2013 International Conference on Computer Communication and Informatics (ICCCI -2013), Jan. 04 – 06, 2013,

Coimbatore, INDIA

Abstract—A novel digital image watermarking scheme based on

Contourlet Transform (CT) and QR factorization method is

proposed in this paper. Contourlet Transform is applied to the

original and watermark image so that it decomposes into

subbands. The lowest frequency coefficients are divided into

blocks. The standard deviation (SD) of each block is calculated

and the blocks that have SD greater than a predefined threshold

are decomposed by QR based factorization method. The

watermark is permuted after the application of CT. After the

embedding process the blocks are joined again to obtain the

watermarked image. It has been shown experimentally that even

after application of attacks on the watermarked image, the

watermark can be efficiently extracted from at least one block of

lowest frequency subband. The preprocessing of the watermark

and division into blocks has made the scheme more robust to

image processing attacks such as Scaling, Cropping, Rotation,

Gaussian noise and Compression.

Index Terms— Digital Image Watermarking, QR

factorization, Permutation, Contourlet Transform, Signal

Processing attacks.

I. INTRODUCTION

he advancement in the world wide web has made the

digital multimedia easily available to manipulate, copy

and store the content. It requires the protection of

multimedia content from unauthorized attacker which has

been made possible with the technique called Digital

watermarking. It is a technique which secures the original

information from unauthorized manipulation. It authenticates

the multimedia content and provides copyright protection [1].

Digital watermark is invisible copyright information that is

embedded into the cover image. To prove the ownership, the

watermark is extracted and compared with the original

watermark. This watermarking technique can be classified as

spatial domain and frequency domain. The spatial domain

watermarking is based on the pixel values of the image. This

simplest technique modifies the pixels of cover image in

accordance with the watermark [2]. It has the disadvantage

that it cannot withstand compression attacks. The frequency

domain watermarking techniques are mostly used for robust

watermarking. In this technique, the frequency components of

cover image are modified in accordance with the watermark.

The frequency domain watermarking is of many types. Some

of these are Discrete Wavelet Transform (DWT), Discrete

Cosine Transform (DCT), and Discrete Fourier Transform

(DFT) [3] etc. The watermarking using DCT and DWT is able

to withstand signal processing attacks. The DFT based

watermarking is resilient against geometric attacks in addition

to the signal processing attacks. The performance of DWT is

better than the other transforms because of its multi-resolution

representation and it can be expressed both in time and

frequency. However, this technique is not able to capture

directional information. Contourlet Transform (CT) proposed

by Do and Vetterli [4], has the property to capture directional

information. This additional feature makes it better than DWT.

On comparing DWT with CT, it is found that the DWT is able

to capture one dimensional signal efficiently but when it

comes to two dimensions, it is not able to capture the

discontinuities, smoothness and contours. CT represents

images with contours and discontinuities efficiently. While,

Contourlet Transform gives directional decomposition of

image to any number at each level whereas wavelet provide

directional decomposition of three levels only. Thus,

Contourlet Transform is proved to be better technique than

wavelets [5]. Contourlet transform has been used in the work

by Khalighi et al. [6]. Here, the CT has been performed on the

cover image and the embedding of watermark has been done

on the highest frequency directional subband. The payload

embedded can be of a large value. This provides resistance

against image processing attacks. At the same time it provides

a good visual quality.

Many matrix decomposition techniques have been used for

watermarking such as Singular Value Decomposition (SVD),

Non Negative Matrix Factorization (NMF), Schur

Factorization, QR Factorization etc. An algorithm proposed by

Yavuz et al. [7] deals with the ambiguities in SVD. The SVD

of watermark is computed and is used as a control parameter

to solve the problems related to ambiguities. Bi et al. [8]

decomposed the lowest frequency coefficients of Contourlet

transformed image. The watermark was scrambled using

Arnold Scrambling and Euclidean norm was used to embed

into the largest singular value. Thus the scheme performs a

fusion of CT with SVD method for watermarking.

