robust color image watermarking using nonsubsampled contourlet transform

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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 3, March 2011

Robust Color Image Watermarking Using

Nonsubsampled Contourlet Transform

C.Venkata Narasimhulu K.Satya Prasad

Professor, Dept of ECE Professor, Dept of ECE,HIET, Hyderabad, India JNTU Kakinada, India

[email protected] [email protected],

Abstract-

In this paper, we propose a novel hybrid spreadspectrum watermarking scheme for authentication of color images using nonsubsampled contourlet transformand singular value decomposition. The host color imageand color watermark images are decomposed intodirectional subbands using Nonsubsampled contourlettransform and then applied Singular value decomposition

to mid frequency sub-band coefficients. The singularvalues of mid frequency sub-band coefficients of colorwatermark image are embedded into singular values of mid frequency sub-band coefficients of host color image inRed, Green and Blue color spaces simultaneously based onspread spectrum technique. The experimental resultsshows that the proposed hybrid watermarking scheme isrobust against common image processing operations suchas, JPEG, JPEG 2000 compression, cropping, Rotation,histogram equalization, low pass filtering ,medianfiltering, sharpening, shearing ,salt & Pepper noise,Gaussian noise, grayscale conversion etc. It has also beenshown the variation of visual quality of watermarkedimage for different scaling factors. The comparativeanalysis reveals that the proposed watermarking scheme

out performs the color image watermarking schemesreported recently.

Keywords: Color image watermarking, Nonsubsampled Contourlet Transform, Singular value decomposition, Peaksignal to noise ratio, normalized Correlation coefficient.

1. INTRODUCTION:

In recent years, multimedia products were rapidlydistributed over the fast communication systems suchas Internet, so there exist strong requirement to protectthe ownership and authentication of the multimediadata. Digital watermarking is a method of securing thedigital data by embedding additional information calledwater mark into the digital multimedia content. This

embedding information can be later extracted from or detected in the multimedia to make an assertion aboutthe data authenticity. Digital watermarks remain intactunder transmission/transformation, allowing us toprotect our ownership rights in digital form. Absence of watermark in a previously watermarked image wouldlead to the conclusion that the data content has beenmodified. A watermarking algorithm consists of watermark structure, an embedding algorithm andextraction or detection algorithm. In multimedia

applications, embedded watermark should be invisible,robust and have a high capacity. Invisibility refers todegree of distortion introduced by the watermark and itsaffect on the viewers and listeners. Robustness is theresistance of an embedded watermark againstintentional attack and normal signal processingoperations such as noise, filtering, rotation, scaling,cropping and lossey compression etc. Capacity is theamount of data can be represented by embeddedwatermark.[1]

Watermarking techniques may be classified indifferent ways. The classification may be based on thetype of watermark being used, i.e., the watermark maybe a visually recognizable logo or sequence of randomnumbers. A second classification is based on whether the watermark is applied in the spatial domain or thetransform domain. In spatial domain, the simplestmethod is based on embedding the watermark in theleast significant bits (LSB) of image pixels. However,spatial domain techniques are not resistant enough toimage compression and other image processing

operations.

Transform domain watermarking schemes such asthose based on the discrete cosine transform (DCT), thediscrete wavelet transform (DWT), contourlettransforms along with numerical transformations suchas Singular value Decomposition (SVD) and Principlecomponent analysis (PCA) typically provide higher image fidelity and are much robust to imagemanipulations.[2]Of the so far proposed algorithms,wavelet domain algorithms perform better than other transform domain algorithms since DWT has a number of advantages over other transforms including timefrequency localization, multi resolution representation,

superior HVS modeling, and linear complexity andadaptively and it has been proved that wavelets aregood at representing point wise discontinuities in onedimensional signal. However, in higher dimensions,e.g. image, there exists line or curve-shapeddiscontinuities. Since, 2D wavelets are produced bytensor products of 1D wavelets; they can only identifyhorizontal, vertical, diagonal discontinuities (edges) inimages, ignoring smoothness along contours andcurves. Curvelet transform was defined to represent two

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dimensional discontinuities more efficiently, with leastsquare error in a fixed term approximation. Curvelettransform was proposed in continuous domain and itsdiscretisation was a challenge when critical sampling isdesired. Contourlet transform was then proposed by DOand Vetterli as an improvement of Curvelet transform.The Contourlet transform is a directional multi

resolution expansion which can represents imagescontains contours efficiently. The CT employsLaplacian pyramids to achieve multi resolutiondecomposition and directional filter banks to achievedirectional decomposition [3] Due to down samplingand up sampling, the Contourlet transform is Shiftvariant. However shift invariance is desirable in imageanalysis applications such as edge detection, Contour characterization, image enhancement [4] and imagewatermarking. Here, we present a NonSubsampledContourlet transform (NSCT) [5] which is shiftinvariant version of the contourlet transform. TheNSCT is built upon iterated nonsubsampled filter banksto obtain a shift invariant image representation.

