fig. 2.1(a). It

consists of the following steps:

1. Encoding the message with T-codes resulting into the

secret message,

2. Decomposing the cover image with 2-D SLT resulting

into low and high subbands, HH, LH, HL, L,

respectively.

3. Applying 8-bit quantization to frequency coefficients of

high subbands.

4. Embedding the secret message into the selected location

of frequency coefficients of high subbands using the

respective techniques.

(a)




(b)

Figure 2.1: (a) The Block diagram of the embedding process, (b) The Block

diagram of the extraction process

The extraction is the reverse process illustrated in Fig. 2.1(b).

One of the major problems in the digital communication through

different channel is the Loss of synchronization. During the

communication through channel, the information usually goes

through compression JPEG standards and others which use

variable length coding. During this communication through

channel, a single bit error can cause the decoder to lose

synchronization. Titchner [9] introduced new VLCs, called

T-codes that have added self-synchronizing ability.

According to Ulrich [10], T-codes re-synchronize within one

to three code -words. Manoharan [1] proposed the use of

T-codes to encode messages prior to embedding the messages

in the cover media. The extracted messages need to he decoded

before use. According to him, this system will be more tolerant

to media transformations that result in some bit losses or bit

inversions in the hidden message.

III. SLT BASED FUSION METHOD

In this section, the proposed image steganographic embeding

and extraction algorithms based SLT using fusion method are

summarized as follows:

Algo 3.1: Embedding

………………………………………..

Input: Image, alpha (pre-processing parameter), no. of

embedding, data to be embedded

Output: Stego image

Step 1. Normalize the color image and choose alpha

(preferably 0.05) and reconstruct pixels to lie in

interval [alpha, 1-alpha].

Step 2. Apply 2-level of SLT to obtain 3 high subbands and

for each color plane of image and one low

frequency subband.

Step 3. Obtain the binary form of the secret data to be

embedded.

Step 4. Generate pseudorandom permutation, using a

stego-key, of the size of a high frequency subband.

Step 5. Enter the number of times the secret message to be

embedded

Step 6. Embed the message by adding or subtracting the

alpha in the randomized coefficients of high

frequency subbands according to message bit is 1

or 0.

Step 7. Apply inverse of 2-D SLT on each color plane

separately.

Step 8. Obtain the stego image by normalizing the

resultant image.

………………………………………..

In the step 3, the secret data is obtained from the original

message by applying the SSVLC, T-codes. In step 5, one can

choose the number of times to be 10. In step 6, (which is the

fusion of the secret binary bits with the selected location of high

sub-band value: x‟ = x +(-) alpha* x), alpha can be any value

between 0 and 1, usually taken as 0.05.

Algo 3.2: Extraction

………………………………………..

Input: Stego image, original image, alpha, length of

embedded message, no. of embedding, stego-key

Output: Original message

Step 1. Apply 2-D SLT on each color plane of the

stego-image.

Step 2. Using the pseudorandom permutation based on the

stego-key , Obtain the selected embedded

coefficients.

Step 3. Obtain the secret message bit ‘s’ by subtracting the

transformed coefficients of original image from the

transformed stego image coefficients obtained by

using 2-D SLT.

Step 4. If the value of ‘s’ is positive, embedded bit is 1 and

the embedded bit is 0 if s is negative.

Step 5. Convert the secret message into the original

message.

………………………………………..

IV. EXPERIMENTAL RESULTS

In this section, we present the performance of the proposed

algorithm in terms of in terms of PSNR, SSIM and KLDiv.

Imperceptibility

We first summarize the results of imperceptibility in terms of

four different metrics, PSNRE, PSNRY, CQM and PSNR with

payload of 4000 bytes with alpha=0.05 and number of times

embedding done is =5in the Tables 4.1 (a) – (d).



4


Table 4.1(a): Comparison of PSNR between Haar wavelet and SLT based on

fusion method with capacity= 2000 bytes, alpha=0.05 and N=5

Image HAAR Slantlet

verona.jpg 75.557064 75.568807

C3.jpg 76.425531 76.451972

Tulips.jpg 76.507162 76.527701

Tooth1.jpg 76.067290 76.093416

New7.tif 76.167475 76.190981

New8.tif 76.112783 76.136289

New11.tif 75.610688 75.619879

New12.tif 76.524789 76.495759

Peppers.png 76.187556 76.214898

C1.png 77.331675 77.303646

C2.bmp 78.167974 75.428561

Baboo.bmp 76.821661 76.793867

Table 4.1(b): PSNRY values for Algo 3.1 based on SLT with capacity= 4000,

alpha=0.05 and No. of embedding=5

Table 4.1(c): CQM values for Algo 3.1 based on SLT with capacity= 4000,

alpha=0.05 and No. of embedding=5

Table 4.1(d): PSNRE values for Algo 3.1 and for other transforms with

capacity= 4000 (alpha=0.05, No. of times embedding done=5)