Nonnegative Matrix Factorization has been implemented

along with CT by Silja et al. [9]. The technique decomposes

A Statistical Property based Image

Watermarking using Permutation and CT-QR

Priyanka Mitra1, Reena Gunjan

2

Department of Computer Engineering

Malaviya National Institute of Technology

Jaipur, Rajasthan, India, 302017

{ mitra.priyanka111 | reenagunjan

2 }@gmail.com

T

978-1-4673-2907-1/13/$31.00 ©2013 IEEE

2013 International Conference on Computer Communication and Informatics (ICCCI -2013), Jan. 04 – 06, 2013,

Coimbatore, INDIA

the cover image into subbands using CT. Then, the highest

frequency subband is further decomposed by using NMF and

SVD. This makes the method more robust than the SVD based

techniques. QR Factorization is an effective approach for

authenticating color images [10]. The red and green channels

are factorized to develop two watermarks. The replacement of

blue channel least significant bit plane is done according to the

scheme.

In this paper, a new method is proposed using Contourlet

Transform and QR matrix decomposition techniques. The

scheme uses permutation and combines CT with QR. It is

compared with Silja et al. [9] using the Normalized

Correlation values. The proposed scheme has been proved to

be robust against signal processing attacks.

The paper is organized in the following manner. The

description of Contourlet Transform is given in Section 2. An

overview of QR factorization method is given in Section 3.

Section 4 describes the proposed scheme. Section 5 elaborates

upon the quality metrics. Section 6 discusses the Experimental

results and the performance under attacks. The conclusions are

put forward in Section 7.

II. CONTOURLET TRANSFORM

The Contourlet Transform [11] is a frequency domain

watermarking technique which consists of double filter bank

structure. The image has multi resolution representation when

it is decomposed by Contourlet Transform. The Laplacian

Pyramid (LP) Filter bank structure proposed by Burt and

Adelson [12] captures the discontinuities at edge points. The

Directional Filter Bank Structure (DFB) [13] links the

discontinuities into linear structure. These two filters together

constitute Pyramidal Directional Filter Bank Structure. Thus

Contourlet Transform (CT) captures the discontinuities and

the smoothness of contours and represents the image in the

form of contour segments. The LP decomposes the original

image into band-pass and low-pass version at each level. The

k level DFB decomposes the band-pass image into 2k

directional wedge shaped subbands. So the image can be

decomposed iteratively into a set of low-pass and band-pass

image thus resulting in multi-scale decompositions. The multi-

scale decomposition using Contourlet Transform of „Lena‟ as

cover image for the proposed scheme is shown in Figure 1.

The watermark taken for the proposed scheme is „Logo‟ and

its CT decomposition is shown in Figure 2.

The matrix decomposition techniques have been used with

Contourlet Transform recently to make the decomposition

more complex and thus difficult to decrypt by the

unauthorized intruders. The proposed algorithm uses QR

decomposition technique on selected blocks of CT

decomposed image.

III. QR DECOMPOSITION

QR Decomposition is a matrix decomposition technique which

reduces the image matrix into more canonical form. The Eigen

values or linear equation solutions are the basis for the

decomposition. There are various matrix decomposition

techniques such as SVD (Singular Value Decomposition),

Schur Factorization, LU Decomposition, QZ Decomposition

etc. In linear algebra, QR decomposition technique can be

used for the factorization of square and rectangle matrix. QR

decomposes the matrix into an orthogonal and triangular

matrix. Consider an image matrix P of size AxB where

coefficients of image matrix are its pixel values. QR factorizes

the matrix P as:

P = Q R. (1)

P = [

] = QR. (2)

P = [

] [

]. (3)

Where, the orthogonal matrix is defined by matrix Q of size

AxA and the upper triangular is defined by matrix R of size

AxB. The orthogonal matrix Q has the following property:

QT.Q = I. (4)

Theorem: The image matrix P has a unique factorization [10].

Proof: Suppose matrix P can be decomposed into orthogonal

and triangular matrix as below.

P=Q1 R1 = Q2 R2. (5)

Where the triangular matrices are R1 and R2 and orthogonal

matrices are Q1, Q2. Thus, we have

S=

. (6)

Where, S matrix is orthogonal as well as triangular.

S = diagonal (s1, s2,,s3 ,…., sm). (7)

Where, R1=SR2. and . Thus we can say

that:

S= I, Q1 = Q2, R1 = R2. (8)

The above theorem states that the image matrix has unique

factorization. QR decomposition technique can be used with

image processing applications such as watermarking schemes.