In all above transform domain watermarking techniques

including NSCT the watermarking bits would be

directly embedded in the locations of sub band

coefficients. Though here the visual of perception of original image is preserved, the watermarked image

when subjected to some intentional attacks like

compression the watermark bits will get damaged.

Coming to the spatial domain watermarking using

numerical transformation like SVD (Gorodetski [6], liuet al [7]) they provide good security against tampering

and common manipulations for protecting rightful

ownership. But these schemes are non adaptive, thusunable to offer consistent perceptual transparency of

watermarking of different images. To provide adaptive

transparency, robustness to the compressions and

insensitivity to malicious manipulations, we propose a

novel image hybrid watermarking scheme using NSCTand SVD.

In this paper, proposed method is compared withanother which is based on Contourlet Transform and

singular value decomposition (CT-SVD). The peak

signal to noise ratio (PSNR) between the original image

and watermarked image and the normalized correlation

coefficients (NCC) and bit error rate (BER) between

the original watermark and extracted were calculated

with and without attacks. The results show highimprovement detection reliability using proposed

method. The rest of this paper is organized as follows.Section 2 describes the Nonsubsampled contourlet

transform, section 3 describes singular value

decomposition, section 4 illustrates the details of

proposed method, in section 5 experimental results are

discussed without and with attacks, conclusion andfuture scope are given in section 6.

2. NONSUBSAMPLED CONTOURLETTRANSFORM

The Nonsubsampled contourlet transform is a newimage decomposition scheme introduced by Arthur

L.Cunha, Jianping Zhou and Minh N.Do [8]. NSCT is

more effective in representing smooth contours in

different directions of in an image than contourlettransform and discrete wavelet transform. The NSCT is

fully shift invariant, Multi scale and multi direction

expansion that has a fast implementation. The NSCT

exhibits a similar sub band decomposition as that of contourlets, but without down samplers and up samplers

in it. Because of its redundancy the filter design problem

of nonsubsampled contourlet is much less constrained

than that of contourlet. The NSCT is constructed by

combining nonsubsampled pyramids andnonsubsampled directional filter bank as shown in

figure (1).The nonsubsampled pyramid structure results

the multi scale property and nonsubsampled directional

filter bank results the directional property.

(a) (b)

Figure 1 The nonsubsampled contourlet transform (a)nonsubsampled filter bank structure that implements the NSCT.(b) Idealized frequency partitioning obtained with NSCT

2.1 Nonsubsampled Pyramids

The nonsubsampled pyramid is a two channelnonsubsampled filter bank as shown in figure2(a).The H0(z) is the low pass filter and one then setsH1(z) =1-H0(z). the corresponding synthesis filters

G0(z) =G1(z)=1.

the perfect reconstruction condition is given byBezout identity

H0(z)G0(z)+H1(Z) G1 (Z) =1………………(1)

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:

(a) (b)

Figure (2): Nonsubsampled pyramidal filter (a). Ideal frequency response of nonsubsampled pyramidal filter (b).The cascading analysis of three stages nonsubsampled pyramid by iteration of two channels

Nonsubsampled filter banks.

Multi scale decomposition is achieved fromnonsubsampled pyramids by iterating the

nonsubsampled filter banks by up sampling all filters

by 2 in both direction the next level decomposition is

achieved. The complexity of filtering is constantwhether the filtering is with H(z) or an up sampled

filter H(z m ) computed a Trous algorithm The

cascading of three stage analysis part is shown infigure 2( b)

2.2 Nonsubsampled directional Filter Banks:

The directional filter bank (DFB) is constructed fromthe combination of critically-sampled two-channel

fan filter banks and resampling operations. The

outcome of this DFB is a tree-structured filter bank

splitting the 2-D frequency plane into wedges. The

nonsubsampled directional filter bank which is shift

invariant is constructed by eliminating the down andup samplers in the DFB.The ideal frequency response

of nonsubsampled filter banks is shown in figure3 (a)

To obtain multi directional decomposition, thenonsubsampled DFBs are iterated. To obtain the

next level decomposition, all filters are up

sampled by a quincunx matrix given by

Q =

……………..(2)

The analysis part of iterated nonsubsampled filter

bank is shown in figure 3 (b)

(a) (b)

Figure (3) Nonsubsampled directional filter bank (a) idealized frequency response of nonsubsampled directional filter bank.(b) Theanalysis part of an iterated nonsubsampled directional bank.

