Robust Watermarking using Walsh Wavelets and SVD

International Journal of Advances in Science and Technology, Vol. 6, No.4, 2013

Robust Watermarking using Walsh Wavelets and SVD H. B. Kekre1 and Tanuja Sarode2 and Shachi Natu3 1

MPSTME, Department of Computer Engineering, NMIMS University, Mumbai, India [email protected] 2

Department of Computer Engineering, TSEC, Mumbai University, India [email protected]

3

Ph. D. Research Scholar, MPSTME, NMIMS University, Mumbai, India [email protected]

Abstract In this paper, a wavelet domain based watermarking technique is proposed. However instead of using traditional Haar wavelet functions, Walsh wavelet transform is used that is derived from orthogonal Walsh transform matrices of different sizes. 256*256 Walsh wavelet is generated using 128*128 and 2*2 Walsh transform matrix and then using 64*64 and 4*4Walsh matrix which depicts the resolution of host image taken into consideration. It is supported by DCT and SVD to increase the robustness. Walsh wavelet based technique is then compared with DCT wavelet based method. Performance of three techniques is compared against various attacks and they are found to be almost equivalent. However, computationally Walsh wavelet is preferable over DCT wavelet. Also Walsh wavelet obtained by 64*64 and 4*4 is preferable over DCT wavelet and Walsh wavelet obtained from corresponding orthogonal transform matrix of size 128*128 and 2*2.

Keywords: DCT Wavelet, Walsh Wavelet, DCT, SVD, Watermarking. 1. Introduction The immense popularity of World Wide Web opened a new gateway for transmission of multimedia contents over the network. However such transmission of digital contents over network has two serious problems. First, these contents are easily downloadable and can be easily reproduced. Second, because of powerful multimedia manipulation tools, credibility of multimedia data such as images, audios and videos is decreased. Thus copyright protection of digital contents is the driving force of research in digital watermarking. Digital watermarking is the process of embedding some signal in a multimedia content to preserve its copyright/ownership information. Depending on the type of digital contents to be protected it can be text, image, audio, or video watermarking. Digital image watermarking is the process of inserting some image called watermark into another image called host image. Insertion of watermark image should be done in such a way that the watermark is extractable from host image. Especially when host image is transmitted over network, many intentional and unintentional alterations can be performed on it. In such cases, survival of watermark image is desirable. Basic requirements of watermarking are security, imperceptibility, robustness and capacity [1]. Security refers to the difficulty in extracting the embedded watermark or altering it from host image without damaging host image. Imperceptibility refers to the perception of transparency of image watermark. There should not be any perceptual difference between original host image and watermarked image. Imperceptibility can be achieved by embedding watermark in perceptually insignificant areas of image. Robustness refers to the capability of watermark to survive signal manipulations. Robustness can be increased by embedding watermark in perceptually significant parts of an image. Hence it survives lossy compression. But since this area of host image is susceptible to alterations, watermark embedding may cause significant distortion in host image. Capacity refers to the amount of information that can be embedded into host image. There is always a trade-off between capacity and robustness and imperceptibility of watermarking. Higher capacity leads to reduced robustness or reduced imperceptibility or both. Another category of image watermarking classification is visible and invisible watermarking. In visible watermarking, the watermark image is intentionally visible to observer. In invisible watermarking watermark is not perceptible to observer but can be extracted from cover image by using computer program. One more classification of watermarking is based on the necessary data for watermark extraction. If original cover image is required to perform watermark extraction, it is known as informed or private watermarking. If original cover image is not required for watermark extraction, it is called as blind or public watermarking [2]. Insertion of watermark into image requires modification of some features of cover image. These