QR Decomposition with Contourlet Transform is in use

recently as it provides enhanced security and robustness

against attacks.

IV. PROPOSED ALGORITHM

This paper proposes a watermarking scheme which uses

Contourlet Transform with QR factorization method. The

scheme embeds the watermark into the coefficients of cover

image. Other schemes embed watermark using Contourlet

Transform, the proposed scheme further improves the process

of watermarking by using QR factorized watermark to embed

into the selected blocks of QR factorized original image.

Contourlet Transform decomposes the original image into

approximate subband and detail subbands. The lowest

frequency subband of Contourlet domain represents the area

2013 International Conference on Computer Communication and Informatics (ICCCI -2013), Jan. 04 – 06, 2013,

Coimbatore, INDIA

of image which is highly smooth but which degrades the

image quality on modifications on pixel values. When the

watermark is embedded in the lowest frequency subband, then

it is found to be resistant against attacks but the watermark is

visible [6]. When the embedding of watermark is in highest

frequency subband, then the watermark is not perceptual but

this region is found to be susceptible to image processing

attacks. So the region chosen for the embedding is the lowest

frequency subband using a low visibility factor. This results in

a watermarked image in which watermark is not visible and is

resistant to image processing attacks as well.

Moreover, this subband is divided into blocks and the

embedding is done on the selected blocks in which the

threshold value is taken as the lower bound for the standard

deviation of each block. The blocks whose standard deviation

is greater than the threshold value is taken for the embedding

of watermark. The selected blocks are then decomposed using

QR Factorization. The lowest frequency subband of

watermark is selected after CT decomposition and permutation

is applied on it. This permuted watermark is taken for the

embedding scheme so that the attacker is unable to determine

the identity of watermark.

A. Watermark Embedding

The size of cover image P is taken as AxB and the size of

watermark image V of size CxD. The scheme for embedding is

shown in Figure 3 which first decomposes the cover image

and then watermark image using CT decomposition technique.

The selective block lowest frequency coefficients of cover

image are decomposed by QR factorization. The lowest

frequency subband of watermark is permuted and then

factorized using QR decomposition technique. The algorithm

for embedding watermark is as follows:

Step1: The cover image is factorized into subbands of required

number of levels by using Contourlet Transform

decomposition.

Step2: The lowest frequency subband of cover image is

selected and is further divided into blocks.

Step3: The statistical analysis of blocks is done and the blocks

that have standard deviation value higher than the threshold

value x are selected.

Step4: The LF subband blocks that are statistically selected are

factorized with the QR decomposition technique.

Step5: The watermark is factorized into subbands of required

number of levels by using Contourlet Transform.

Step6: The LF subband of the CT decomposed watermark

image is permuted.

Step7: The permuted LF subband of watermark image is

further factorized using QR decomposition technique.

Step8: The permuted and QR factorized watermark image is

embedded into the QR factorized cover image in the selected

blocks as shown:

U‟ = U + α M. (9) (4)

Where, U is the matrix of QR decomposed cover image and M

is the matrix of the processed watermark image. U’ is the

matrix of the watermarked cover image and the visibility

factor is taken as α.

Step9: The modified coefficients of cover image are then

applied with inverse QR technique.

Step10: The modified QR factorized blocks are then rejoined

and then inverse CT is applied to get the watermarked image.

B. Watermark Extraction

The extraction procedure is shown in Figure 4 which is the

reverse scheme of embedding. The input image for the

extraction scheme is the watermarked image which is

decomposed by Contourlet Transform. The lowest frequency

coefficients are divided into blocks and then QR

decomposition is applied on the selected blocks where

embedding was performed. The selected blocks are then QR

factorized and the QR factorized coefficients of cover image

are then subtracted from it and divided with the visibility

factor to obtain the coefficients of watermark. The coefficients

are then applied with inverse QR and then re-permutation. The

inverse CT is applied on the extracted coefficients to get the

watermark. The steps for watermark extraction are as follows:

Step1: The watermarked image is factorized using Contourlet

Transform into subbands of required number of levels.

Step2: The lowest frequency subband of watermarked image

is divided into blocks.

