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TRIBHUVAN UNIVERSITY

INSTITUTE OF ENGINEERING

PULCHOWK CAMPUS

THESIS NO.: 069/MSI/603

IMPROVED IMAGE STEGANOGRAPHY TECHNIQUE USING

DAUBECHIES DISCRETE WAVELET TRANSFORM

BY

AJAYA SHRESTHA

AFINAL

THESIS REPORT

SUBMITTED TO THE DEPARTMENT OF ELECTRONICS AND

COMPUTER ENGINEERING IN PARTIAL FULFILMENT OF THE

REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN

INFORMATION AND COMMUNICATION ENGINEERING

DEPARTMENT OF ELECTRONICS AND COMPUTERENGINEERING

October, 2014

IMPROVED IMAGE STEGANOGRAPHY TECHNIQUE USING

DAUBECHIES DISCRETE WAVELET TRANSFORM

By

AJAYA SHRESTHA

069/MSI/603

Thesis Supervisor

Dr. Arun Kumar Timalsina

A thesis submitted in partial fulfillment of the requirements for the

degree of Master of Science in Information and Communication

Engineering

Department of Electronics and Computer Engineering

Institute of Engineering, Pulchowk Campus Tribhuvan University

Lalitpur, Nepal

October, 2014

ii

COPYRIGHT©The author has agreed that the library, Department of Electronics and Computer

Engineering, Institute of Engineering, Pulchowk Campus, may make this thesis freely

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professor(s), who supervised the thesis work recorded herein or, in their absence, by

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Electronics and Computer Engineering, Pulchowk Campus in any use of the material

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without approval of the Department of Electronics and Computer Engineering,

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thesis in whole or part should be addressed to:

Head

Department of Electronics and Computer Engineering

Institute of Engineering, Pulchowk Campus

Pulchowk, Lalitpur, Nepal

iii

RecommendationThe undersigned certify that they have read and recommended to the Department of

Electronics and Computer Engineering for acceptance, a thesis entitled “Improved

Image Steganography Technique Using Daubechies Discrete Wavelet

Transform”, submitted by Ajaya Shrestha in partial fulfillment of the requirement

for the award of the degree of “Master of Science in Information and

Communication Engineering”.

……………………………………

Dr. Arun Kumar Timalsina

Department of Electronics and Computer

Central Campus, Institute of Engineering

Trubhuvan University

iv

AcknowledgementI would like to express my sincere gratitude to the Department of Electronics

and Computer Engineering, Institute of Engineering for accepting my thesis on

“Improved Image Steganography Technique Using Daubechies Discrete Wavelet

Transform”. I would like to extend my sincere thanks for providing me with all the

essential co-operation, valuable suggestions for choosing the thesis topic.

I am grateful to my supervisor Dr. Arun Kumar Timalsina for providing

useful information and guidance regarding this thesis. I am also grateful to Dr.

Surendra Shrestha, Program Coordinator, Masters of Science in Information and

Communication Engineering, Pulchowk Campus for providing coordination and

support related to this thesis. I am indebted to Asst. Campus Chief, Asst. Prof. Sharad

Kumar Ghimire for providing all the information regarding to the thesis.

Last but not the least I would like to express my heartfelt thanks to respected

teachers, my families and friends who have helped and supported me directly and

indirectly during the thesis.

v

AbstractThe world in modern days is being more and more tied up to the use of

technology for facilitating day to day tasks. In this regard, information security is

turning to be great challenge when sending information from one place to another

with the aid of technology. Strong security techniques are being evolved from time to

time. Steganography is one of the techniques for the safe transmission which involves

hiding information generally with other information that only the receiver will know.

In this thesis, an improved technique of steganography is implemented using

Daubechies Discrete Wavelet Transform (DWT). First the cover image is transformed

using Daubechies DWT and encoded secret information is embedded in coefficients

of Daubechies DWT which gives stego image. Reverse process is applied to obtain

secret information from stego image. The performance of the proposed approach is

evaluated using PSNR, MSE and computation time. Also analysis is done to find the

best sub-band to hide information among different sub-bands of Daubechies DWT.

Keywords: Stego Image, Discrete Wavelet Transform (DWT), Cover Image, Peak

Signal to Noise Ratio (PSNR), Mean Square Error (MSE)

List of Figures

vi

Figure 1.1: Basic Block Diagram of Steganography.....................................................2

Figure 1.2: Block Diagram of 1-Step 2-D DWT...........................................................3

Figure 1.3: First level wavelet Decomposition..............................................................3

Figure 1.4: Second Level Wavelet Decomposition.......................................................4

Figure 3.1: Embedding Process...................................................................................10

Figure 3.2: Extracting Process.....................................................................................11

Figure 4.1: (a) Cover Image (image12) (b) Stego Image (c) Wavelet Transform of an

image (d) Original Secret Image (e) Extracted Secret Image....................................39

Figure 4.2: (a) Cover Image (image 37) (b) Stego Image (c) Wavelet Transform of

an image (d) Original Secret Image (e) Extracted Secret Image...............................40





Figure 4.5: (a) Cover Image (image11) (b) Stego Image (c) 2-level Wavelet

Transform of an image (d) Original Secret Image (e) Extracted Secret Image…….

List of Tables

vii

Table 4.1: Calculation of MSE and PSNR at different bands with roses.jpg as secret

image............................................................................................................................13

Table 4.2: Calculation of MSE and PSNR at different bands with house1.jpg as secret

image............................................................................................................................14

Table 4.3: Calculation of MSE and PSNR at different bands with sec.jpg as secret

image............................................................................................................................15

Table 4.4: Calculation of MSE and PSNR at different bands with imm.jpg as secret

image............................................................................................................................16

Table 4.5: Calculation of MSE and PSNR at different bands with secr.jpg as secret

image............................................................................................................................17

Table 4.6: Mean square error of different images with Daubechies and Haar wavelet

transform (Secret images: imm.jpg, secr.jpg and sec.jpg)...........................................20


transform (Secret image: roses.jpg and house1.jpg)....................................................22

Table 4.8: Computation time in seconds of different images of Haar and Daubechies

Wavelet Transform......................................................................................................23

Table 4.9: Calculation of MSE and PSNR at different bands with secret7.jpg as secret

image............................................................................................................................25

Table 4.10: Calculation of MSE and PSNR at different bands with secret2.jpg as

secret image.................................................................................................................26


secret image.................................................................................................................27


secret image.................................................................................................................28


secret image.................................................................................................................29


transform (Secret images: secret7.jpg, secret2.jpg and secret9.jpg)............................30

viii


transform (Secret images: secret6.jpg and secret4.jpg)...............................................32

Table 4.16: Mean square error of different images with 1-level and 2-level

Daubechies wavelet transform (Secret images: imm.jpg, roses.jpg and sec.jpg)........36


Daubechies wavelet transform (Secret images: house1.jpg and secr.jpg)...................37

ix

List of AbbreviationsAbbreviations Full Form

DCT Discrete Cosine Transform

DWT Discrete Wavelet Transform

HPF High Pass Filter

LPF Low Pass Filter

LSB Least Significant Bit

MSE Mean Square Error

PSNR Peak Signal to Noise Ratio

RGB Red Green Blue

x

Table of ContentsContents Page No

.

COPYRIGHT©............................................................................................................iii

Recommendation..........................................................................................................iv

Acknowledgement.........................................................................................................v

Abstract.........................................................................................................................vi

List of Figures..............................................................................................................vii

List of Tables..............................................................................................................viii

List of Abbreviations.....................................................................................................x

1. Introduction................................................................................................................1

1.1 Background..........................................................................................................1

1.2 Related Theory.....................................................................................................2

1.2.1 Discrete Wavelet Transform.........................................................................2

1.2.2 Haar Wavelet.................................................................................................4

1.2.3 Daubechies Wavelet......................................................................................5

1.2.4 Cover Image..................................................................................................5

1.2.5 Stego image...................................................................................................5

1.3 Problem Statement...............................................................................................6

1.4 Objectives.............................................................................................................6

1.5 Application...........................................................................................................6

2. Literature Review......................................................................................................7

3. Methodology..............................................................................................................9

3.1 Embedding Process..............................................................................................9

3.2 Extracting Process................................................................................................9

3.3 Evaluation Metrics.............................................................................................11

4. Result and Analysis.................................................................................................12

4.1 Simulation Parameters for Grayscale Image......................................................12

4.2 Simulation Parameters for Color Image.............................................................12

4.3 Comparison of different bands of Daubechies wavelet transform for embedding

secret image (Grayscale Images).............................................................................12

4.4 Comparison of Haar and Daubechies Wavelet Transform (Grayscale Image)..18

4.5 Computation time comparison of Haar and Daubechies Wavelet Transform.. .23

4.6 Comparison of different bands of Daubechies wavelet transform for embedding

secret image (Color Images)....................................................................................25

4.7 Comparison of Haar and Daubechies Wavelet Transform (Color Image).........30

4.8 Comparison of Stego and Original Image in 1-level and 2-level Daubechies

Wavelet Transform..................................................................................................34

4.9 Some experiment images and results.................................................................39

5. Conclusion...............................................................................................................44

References....................................................................................................................45

Appendix A..................................................................................................................47

Appendix B..................................................................................................................50

1. Introduction

1.1 BackgroundTransmission of information from one place to another always has potential

threats of being leaked before it reaches the destination. Especially when one has to

transmit secure and confidential message, this risk is always high. To address these

threats, people always seek and invent technologies for securely transmitting

messages. One of the techniques is information hiding.