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International Journal of Advances in Science and Technology, Vol. 6, No.4, 2013 features can be pixels of the cover image or transform coefficients. Based on this, digital image watermarking can be classified as spatial domain and transform domain watermarking respectively. Spatial domain techniques are simple and have high capacity. Spatial domain techniques have higher control on perceptual quality as compared to frequency domain techniques. Also spatial domain techniques have low computational cost. But in frequency domain watermarking, we can achieve more robustness against various attacks. Lot of work has been done in transform domain watermarking using DCT [3], [4], [5], wavelet transform [6], [7], [8] singular value decomposition [2], [9], [10] and wavelet packet transform [11]. Methods are also proposed using combination of two or more transforms like DWT-DCT [12], DWT-SVD [13], DCT-SVD [14], DWT-DCT-SVD [15]. Combination of two or more transforms has proved to be more robust than using any single transformation technique. Attempts are still made to improve the performance of transform based techniques. G. Bhatnagar, B. Raman and Q. M. J. Wu [10] have proposed a robust watermarking scheme using fractional wavelet packet transform. In their proposed technique, image is decomposed by means of fractional wavelet packet transform. Then positions of all frequency sub-bands at each level are changed with respect to some rule which is secret and known only to owner. Then inverse fractional wavelet transform is performed to obtain the reference image. For embedding, reference image is divided into non-overlapping blocks and then watermark is embedded in reference image by modifying its singular values. The size of blocks is same as size of watermark. K. Ramanjaneyulu and K. Rajarajeswari [16] have proposed a wavelet based image watermarking scheme using genetic algorithm. Here the cover image is subjected to three level DWT. Third and second level horizontal detail sub-band (LH2 and LH3) coefficients are grouped into different blocks. In each block first minimum and second minimum are identified and modified according to the watermark bit. After watermark insertion, inverse DWT is applied to the sub-bands with modified coefficients to obtain the watermarked image. A threshold based decoder is designed for extraction process. PSNR of watermarked image and Normalized Cross Correlation (NCC) of extracted watermark are the parameters used to measure the performance of this technique. Since maximization of PSNR decreases the value of NCC and both the values must be as large as possible, genetic algorithm is used to optimize values of PSNR and NCC. A dual watermarking scheme has been proposed by Saraju Mohanty, K. R. Ramkrishnan and Mohan Kankanhalli [17]. Dual watermarking refers to combination of visible and invisible watermarks. In visible watermarking grey values of host image are modified based on its local as well as global statistics like mean and variance. Both host image and watermark image are divided into equal size blocks. Appropriate values of scaling factor (α) and embedding factor (β) are obtained to perform insertion of watermark block wise. Choice of α and β are governed by certain characteristics of Human Visual System (HVS). Visible watermarking is then followed by invisible watermarking carried out in spatial domain. Logical Ex-OR operation is used instead of simple addition to increase the robustness of the scheme. A wavelet based watermarking scheme for colour images is given by D. Dejey and R. S. Rajesh [18]. After decomposing an image into its coefficients, suitable bands of these coefficients are selected. This selected band is then subjected to Fan Beam Transform. Watermark is then embedded by altering the fan beam transform coefficients. The schemes are used on chrominance alone and on luminance and chrominance. Mei Jiansheng, Li Sukang and Tan Xiomei [19] have proposed a DCT and DWT based image watermarking. Here watermark image is first Discrete Cosine Transformed. The host image is decomposed through DWT and appropriate DWT moduli in the high frequency level are selected for embedding watermark. Another wavelet based approach for digital image watermarking is proposed by M. Mohamed Sathik and S. S. Sujatha [20] in which watermark is generated using distorted perceptual information of the image contents using Arnold Transform. This watermark is then embedded in high frequency components of Wavelet transformed host image. The robustness of the scheme is claimed due to multifaceted procedure used to construct the watermark. Ali Al-Haj [21] has proposed a combined DWT-DCT based watermarking scheme. According to their scheme, host image is first subjected to wavelet decomposition. HL1 or HH1 sub-band is again decomposed to get HL2 or HH2 sub-band respectively. HL2/HH2 is then divided into 4*4 blocks and DCT is applied to these blocks. Greyscale watermark image is reformulated into a vector of zeros and ones. Two uncorrelated pseudorandom sequences are generated to embed watermark bit zero and one. Combination of DWT and DCT improves the robustness of watermarking as compared to only DWT based approach. Xiangui Kang, Jiwu Huang[22] proposed a DWT-DFT watermarking scheme in which a spread spectrum based informative watermark with a training sequence are embedded in the coefficients of LL sub band in the DWT domain and template is embedded in middle frequency components in DFT domain.

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2. Walsh wavelet Discrete Wavelet Transform has been widely used in many image processing applications like image compression, feature detection and recognition, information hiding, biometric techniques, digital watermarking etc. Especially in watermarking, the techniques based on DWT are proved to be more robust than any other transform as well as when combined with other transformation techniques. This is due to excellent spatial localization and multi-resolution properties of wavelet. Haar wavelets are most popular in watermarking and other applications. But recently the wavelets are generated from other orthogonal transforms like DCT, Walsh, Hartley and Kekre transform [23], [24] using Kekre algorithm [25] and are successfully used in various image processing applications like steganography [26], image compression [25], CBIR [27], [28] retinal scan recognition [29] digital image watermarking [30] and many more. In this paper an attempt has been made to exploit the wavelet properties of Walsh wavelet generated from Walsh transform for digital image watermarking in combination with DCT and SVD.

3. DCT and SVD Discrete Cosine Transform (DCT) is one of the most popular orthogonal transformation techniques used in image processing. High energy compaction property of DCT is the reason. In watermarking, this property helps in deciding the location in image to embed the watermark with maximum possible robustness. Singular Value Decomposition (SVD) decomposes an M*N image I into a product of three matrices as I=USVT, where U and V are orthogonal matrices of size M*M and N*N respectively. S is a matrix of size M*N whose first r diagonal values are Eigen values of positive definite matrix IT*I [31]. Elements of U, S or V can be selected and modified for embedding watermark into an image.

4. Proposed method Generation of wavelet transform from any orthogonal transform is discussed in detail in [25]. Using the method in [25] we can generate Walsh wavelet of size MN*MN from Walsh transform matrices of size M*M and N*N respectively where M and N are power of 2. By changing the size of Walsh transform matrix, we can achieve desired level resolution of local properties suitable for application. In the proposed method Walsh wavelet matrix of size 256*256 has been generated using two distinct pairs of Walsh transform matrix i)128* 128 and 2*2 and ii) 64*64 and 4*4 to study the effect of selection of resolution level on robustness and imperceptibility of watermarking. For some applications selection of higher resolution i.e. emphasizing on local properties gives better results whereas for some applications emphasizing on global properties gives better results. Here 128*128 and 2*2 combination gives higher resolution than 64*64 and 4*4 pair of Walsh transform.