Step3: The selected embedded blocks are factorized using QR

decomposition technique.

Step4: The QR decomposed coefficients of watermark from

the lowest frequency subband are extracted using the

following equation.

M = ( U‟ – U ) / α . (10) (5)

Step5: The extracted coefficients are then subjected to inverse

QR decomposition technique.

Step6: The re-permutation is then applied on the extracted

coefficients and then inverse CT is performed to obtain the

watermark.

V. QUALITY METRICS

The quality metrics used for the watermarked image are MSE

(Mean Squared Error) and PSNR (Peak Signal to Noise

Fig. 2. Contourlet Transformed Logo Image with 2 LP levels and 8

directions.

Contourlet coefficients of watermark image

Fig. 1. Contourlet Transformed Lena Image with 2 LP levels and 8 directions.

Contourlet coefficients of original image

2013 International Conference on Computer Communication and Informatics (ICCCI -2013), Jan. 04 – 06, 2013,

Coimbatore, INDIA

Ratio). The average difference in the quality of image between

the original image and the distorted image is measured by

using MSE. While PSNR measures the effect on the quality of

image on applying the embedding scheme. So PSNR is a

technique which computes the maximum signal power to

noise power ratio. It is calculated to measure the similarity

between the original image and the watermarked image. The

high value of PSNR represents the good quality of

watermarked image and a smaller value shows that the image

is noisy. PSNR is measured in terms of logarithmic decibel

scale and is defined as:

(

) (11)

∑ ∑

(12)

The image matrix can be taken of size AxB. For square image

A=B. The number of bits per pixel for grayscale image is

taken as m=8. u’ represents the watermarked image and u

represents the original image intensity values. The PSNR

measured is 40.46 dB, 40.46dB, 41.36dB for Lena, Opera

House and Flower respectively. The PSNR values show that

the perceptual quality of the image does not degrades with the

proposed scheme. NC (Normalized Correlation), another

quality metrics is used to measure similarity between the

original watermark (M) and the extracted watermark (M*). It

is defined as follows:

∑ ∑

√∑ ∑ ∑ ∑

(13)

VI. EXPERIMENTAL RESULTS

The experiments were performed using „Lena‟, „Opera

House‟ and „Flower‟ images as the cover images. The images

were converted to 8 bit gray scale of size 512x512 as shown in

Figure 5. The watermark image used was the „Logo‟ of size

256x256. The conversion of watermark was done to gray scale

as shown in Figure 6. The watermarked images without the

application of attacks are displayed in Figure 7. The

watermarks extracted are shown in Figure 8. The “pkva”

filters were used by Contourlet Transform for the LP and DFB

structure. For the cover image, the lowest frequency sub-band

was of size 128x128. After the CT had been performed on

watermark, its lowest frequency subband coefficients of size

64x64 pixels had been used to modify the cover image. The

watermark was embedded and extracted from the selected

subband. The tool used for the computation is Matlab.

(a) Lena (b) Opera House (c) Flower

Fig. 5. Cover Images

Fig. 4. Watermark Extraction

Fig. 3. Watermark Embedding

2013 International Conference on Computer Communication and Informatics (ICCCI -2013), Jan. 04 – 06, 2013,

Coimbatore, INDIA

A. Performance under attacks

The images have been subjected various image processing

attacks and the performance of the proposed scheme is tested.

The proposed scheme is evaluated for robustness against

attacks such as Scaling, Rotation, Cropping, Gaussian noise

and JPEG compression. The visibility factor of the proposed

scheme is , so the watermarked image looks

perceptually similar to original image. The Normalized

Correlation (NC) is computed for various attacks as shown in

Table I, II and III. The attacks, NC values and extracted

watermarks are shown in tables.

1) Gaussian Noise Attack

To evaluate the performance of the proposed scheme, the

watermarked image is subjected to Gaussian Noise attack.

The Gaussian Noise attack is applied for different values of

variance. The results show that the proposed scheme has NC

value of 1 for the images. It is evident that that the proposed

scheme is resistant against Gaussian Noise attack.

2) Scaling Attack

The scaling attack involves the resizing of the image. Here,

the image has been reduced in size to 75%, as also magnified

to 125% and 150% of its size. Results show that the proposed

scheme is robust against attacks having different scaling

factors. The tables show better NC values of the test images as

compared to Silja‟s scheme. Thus, the watermark has been

accurately extracted even after the attacks.