There are many techniques of information hiding including cryptography,

watermarking and steganography. Cryptography is art of protecting information by

transforming or encrypting it into an unreadable format, called cipher text. Only those

who possess a secret key can decipher or decrypt the message into plain text.

Watermarking is a pattern of bits inserted into a digital image, audio or video file that

identifies the file's copyright information (author, rights, etc.)

Steganography is an art of covert communication in which a secret message is

communicated by hiding it in a cover file, so that the very existence of the secret

message is not detectable. The cover file can be image, audio or video; the most

commonly being the image files.

Steganography dates back to ancient Greece, where common practices

consisted of etching messages in wooden tablets and covering them with wax, and

tattooing a shaved messenger's head, letting his hair grow back, and then shaving it

again when he arrived at his contact point.

The advantage of steganography over cryptography alone is that the intended

secret message does not attract attention to itself as an object of scrutiny. Plainly

visible encrypted messages no matter how unbreakable will arouse interest, and may

in themselves be incriminating in countries where encryption is illegal. Thus, whereas

cryptography is the practice of protecting the contents of a message alone,

1

Secret Message

Cover Image

Embedding Function Stego Image

Extraction Function

Secret Message

steganography is concerned with concealing the fact that a secret message is being

sent, as well as concealing the contents of the message.

Figure 1.1: Basic Block Diagram of Steganography

This thesis mainly focuses on steganography and improved method of image

steganography will be implemented using daubechies discrete wavelet transform.

1.2 Related Theory

1.2.1 Discrete Wavelet Transform

The wavelet domain is growing up very quickly. Wavelets have been utilized

as a powerful tool in many diverse fields, including approximation theory; signal

processing, physics, astronomy, and image processing. A wavelet is simply, a small

wave which has its energy concentrated in time to give a tool for the analysis of

transient, non-stationary or time-varying phenomena. A signal can be better analyzed

if expressed as a linear decomposition of sums of products of coefficient and

functions. A two-parameter system is constructed such that one has a double sum and

coefficient with two indices. The set of coefficients are called the DWT of a signal.

The DWT splits the signal into high and low frequency parts. The high

frequency part contains information about the edge components, while the low

frequency part is split again into high and low frequency parts which is shown in

figure 1.2 [1].

2

Figure 1.2: Block Diagram of 1-Step 2-D DWT

The high frequency components are usually used for steganography since the

human eye is less sensitive to changes in edges [2]. In two dimensional applications,

for each level of decompositions, we first perform the DWT in the vertical direction,

followed by the DWT in the horizontal direction. As we can see in figure 1.3 [2],

after the first level of decomposition, there are four sub-bands: LL, LH, HL and HH

.

Figure 1.3: First level wavelet Decomposition

Similarly, second level of decomposition is shown in figure 1.4 [2].

3

Figure 1.4: Second Level Wavelet Decomposition

1.2.2 Haar Wavelet

Haar wavelet is one of the oldest and simplest wavelet. Hence, any discussion

of wavelets starts with the Haar wavelet. It is also the symmetric wavelet. In discrete

form Haar wavelets are related to a mathematical operation called the Haar transform.

The Haar transform works as a prototype for all other wavelet transforms. In

mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions

which together form a wavelet family or basis. Wavelet analysis is homogeneous to

Fourier analysis in that it allows a target function over an interval to be represented in

terms of an orthonormal function basis. It represents the same wavelet as Daubechies

db1. The Haar wavelet transform has a number of advantages such as it is

conceptually fast, simple, memory efficient, since it can be calculated in place

without a temporary array.

The Haar wavelet also has limitations. In generating each of averages for the

next level and each set of coefficients, the Haar transform performs an average and

difference on a pair of values. Then the algorithm shifts over by two values and

calculates another average and difference on the next pair. The high frequency

4

coefficient spectrum should reflect all high frequency changes. The Haar window is

only two elements wide. If a big change takes place from an even value to an odd

value, the change will not be reflected in the high frequency coefficients.

1.2.3 Daubechies Wavelet

Daubechies wavelets are the most popular wavelets. They represent the

foundations of wavelet signal processing and are used in various applications. These

are also called Maxflat wavelets as their frequency responses have maximum flatness

at frequencies 0 and π. The Daubechies wavelet transforms are defined in the same

way as the Haar wavelet transform—by computing running averages and differences

via scalar products with scaling signals and wavelets—the only difference between

them consists in how these scaling signals and wavelets are defined. For the

Daubechies wavelet transforms, the scaling signals and wavelets have slightly longer

supports, i.e., they produce averages and differences using just a few more values

from the signal. This slight change, however, provides a tremendous improvement in

the capabilities of these new transforms. The names of the Daubechies family

wavelets are written dbN, where N is the order, and db the "surname" of the wavelet.

1.2.4 Cover Image

It is defined as the original image into which the required secret message is

embedded. It is also termed as innocent image or host image. The secret message

should be embedded in such a manner that there are no significant changes in the

statistical properties of the cover image. Good cover images range from gray scale

image to colored image in uncompressed format.

1.2.5 Stego image

It is the final image obtained after embedding the secret information (in a

form of image, text, audio etc.) into a given cover image. It should have similar

statistical properties to that of the cover image.

5

1.3 Problem StatementSteganography means hiding some secret information into a cover file. Cover

files may by audio, image, video etc. The main issue in steganography is to hide

information in such a way that there is no significant change in quality and quantity

of cover file.

1.4 ObjectivesThe main objectives of this thesis are

To improve the image steganography technique using Daubechies Discrete

Wavelet Transform and compare with Haar Discrete Wavelet Transform

To analyze the sub-bands of discrete wavelet transform for obtaining best sub-

band to hide information.

1.5 ApplicationThe outcomes of this thesis will be applicable in various sectors where security in

information sending is of great concern. Some of the major target sectors are:

Military Sector: for the purpose of sending secret files

Banking Sector: to send passwords to the customers and/or employees over

the internet

Corporate Sector: for the purpose of sharing company strategies among their

management team

Government Sector: for the purpose of sending secret information and/or

confidential data

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2. Literature ReviewInformation security is one of the prime concerns in the modern world since

information is shared a lot in the internet and chances of information leakages are

increasing. Information can be made secure by sharing information using

steganography in which a secret message is communicated by hiding it in a cover file.

There are many steganography techniques which are capable of hiding data

within an image. These techniques can be classified into two categories based on their

algorithms: (1) spatial domain based techniques; (2) transform domain based

techniques. The spatial domain based steganography technique use either the LSB or

Bit Plane Complexity Segmentation algorithm. The most widely used technique to

hide data is the usage of the LSB [5]. The existing techniques are mainly based on

LSB (Least Significant Bit) where LSBs of the cover file are directly changed with

message bits. S. M Karim et al. [6] has proposed a LSB technique for RGB true color

image by enhancing the existing LSB substitution techniques to improve the security

level of hidden information. LSB matching image steganography and edge adaptive

scheme was proposed which can select the embedding regions according to the size

of secret message and the difference between two consecutive pixels in the cover

image. In [7] designing of robust and secure image steganography based on LSB

insertion and RSA encryption technique has been used.

M. A. Ahmed et al. [8] proposed a method in which a message hidden inside

an image by using Least Significant Bit technique and after creation of the hidden

message, the image will pass it in hash function to obtain hashing value using the

MD5 technique. In [9] a hash based approach proposed for secure keyless

steganography in lossless RGB images that an improved steganography approach for

hiding text messages in lossless RGB images.