3. SINGULAR VALUE DECOMPOSITION

Singular value decomposition (SVD) is apopular technique in linear algebra and it hasapplications in matrix inversion, obtaining lowdimensional representation for high dimensional

data, for data compression and data denoising. If A is any N x N matrix, it is possible to find adecomposition of the form

1 1

1 ‐1


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A=USVT

Where U and V are orthogonal matrices of order

N x N and N x N such that UTU=I,VTV=I , and the

diagonal matrix S of order N x N has elements λ i (i=1,2,3,..n) , I is an identity matrix of order N x N.

The diagonal entries are called singular values of

matrix A, the columns of U matrix are called the left

singular values of A, and the columns of V are

called as the right singular values of A.The general properties of SVD are [1], [2], [9]

a) Transpose: A and its transpose AT have the

same non-zero singular values.b) Flip: A, row-flipped Arf , and column-flipped Acf have the same non-zero singular values.

c) Rotation: A and Ar (A rotated by an

arbitrary degree) have the same non-zero singular values.

d) Scaling: B is a row-scaled version of A by

repeating every row for L1 times. For each non-zero

singular value λ of A, B has √L1λ . C is a column-

scaled version of A by repeating every column for L2 times. For each nonzero singular value λ of A, C

has √L2λ . If D is row-scaled by L1 times and

column-scaled by L2 times, for each non-zerosingular value λ of A, D has √L1L2λ .

e) Translation: A is expanded by adding rowsand columns of black pixels. The resulting matrixAe has the same Non-zero singular values as A.

The important properties of SVD from the view

point of image processing applications are:

1. The singular values of an image have verygood stability i.e. When a small perturbation is

added to an image, their singular values do not

change significantly.

2. Singular value represents intrinsic algebraic

image properties.

Due to these properties of SVD, in the last fewyears several watermarking algorithms have been

proposed based on this technique. The main idea of this approach is to find the SVD of a original image

and then modify its singular values to embedded the

watermark. Some SVD based algorithms are purely

SVD based in a sense that only SVD domain is used

to embed watermark into original image. Recentlysome hybrid SVD based algorithms have been

proposed where different types of transform domain

including discrete cosine transform (DCT), discrete

wavelet transform (DWT), Contourlet transform(CT) etc have been used to embed watermark into

original image. here the proposed scheme uses

nonsubsampled contourlet transform(NSCT) alongwith SVD for watermarking to obtain better

performance compared to existing hybrid

algorithms.

4. PROPOSED ALGORITHM

In this paper, Nonsubsampled Contourlet

Transform and SVD based hybrid technique isproposed for color image watermarking that uses

true color images for both watermark and host

images. The robustness and visual quality of

watermarked image is tested with three quantifierssuch as PSNR, NCC and Bit Error Rate. It is

investigated whether the NSCT-SVD advantages

over CT-SVD for color image watermarking with

their extra features would provide any significance

in terms of watermark robustness and invisibility.4.1 , 4.2 explain the watermark embedding and

extraction algorithm [10],[11]

4.1 Watermark Embedding Algorithm

The proposed watermark embedding algorithm

is shown in Figure 4. The steps of watermark embedding algorithm are as follows.

Step1: Separate the R G B color spaces of both

host and watermark color images.

Step2: Apply Nonsubsampled Contourlet

Transform to the R color space of both host image

and watermark image to decompose them into subbands.

Step3: Apply SVD to mid frequency sub-band of

CT of R color space of both host and watermark

image.

Step4: Modify the singular values of midfrequency sub-band coefficients of R color space of

host image with the singular values of mid

frequency sub-band coefficients of R color space of watermark image using spread spectrum technique.

i.e. λ I’ = λ I + α λ W.,

Where α is scaling factor [9], λ I is singular valueof R color space of host image, λ W is singular valueof R color space of watermark and λ I’

becomes

singular value of R color space watermarked image.

Step5: Apply inverse SVD on modified singular

values obtained in step4 to get the mid frequency

sub-band coefficients of watermarked image.

Step6: Apply inverse Nonsubsampled

Contourlet Transform to the mid frequency sub-


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band coefficients obtained in step 5 to get the R

color space of watermarked image.