5. Embedding Algorithm Step 1. Generate 256*256 Walsh-wavelet matrix from 128*128 and 2*2 pair / 64*64 and 4*4 pair of Walsh matrices as explained in section 3. Step 2. Generate 128*128 Walsh-wavelet matrix from 64*64 and 2*2 pair / 32*32 and 4*4 pair of Walsh matrices. Step 3. Generate 64*64 Walsh-wavelet matrix from 32*32 and 2*2 pair / 16*16 and 4*4 pair of Walsh matrices. These matrices are required to obtain the wavelet transformed image from cover image and watermark image. Step 4. Take 2-level Walsh-wavelet transform of Red, Green and Blue planes of cover image separately using transformation matrices generated in step 1 and step 2. Step 5. Select HL2 sub-band of Walsh -wavelet transformed cover image and apply DCT to it. Step 6. Arrange Walsh -wavelet-DCT transformed HL2 sub-band in a zigzag manner and get four quadrants out of it. Step 7. Decompose these four quadrants using SVD and get singular values of each quadrant. Step 8. Take 2-level Walsh -wavelet transform of Red, Green and Blue planes of watermark image separately using transformation matrices generated in step 2 and step 3. Step 9. Select HL2 sub-band of Walsh -wavelet transformed watermark image and apply DCT to it. Step 10. Decompose Walsh -wavelet-DCT transformed watermark image using SVD to obtain its singular values. Step 11. Scale the singular values of watermark image obtained in step 10 by scaling factor k and add them to corresponding singular values of four quadrants of cover image obtained in step 7. S”=S+KS’ (1)

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International Journal of Advances in Science and Technology, Vol. 6, No.4, 2013 Where, S is the singular value matrix of each quadrant, S’ is the singular value matrix of watermark and S” is the modified singular value matrix of cover image. Step 12. Reconstruct the watermarked image by following inverse zigzag, inverse DCT and inverse 2-level Walsh wavelet in sequence. Step 13. Calculate Mean Absolute Error (MAE) between cover image and watermarked image as a measure of imperceptibility.

6. Extraction algorithm Step 1. Take 2-level Walsh -wavelet transform of Red, Green and Blue planes of watermarked image separately using transformation matrices generated in step 1 and step 2 of embedding algorithm. Step 2. Select HL2 sub-band of Walsh -wavelet transformed watermarked image and apply DCT to it. Step 3. Arrange Walsh -wavelet-DCT transformed HL2 sub-band in a zigzag manner and get four quadrants out of it. Step 4. Decompose these four quadrants using SVD and get singular values of each quadrant. Step 5. Extract singular values of watermark from singular values of watermarked image and singular values of cover image. S’= (S”-S)/K (2) Step 6. Construct DCT coefficients of watermark using the singular values extracted in Step 5. Step 7. Take inverse DCT and then 2-level inverse Walsh -wavelet to extract watermark from watermarked image. Step 8. Calculate Mean Absolute Error (MAE) between original watermark and extracted watermark as a major of robustness. Figure 1 and Figure 2below show the ten images used as cover images and five images/logos used as watermarks for implementation.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Figure 1.Cover images used for experimentation (a)Lena (b)Mandrill (c)Peppers (d)Balls (e)Puppy (f)Tiger (g)Flower (h)Ganesh (i)Titanic (j)Waterlili

(a)

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(d)

(e)

Figure 2.Watermark images used for experimentation (a) austral (b) bear (c) ccd (d) logo (e) nmims

7. Results Figure 3 and Figure 4 below show the watermarked images with ‘austral’ watermark embedded into it for scaling factor 0.2 using Walsh wavelet obtained from (128,2) and (64,4) Walsh transform respectively.

MAE=5.62

MAE=11.67

MAE=8.07

MAE=4.72

MAE=4.72

(a)

(b)

(c)

(d)

(e)

MAE=6.04

MAE=10.05

MAE=20.86

MAE=7.03

MAE=7.70

(f)

(g)

(h)

(i)

(j)

Figure 3.Watermarked images with ‘austral’ watermark embedded into it for scaling factor 0.2 using Walsh wavelet obtained from (128, 2) Walsh transform

MAE=5.61

MAE=11.67

MAE=8.09

MAE=4.75

MAE=4.73

(a)

(b)

(c)

(d)

(e)

MAE=6.06

MAE=10.03

MAE=20.85

MAE=7.03

MAE=7.71

(f)

(g)

(h)

(i)

(j)

Figure 4.Watermarked images with ‘austral’ watermark embedded into it for scaling factor 0.2 using Walsh wavelet obtained from (64, 4) Walsh transform

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International Journal of Advances in Science and Technology, Vol. 6, No.4, 2013 Table 1below shows Average Mean Absolute Error (MAE) between host and watermarked image using Walsh wavelet generated using (128, 2) and (64, 4) pair of Walsh transform. Ten host images and five different watermarks as shown above are used to find MAE between host and watermarked image. For each watermark Average MAE over ten host images is then calculated. Table 1.Average Mean Absolute Error (MAE) between host and watermarked image for five different logos using Walsh wavelet generated using (128, 2) and (64, 4) pair of Walsh transform. Watermark austral

bear

ccd

logo

nmims

K

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

0.05

8.215

8.215

8.181

8.181

8.225

8.227

8.198

8.198

8.275

8.278

0.1

8.311

8.313

8.201

8.201

8.336

8.339

8.243

8.244

8.505

8.511

0.2

8.653

8.657

8.264

8.265

8.718

8.728

8.391

8.395

9.256

9.275

0.4

9.772

9.781

8.488

8.490

9.935

9.962

8.881

8.892

11.450

11.497

0.6

11.261

11.274

8.824

8.827

11.526

11.570

9.553

9.575

14.141

14.220

From Table 1 it is clear that MAE obtained by Walsh wavelet from (64, 4) pair is negligibly higher than MAE obtained by Walsh wavelet from (128, 2) pair of Walsh transform. Table 2 shows the Average MAE between original watermark and extracted watermarks when there is no attack performed on watermarked image. These values are for different values of scaling factor (K) and for both types Walsh wavelets generated Table 2.Average MAE between original watermark and extracted watermarks when there is no attack performed on watermarked image Watermark austral