Transform domain techniques embed secret information in a transform space

of the signal; means the process of embedding data in the frequency domain of a

7

signal to make them more robust to attack such as adding noise, compression,

cropping, some image processing etc[10]. Many transform domain variations exist.

One method is to use the Discrete Cosine Transformation (DCT) as a vehicle to

embed information in image. Another method would be the use of wavelet

transforms. Advantages of transform domain include higher level of robustness

against simple statistical analysis.

JSteg sequentially replaces the LSB of the non-zero quantized DCT

coefficients with secret message bits whereas in JPHide, the quantized DCT

coefficients are not selected sequentially but selected randomly by a pseudo-random

number generator [10]. F5 comes after a series of F3 and F4 [11]. F5 steganographic

algorithm was introduced by Westfield and it embeds message bits into randomly

chosen DCT coefficients. F5 algorithm employs matrix embedding that minimizes the

necessary number of changes to hide a message of certain length.

Discrete wavelet transform (DWT) method is favored over DCT method in

steganography because DWT provides better image resolution at various levels. DWT

converts spatial domain information to the frequency domain information and it

clearly partitions the high-frequency and low-frequency information on a pixel by

pixel basis [12]. Wavelets are mathematical functions that divide data into frequency

components, which makes them ideal for image compression. Haar wavelet transform

is the widely used wavelet transform due to the simplicity in implementation [13].

H. Rohil et al. [13] proposed an algorithm in which 2-level Haar DWT

transform on the image. This will result in the formation of four bands i.e. LL1, HL1,

LH1 and HH1 and LL2 band is selected to embed the secret. Cover image is divided

into higher and lower frequency sub-bands and data is embedded into higher

frequency sub-bands. Arnold Transformation is used to increase the security.

8

3. MethodologyThe process in the thesis consists of two parts: Embedding Process and

Extracting Process.

3.1 Embedding ProcessEmbedding process of secret information is done as follows:

1. Get cover image and secret image.

2. Calculate daubechies wavelet transform of the cover image.

3. Encrypt the pixel value of secret image by XORing pixel value with secret

key.

4. Embed the encrypted pixel values of secret image into the wavelet

coefficients. This is done in following method.

i. Select any two bands (i.e. HL/HH or LH/HH or HL/LH).

ii. Get the secret information (image).

iii. Get lower four bits of secret information and embed into the lower

four bits of wavelet coefficients of one of the band selected.

iv. Get higher four bits of secret information and embed into the lower

four bits of wavelet coefficients of other band selected.

5. Calculate inverse daubechies wavelet transform.

6. Stego image is generated.

3.2 Extracting ProcessExtracting process is done as follows.

1. Get stego image.

2. Calculate daubechies wavelet transform of the stego image.

3. Obtain the coefficients of the selected band where the pixel value of secret

image is hidden.

9

4. Extract the pixel values of secret image from wavelet coefficients. The

extraction is done in following method.

i. Get coefficients from one of the selected bands of wavelet.

ii. Obtain lower four bits of the coefficients.

iii. Get coefficients from other selected bands of wavelet.

iv. Obtain lower four bits of the coefficients.

v. Combine this four bits with the four bits obtained in (ii) by making this

four bits as higher bits and other four bits as lower bits.

vi. Decrypt the obtained value by XORing it with secret key.

5. Secret image is generated.

Figure 3.5: Embedding Process

10

Cover Image

Daubechies DWT

Embed encrypted message in the Daubechies DWT coefficient

Secret Image

Stego Image

Apply Inverse

Daubechies DWT

XOR pixel value with

secret key

Figure 3.6: Extracting Process

3.3 Evaluation MetricsTo check the performance of the proposed approach, two evaluation metrics

will be used. They are

Peak Signal to Noise Ratio (PSNR): It is the measure of reconstruction of the

transformed image. This metric is used for discriminating between the cover

and stego image which is given by equation 3.1 [13]

PSNR=10 log102552/MSE (3.1)

Mean Square Error (MSE): It is one of the most frequently used quality

measurement technique followed by PSNR. The MSE can be defined as the

measure of average of the squares of the difference between the intensities of

the stego image and the cover image. It is popularly used because of the

mathematical tractability it offers. It is represented in equation 3.2 [13]:

MSE= 1MN ∑

i=1

M

∑j=1

N

( f (i , j )−f ' (i , j ) )2 (3.2)

11

Stego Image Daubechies DWT Daubechies DWT coefficents

Decode the encrypted pixel value

from corresponding coefficients

Secret

Image

Decrypt the pixel value by

XORing with secret key

coefficients

4. Result and Analysis

4.1 Simulation Parameters for Grayscale Image Coding Platform: Matlab

Cover and Secret Image: 8-bit grayscale

Cover Image size: 512 X 512

Secret Image size: 128 X 128

4.2 Simulation Parameters for Color Image Coding Platform: Matlab

Cover and Secret Image: 24-bit color

Cover Image size: 512 X 512

Secret Image size: 128 X 128

4.3 Comparison of different bands of Daubechies wavelet transform

for embedding secret image (Grayscale Images)5 different secret images and 30 different cover images are taken and secret

image is embedded in different combination of bands (horizontal/diagonal,

vertical/diagonal, vertical/horizontal) and performance is evaluated in terms of mean

square error and peak signal to noise ratio.

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Table 4.1: Calculation of MSE and PSNR at different bands with roses.jpg as secret

image

Cover Image

roses (Secret Image)horizontal/diagonal vertical/diagonal vertical/horizontal

MSE PSNR MSE PSNR MSE PSNRlina1 227.0067 24.57042 223.0057 24.64764 630.069 20.13692image11 2538.8 14.08452 2664.4 13.87481 3065.9 13.26522image2 1111 17.67366 1124.1 17.62275 2683.4 13.84395test 405.8065 22.04761 424.1797 21.8553 6196 10.20969chess 208.5411 24.93889 223.9547 24.6292 300.5876 23.35109aaa 193.5825 25.26214 171.9372 25.77711 439.0814 21.70535aa 189.594 25.35256 201.1265 25.09611 1219.4 17.26934drae 553.144 20.70242 594.3964 20.39004 812.5802 19.03214test1 198.9744 25.14283 200.0817 25.11873 373.3772 22.40933noise 217.6369 24.75348 219.5092 24.71628 5544.2 10.69241highpass 204.1147 25.03206 214.7119 24.81224 830.8343 18.93566rose 176.1932 25.67091 178.9166 25.6043 1030.4 18.00075image12 180.6531 25.56235 178.3638 25.61774 638.3116 20.08048image14 4141.2 11.95954 4149.4 11.95095 4573 11.52879image16 423.2897 21.86443 446.4719 21.63286 1866.3 15.42099image17 165.3695 25.94625 171.9332 25.77721 169.64 25.83552image20 190.9529 25.32154 202.0372 25.07649 1430.8 16.57501image21 225.8375 24.59284 238.2367 24.36072 336.1237 22.86581image24 1878 15.39385 1884.6 15.37861 2192.2 14.722image30 177.3276 25.64304 190.3532 25.3352 568.7062 20.58192image31 2049.4 15.01454 2105.1 14.89808 2427.5 14.27921image32 640.2269 20.06746 721.5757 19.54798 2463.6 14.2151image33 359.5592 22.5731 363.8241 22.52189 701.0541 19.67329image34 209.3379 24.92232 221.3373 24.68026 266.7036 23.87051image36 193.166 25.2715 227.5934 24.55921 1400 16.66952image37 435.712 21.73881 496.0349 21.17568 4825.6 11.29529image39 186.1259 25.43274 190.2888 25.33667 203.76 25.03961image40 235.5389 24.41018 227.8763 24.55381 1681.1 15.87487image26 1730.1 15.75009 1898.6 15.34647 2248.8 14.6113moon 232.7104 24.46265 252.3342 24.11104 985.8918 18.19251

In this case out of 30 tests, 26 give less mean square error and hence more

peak signal to noise ratio in horizontal/diagonal band and 4 give less mean square

error in vertical/diagonal band.