From Tables 4.1(a)-(d), it can be seen that the SLT based

Fusion method shows reasonably good imperceptibility almost

equivalent to HWT based Fusion method in terms of different

metrics defined for color images: PSNR, PSNRE, PSNRy, and

CQM.

Image PSNRY

(HAAR)

PSNRY

(SLT)

C3.jpg 31.193871 30.838038

Tooth1.jpg 31.206736 30.846488

Tooth1.jpg 31.320985 30.960045

C2.bmp 31.145258 30.798501

Baboo.bmp 31.169689 30.797895

C1.png 31.154102 30.777346

Peppers.png 31.158752 30.802512

New7.tif 31.205343 30.843205

New8.tif 31.168077 30.803366

New11.tif 31.174614 30.803799

New12.tif 31.156383 30.794555

Image CQM

(HAAR)

CQM

(SLT)

C3.jpg 26.390721 26.049582

Tulips.jpg 26.628155 26.286139

Tooth1.jpg 26.600644 26.253537

C2.bmp 26.342996 26.047007

Baboo.bmp 26.407459 26.039967

C1.png 26.386601 25.998446

Peppers.png 26.381137 26.065181

New7.tif 26.413651 26.074144

New8.tif 26.380416 26.035328

New11.tif 26.394636 26.052637

New12.tif 26.362901 26.019283

Image CDF9/7 HAAR SLT

C3.jpg 19.883235 26.390550 26.049399

Tooth1.jpg 19.653746 26.515350 26.173700

C1.png 18.924709 25.370889 25.026339

C2.bmp 19.848411 26.074336 25.734735

Baboo.bmp 18.432017 26.381020 26.039853

New7.tif 18.362459 25.287807 24.948299

New12.tif 19.046590 25.872436 25.528819

Image PSNRY

(HAAR)

PSNRY

(SLT)

C3.jpg 31.193871 30.838038

Tooth1.jpg 31.206736 30.846488

Tooth1.jpg 31.320985 30.960045

C2.bmp 31.145258 30.798501

Baboo.bmp 31.169689 30.797895

C1.png 31.154102 30.777346

Peppers.png 31.158752 30.802512

New7.tif 31.205343 30.843205

New8.tif 31.168077 30.803366

New11.tif 31.174614 30.803799

New12.tif 31.156383 30.794555




Fig. 4.1:The results of PSNR vs Payload for Fusion method using Haar and

Slantlet transforms

We have implemented the proposed Algo 2.1 using number of

test images of different formats. The embedding capacity used

varying from low 500 bytes to high 6000 bytes. Experiments

have been performed using MATLAB 7.0.

Structural similarity

Next we present the some of the results structural similalrity

using the metrics SSIM for the proposed algorithms

implemented on different image formats. The results are

summarized in Table 4.2.

Table 4.2:Comparison of SSIM values between Wavelets and Slantlet

transform based on fusion method with capacity= 4000 (alpha=0.05, No. of

times embedding done=5)

Fig. 4.2: The results of MSSIM vs Payload for Fusion method using Haar and

Slantlet transform

From the Fig. 4.2, it can be seen that performance of SLT based

fusion scheme is almost same as of Haar based fusion scheme in

terms of structural similarity.

Provable Security

In the Table 4.3, we summarize the results of provable security

using the metrics KLdiv for the proposed algorithm using

different image formats with embedding capacity 4000 bytes,

alpha=0.05 and number of times embedding done = 5.