3) Rotation Attack

On applying the rotation attack, the image is rotated by a few

degrees. In the proposed scheme, the Lena, Opera House and

Flower images show good results against rotation attacks. It

has been found that this value is one showing better

performance of the proposed scheme than Silja‟s scheme.

4) JPEG Compression Attack

The JPEG Compression attack with quality factors 60, 90 and

100 had been applied to the watermarked image. The scheme

has shown good results for the JPEG compression. The results

of Silja‟s scheme are slightly higher but NC values of 0.9

shows a very good extraction of watermark.

TABLE II RESULTS OF ATTACKS ON PROPOSED FOR OPERA HOUSE

IMAGE

Attack on Opera

House Image

Results

NC Proposed

scheme

Extracted

Watermark

NC Silja’s scheme

[9]

No

Attack 1.0000

0.9919

Gaussian Noise

0.001 1.0000

0.9407 0.003 1.0000

0.005 1.0000

Scaling

75% 0.9962

0.9100 125% 0.9998

150% 0.9997

Rotation 0.1 1.0000

0.8295

Cropping

0.4% 0.9998 0.9892

1.6% 0.9998

JPEG

Compres-sion

Quality

factor 60 0.9640

0.9869 Quality

factor 90 0.9648

Quality

factor 100 0.9646

TABLE I RESULTS OF ATTACKS ON PROPOSED FOR LENA IMAGE

Attack on Lena image

Results

NC Proposed

scheme

Extracted

Watermark

NC Silja’s scheme

[9]

No

Attack 1.0000

0.9919

Gaussian Noise

0.001 1.0000

0.9407 0.003 1.0000

0.005 1.0000

Scaling

75% 0.9755

0.9100 125% 0.9964

150% 0.9989

Rotation 0.1 1.0000

0.8295

Cropping

0.4% 0.9998 0.9892

1.6% 0.9998

JPEG

Compres-sion

Quality

factor 60 0.9326

0.9869 Quality

factor 90 0.9321

Quality

factor 100 0.9365

(a) (b) (c)

Fig. 8. Watermarks extracted from (a) Lena (b) Opera House (c) Flower

(a)Lena (b) Opera House (c) Flower

Fig. 7. Images after Watermarking

Fig. 6. Watermark

2013 International Conference on Computer Communication and Informatics (ICCCI -2013), Jan. 04 – 06, 2013,

Coimbatore, INDIA

5) Cropping Attack

Cropping is used to cut a part of an image from a picture so

that the watermark is corrupted. The Cropping attack with

different sizes of 0.4% and 1.6% is applied to the watermarked

image. The proposed algorithm resists the cropping attack

effectively as compared to Silja‟s scheme.

B. Comparisons with other watermarking scheme

In this section, the experimental results of the proposed

scheme were evaluated and compared with the Silja‟s scheme

for watermarking of image [9]. The comparison of the NC

values of the proposed scheme with the Silja‟s scheme for

Gaussian Noise Attack, Scaling Attack, Cropping Attack,

Rotation Attack and JPEG Compression was performed. It

was observed that the NC values of the proposed scheme

based on CT and QR Factorization techniques were better than

Silja‟s scheme. The NC value with no attacks calculated to be

1.0000 for all the images whereas it was 0.9919 in Silja‟s

scheme meaning that the embedding of watermark had caused

disturbance in the watermarked image. Thus, the proposed

algorithm was found to be more accurate and robust. For

Gaussian noise attack, the NC value was computed to be

1.0000. For scaling attack, this value was approximately 1 for

resizing of 75%, 125 % and 150%. The NC values for rotation

attack was also 1 showing that watermark was accurately

extractable and the values were found to be better than Silja‟s

scheme. Thus, the proposed method has better robustness and

imperceptibility for all the test images. The comparisons show

that the proposed scheme outperforms the compared scheme.