bear

ccd

logo

nmims

K

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

0.05

11.274

11.281

6.387

6.386

9.635

9.645

5.480

5.492

19.008

19.009

0.1

11.150

11.147

6.312

6.312

9.500

9.505

5.247

5.248

18.933

18.931

0.2

11.132

11.130

6.276

6.275

9.470

9.469

5.171

5.172

18.966

18.968

0.4

11.183

11.183

6.273

6.271

9.522

9.521

5.174

5.173

19.143

19.142

0.6

11.263

11.261

6.276

6.275

9.594

9.594

5.191

5.192

19.353

19.346

Since response of watermarking technique to various attacks on image decides its robustness, response of proposed watermarking technique to various attacks like contrast stretching, image cropping, Gaussian noise, histogram equalization and image resizing is tabulated below. These values are obtained for each of the five different watermarks embedded into ten host images and for various values of scaling factor. In contrast stretching, the intensity values below 0.3 and above 0.7 of host image are clipped to 0.1 and 0.9 respectively. In cropping, 256*36 size vertical strip at the rightmost end of 256*256 watermarked images is cropped. In Gaussian noise attack, Gaussian noise of variance 0.1 is added to watermarked image. Image resizing is performed by reducing the image to half of its original size using bicubic interpolation and then bringing it to original size again. Figure 5and Figure 6show the Lena image watermarked using Walsh wavelet (128, 2) and Walsh wavelet (64, 4) with various attacks performed on it.

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(a)

(b)

(c)

(d)

(e)

Figure 5.Watermarked ‘Lena’ image using Walsh wavelet (128,2) with various attacks on it(Watermark=’austral’, K=0.2),(a)Contrast stretching (b)Cropping (c)Gaussian noise, variance=0.1(d)Histogram Equalization(e)Resizing

(a)

(b)

(c)

(d)

(e)

Figure 6.Watermarked ‘Lena’ image using Walsh wavelet (64,4) with various attacks on it(Watermark=’austral’, K=0.2),(a)Contrast stretching (b)Cropping (c)Gaussian noise, variance=0.1(d)Histogram Equalization(e)Resizing Table 3 shows the values of Average Mean Absolute Error between original watermark and average MAE values of extracted watermarks from four quadrants when contrast stretching attack is performed on watermarked image. Table 3.Average Mean Absolute Error between original watermark and average MAE values of extracted watermarks from four quadrants for contrast stretching attack on host image for different scaling factors (K) and Walsh wavelet (128,2) and Walsh wavelet(64,4) Watermark austral

bear

ccd

logo

nmims

K

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

0.05

27.051

27.196

37.851

38.181

24.010

24.121

26.414

26.595

35.884

36.038

0.1

19.319

19.353

23.389

23.505

16.993

17.024

16.534

16.586

27.567

27.595

0.2

14.968

14.956

14.145

14.157

13.209

13.219

10.673

10.701

23.046

23.024

0.4

12.830

12.798

9.421

9.4092

11.398

11.393

7.7469

7.7614

20.999

20.977

0.6

12.183

12.1554

8.015

7.999

10.851

10.843

6.8462

6.851

20.460

20.436

From Table 3 we can see the effect of change in resolution on Average MAE values between original watermark and watermarks extracted from four quadrants of HL2 sub-band of image. For higher resolution i.e. for (128*128, 2*2) pair Walsh wavelet, MAE value is less than that of (64*64, 4*4) pair Walsh wavelet. Thus higher resolution or use of local properties of host image for embedding watermark is more robust in case of contrast stretching attack. Figure 7 (a)-(d) and Figure 8 (a)-(d) show ‘austral’ watermark extracted from four quadrants of HL2 sub-band of watermarked image ‘Lena’ watermarked using Walsh wavelet (128,2) and Walsh wavelet (64,4) respectively. These extracted watermarks are for contrast stretching attack and for scaling factor 0.2.

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Original Watermark

MAE=14.06

MAE=15.11

MAE=15.18

MAE=14.72

(a)

(b)

(c)

(d)

Figure 7. ‘austral’ watermark extracted from contrast stretched watermarked image ‘Lena’ watermarked using Walsh wavelet (128, 2) for scaling factor 0.2.

Original Watermark

MAE=14.32

MAE=14.90

MAE=15.17

MAE=14.87

(a)

(b)

(c)

(d)

Figure 8. ‘austral’ watermark extracted from contrast stretched watermarked image ‘Lena’ watermarked using Walsh wavelet (64, 4) for scaling factor 0.2. Table 4 shows the response of proposed watermarking technique to image cropping attack. Average MAE values between original watermark and extracted watermark (average of four watermarks extracted from four quadrants) are shown in Table 4. Table 4.Average MAE values between original watermark and extracted watermark from cropped watermarked image cropping for different scaling factors (K) and Walsh wavelet (128,2) and Walsh wavelet(64,4) Watermark austral

bear

ccd

logo

nmims

K

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

0.05

16.256

15.890

12.849

12.350

14.174

13.902

10.439

10.195

24.135

23.705

0.1

13.450

13.245

8.947

8.571

11.724

11.571

7.602

7.450

21.429

21.220

0.2

12.255

12.159

7.297

7.108

10.608

10.550

6.299

6.217

20.313

20.223

0.4

11.801

11.762

6.667

6.586

10.167

10.158

5.734

5.703

19.967

19.929

0.6

11.730

11.704

6.514

6.467

10.092

10.100

5.584

5.571

20.014

19.981

For (128*128, 2*2) pair of Walsh wavelet, MAE values are slightly higher than (64*64, 4*4) pair Walsh wavelet. In contrast to contrast stretching attack, selection of lower resolution proves to be better for cropping attack. Figure 9(a)-(d) and Figure 10 (a)-(d) show ‘austral’ watermarks extracted from four quadrants of HL2 sub-bands of cropped Lena image along with Mean Absolute Error with scaling factor 0.2 for Walsh wavelet (128,2) and Walsh wavelet (64,4) respectively.