Table 4.3:Comparison of KLDiv values between Wavelets and Slantlet

transform based on fusion method with capacity= 4000 (alpha=0.05, No. of

times embedding done=5)

Image HAAR SLT

C3.jpg 0.604029 0.589851

Tooth1.jpg 0.669087 0.656311

C1.png 0.626427 0.609857

C2.bmp 0.475631 0.460202

Baboo.bmp 0.787558 0.776552

New7.tif 0.599148 0.585937

New12.tif 0.516617 0.501535

Image HAAR SLT

C1.png 0.002239 0.002443

Peppers.png 0.001967 0.002159

C2.bmp 0.001801 0.001740

Baboo.bmp 0.002162 0.002375

C3.jpg 0.002686 0.002944

Tulips.jpg 0.002574 0.002867

Tooth1.jpg 0.002964 0.003151

New7.tif 0.003912 0.004345

New8.tif 0.003693 0.003983

New11.tif 0.003567 0.003793

New12.tif 0.002052 0.002264



6


Fig. 4.3: The results of KLDiv for Fusion method using Haar and Slantlet

transform

It is observed that there is no difference in the performance of

Haar and SLT in terms KLDiv, so they both provide provable

security. Also, the KLDiv is observed to be independent of the

image formats for the SLT/Haar based Fusion method as can be

seen from Figure 5.3.

In Figure 4.4, the results of KLDiv for image: „Lena.jpg‟ is

shown for the proposed algorithm alongwith corresponding

Haar based Fusion method. It is observed that initially for the

bpp till 0.075 the Haar is showing better results than SLT, but

then SLT based KLDiv values shows improvement over the

Haar based KLDiv values. Anyway it is clear that in both Haar

as well as SLT based Fusion method cases Provable security is

affected as the embedding capacity is increased.

Fig. 4.4: The KLDiv vs BPP for Fusion method based on Haar and SLT using

Image: „Lena.jpg‟

V. CONCLUSION

This paper presents the study of performance of high

embedding rate steganography algorithm using the Slantet

Fusion method for color images using self-synchronizing

variable length encoder, viz., T-codes. The secret message to be

embedded is obtained from original text by applying T-codes. It

is observed Slantlet Fusion method is as good as Wavelet

fusion method when compared the results of PSNRY, CQM,

SSIM and KLDiv, but it is well known fact that SLT retain

higher percentage of energy after compression as compared to

the DWT approach. Selesnick [4] has also shown the

improvement in denoising through example. S. Kumar et al

[7][8] have also observed SLT to be a better option than the

other basic transforms.

APPENDIX (PERFORMANCE MEASURES)

The performance of the proposed technique given in the paper

is evaluated according to the widely used metrics: PSNR, SSIM

and KLDiv

(A) The Peak Signal to Noise Ratio (PSNR) for an

image of size N x N is given as follows:

PSNR = 10 log10 (cmax 2/ MSE) (dB),

MSE=(1/N*N) ∑∑ (xij – xij )2 ,

1 in normalized double

precision

range

where cmax =

255 in 8-bit unsigned integer

values

A high value of PSNR means better image quality (less

distortion), it is recorded that in grayscale images that the

human visual system (HVS) can‟t detect any distortions in

stego-images having PSNR that goes beyond 36 dB.

There exist different approaches for computing the PSNR of a

color image. According to Mathworks

(http://www.mathworks.in/help/vision/ref/psnr.html), the

PSNR for color images can be computed by first converting the

image to a color space that separates the intensity (luma)

channel, such as YCbCr and then the PSNR can be obtained

only on the luma channel, (denoted by PSNRY). The

recommendation for this approach is suggested because the

human eye is most sensitive to luma information, the Y (luma),

in YCbCr represents a weighted average of R, G and B and G is

given the most weight, again because the human eye perceives

it most easily.

Alternately, for color images with three RGB values per pixel,

the definition of PSNR is the same as for a noise free (m x n)

monochrome image, except the MSE is the sum over all

squared value differences divided by image size and by three

(http://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio).

http://www.mathworks.in/help/vision/ref/psnr.html

http://en.wikipedia.org/wiki/Color_image

http://en.wikipedia.org/wiki/RGB

http://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio




This is denoted as PSNRE in the paper.

The performance of the proposed techniques given in the thesis

is evaluated according to the widely used metrics: PSNR, SSIM

and KLDiv and Embedding efficiency.

Another simple and effective full-reference color image quality

measure (CQM) based on reversible luminance and

chrominance (YUV) color transformation and peak

signal-to-noise ratio (PSNR) measure. The CQM value is given

as:

where the CQM is composed of the weighted luminance quality

measure (PSNRY×RW) and weighted color quality measure

(PSNRU + PSNRV) ×CW) components. CW is the weight on the

human perception of the cones and RW, is the weight on the

human perception of the rods. The values of Cw and Rw are

calculated as 0.0551 and 0.9449, respectively. The notation

PSNR used for color images will mean the average value of

PSNR calculated for each of the Red, Green and Blue channels.