13

Table 4.2: Calculation of MSE and PSNR at different bands with house1.jpg as

secret image

Cover Image

house1 (Secret Image)horizontal/diagonal vertical/diagonal vertical/horizontalMSE PSNR MSE PSNR MSE PSNR

lina1 224.3099 24.622319 263.9912 23.915 618.1324 20.21999image11 284.4663 23.590495 351.2156 22.675 456.9362 21.53225image2 643.054 20.048329 615.2386 20.24 1086.9 17.76891test 451.5289 21.583948 752.8693 19.364 1298.4 16.99672chess 321.5059 23.058914 353.2876 22.65 259.099 23.99615aaa 216.0289 24.785685 267.5063 23.857 213.7628 24.83148aa 289.7525 23.510532 301.6014 23.336 650.0114 20.00159drae 677.1614 19.823882 874.7213 18.712 1099.5 17.71885test1 233.6724 24.444729 233.1108 24.455 338.2643 22.83824noise 241.8947 24.29454 450.332 21.595 779.9642 19.21006highpass

223.6788 24.634555 196.6776 25.193 306.6747 23.26402rose 335.9387 22.868203 339.3306 22.825 652.0356 19.98809image12 197.0387 25.185288 211.3 24.882 479.2419 21.32526image14 915.4968 18.514235 1100.6 17.715 4616 11.48815image16 489.2836 21.235197 484.0939 21.282 1283.6 17.04651image17 242.9184 24.276199 258.9008 23.999 256.997 24.03152image20 205.7913 24.996534 205.7495 24.997 438.126 21.71481image21 187.6199 25.398015 413.787 21.963 265.3393 23.89279image24 256.1647 24.045611 247.5874 24.194 343.243 22.77479image30 200.5266 25.109084 206.3627 24.984 540.0852 20.80618image31 851.8571 18.827136 975.4838 18.239 987.8709 18.1838image32 483.0316 21.291048 337.7449 22.845 705.2938 19.6471image33 288.7723 23.525248 201.3334 25.092 370.319 22.44504image34 400.1071 22.109041 210.0988 24.907 327.0353 22.98486image36 209.5191 24.918567 201.5491 25.087 412.2944 21.97873image37 264.9592 23.899014 377.5391 22.361 1418.5 16.61251image39 313.3872 23.169991 320.5284 23.072 298.7421 23.37784image40 354.2698 22.637462 206.912 24.973 928.6486 18.45229image26 302.6871 23.320864 335.7319 22.871 443.2863 21.66396moon 366.0989 22.494819 345.3344 22.748 406.8639 22.03631


peak signal to noise ratio in horizontal/diagonal band, 12 give less mean square error

in vertical/diagonal band and 2 in vertical/horizontal band.

14

Table 4.3: Calculation of MSE and PSNR at different bands with sec.jpg as secret

image

Cover Image

sec (Secret Image)horizontal/diagonal vertical/diagonal vertical/horizontal

MSE PSNR MSE PSNR MSE PSNRlina1 336.0264 22.86707 232.3139 24.47 522.2986 20.95161image11 1227.2 17.24165 1714.1 15.79 3075.7 13.25136image2 832.741 18.9257 877.9965 18.696 1518.4 16.31694test 330.733 22.93603 514.2712 21.019 1801.6 15.57422chess 280.5366 23.65091 301.1914 23.342 492.1562 21.20977aaa 262.0065 23.94768 264.8839 23.9 406.468 22.04054aa 301.1351 23.34319 320.6244 23.071 760.0464 19.3224drae 799.9365 19.10025 875.1922 18.71 1053.4 17.90487test1 356.9564 22.60465 398.4433 22.127 436.6625 21.72934noise 417.676 21.92241 414.0279 21.961 1405 16.65404highpass 318.0975 23.1052 339.6024 22.821 324.6218 23.01703rose 295.3685 23.42716 296.3103 23.413 593.2756 20.39824image12 270.9931 23.80122 331.6098 22.925 708.8446 19.62529image14 5214.7 10.95851 5160.8 11.004 6497.4 10.00341image16 421.5468 21.88235 448.6499 21.612 1499.9 16.37018image17 249.9127 24.15292 261.0217 23.964 492.8276 21.20385image20 252.2028 24.1133 377.8871 22.357 812.4347 19.03292image21 342.4185 22.78523 327.759 22.975 596.8591 20.37209image24 2050.6 15.01199 1898.5 15.347 2187.5 14.73132image30 290.1818 23.5041 295.2054 23.43 378.3547 22.35181image31 1304.9 16.97503 1151.8 17.517 1411.7 16.63338image32 421.9924 21.87776 405.8443 22.047 1282.8 17.04921image33 413.2877 21.96828 414.5646 21.955 611.6548 20.26574image34 327.9899 22.9722 327.2231 22.982 374.7996 22.39281image36 323.9753 23.02568 349.3306 22.698 724.4454 19.53075image37 580.8964 20.48982 527.8282 20.906 1722.3 15.76972image39 306.4636 23.26701 299.2375 23.371 520.231 20.96884image40 349.5421 22.69581 379.8043 22.335 1066.8 17.84997image26 2270.1 14.57035 3006.2 13.351 3295.5 12.95159moon 418.1559 21.91742 408.3144 22.021 584.6746 20.46166




15

Table 4.4: Calculation of MSE and PSNR at different bands with imm.jpg as secret

image

Cover Image

imm (Secret Image)horizontal/diagonal vertical/diagonal vertical/horizontal

MSE PSNR MSE PSNR MSE PSNRlina1 322.8702 23.04052 376.9686 22.368 813.2798 19.0284image11 2268.2 14.57399 2717.2 13.79 3145.4 13.15404image2 949.3478 18.35655 995.0606 18.152 2228.4 14.65087test 429.1101 21.80512 417.7761 21.921 4193.8 11.90473chess 336.686 22.85855 255.3652 24.059 583.5169 20.47027aaa 316.5553 23.12631 331.6295 22.924 632.0129 20.12354aa 349.6396 22.6946 350.6082 22.683 1028.6 18.00834drae 606.0934 20.30541 861.2502 18.78 992.7291 18.1625test1 283.8168 23.60042 286.2129 23.564 489.5773 21.23259noise 396.149 22.15222 381.9446 22.311 3766.8 12.37108highpass 346.3035 22.73623 343.0537 22.777 879.8193 18.68687rose 297.088 23.40195 342.7798 22.781 950.3099 18.35215image12 237.4118 24.37578 265.3546 23.893 582.3695 20.47882image14 3863.8 12.26066 3880.2 12.242 4444.4 11.65267image16 405.4139 22.05182 623.9517 20.179 1778.5 15.63026image17 240.2191 24.32473 252.2642 24.112 247.2172 24.20002image20 337.5687 22.84718 341.8209 22.793 931.0502 18.44107image21 270.9183 23.80242 267.3243 23.86 483.9779 21.28255image24 1887.6 15.3717 1924.1 15.289 2263.3 14.58338image30 277.6959 23.69511 275.4467 23.73 719.744 19.55902image31 1418.1 16.61374 1509.8 16.342 1788.3 15.6064image32 560.4141 20.64571 546.3968 20.756 1661 15.92711image33 402.9062 22.07876 391.8541 22.2 480.2963 21.31571image34 261.8513 23.95026 362.5798 22.537 384.4582 22.28231image36 309.474 23.22456 362.054 22.543 1055.7 17.8954image37 595.2593 20.38374 579.0436 20.504 3172.8 13.11638image39 283.8746 23.59954 292.3875 23.471 311.2159 23.20019image40 367.3627 22.47985 364.527 22.514 1191.9 17.36841image26 1654.2 15.94492 1888.7 15.369 2316.7 14.48211moon 390.688 22.2125 409.4083 22.009 1133.2 17.58774




16

Table 4.5: Calculation of MSE and PSNR at different bands with secr.jpg as secret

image

Cover Image

secr (Secret Image)horizontal/diagonal vertical/diagonal vertical/horizontalMSE PSNR MSE PSNR MSE PSNR

lina1 247.3735 24.197272 262.3742 23.942 390.0919 22.21913image11 1491.1 16.395736 1600.6 16.088 1953.1 15.22356image2 1277.2 17.068215 1260.3 17.126 2677.2 13.854test 245.6612 24.227438 257.4182 24.024 2755.2 13.72927chess 193.5219 25.263502 195.8959 25.211 204.7261 25.01907aaa 234.8042 24.423745 244.9876 24.239 244.9091 24.24075aa 240.9103 24.31225 280.5471 23.651 810.886 19.04121drae 615.5201 20.238381 627.1213 20.157 907.0526 18.55448test1 257.7365 24.019044 256.7739 24.035 368.0475 22.47176noise 252.9445 24.100551 287.3444 23.547 2946 13.43848highpass