Step7: Apply the same Steps from Step2 to

Step6 for the G and B color subspaces.

Step 8: Combine the R,G and B color spaces of watermarked image to obtain the color watermarked

image.

Figure 4 Watermark Embeddign Algorithm

4.2 Watermark Extraction Algorithm

The watermark extraction algorithm is shown in

Figure 5. The Steps of watermark extractionalgorithm are as follows.

Step1: Separate the R,G,B color spaces of

watermarked image.

Step2: Apply Nonsubsampled Contourlet

Transform to the R color space obtained in step1.

Step3: Apply SVD to mid frequency sub-band of

R color space of transformed watermarked image.

Step4: Extract the singular values from mid

frequency sub-band of R color space of

watermarked and host image

i, e λ W = ( λ I’ - λ I )/ α

Where λ I is singular value of watermarked image.

Step5: Apply inverse SVD to obtain mid

frequency coefficients of R color space of

transformed watermark image using Step 3.

Step6: Apply inverse NSCT using the

coefficients of the mid frequency sub-band to obtainthe R color space of Watermark image.

Step7: Repeat the Steps 2 to 6 for G and B color

spaces.

Step8: Combine the R,G and B color spaces to

get the color watermark.

Figure 5 Watermark Extracting Algorithm

5. EXPERIMENTAL RESULTS

In the experiments, we use the true color “tajmahal.jpg” of size 256X256 as host image asshown in the Figure 6 and true color “lena.jpg” of size 128 X 128 as watermark as shown in Figure 7.The experiment is performed by taking scalingfactor alpha as 0.5.The results show that there are noperceptibly visual degradations on the watermarkedimage shown in Figure 8 with a PSNR of 45.2253dB. Extracted watermark without attack isshown in Figure 9 with NCC around unity and BER of 0.1339. MATLAB 7.6 version is used for testingthe robustness of the proposed method.

The proposed algorithm is tested for different host

images such as “lotus.jpg”, ”Baboon.jpg”,

”Barbara.jpg”, ”Way.jpg” ,”Horse.jpg” and“Wheel.jpg” as shown in Table 1 and it is observed

that there are no visual degradations on the respected


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watermarked images. For all the different Host test

images, the watermark is effectively extracted with

around unity NCC. Various intentional and non-

intentional attacks are tested for robustness of the

proposed watermark algorithm includesJPEG,JPEG2000compressions, low pass filtering,

Rotation, Histogram Equalization ,Median Filtering,

Salt &Pepper Noise, Weiner Filtering, GammaCorrection, Gaussian Noise, Rescaling, Sharpening

Blurring ,Contrast Adjustment ,Automatic cropping,

Dilation, Row Colum Copying, Row Colum

removing, color to Gray scale conversion ,shearing

and sharpening. The term robustness describes thewatermark resistance to these attacks and can be

measured by the bit-error rate which, is defined as the

ratio of wrong extracted bits to the total number of embedded bits.

In table 2, extracted watermark and attacked

watermarked image with NCC and BER are shown.

The quality and imperceptibility of watermarkedimage is measured by using PSNR. The PSNR iscalculated separately for R, G, B color space of

watermarked image with respect to the respective

color space of host image using eq.3 [12]. The

final PSNR of watermarked image is taken as meanof PSNR obtained with three color spaces. The

similarity of extracted watermark with original

watermark embedded is measured using NCC. The

NCC is calculated using eq. (4) [13]for the three

color spaces and their mean is taken as the resultant

Normalized Correlation coefficient. The proposedmethod is also tested for binary and grayscale

watermark image of size 128x128 and watermarked

and extracted watermark are shown in table 3.

……….….(3)

Normalized Correlation Coefficient:

………..(4)

Fig 6:Original image-"Tajmahal.jpg”

Fig 7:Watermark image-"Lena.jpg”

Fig 8:Watermarked LenaPSNR= 45.2253

Fig 9:ExtractedWatermark

Ncc=0.9991,Ber=0.1339

TABLE 1: WATERMARKED AND EXTRACTED WATERMARK WITH PSNR, NCC, AND BER FOR DIFFERENT ORIGINALIMAGES.