(B) The mean similarity measure of stego-image, F with

respect to the original image, E, given by

1 2

2 2 2 2

1 2

( ) (2 )( , )

( ) ( )

x y xy

x y x y

C CSSIM E F

C C

where µx , µy , σx, σy and σxy local statistics parameters of the two

images E and F and C1, C2 are constants used to make it finite.

The SSIM index models any distortion as a combination of three

different factors: loss of correlation, luminance distortion and

contrast distortion. The mean similarity measure MSSIM varies

in the interval [-1, 1]. The best value 1 is achieved if and only if

E=F.

(C) K. L. divergence is a measure of distance between two

probability distributions.

Let random variable C and S denote the cover image and stego

image respectively and let PC and PS represent the probability

mass functions (pmfs) of C and S, respectively. The K-L

divergence between these two pmfs, PC and PS, is defined as:

D (PC||PS) =∑g∈G [PC (g) log (PC (g)/PS (g)]

where g ∈ G ≈ { 0, 1, 2, ..., 255} is the pixel value in grayscale

images.

The stego system is considered perfectly secure in the Cachin‟s

sense if D (PC||PS) = 0. It is called ε -secure, if D (PC||PS) ≤ ε. It

is proved that there exists a perfectly secure steganographic

system .

Some of the tested images are shown in Fig. A.1

Fig. A.1 Test Images

ACKNOWLEDGMENT

The author would like to thank Professor Ivan W.

Selesnick, Polytechnic University, New York, for his

valuable 2-D Slantlet transform Matlab codes

(http://eeweb.poly.edu/iselesni/WaveletSoftware/).

REFERENCES

[1] Manhoran, S. (2003). Towards robust steganography using T-codes.

Proceedings of Video/Image Processing and Multimedia

communications.

[2] Muttoo S.K. and Sushil Kumar, “Secure image Steganography

based on Slantlet transform”, ICM2CS-09, JNU, New Delhi,

India, 2009

[3] Panda G. and Meher S.K., “An efficient approach to signal

compression using slantlet transform”, IETE Journal of Research, Vol.

46, No. 5, September, pp. 299-307, 2000.

[4] Selesnick Ivan W., “The Slantlet Transform”, IEEE transactions on

signal processing, Vol. 47, No. 5, May, pp. 1304-1312,1998

[5] Sushil Kumar, “ Data Hiding in Digital Images using Steganography”,

Ph.D. Thesis, University of Delhi, Delhi, December 2013.

[6] Sushil Kumar, S.K. Muttoo, “Data Hiding techniques based on

Wavelet-like Transform and Complex Wavelet Transform”,

International Symposium on Intelligence Information Processing and

Trusted Computing, IPTC 2010, Huanggang, China, Oct. 28-29, 2010

[7] Sushil Kumar, S.K. Muttoo, “A comparative study of Image

algorithms in Wavelet domain”, International Journal Of Computer

Science And Mobile Computing (IJCSMC) ,Febuary 2013.

[8] Sushil Kumar and S.K. Muttoo, “Distortionless Data Hiding based on

Slantlet Transform”, Proceeding of the first International conference

on Multimedia Information Networking & Security (Mines, 2009),

Wuhan, China, Nov. 17- 20, Vol. 1, pp. 48-52, IEEE Computer Society

Press, 2009

[9] Titchener, M. R., “Generalised T-codes: extended construction

algorithm for self- synchronization codes”, IEE Proc. Commun., Vol.

143, No.3, pp. 122-128, 2006.

[10] Ulrich G., “Robust Source Coding with Generalised T-codes”, a thesis

submitted in the University of Auckland, 1998.



8


Dr. Sushil Kumar (nee‟ Sushil Kumar Azad) is an associate

professor in the Department of Mathematics, Rajdhani

College, University of Delhi, New Delhi. He has received his

M.Sc. degree in mathematics, MPhil in mathematics, M.Tech.

degree in computer science and Ph.D. degree in computer

science from University of Delhi, Delhi.

He has been teaching graduate and under-graduate students

for last 36 years. He is the author of three books with titles as

Computer fundamental and Software, Scientific and

Statistical Computations using Fortran 77 and Theory of

Computations.

Dr. Kumar is a reviewer of national and international journals.

He has presented talks, attended national and international

conferences and published number of research papers on

different subjects such as Image steganography, Cloud

computing, Fuzzy topology, Parallel computing. He is a life

member of CSI.

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