218.6307 24.733692 191.5765 25.307 374.4696 22.39664rose 204.9199 25.014962 194.2748 25.247 668.5211 19.87965image12 207.4206 24.962285 208.5787 24.938 565.6366 20.60543image14 3236 13.030718 3238.3 13.028 4096.2 12.00699image16 494.5818 21.188422 472.5336 21.386 1422.3 16.60089image17 196.8328 25.189829 201.6071 25.086 199.4324 25.13285image20 252.1632 24.113987 270.4713 23.81 1128.9 17.60425image21 245.9616 24.222131 244.8299 24.242 359.9957 22.56783image24 1481.9 16.422615 1355.6 16.809 1677.1 15.88521image30 191.5515 25.307948 215.6621 24.793 309.0566 23.23042image31 1719.1 15.777792 1669.9 15.904 1983.9 15.15561image32 544.9973 20.76686 592.963 20.401 1773 15.64372image33 355.4284 22.623282 341.4385 22.798 661.1539 19.92778image34 192.3648 25.289548 220.2045 24.703 201.5913 25.08609image36 267.0773 23.864434 237.471 24.375 948.8707 18.35873image37 422.3401 21.87418 416.7313 21.932 2898 13.50982image39 223.5789 24.636495 219.702 24.712 242.4744 24.28414image40 240.4617 24.320344 265.5273 23.89 1173.4 17.43634image26 1065.5 17.855269 1522.3 16.306 2099.1 14.91047moon 289.8643 23.508856 271.9287 23.786 412.925 21.97209




17

In above five tables, out of 150 tests, 98 give less mean square error in

horizontal/diagonal band, 50 give less mean square error in vertical/diagonal band

and 2 give less mean square error in vertical/horizontal band. Horizontal/diagonal

band has slightly more images with less mean square error and vertical/diagonal band

also contains significant number of images with less mean square error. Hence, it can

be concluded that diagonal band contains less information of an original image and

can be used to embed the secret information with less distortion in original image.

4.4 Comparison of Haar and Daubechies Wavelet Transform

(Grayscale Image)5 different secret images and 20 different cover images are taken and

performance of Haar and Daubechies wavelet transform is compared on these images

in terms of mean square error.

In table 4.6 mean square error is calculated with different secret images. Table

4.6 can be analysed as follows:

Case I:- Secret Image: imm.jpg

In this case, there are 17 cover images out of 20 images where the

mean square error of Daubechies wavelet transform is less than Haar wavelet

transform.

imag

e2 test

power1im

age2

0im

age2

1im

age2

4im

age3

1im

age3

7im

age4

0im

age1

6im

age1

7 aaa

draeim

age3

3im

age3

4im

age1

2im

age1

8moon

imag

e23

imag

e29

0

500

1000

1500

2000

2500

3000DaubechiesHaar

Cover Image

MSE

18

Case II:- Secret Image: secr.jpg



transform.im

age2 tes

tpower1im

age2

0im

age2

1im

age2

4im

age3

1im

age3

7im

age4

0im

age1

6im

age1

7 aaa

draeim

age3

3im

age3

4im

age1

2im

age1

8moon

imag

e23

imag

e29

0

500

1000

1500

2000

2500

DaubechiesHaar

Cover Image

MSE

Case III:- Secret Image: sec.jpg



transform.

imag

e2 test

power1im

age2

0im

age2

1im

age2

4im

age3

1im

age3

7im

age4

0im

age1

6im

age1

7 aaa

draeim

age3

3im

age3

4im

age1

2im

age1

8moon

imag

e23

imag

e29

0

500

1000

1500

2000

2500

DaubechiesHaar

Cover Image

MSE

19


transform (Secret images: imm.jpg, secr.jpg and sec.jpg)

Cover Image

Secret Image: imm.jpg Secret Image: secr.jpg Secret image: sec.jpgDaubechies Haar Daubechies Haar Daubechies Haar

image2 949.3478 1228.7 1277.2 1532.6 832.741 968.6671test 429.1101 599.8784 245.6612 316.6432 330.733 491.7958power1 771.4604 1306.9 635.4859 803.7192 843.6862 1046.3image20 337.5687 347.4767 252.1632 277.0934 252.2028 340.8303image21 270.9183 330.593 245.9616 251.9816 342.4185 403.7371image24 1887.6 2407.8 1481.9 1594.4 2050.6 2146.9image31 277.6959 317.0563 1719.1 1960.3 1304.9 1324.8image37 595.2593 1032.8 422.3401 889.0158 580.8964 912.1024image40 237.4118 277.8547 240.4617 409.7321 349.5421 727.8544image16 405.4139 879.0896 494.5818 198.2993 421.5468 888.4167image17 240.2191 245.9316 196.8328 692.2786 249.9127 288.9265aaa 316.5553 371.8646 234.8042 209.4868 262.0065 336.8728drae 606.0934 856.9799 615.5201 708.8082 799.9365 937.4206image33 402.9062 393.9998 355.4284 373.2648 413.2877 444.6382image34 261.8513 381.7764 192.3648 269.4603 327.9899 307.9075image12 237.4118 277.8547 207.4206 275.8674 270.9931 448.6489image18 339.2261 288.2324 230.158 218.1385 279.9133 332.1898moon 390.688 324.1594 289.8643 354.7383 418.1559 497.0123image23 1312.4 1572.7 1058.5 1609 1183.7 1443.5

image29 318.7376 467.8544 254.2525 419.7769 298.9232 334.7615

In table 4.7 mean square error is calculated with different secret images. Table 4.7

can be analysed as follows:

20

Case IV:- Secret Image: roses.jpg



transform.im

age2 Test

power1im

age2

0im

age2

1im

age2

4im

age3

1im

age3

7im

age4

0im

age1

6im

age1

7Aaa

Draeim

age3

3im

age3

4im

age1

2im

age1

8Moon

imag

e23

imag

e29

0

500

1000

1500

2000

2500

3000

DaubechiesHaar

Cover Image

MSE

Case V:- Secret Image: house1.jpg



transform.

imag

e2 Test

power1im

age2

0im

age2

1im

age2

4im

age3

1im

age3

7im

age4

0im

age1

6im

age1

7Aaa

Draeim

age3

3im

age3

4im

age1

2im

age1

8Moon

imag

e23

imag

e29

0

200

400

600

800

1000

1200

1400

1600DaubechiesHaar

Cover Image

MSE

21


transform (Secret image: roses.jpg and house1.jpg)

Cover Image

Secret Image: roses.jpg Secret Image: house1.jpgDaubechies Haar Daubechies Haar

image2 1124.1 1475.9 643.054 602.1916test 424.1797 484.7471 451.5289 564.8176power1 803.7977 1229.3 222.887 227.5679image20 202.0372 226.5262 205.7913 373.8927image21 238.2367 203.6461 187.6199 433.3782image24 1884.6 2349.7 256.1647 350.3449image31 2105.1 2559.9 851.8571 921.4156image37 496.0349 1282 264.9592 591.0016image40 227.8763 436.7521 354.2698 532.4647image16 446.4719 783.9743 489.2836 944.463image17 171.9332 158.3301 242.9184 327.0615aaa 171.9372 206.6008 216.0289 385.1224drae 594.3964 700.3987 677.1614 990.3748image33 363.8241 461.0787 288.7723 436.048image34 221.3373 248.1956 400.1071 416.3519image12 178.3638 284.2126 197.0387 230.2736image18 201.0585 194.7806 194.4127 207.1558moon 252.3342 272.1696 366.0989 381.9606image23 252.3342 272.1696 1414.8 1224.2image29 237.9325 452.0146 321.5128 177.0512

In above 5 cases, a total of 87 out of 100 tests give less mean square error in

Daubechies wavelet transform than Haar wavelet transform. Hence it can be

concluded that Daubechies wavelet transform gives better quality of secret image

extracted from stego image.

22

4.5 Computation time comparison of Haar and Daubechies Wavelet

Transform5 different secret images and 8 different cover images are taken and

computation of Haar and Daubechies wavelet transform is compared on these images.

In table 4.8, in all cases Daubechies wavelet transform has slightly higher

computation time than Haar wavelet transform.