Original image“lotus.jpg”

Watermark image“LENA.jpg”

Watermarked image withPSNR=46.2785

Extracted imageNCC= 0.9983,Ber=0.1610


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Original image“baboon.jpg”


Watermarked image with

PSNR=44.8322Extracted image

NCC=0.9992, Ber=0.1342

Original image

“barbara.jpg”

Watermark image

“LENA.jpg”


PSNR=44.4930

Extracted image

NCC=0.9994,Ber=0.1299

Original image

“way.jpg”

Watermark image

“LENA.jpg”


PSNR=44.7550

Extracted image

NCC= 0.9994, Ber=0.1140

Original image

“horse.jpg”

Watermark image

“LENA.jpg”


PSNR= 44.7308

Extracted image

NCC= 0.9994, Ber=0.1201

Original image“wheeljpg”


Watermarked image withPSNR= 45.5204

Extracted imageNCC= 0.9985, Ber=0.1614


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TABLE 2: EXTRACTED WATERMARKS WITH NCC AND BER FOR DIFFERENT ATTACKS ALONG WITH ATTACKEDWATERMARKED IMAGE

Jpeg compression Ncc= 0.9985,Ber=0.3306 Jpeg2000Ncc= 0.9995,Ber=0.1056

Salt & pepper noise Ncc= 0.6948, Ber=0.4503 Low Pass filtering Ncc= 0.9729 Ber=0.2995

utomatic cropping Ncc= 0.9538 Ber=0.3449 Histogram Equalization Ncc= 0.9808 Ber=0.3128

Rotation Ncc= 0. 0.9951 Ber=0.2958 Median filtering Ncc= 0.9484 Ber=0.3178

Contrast adjustment Ncc= 0.9985 Ber= 0.1613 Weiner filter Ncc= 0.9982 Ber=0.2051


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Gamma correction Ncc= 0.9989 Ber=0.1387 Gaussian Noise Ncc= 0.8399 Ber=0.3120

Sharpening Ncc= 0.8379 Ber=0.3967 Gaussian Blurring Ncc= 0.9719 Ber=0.3003

Shearing Ncc= 0.9744 Ber=0.2889 Dilatations= 0.9443 Ber=0.3332

Color to grayscale Ncc= 0.8163 Ber=0.3490 Row & column removal Ncc=0.9977 Ber=0.1930


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Row column copying Ncc= 0.9902 Ber=0.9734 Scaling (150%) Ncc = 0.9187

TABLE 3: WATERMARKED AND EXTRACTED WATERMARK IMAGES FOR BINARY AND GRAYSCALE WATERMARK

Original image“tajmahal.jpg

Binary Watermark image“ksp.bmp”.

Watermarked imagePSNR= 47.6710

Extracted imageNcc= 0.9995, Ber=0.0157

Original image“tajmahal.jpg

Binary Watermark image“lena.bmp”.

Watermarked imagePSNR= Inf

Extracted imageNcc= 1,Ber= 0

Original image “tajmahal.jpg Gray scale Watermark image“Lena.jpg”.

Watermarked imagePSNR=45.2629

Extracted imageNcc= 0.9992,Ber= 0.1345

In table 4, the proposed method is compared

with contourlet and SVD based algorithm [11].Itdemonstrates that proposed method is superior to

salt pepper noise, Rotation, Gaussian Noise,

Sharpening, Row and Colum removal and Rowand column copying.


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TABLE 4: COMPARISON OF CT+SVD ANDNSCT + SVD

S.No ATTACK Normalized Correlation

NSCT+SVD CT+SVD

1 Jpegcompression

0.9985 0.9996

2 Jpeg2000 0.9995 0.99963 Salt & pepper

noise

0.6948 0.6823

4 Low passfiltering

0.9729 0.9839

5 Automaticcropping

0.9538 0.9658

6 HistogramEquation

0.9808 0.9733

7 Rotation 0.9958 0.9750

8 Medianfiltering

0.9484 0.9680

9 Contrastadjustment

0.9985 0.9991

10 Weiner filter 0.9982 0.9989

11 Gammacorrection

0.9989 0.9995

12 Gaussian Noise 0.8399 0.7538

13 Sharpening 0.8379 0.8212

14 GaussianBlurring

0.9719 0.9841

14 Shearing 0.9744 0.9857

16 dilatations 0.9443 0.9678

17 Color tograyscale

0.8163 0.8693

18 Row & Columremoval

0.9977 0.9972

19 Row Columcopying

0.9902 0.9820

20 Scaling (150%) 0.9187 0.9417

6. CONCLUSION:

In this paper, a novel robust hybrid watermarking

scheme is proposed for authentication of color images using nonsubsampled contourlet transform

and singular value decomposition. Watermark is

embedded in all color spaces of host image by

modifying singular values of mid frequency sub band

coefficients with respect to watermark mid frequency

sub band coefficient with suitable scaling factor. Therobustness of watermark is improved for common

image procession operations by combining both theconcepts of nonsubsampled contourlet transform andsingular value decomposition. The proposed

algorithm is tested for different host images and

respective watermark images are obtained without

any visual degradation. The proposed algorithm

preserves high perceptual quality of the watermarked

image and shows an excellent robustness to attackslike Salt and Pepper Noise, Gaussian Noise, Row

Column Copying, and Row Column Removal.