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Original Watermark

MAE=11.20

MAE=11.37

MAE=11.75

MAE=12.42

(a)

(b)

(c)

(d)

Figure 9. ‘austral’ watermarks extracted from cropped ‘Lena’ image with scaling factor 0.2 for Walsh wavelet (128, 2).

Original Watermark

MAE=11.41

MAE=11.45

MAE=11.59

MAE=12.26

(a)

(b)

(c)

(d)

Figure 10. ‘austral’ watermarks extracted from cropped ‘Lena’ image with scaling factor 0.2 for Walsh wavelet (64, 4). Table 5 shows the effect of Gaussian noise attack on watermarked images. Gaussian noise with variance 0.1 is added to the watermarked image. Average MAE values between original watermark and watermark extracted from noise added image are shown in Table 5. These values are the average MAE values over ten different host images for each of the five different watermarks. Table 5.Average MAE values between original watermark and watermark extracted from Gaussian noise (variance=0.1) added image for different scaling factors (K) and Walsh wavelet (128, 2) and Walsh wavelet (64, 4) Watermark austral

bear

ccd

logo

nmims

K

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

0.05

19.806

19.491

23.161

22.723

17.472

17.152

16.643

16.614

27.164

26.970

0.1

14.518

14.419

13.520

13.061

12.977

12.790

10.357

10.256

22.200

22.028

0.2

12.289

12.262

8.607

8.551

10.970

10.932

7.419

7.347

20.184

20.161

0.4

11.573

11.564

6.874

6.840

10.200

10.175

6.103

6.063

19.677

19.670

0.6

11.512

11.505

6.521

6.507

10.046

10.021

5.751

5.723

19.788

19.754

MAE values for (64*64, 4*4) Walsh wavelet are less than MAE value for (128*128, 2*2) Walsh wavelet. Thus embedding watermark into higher resolution host image increases the difference between MAE value of original watermark and extracted watermark. Hence it can be concluded that selection of low resolution host image is more robust for Gaussian noise attack. Figure 11(a)-(d) and Figure 12(a)-(d) show the ‘austral’ watermarks extracted from four quadrants of HL2 frequency bands of Gaussian noise added watermarked image ‘Lena’ when (128,2) and (64,4) Walsh wavelets are used respectively (K=0.2).

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Original Watermark

MAE=12.85

MAE=12.38

MAE=12.26

MAE=12.26

(a)

(b)

(c)

(d)

Figure 11. ‘austral’ watermarks extracted from four quadrants of Gaussian noise added watermarked image ‘Lena’ when (128, 2) is used

Original Watermark

MAE=12.41

MAE=12.28

MAE=12.48

MAE=12.27

(a)

(b)

(c)

(d)

Figure 12. ‘austral’ watermarks extracted from four quadrants of Gaussian noise added watermarked image ‘Lena’ when (64, 4) Walsh wavelets is used Table 6 shows the Average MAE between original and extracted watermark when histogram equalization is applied to watermarked image. Table 6.Average MAE between original and extracted watermark when histogram equalization is applied to watermarked image Watermark austral

bear

ccd

logo

nmims

K

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

0.05

28.240

28.043

38.391

38.490

25.143

25.048

26.876

26.954

36.786

36.786

0.1

20.479

20.383

24.763

24.836

17.849

17.822

17.258

17.255

28.553

28.588

0.2

15.853

15.824

15.718

15.769

13.639

13.636

11.251

11.289

23.685

23.689

0.4

13.343

13.321

10.624

10.648

11.447

11.418

8.063

8.093

21.081

21.063

0.6

12.441

12.422

8.914

8.932

10.699

10.674

7.009

7.023

20.206

20.188

From Table 6 it can be observed that MAE values are smaller for (64*64, 4*4) pair Walsh wavelet. Thus for histogram equalization also, performance of low resolution wavelet is better in terms of robustness. Figure 13(a)-(d) and Figure 14 (a)-(d) show the watermarks extracted from four quadrants of HL2 frequency bands histogram equalized watermarked using Walsh wavelet (128, 2) and (64,4).

Original Watermark

MAE=16.25

MAE=16.91

MAE=17.06

MAE=17.14

(a)

(b)

(c)

(d)

Figure 13.Watermarks extracted from histogram equalized watermarked using Walsh wavelet (128, 2)

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Original Watermark

MAE=16.59

MAE=16.84

MAE=17.05

MAE=17.14

(a)

(b)

(c)

(d)

Figure 14.Watermarks extracted from histogram equalized watermarked using Walsh wavelet (64, 4) Table 7depicts the response of image resizing to high resolution and low resolution watermarked image. Average MAE between original watermark and extracted watermark for image resizing attack are shown in Table 7. Table 7.Average MAE between original watermark and extracted watermark for image resizing attack for various scaling factor values and both types of Walsh wavelets. Watermark austral

bear

ccd

logo

nmims

K

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

(128,2)

(64,4)

0.05

28.632

28.756

29.799

30.013

25.128

25.239

22.237

22.384

39.569

39.647

0.1

20.285

20.278

17.756

17.808

17.904

17.912

14.119

14.180

30.004

29.962

0.2

16.061

16.012

11.461

11.458

14.157

14.125

9.749

9.758

25.381

25.312

0.4

14.229

14.178

8.649

8.628

12.431

12.388

7.650

7.641

23.437

23.350

0.6

13.740

13.686

7.861

7.837

11.939

11.890

7.014

6.998

22.986

22.891

From Table 7 it can be seen that higher resolution of host image works better for resizing attack than lower resolution. From Table 3 to Table 7 we can say that for certain attacks, higher resolution of host image is more robust whereas for some attacks, low resolution of host image gives better robustness. Figure 15(a)-(d) and Figure 16(a)-(d) show the watermarks extracted from four quadrants of HL2 frequency bands resized watermarked image for two combinations of Walsh wavelet (128,2) and (64,4) respectively for K=0.2.