Table 4.8: Computation time in seconds of different images of Haar and Daubechies

Wavelet Transform

Cover Image

Secret Image: roses.jpgDaubechies Haar

lina1 3.29396 3.1413image11 3.21348 3.11084moon 3.27274 3.176chess 3.2272 3.12892highpass 3.27312 3.18572image12 3.17134 3.0983image14 3.28502 3.14894image30 3.2068 3.1347 (a)

Cover Image

Secret Image: house1.jpgDaubechies Haar

lina1 3.2251 3.15256image11 3.21554 3.13064moon 3.21462 3.10704chess 3.2315 3.10958highpass 3.25102 3.14916image12 3.18642 3.05536image14 3.26328 3.15696image30 3.2524 3.13812 (b)

23

lina1

image11

moonchess

highpass

image12

image14

image30

3

3.05

3.1

3.15

3.2

3.25

3.3

3.35Daubechies Haar

Cover Image

Com

puta

tion

Tim

e (S

ec)

lina1

image11

moonchess

highpass

image12

image14

image30

2.953

3.053.1

3.153.2

3.253.3 Daubechies Haar

Cover Image

Com

puta

tion

Tim

e (S

ec)

Cover Image

Secret image: imm.jpg

Daubechies Haarlina1 3.24748 3.13998image11 3.20044 3.11785moon 3.24682 3.13518chess 3.23762 3.08232highpass 3.25612 3.09272image12 3.20276 3.03058image14 3.21056 3.09472image30 3.22296 3.10634 (c)

(d)

24

lina1

image11

moonchess

highpass

image12

image14

image30

2.953

3.053.1

3.153.2


Cover Image

Com

puta

tion

Tim

e (S

ec)

lina1

image11

moonchess

highpass

image12

image14

image30

2.92.95

33.05

3.13.15

3.23.25


Cover Image

Com

puta

tion

Tim

e (S

ec)

Cover Image

Secret Image: sec.jpgDaubechies Haar

lina1 3.18842 3.08426image11 3.24638 3.12276moon 3.23316 3.09742chess 3.18128 3.05982highpass 3.2417 3.11716image12 3.18242 3.09956image14 3.23134 3.13984image30 3.1812 3.10534

Cover Image

Secret Image: secr.jpgDaubechies Haar

lina1 3.27114 3.13636image11 3.20362 3.05072moon 3.27206 3.15902chess 3.18508 3.08886highpass 3.226 3.11844image12 3.19856 3.05642image14 3.28742 3.12932image30 3.27346 3.11522

(e)

25

lina1

image11

moonchess

highpass

image12

image14

image30

2.92.95

33.05

3.13.15

3.23.25


Cover Image

Com

puta

tion

Tim

e (S

ec)

4.6 Comparison of different bands of Daubechies wavelet transform

for embedding secret image (Color Images)5 different secret images and 17 different cover images are taken and secret

image is embedded in different combination of bands (horizontal/diagonal,

vertical/diagonal, vertical/horizontal) and performance is evaluated in terms of mean

square error and peak signal to noise ratio.


secret image

Cover Image

secret7.jpg (Secret Image)horizontal/diagonal vertical/diagonal vertical/horizontalMSE PSNR MSE PSNR MSE PSNR

im 398.1939 22.12986 229.7115 24.51898 628.3327 20.14891

image1 172.5045 25.7628 321.5735 23.058 1238.5 17.20184

image2 203.7023 25.04084 182.5424 25.51717 696.4052 19.70218

image3 209.7872 24.91301 237.5225 24.37376 505.0389 21.09756

image4 233.7363 24.44354 325.8801 23.00023 1.52E+03 16.30523

image5 131.9064 26.92814 284.6853 23.58715 973.3164 18.24826

image6 228.9882 24.53267 244.3595 24.25051 365.1028 22.50665

image8 203.7938 25.03889 260.0745 23.97983 473.5481 21.37716

image10 158.2519 26.13731 183.4217 25.4963 338.4968 22.83526

image11 174.9615 25.70138 298.3261 23.38389 455.5225 21.54571

image12 170.9043 25.80327 297.5184 23.39567 430.3819 21.79226

image13 190.3149 25.33608 291.0683 23.49085 1.23E+03 17.24342

image14 941.9796 18.39039 238.5145 24.35566 615.6075 20.23776

image15 294.7213 23.43669 259.2513 23.99359 890.1537 18.63615

image16 240.8902 24.31261 251.7532 24.12105 1038.5 17.96674

image17 221.8758 24.6697 243.3937 24.26771 411.7581 21.98438

image19 178.6816 25.61001 164.1212 25.97916 279.5104 23.66682

26





secret image

Cover Image


im 2502 14.14758 394.0375 22.17543 245.639 24.22783

image1 732.4719 19.48289 872.8405 18.72145 3807.9 12.32395

image2 419.8701 21.89965 595.4296 20.3825 2139.7 14.82727

image3 637.3083 20.08731 730.6192 19.49389 1638.6 15.98607

image4 708.2591 19.62888 3984.4 12.12717 4486.1 11.61211

image5 528.3311 20.90174 791.0909 19.14854 3155.2 13.14053

image6 504.8779 21.09894 809.0752 19.05091 816.4483 19.01152

image8 483.7021 21.28502 384.7709 22.27878 1232.7 17.22223

image10 581.2159 20.48743 581.682 20.48395 854.1317 18.81556

image11 573.8735 20.54264 790.8591 19.14981 1127.5 17.60964

image12 505.7425 21.09151 628.611 20.14698 889.4068 18.6398

image13 493.964 21.19385 814.7021 19.02082 3818.5 12.31188

image14 214.8173 24.81011 778.6281 19.2175 2156.9 14.7925

image15 512.3076 21.0355 776.525 19.22925 2132.5 14.84191

image16 596.62 20.37383 583.5994 20.46966 2508 14.13753

image17 485.8181 21.26607 480.7594 21.31153 720.3469 19.55539

image19 715.7114 19.58342 515.0185 21.01258 675.6216 19.83377


peak signal to noise ratio in horizontal/diagonal band , 4 give less mean square error

27

in vertical/diagonal band and 1 gives less mean square error in vertical/horizontal

band.