VII. CONCLUSION

This paper presents a combination of Contourlet Transform

scheme with Matrix based factorization method namely QR

decomposition. The watermark has been scrambled to enhance

security. The statistical analysis of the image is done to embed

the watermark in area where it is less detectable. Experimental

results have shown the superiority of the proposed

watermarking scheme in terms of quality and robustness. The

scheme has shown good results for all the attacks except for

the JPEG compression attack where the NC value is slightly

less than that of Silja‟s scheme but still it is greater than the

required NC value of 0.9. For the future perspectives, further

algorithms may be implemented for the improvement of

results for the JPEG compression attack. Moreover, other

matrix factorization methods can be used to implement the

scheme. Also, CT can be used with other matrix factorization

methods. It can be implemented on other subbands of CT.

REFERENCES

[1] L. Tong, Q. Zheng-ding, “The Survey of Digital Watermarking-based Image Authentication Techniques”, 6th International Conference on Signal Processing, 2002, ICSP Proceedings, vol. 2, pp. 1556-1559, Aug. 2002.

[2] R.C.Gonzalez and R.E.Woods, “Digital Image Processing”, 3rd Edition, Pearson Education, 2009.

[3] V.M. Potdar, S. Han, E. Chang, “A survey of digital image watermarking techniques”, 3rd IEEE International Conference on Industrial Informatics, INDIN'05, pp. 709-716, Aug. 2005.

[4] M. N. Do, and M. Vetterli, “Contourlets: a directional multiresolution image representation,” International Conference on Image Processing, vol.1, pp. I-357-I-360, 2002.

[5] R. Javidan, M. A. Masnadi-Shirazi, Z. Azimifar and M. H. Sadreddini, “A Comparative study between wavelet and Contourlet Transorm Features for Textural Image Classification”, Information and Communication Technologies: From Theory to Applications, pp. 1-5, 7-11 April 2008.

[6] S. Khalighi, P. Tirdad and H. R. Rabiee, “A Contourlet-Based Image Watermarking Scheme with High Resistance to Removal and Geometrical Attacks”, EURASIP Journal on Advances in Signal Processing, Hindawi Publishing Corporation, vol. 2010, Article ID 540723, pp. 1-13, 2010.

[7] E. Yavuz and Z. Telatar, “Improved SVD--DWT Based Digital Image Watermarking Against Watermark Ambiguity”, Proceedings of the 2007 ACM symposium on Applied computing, SAC‟07, pp. 1051-1055, 2007.

[8] H. Bi, X. Li, Y. Zhang, Y. Xu, “A blind robust watermarking scheme based on CT and SVD”, 2010 IEEE 10th international conference on Signal Processing, pp. 881-884, Oct. 2010

[9] M. S. Silja and K. P. Soman, “A Watermarking Algorithm Based on Contourlet Transform and Nonnegative Matrix Factorization”, artcom 2009, International Conference on Advances in Recent Technologies in Communication and Computing, pp. 279-281, Oct 2009.

[10] S. Sun, S. Wei, C. Wang, “DPCC and QR factorization-based color medical image authentication algorithm”, International Conference on Image Analysis and Signal Processing, IASP 2009, pp. 81-84, April 2009.

[11] M. N. Do, and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Transactions on Image Processing, vol. 14, no. 12, pp. 2091-2106, 2005.

[12] P. Burt and E. Adelson. “The Laplacian Pyramid as a Compact Image Code”, IEEE Transactions on Communications, vol. 31, no. 4, pp. 532-540, April 1983.

[13] R. H. Bamberger and M. J. T. Smith, “A filter bank for the directional decomposition of images: theory and design”, IEEE Transactions on Signal Processing, vol. 40, no. 4. pp. 882-893, April 1992.

TABLE III RESULTS OF ATTACKS ON PROPOSED FOR FLOWER IMAGE

Attack on Flower

Image

Results

NC

Proposed

scheme

Extracted Watermark

NC Silja’s

scheme

[9]

No

Attack 1.0000

0.9919

Gaussian

Noise

0.001 1.0000

0.9407 0.003 1.0000

0.005 1.0000

Scaling

75% 0.9951

0.9100 125% 0.9996

150% 0.9995

Rotation 0.1 1.0000

0.8295

Cropping 0.4% 1.0000

0.9892 1.6% 1.0000

JPEG

Compres-sion

Quality factor 60

0.9597

0.9869 Quality

factor 90 0.9580

Quality

factor 100 0.9586