Original Watermark

MAE=14.44

MAE=14.33

MAE=14.47

MAE=14.17

(a)

(b)

(c)

(d)

Figure 15. Watermarks extracted from Walsh wavelet (128, 2) watermarked image on resizing attack

Original Watermark

MAE=14.34

MAE=14.32

MAE=14.35

MAE=14.03

(a)

(b)

(c)

(d)

Figure 16. Watermarks extracted from Walsh wavelet (64, 4) watermarked image on resizing attack

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Average MAE between original and extracted watermark for contrast stretching

Apart from studying the effect of selection of resolution of host image, results of proposed method are also compared with the previous work stated in [30]. In [30], DCT wavelet generated from orthogonal DCT transformation matrix of size 128*128 and 2*2 is used for watermarking. Similar to proposed method, DCT wavelet is further supported by DCT and SVD to increase robustness. Comparison of proposed method with DCT wavelet based watermarking method is done on the basis of their response to various attacks stated earlier. Same set of host images and watermarks is used in both cases for fair comparison. Figure 17shows the comparison of MAE for DCT wavelet (128, 2)-DCT-SVD, Walsh wavelet128, 2)-DCT-SVD and Walsh wavelet (64, 4)-DCT-SVD when watermarked image is subjected to contrast stretching for different values of scaling factor (K). 31 27 23

DCT Wavelet (128*2)

19

Walsh wavelet (128*2)

15

Walsh wavelet (64*4)

11 0.05 0.1 0.2 0.4 0.6 Scaling Factor (K)

Figure 17.Comparison of MAE between original and extracted watermark for DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) on contrast stretched watermarked image with different scaling factors

Average MAE between original and extracted watermark for cropping

From Figure 17, it can be observed that Walsh wavelet (128, 2) and Walsh wavelet (64, 4) give MAE values that are negligibly higher than the MAE values obtained by DCT wavelet (128*2). Further, Walsh wavelets are computationally faster as compared to DCT wavelet and hence Walsh wavelet for Watermarking is acceptable over DCT wavelet. Figure 18 shows the comparison of DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) for image cropping attack. 16.5 15.5 14.5

DCT Wavelet (128*2)

13.5 12.5 11.5

Walsh wavelet (128*2)

10.5

Walsh wavelet (64*4)

0.05 0.1 0.2 0.4 0.6 Scaling Factor (K)

Figure 18. Comparison of MAE between original and extracted watermark for DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) watermarked image with different scaling factors for cropping Figure 18shows that Walsh wavelet (64, 4) gives smaller MAE values for image cropping attack than DCT wavelet (128,2) and Walsh wavelet (128,2) for all scaling factor values. Thus robustness of proposed Walsh wavelet based scheme is better for cropping attack. Figure 19 and Figure 20 show the comparison of DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) in terms of MAE for Gaussian noise and histogram equalization attacks, with different scaling factors.

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Average MAE between original and extracted watermark for guassian noise

22 19 16

DCT Wavelet (128*2)

13

Walsh wavelet (128*2)

10

Walsh wavelet (64*4)

0.05 0.1 0.2 0.4 0.6 Scaling Factor (K)

31 28 25 22 19 16 13 10

DCT Wavelet (128*2)

0.6

0.4

0.2

0.1

Walsh wavelet (128*2)

0.05

Average MAE between original and extracted watermark for histogram equalization

Figure 19. Comparison of MAE between original and extracted watermark for DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) watermarked image with different scaling factors for Gaussian noise

Walsh wavelet (64*4)

Scaling Factor (K)

Figure 20. Comparison of MAE between original and extracted watermark for DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) watermarked image with different scaling factors for histogram equalization

Average MAE between original and extracted watermark for resizing

From Figure 19 and Figure 20 it is observed that Walsh wavelet (64, 4) performs better for Gaussian noise attack than DCT wavelet (128, 2) and Walsh wavelet (128, 2). As scaling factor increases from 0.05 to 0.6, difference between MAE obtained by DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) is nil. But since higher value of scaling factor reduces imperceptibility of watermarking scheme, lower value of scaling factor are preferred such that it will not sacrifice robustness. Therefore for lower values of scaling factor, Walsh wavelet (64, 4) is preferable over DCT wavelet (128, 2) and Walsh wavelet (128, 2). Figure 21 shows MAE value comparison for DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) for image resizing attack. 29 27 25 23 21 19 17 15 13 11

DCT Wavelet (128*2) Walsh wavelet (128*2)

0.05 0.1 0.2 0.4 0.6

Walsh wavelet (64*4)

Scaling Factor (K)

Figure 21. MAE value comparison for DCT wavelet (128, 2), Walsh wavelet (128, 2) and Walsh wavelet (64, 4) for resized watermarked image.