secret image

Cover Image


im 493.4117 21.19871 187.3109 25.40517 583.2855 20.47199

image1 153.2008 26.27819 323.1758 23.03642 1111.2 17.67288

image2 184.2325 25.47714 248.4265 24.17882 671.7569 19.85868

image3 199.3165 25.13537 213.7049 24.83266 431.5912 21.78008

image4 342.028 22.79019 399.9489 22.11076 1184.6 17.39509

image5 228.6224 24.53962 272.4623 23.77774 849.6735 18.83828

image6 135.8742 26.79943 236.823 24.38656 292.0013 23.47696

image8 200.5832 25.10786 226.0176 24.58938 415.02 21.95011

image10 178.6397 25.61102 200.5596 25.10837 298.3609 23.38338

image11 205.5393 25.00185 241.2097 24.30686 334.2771 22.88974

image12 166.2846 25.92228 179.0576 25.60088 311.0482 23.20253

image13 244.0035 24.25684 235.6349 24.40841 977.8077 18.22827

image14 237.8765 24.36729 216.4577 24.77707 604.8028 20.31467

image15 229.0612 24.53129 239.0199 24.34646 794.8997 19.12768

image16 196.7889 25.1908 214.6261 24.81398 988.3105 18.18187

image17 190.7451 25.32627 203.1921 25.05174 275.7386 23.72583

image19 180.916 25.55603 157.7709 26.15053 240.3529 24.32231

28





secret image

Cover Image


im 342.739 22.78117 204.0696 25.03302 157.7654 26.15069

image1 225.9264 24.59113 461.115 21.49271 1457.3 16.49531

image2 223.3976 24.64002 214.3335 24.8199 1046.7 17.93258

image3 233.8684 24.44109 260.5305 23.97222 662.0074 19.92218

image4 254.3868 24.07586 879.4688 18.6886 1267.1 17.10269

image5 206.289 24.98604 318.3535 23.10171 1475.9 16.44023

image6 261.3139 23.95918 288.0202 23.53657 289.8026 23.50978

image8 234.5507 24.42844 221.6199 24.67472 487.715 21.24914

image10 186.0707 25.43402 230.5492 24.50317 323.423 23.03309

image11 174.4255 25.7147 342.5715 22.78329 464.5332 21.46064

image12 231.3841 24.48747 202.0849 25.07546 385.4739 22.27085

image13 173.4452 25.73918 299.0996 23.37265 1575.8 16.15579

image14 227.3351 24.56414 377.9499 22.35646 1007.5 18.09835

image15 200.1144 25.11802 272.2527 23.78108 1066.9 17.84957

image16 271.593 23.79162 329.4872 22.95242 1308.3 16.96373

image17 203.5504 25.04408 294.2659 23.4434 329.6635 22.95009

image19 294.1738 23.44476 194.9973 25.23052 296.315 23.41327

29





secret image

Cover Image


im 162.2776 26.02822 243.1709 24.27169 227.5585 24.55987

image1 338.6824 22.83288 867.44 18.74841 1593.8 16.10647

image2 218.337 24.73953 271.8682 23.78722 1069.4 17.8394

image3 304.6215 23.2932 373.6658 22.40597 825.9901 18.96106

image4 332.2241 22.91649 453.2622 21.56731 1263.8 17.11402

image5 272.0327 23.78459 386.6624 22.25748 1474 16.44583

image6 216.5492 24.77524 230.7881 24.49867 357.1386 22.60244

image8 220.3249 24.70017 226.8974 24.57251 770.2026 19.26475

image10 308.5724 23.23723 302.5938 23.3222 400.9387 22.10002

image11 238.7778 24.35086 343.8502 22.76711 504.2259 21.10455

image12 268.7335 23.83759 315.1184 23.14607 458.7786 21.51477

image13 265.4314 23.89128 412.873 21.97264 1717 15.7831

image14 156.5284 26.18487 358.2187 22.58932 1082.1 17.78813

image15 333.9457 22.89405 366.5487 22.48949 1029.3 18.00538

image16 324.9079 23.0132 341.8552 22.79238 1231.6 17.22611

image17 218.6883 24.73255 226.7877 24.57461 421.9114 21.87859

image19 256.9503 24.03231 249.3694 24.16237 199.9656 25.12125

30




In above five tables, out of 85 tests, 64 tests give less mean square error in

horizontal/diagonal band, 20 tests give less mean square error in vertical/diagonal

band and 1 test gives less mean square error in vertical/horizontal band.

Horizontal/diagonal band has more images with less mean square error and

vertical/diagonal band also contains some number of images with less mean square

error. Hence, it can be concluded that diagonal band contains less information of an

original image.

4.7 Comparison of Haar and Daubechies Wavelet Transform (Color

Image)5 different secret images and 17 different cover images are taken and

performance of Haar and Daubechies wavelet transform is compared on these images

in terms of mean square error.


transform (Secret images: secret7.jpg, secret2.jpg and secret9.jpg)

Cover Image

Secret Image: secret7.jpg



Daubechies Haar Daubechies Haar

Daubechies Haar

im 398.1939 568.3043 625 2922 493.4117 868.3666image1 172.5045 224.3552 732.4719 1507.3 153.2008 211.2879image2 203.7023 201.2225 419.8701 477.3989 184.2325 184.2972image3 209.7872 251.1179 637.3083 867.3118 199.3165 267.3142image4 233.7363 383.8844 708.2591 913.5079 342.028 310.868image5 131.9064 221.4519 528.3311 471.6635 228.6224 196.4583image6 228.9882 200.8243 504.8779 468.3548 135.8742 181.6099image8 203.7938 206.1901 483.7021 524.658 200.5832 182.3865image10 158.2519 174.7525 581.2159 578.8668 178.6397 201.5325

31

image11 174.9615 235.3116 573.8735 573.5831 205.5393 205.0389image12 170.9043 296.0749 505.7425 818.0785 166.2846 206.3234image13 190.3149 269.7852 493.964 531.0606 244.0035 252.3329image14 941.9796 970.7701 214.8173 346.3505 237.8765 297.2593image15 294.7213 348.1616 512.3076 1081.7 229.0612 485.31image16 240.8902 632.5615 596.62 1926.4 196.7889 403.7838image17 221.8758 220.7456 485.8181 510.8235 190.7451 190.4981image19 178.6816 227.0378 715.7114 623.5331 180.916 195.1315

In table 4.14 mean square error is calculated with different secret images.

Table 4.14 can be analysed as follows:

Case I:- Secret Image: secret7.jpg

In this case, 14 cover images out of 17 images have less mean square

error in Daubechies wavelet transform than in Haar wavelet transform.

imim

age1

image

2

image

3

image

4

image

5

image

6

image

8

image

10

image

11

image

12

image

13

image

14

image

15

image

16

image

17

image

190

200

400

600

800

1000

1200

DaubechiesHaar

Cover Image

MSE

Case II:- Secret Image: secret2.jpg



32

imim

age1

image

2

image

3

image

4

image

5

image

6

image

8

image

10

image

11

image

12

image

13

image

14

image

15

image

16

image

17

image

190

500

1000

1500

2000

2500

3000

3500

DaubechiesHaar

Cover Image

MSE

Case III:- Secret Image: secret9.jpg


error of Daubechies wavelet transform than in Haar wavelet transform.

imim

age1

image

2

image

3

image

4

image

5

image

6

image

8

image

10

image

11

image

12

image

13

image

14

image

15

image

16

image

17

image

190

100200300400500600700800900

1000DaubechiesHaar

Cover Image

MSE


transform (Secret images: secret6.jpg and secret4.jpg)

Cover Secret Image: secret6.jpg Secret Image: secret4.jpg

33

Image Daubechies Haar Daubechies Haarim 342.739 467.0845 162.2776 153.5925image1 225.9264 439.2729 338.6824 331.5501image2 223.3976 244.0339 218.337 278.2767image3 233.8684 262.3655 304.6215 308.6364image4 254.3868 528.1992 332.2241 333.6193image5 206.289 393.898 272.0327 292.0546image6 261.3139 259.5599 216.5492 324.2621image8 234.5507 253.7041 220.3249 319.811image10 186.0707 237.8682 308.5724 378.0647image11 174.4255 224.2154 238.7778 261.0881image12 231.3841 270.1278 268.7335 279.6169image13 173.4452 407.0945 265.4314 235.7293image14 227.3351 206.2585 156.5284 128.7204image15 200.1144 682.4434 333.9457 510.7621image16 271.593 652.4881 324.9079 975.1453image17 203.5504 269.4754 218.6883 334.4228image19 294.1738 255.9894 256.9503 345.5191



Case IV:- Secret Image: secret6.jpg



imim

age1

image

2

image

3

image

4

image

5

image

6

image

8

image

10

image

11

image

12

image

13

image

14

image

15

image

16

image

17

image

190

100

200

300

400

500

600

700

800DaubechiesHaar

Cover Image

MSE

Case V:- Secret Image: secret4.jpg

34



imim

age1

image

2

image

3

image

4

image

5

image

6

image

8

image

10

image

11

image

12

image

13

image

14

image

15

image

16

image

17

image

190

200

400

600

800

1000

1200

Daubechies Haar

Cover Image

MSE


Daubechies wavelet transform than Haar wavelet transform. Hence it can be

concluded that Daubechies wavelet transform gives better quality of secret image

extracted from stego image.

4.8 Comparison of Stego and Original Image in 1-level and 2-level

Daubechies Wavelet Transform5 different secret images and 30 different cover images are taken and

performance of 1-level and 2-level Daubechies Wavelet Transform is compared on

these images in terms of mean square error.



Case I:- Secret Image: imm.jpg

35


mean square error of 2-level Daubechies wavelet transform is less than 1-level

Daubechies wavelet transform.

lina1

image

11

image

2 test

aaa aadrae tes

t1noise

highpass rose

image

12

image

16

image

20

image

24

image

30

image

31

image

32

image

33

image

34

image

37

image

39

image

40

image

26moon

0

50

100

150

200

250

1-level DWT2-level DWT

Cover Image

MSE

Case II:- Secret Image: roses.jpg




36

lina1

image

11

image

2 test

aaa aa draetest1

noise

highpass rose

image

12

image

16

image

20

image

24

image

30

image

31

image

32

image

33

image

34

image

37

image

39

image

40

image

26moon

0

50

100

150

200

250


Cover Image

MSE

Case III:- Secret Image: sec.jpg




lina1

image

11

image

2 test

aaa aadraetes

t1noise

highpass rose

image

12

image

16

image

20

image

24

image

30

image

31

image

32

image

33

image

34

image

37

image

39

image

40

image

26moon

020406080

100120140160180


Cover Image

MSE


Daubechies wavelet transform (Secret images: imm.jpg, roses.jpg and sec.jpg)