7. REFERENCES:

[1]. C.Venkata Narasimhulu &K.Satya Prasad:”A novel robust

watermarking technique based on nonsubsampled contourlet

transform and SVD”, International Journal of multimedia and

Applications.vol.3, no.1, Feb2011.

[2]. C.Venkata Narasimhulu &K.Satya Prasad:”A hybrid

watermarking scheme using contourlet transform andsingular value Decomposition”, IJCSNS: International

Journal of Computer Science and Network Security.vol.10,

no.9, Sep2010.

[3] Minh N. Do, and Martin Vetterli, “The Contourlet

Transform: An Efficient Directional Multiresolution ImageRepresentation” IEEE Transaction on image processing, vol

14, issue no 12, pp 2091-2106, Dec 2005

[4] Jianping Zhou; Cunha, A.L, M.N.Do, “Nonsubsampled

contourlet transform construction and application in

enhancement” IEEE Trans. Image Proc Sept. 2005.

[5] Arthur L. Cunha, J. Zhou, and M. N. Do, “Nonsubsampled

contourlet transform: filter design and applications in

denoising” IEEE International conference on image

processing, September 2005.

[6] V.I.Gorodetski L.J.Popyack, and V.Samoilov, “SVD-based

approach to transparent embedding data into digital

images,” in proc. int. Workshop, MMM-ACNS,St Peterburg, Russia, May 2001, pp.263-274.10.

[7] R.Liu and T.Tan, “An SVD-Based Watermarking scheme

for Protecting rightful ownership,” IEEE Trans. Multimedia,vol.4, no.1, pp.121-128, Mar.2002.

[8] A. L. Cunha, J. Zhou, and M. N. Do, “The Nonsubsampled

contourlet transform: theory, design and applications,”

IEEE Trans. Image Proc., vol.15, no.10, October 2006.

[9] Emir Ganic and ahmet M. Eskicioglu “ Robust embedding

of visual watermarks using discrete wavelet transform and

singular value decomposition Journal. Of Electron.Imaging, Vol. 14, 043004 (2005); doi:10.1117/1.2137650

Published 12 December 2005

[10] Dongyan liu,wenbo Liu,Gong Zhang,”An adaptive

watermarking scheme based on nonsubsampled contourlettransform for color image authentication”.Proceedings of

the 2008 the 9th international conference for Young

computer Scientist,ISBN:978-0-7695-3398-8.

[11] C.Venkata Narasimhulu &K.Satya Prasad:”A new SVD

based hybrid color image watermarking for copy right

\ protection using Contourlet transform”, Communicated

to International Journal of computer and

Applications(IJCA) in March 2011.

[12] Ashraf. K. Helmy and GH.S.El-Taweel “AuthenticationScheme Based on Principal Component Analysis for

Satellite Images” International Journal of Signal

Processing, Image Processing and Pattern RecognitionVol. 2, No.3, September 2009.

[13] Matlab 7.6 version, Image Processing Tool Box.


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AUTHORS PROFILE:

C.V Narasimhulu

He received his Bachelor degree in Electronics and

Communication Engineering from S.V. University,Tirupati, India in 1995 and Master of Technology in

Instruments and Control Systems from Regional

Engineering College Calicut, India in 2000.He is

currently pursuing the Ph.D degree in the departmentof Electronics and Communication Engineering from

Jawaharlal Nehru Technological University

Kakinada, India. He has more than 15 years

experience of teaching under graduate and post

graduate level. He is interested in the areas of signalprocessing and multimedia security

K.Satya Prasad

Received his Ph.D degree from IIT Madras, India. He

is presently working as professor in ECE department,

JNTU college of Engineering Kakinada and Rector of

JNT University, Kakinada, India. He has more than

30 years of teaching and research experience. He

published 30 research papers in international and 20research papers in National journals. He guided 8

Ph.D thesises and 20 Ph.D thesises are under his

guidance. His area of interests is digital signal andimage processing, communications, adhoc networks

etc..,


robust color image watermarking using nonsubsampled contourlet transform

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