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International Journal of Advances in Science and Technology, Vol. 6, No.4, 2013 For smaller values of scaling factor, DCT wavelet (128*2) is better than Walsh wavelet (128, 2) and Walsh wavelet (64, 4). Since the difference is very negligible, Walsh wavelet can be preferred over DCT wavelet by considering its computational efficiency.

8. Conclusion Following conclusions can be drawn based on the proposed method and its comparison with DCT wavelet based method in [30]. As scaling factor increases, robustness of watermarking scheme against various attacks also increases but at the cost of imperceptibility. Hence proper selection of scaling factor plays a major role in watermarking scheme. Selection of details of an image (resolution) also plays important role in watermarking. For some attacks, higher resolution turns out to be more robust over low resolution. For majority of attacks stated in proposed method, Walsh wavelet (64, 4) has been proved better due to low resolution of host image

9. References [1] Malihe Soleimani, Faezeh Sanaei Nezhad et. al, “A robust digital blind image watermarking based on spread spectrum in DCT domain”, Science Academy Transactions on Computer and Communication Network, Vol. 2, No. 2, June 2012, pp. 122-126. [2] Habibollah Danyali, Morteza Makhloghi and Fardin Akhlagian Tab, “Robust blind DWT based digital image watermarking using singular value decomposition, International Journal of Innovative Computing, Information and control, vol. 8, number 7(A), July 2012, pp.4691-4703. [3] Wai Chu, “DCT-Based Image Watermarking Using Subsampling”, IEEE transactions on multimedia, vol. 5, no. 1, March 2003, pp. 34-38. [4] Adrian G. Bor_s and Ioannis Pitas, “Image watermarking using block site selection and DCT domain constraints”, Optics Express, Vol. 3, No. 12, 1998, pp.512-523. [5] Rajesh Kannan Megalingam, Mithun Muralidharan Nair, Rahul Srikumar, Venkat Krishnan Balasubramanian and Vineeth Sarma Venugopala Sarma, “A Comparative Study on Performance of Novel, Robust Spatial Domain Digital Image Watermarking with DCT Based Watermarking”, International Journal of Computer Theory and Engineering, Vol. 2, No. 4, August, 2010, pp. 647-653. [6] Dr. B. Eswara Reddy, P. Harini, S. Maruthu Perumal & Dr. V. Vijaya Kumar, “A New Wavelet Based Digital Watermarking Method for Authenticated Mobile Signals”, International Journal of Image Processing (IJIP), Volume (5): Issue (1): 2011 pp. 13-24. [7] Nagaraj V. Dharwadkar & B. B. Amberker, “Determining the Efficient Subband Coefficients of Biorthogonal Wavelet for Grey level Image Watermarking”, International Journal of Image Processing Volume (4): Issue (2), pp. 89-105. [8] Yiwei Wang, , John F. Doherty, and Robert E. Van Dyck, “A Wavelet-Based Watermarking Algorithm for Ownership Verification of Digital Images”, IEEE transactions on image processing, vol. 11, no. 2, FEBRUARY 2002, pp.77-88. [9] Ruizhen Liu and Tieniu Tan, “An SVD-Based Watermarking Scheme for Protecting Rightful Ownership”, IEEE transactions on multimedia, vol. 4, no.1, MARCH 2002 pp. 121-128. [10] Kapre Bhagyashri, S.; Joshi, M.Y.; , "Robust image watermarking based on singular value decomposition and discrete wavelet transform," Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on , vol.5, no., pp.337-341, 9-11 July 2010 [11] G. Bhatnagar, B. Raman, Q. M. J. Wu, “ Robust watermarking using fractional wavelet packet transform”, IET Image Processing, vol. 6, issue 4, 2012, pp. 386-397. [12] Ahmed Abdulfetah, XingmingSun, Hengfu Yang and Nur Mohammad, “Robust adaptive image watermarking using visual models in DWT and DCT domain”, Information Technology journal 9(3), 2010, pp. 460-466. [13] Mohsen Kariman Khorasani, Mohammad Mojtaba Sheikholeslami, “An DWT-SVD Based Digital Image Watermarking Using a Novel Wavelet Analysis Function”, Fourth International Conference on Computational Intelligence, Communication Systems and Networks, 2012, pp. 254-256. [14] A.Sverdlov, S. Dexter and A.M.Eskicioglu, “Robust DCT-SVD domain image watermarking for copyright protection : Embedding data in all frequencies, in proc. the 2004 Multimedia and SecurityWorkshop, ACM press, September 2004,pp. 166-174. [15] Navas, K.A.; Ajay, M.C.; Lakshmi, M.; Archana, T.S.; Sasikumar, M., "DWT-DCT-SVD based watermarking," Communication Systems Software and Middleware and Workshops, 2008. COMSWARE 2008. 3rd International Conference on , vol., no., pp.271-274, 6-10 Jan. 2008