Cover Secret Image: imm.jpg Secret Image: roses.jpg Secret image: sec.jpg

37

Image 1-level DWT

2-level DWT

1-level DWT

2-level DWT

1-level DWT

2-level DWT

lina1 69.263 55.6037 41.5012 53.4207 23.5212 18.8902image11 86.3989 32.4427 20.1064 39.3874 28.8866 14.7607image2 6.7769 20.829 10.5945 22.9832 8.4757 23.3053test 27.9439 15.6591 35.707 15.652 20.195 7.9869aaa 210.0028 157.7097 222.5804 155.9189 170.7238 93.5402aa 171.6717 109.3588 189.7067 115.5015 138.3215 91.8172drae 28.8077 10.3062 25.4865 7.8945 25.7562 18.9411test1 48.4592 12.0588 44.5792 13.0256 25.1044 11.3857noise 21.6844 11.7137 16.0085 12.8348 23.4008 17.541highpass 100.796 42.7923 79.4167 44.0782 125.5963 58.2303rose 79.5021 40.7063 54.5376 31.3504 91.1024 41.2349image12 16.1012 10.4295 15.5793 17.1226 10.031 13.6404image16 11.7778 6.3925 15.4712 9.1019 16.9137 12.3951image20 6.7078 8.7152 5.3653 17.5046 19.968 7.5495image24 154.7545 54.2682 155.7083 57.9516 95.0769 32.7753image30 66.6672 19.3326 69.008 19.2329 37.577 13.3198image31 14.0608 7.0694 10.136 8.1792 16.2166 11.728image32 20.7552 11.2582 28.2165 7.1292 6.775 8.1343image33 105.4483 30.2575 110.3561 26.9071 91.4881 23.9379image34 114.2732 40.5746 157.358 47.9621 36.6758 12.3637

image37 7.4781 23.6552 5.8902 6.8154 4.8961 5.6851image39 6.2222 22.1737 6.9394 19.9322 7.3017 8.0031image40 30.6817 7.6224 34.4693 8.3059 13.0789 9.4301image26 67.26 86.7173 69.7705 90.0749 65.3833 53.6875moon 106.4508 101.9788 119.7945 61.2113 116.9564 70.9453


Daubechies wavelet transform (Secret images: house1.jpg and secr.jpg)

38

Cover Image

Secret Image: house1.jpg Secret Image: secr.jpg1-level DWT 2-level DWT 1-level DWT 2-level DWT

lina1 43.2159 42.6108 19.1232 33.9433

image11 56.7374 27.8726 40.6513 20.4093

image2 11.2237 24.4318 12.1635 10.3764

test 28.8895 14.671 60.842 11.1295

aaa 164.9981 108.9386 93.0709 80.7572

aa 133.9229 80.1809 107.8136 73.1583

drae 25.7644 14.9114 24.4353 13.838

test1 49.3116 21.2489 19.6917 11.9043

noise 25.8955 16.1199 15.4836 8.6047

highpass 139.4828 89.574 115.7898 50.1417

rose 168.195 70.1468 96.9314 48.7909

image12 13.1434 11.6343 26.1999 12.5616

image16 19.265 21.6625 27.3666 8.5831

image20 22.0457 12.622 8.181 8.1393

image24 117.7584 50.5827 71.5436 30.1581

image30 45.0292 17.7184 18.1149 12.7171

image31 16.4022 12.6851 21.3668 7.2775

image32 14.0223 12.6516 11.1747 11.6017

image33 76.3702 34.1236 84.3519 22.9537

image34 82.3744 20.6973 30.3422 7.9234

image37 6.0175 8.8844 3.5589 10.525

image39 9.3479 13.9997 5.4536 5.6625

image40 18.3287 8.9739 18.3843 6.2147

image26 83.3823 64.4212 77.2836 58.9217

moon 136.7432 123.4857 120.4071 84.6188



Case IV:- Secret Image: house1.jpg

39




lina1

image

11

image

2 test

aaa aa draetest1

noise

highpass rose

image

12

image

16

image

20

image

24

image

30

image

31

image

32

image

33

image

34

image

37

image

39

image

40

image

26moon

020406080

100120140160180


Cover Image

MSE

Case V:- Secret Image: secr.jpg




lina1

image

11

image

2 test

aaa aadraetes

t1noise

highpass rose

image

12

image

16

image

20

image

24

image

30

image

31

image

32

image

33

image

34

image

37

image

39

image

40

image

26moon

0

20

40

60

80

100

120

140


Cover Image

MSE

40


2-level Daubechies wavelet transform than 1-level Daubechies wavelet transform. So,

original image is less distorted while using 2-level Daubechies wavelet transform.

4.9 Some experiment images and results

41

(a)

(c)

(d) (e)


image (d) Original Secret Image (e) Extracted Secret Image

42

(a)

(c)

Figure 4.8: (a) Cover Image (image 37) (b) Stego Image (c) Wavelet Transform of

an image (d) Original Secret Image (e) Extracted Secret Image

43

(b)

(c)

(d) (e)


image (d) Original Secret Image (e) Extracted Secret Image

Figure 0.10: (a) Cover Image

(image8) (b) Stego Image (c)

Wavelet Transform of an image (d)

Original Secret Image (e) Extracted Secret

Image

44

(b)

(d) (e)

Figure 0.5: (a) Cover Image (image11) (b) Stego Image (c) 2- level Wavelet

Transform of an image (d) Original Secret Image (e) Extracted Secret Image

45

(a)

(b)

(c)

(d) (e)

5. ConclusionIn steganography, secret information is to be embedded in such a way that it

doesn’t make significant change to cover file. In this thesis, Daubechies discrete

wavelet transform technique is used to embed the secret information and different

tests have been performed. Different results show that diagonal band of wavelet

transform carries less information of original image and hence coefficients of this

band can be used to embed the secret information without much change to an original

image. Instead of taking single band, embedding secret information in combination of

bands gives better result in terms of MSE and horizontal/diagonal band is best for

embedding.

Analyzing 1-level and 2-level Daubechies DWT, MSE is less while using 2-

level Daubechies DWT while comparing original image and stego image. But there is

not much difference in MSE in both 1-level and 2-level Daubechies DWT while

comparing secret image and extracted secret image.

Also the performance of Daubechies DWT and Haar DWT is evaluated in

terms of MSE and computation time. Different tests show that Daubechies DWT

gives less MSE and hence more PSNR compared to Haar DWT. In terms of

computation time Haar DWT is executed slightly faster than Daubechies DWT. But

analyzing computation time and MSE, it can be concluded that overall performance

of Daubechies DWT is better than Haar DWT.

46

References[1] B. G. Banik and S. K. Bandyopadhyay, “A DWT Method for Image

Steganography”, International Journal of Advanced Research in Computer Science

and Software Engineering, 2013

[2] A. Joseph and T. Narasimmalou, “Optimized Discrete Wavelet Transform based

Steganography”, IEEE Interational Conference on Advanced Communication Control

and Computing Technologies, 2012

[3] Chi-Kwong Chan, L.M. Cheng, “Hiding data in images by simple LSB

substitution”, Pattern Recognition Society, 2004

[4] C. Simpson, "The Rules of Unified English Braille", Round Table on Information

Access for People with Print Disabilities Inc, Australia, 2010

[5] J. M. Guo and T. N. Le, “Secret Communication Using JPEG Double

Compression”, Signal Processing Letters IEEE, 2010.

[6] S. M. Karim et al., “A New Approach for LSB Based Image Steganography using

Secret Key”, International Conference on Computer and Information Technology,

2011

[7] S. Tiwari and R. P. Mahajan, “A Secure Image Based Steganographic Model

Using RSA Algorithm and LSB Insertion”, International Journal of Electronics

Communication and Computer Engineering, 2012

[8] M. A. Ahmad et al., “Achieving Security for Images by LSB and MD5”, Journal

of Advanced Computer Science and Technology Research, 2012

[9] W. Luo et al., “Security Analysis on Spatial 1 Steganography for JPEG

Decompressed Images”, Signal Processing Letters IEEE, 2011.

47

[10] C. P. Sumathi and T. Santanam, “A Study of Various Steganographic

Techniques Used for Information Hiding”, International Journal of Computer Science

& Engineering Survey, 2013

[11] P. Bateman and H. G. Schaathun, “Image Steganography and Steganalysis”,

Master’s thesis in Security Technologies & Applications, University of Surrey, 2008

[12] T. Morkel and J.H.P. Eloff, “An Overview Of Image Steganography”,

Information and Computer Security Architecture (ICSA) Research Group, 2012

[13] H. Rohil et al., “Optimized Image Steganography using Discrete Wavelet

Transform (DWT)”, International Journal of Recent Development in Engineering and

Technology, 2014

48

Appendix AFigures used for cover image and secret image in the thesis (grayscale)

49

Appendix BFigures used for cover image and secret image in the thesis (color)

52

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