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[16] K. Ramanjaneyulu, K. Rajarajeswari, “Wavelet-based oblivious image watermarking scheme using genetic algorithm”, IET Image Processing, vol. 6, issue 4, 2012, pp. 364-373. [17] Saraju Mohanty, K. R. Ramkrishnan and Mohan Kankanhalli, “A dual watermarking technique for images”, ACM Multimedia, 1999, pp. 49-51. [18] D. Dejey and R. S. Rajesh, “Robust discrete wavelet-fan beam transforms-based colour image watermarking”, IET Image Processing, vol. 5, issue 4, 2011, pp. 315-322. [19] Mei Jiansheng, Li Sukang and Tan Xiomei, “A Digital Watermarking Algorithm Based On DCT and DWT”, Proceedings of the 2009 International Symposium on Web Information Systems and Applications (WISA’09) China, May 22-24, 2009, pp. 104-107. [20] M. Mohamed Sathik and S. S. Sujatha, “A novel DWT based invisible watermarking technique for digital images”, International Arab journal of e-Technology, Vol. 2 No. 3, January 2012. [21] Ali Al-Haj, “Combined DWT-DCT digital image watermarking”, Journal of Computer Science, Vol. 3, Issue 9, pp. 740-746, 2007. [22] Xiangui Kang, Jiwu Huang, “A DWT-DFT composite watermarking scheme robust to both affine transform and JPEG compression”, IEEE transactions on circuits and systems for video technology, vol. 13, NO. 8, pp. 776-786, AUGUST 2003. [23] Dr. H. B. Kekre and Sudeep Thepade”, Image Retrieval Using Non-Involutional Orthogonal Kekre’s Transform”, International J. of Multi discipline. Research & Advances in Engineering, IJMRAE, Vol. 1, No. 1, November 2009, pp. 189-203. [24] Dr. H.B. Kekre , Ms. Archana Athawale and Ms. Dipali Sadavarti ,” Algorithm to Generate Kekre’s Wavelet Transform from Kekre’s Transform”, International Journal of Engineering Science and Technology Vol. 2(5), 2010, 756-767,2009. [25] Dr. H. B. Kekre, Archana Athawale & Dipali Sadavarti, “Algorithm to Generate Wavelet Transform from an Orthogonal Transform”, International JournalOfImage Processing (IJIP), Volume (4): Issue (4), pp. 444-455. [26] H. B. Kekre, Archana Athawale, Dipali Sadavarti, “Performance Comparison of Simple Orthogonal Transforms and Wavelet Transforms for Image Steganography”, IJCA vol. 44, Issue 6, April 2012. [27] Dr. H. B. Kekre, Sudeep D. Thepade, Akshay Maloo, “Performance Comparison of Image Retrieval Techniques using Wavelet Pyramids of Walsh, Haar and Kekre Transforms”, International Journal of Computer Applications (IJCA) Volume 4, Number 10, August 2010 Edition, pp. 1-8. [28] Dr. H. B. Kekre, Sudeep D. Thepade, “Image Retrieval using Non-Involutional Orthogonal Kekre’s Transform”, International Journal of Multidisciplinary Research and Advances in Engineering (IJMRAE), Ascent Publication House, 2009, Volume 1, No. I, pp. 189-203. [29] H. B. Kekre, Rita Vora, “ Retinal Scan Recognition using Wavelet Energy Entropy”, Proc. of IEEE International Conference on Communication, Information & Computing Technology (ICCICT)2012, pp.1-6. [30] Dr. H. B. Kekre, Dr. Tanuja Sarode, Shachi Natu, “Hybrid Watermarking of Colour Images using DCT-Wavelet, DCT and SVD”, InternationalJournal of Advances in Engineering and Technology, vol. No. May 2013. [31] H. B. Kekre, Tanuja Sarode, Shachi Natu, “ Performance Comparison of DCT and Walsh Transforms for Watermarking using DWT-SVD”, International Journal of Advanced Computer Science and Applications, Vol. 4, No. 2, 2013, pp. 131-141.

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Authors’ Profile Dr. H. B. Kekre has received B.E. (Hons.) in Telecomm. Engineering from Jabalpur University in 1958, M. Tech (Industrial Electronics) from IIT Bombay in 1960, M.S. Engg. (Electrical Engineering) from University of Ottawa in 1965 and Ph.D. (System Identification) from IIT Bombay in 1970. He has worked Over 35 years as Faculty of Electrical Engineering and then HOD Computer Science and Engg. at IIT Bombay. After serving IIT for 35 years, he retired in 1995. After retirement from IIT, for 13 years he was working as a professor and head in the department of computer engineering and Vice principal at Thadomal Shahani Engg. College, Mumbai. Now he is senior professor at MPSTME, SVKM’s NMIMS University. He has guided 17 PhDs.’, more than 100 M.E./M.Tech and several B.E. / B.Tech projects, while in IIT and TSEC. His areas of interest are Digital Signal processing, Image Processing and Computer Networking. He has more than 450 papers in National / International Journals and Conferences to his credit. He was Senior Member of IEEE. Presently He is Fellow of IETE, Life Member of ISTE and Senior Member of International Association of Computer Science and Information Technology (IACSIT). Recently fifteen students working under his guidance have received best paper awards. Currently eight research scholars working under his guidance have been awarded Ph. D. by NMIMS (Deemed to be University). At present seven research scholars are pursuing Ph.D. program under his guidance. Dr. Tanuja K. Sarode has received M.E. (Computer Engineering) degree from Mumbai University in 2004, Ph.D. from Mukesh Patel School of Technology, Management and Engg. SVKM’s NMIMS University, Vile-Parle (W), Mumbai, INDIA. She has more than 11 years of experience in teaching. Currently working as Assistant Professor in Dept of Computer Engineering at Thadomal Shahani Engineering College, Mumbai. She is member of International Association of Engineers (IAENG) and International Association of Computer Science and Information Technology (IACSIT). Her areas of interest are Image Processing, Signal Processing and Computer Graphics. She has 137 papers in National /International Conferences/journal to her credit. Ms. Shachi Natu has received M.E. (Computer Engineering) degree from Mumbai University in 2010. Currently pursuing Ph.D. from NMIMS University. She has 08 years of experience in teaching. Currently working as Assistant Professor in Department of Information Technology at Thadomal Shahani Engineering College, Mumbai. Her areas of interest are Image Processing, Database Management Systems and Operating Systems. She has 14 papers in International Conferences/journal to her credit.

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