DIGITAL WATERMARKING ANALYSIS USING DCT AND DWT

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11 COPYRIGHT TO IJETIE

DIGITAL WATERMARKING ANALYSIS USING DCT AND DWT

1Arisudan Tiwari

M. Tech Scholar, Department of Computer Science & Engineering, Maharishi Ved Vyas Engineering College Jagadhri, Yamuna Nagar, India,

E-mail:[email protected]

2Anoopa Arya

Assistant Professor, Department of Computer Science & Engineering, Maharishi Ved Vyas Engineering College Jagadhri, Yamuna Nagar, India,

E-mail:[email protected]

3 Shubham Shukla

Assistant Professor, Department of Computer Science & Engineering, Neelkanth Institute of Technology, Meerut, India

E-mail:[email protected] Abstract:

The paper focused on the development computationally efficient and effective method and algorithm for digital watermarking using wavelets. Digital contents are possible to create, transmit, develop, replicate, and distribute in an effortless way, with the success of the internet. It is cost-effective and the promise of higher bandwidth and quality of service (QoS) for both wired and wireless networks, with digital recording and storage devices.

The protection and enforcement of intellectual property rights for digital media has become an important issue. In the paper the digital watermarking is discussed with the cryptographic encryption and decryption technique. We are proposing the watermark extraction using both DCT and DWT technique. The simulation work is carried out in MATLAB 13.1 image processing tool.

Keywords: Discrete Wavelet Transform (DWT), Discrete Cosine Transform (DCT), Quality of Service (QoS), Matrix Laboratory (MATLAB)

1. Introduction

Digital watermarking process is technique used as computer-aided information hiding in a carrier signal. The unwanted and hidden information does not need to contain a relation to the carrier signal. The authenticity or integrity of the carrier signal is authenticated using digital watermarks and may be used to verify the identity of its owners. Integration is prominently used for tracing copyright infringements and for back tone authentication. Digital watermarks are only perceptible under certain conditions or after the use of some algorithms, and imperceptible anytime like traditional watermarks. If a digital watermark is not of any use if it distorts the carrier signal in a way that it gets perceivable. Traditional Watermarks may be applied to visible media like video, images. In digital watermarking methods, the signal may be audio, video, pictures, texts, 2D or 3D models. Different watermarks can be carried by a signal at the same time. The size of a carrier signal is not changed with the help of a watermark unlike

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metadata that is added to the carrier signal.

The properties of a digital watermark depend on the use cases in which it is applied. A digital watermark has to be rather robust against modifications that can be applied to the carrier signal for marking media files with copyright information.

Instead of it, fragile watermark would be applied, if integrity has to be ensured.

Digital watermarking and stenography both employ steganography techniques to embedded data covertly in noisy signals.

Steganography directly aims for imperceptibility to human senses, perceptions, digital watermarking tries to control the robustness as top priority.

2. Watermarking with Encryption and Decryption

Watermarking requires [5] two operations, embedding the watermarks with the information and extraction. Watermark may be an image, plain text data, password,

serial number or authentication key.

According to the type of document, digital watermarking methods can be categorized in four ways, whcih are (i) text watermarking (ii) image watermarking (ii) audio watermarking and (iv) video marketing.

Image watermarking can be classified both in spatial domain and frequency domain.

Visible watermarks can appear to a casual viewer as a visible on careful inspection.

Primary images are embedded with the invisible fragile watermark technique in such a way that modification or manipulation of the image would destroy or alter the watermark. The alteration done to the pixel value is noticeable perceptually and it is possible to recover with appropriate decoding. Human perception classified watermarking as robust and fragile. In image processing, the watermarking techniques are classified into three types, visible watermark, invisible robust watermark and invisible fragile watermark.

Fig. 1 Encryption and decryption

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Fig. 2 Watermark embedding process and extraction process

All watermarking techniques are compatible with hardware, software or both together. There is a close relationship of watermarking and cryptography but watermarking is distinct from encryption.

An original image is embedded with the information carrying the watermark. The watermarked image is stored and transmitted and then decoded by the receiver.

Cryptography helps to resemble the image so that it cannot be understood.

Cryptographic [14] mechanism forms a foundation on network security [7], which help in implementation of security system based networks. There are encryption and decryption cryptographic algorithms. These algorithms suggest the ways by which it is possible to transfer secured data over networks [1]. Encryption is the method of changing plain text or unhidden text to a cipher text or hidden text, to secure against thieves under key management policy [14].

In encryption, [10] the data is locked at one end by the sender with the help of key and routed over network. Decryption is the process to retrieve the same text from the cipher text at another end. In decryption, same data is received, when the receiver is breaks the encrypted data with the help of

key. The encryption and decryption process is shown in fig. 1 and watermark embedding process and extraction process in fig. 2.

A digital watermark could be used either source based or destination based.

From the application point of view, source based watermarks are used for authentication or ownership identification.

In this a unique watermark is identifying that the owner is introduced to all the parallel copies of a particular image being distributed and it also used to identify weather a received image has been tampered with. If the each distributed copy is getting a unique watermark, it could be a destination based watermark and it could be used to determine the buyer in case of illegal reselling. In real time, watermarking will solve the issues of source authentication. In the real time stream exchange, the parties involved to check the authenticity of the data received with the help of watermark extraction bits available in the embedded stream. This watermark can be applied at the source point, channel or at the receiver side as video stream. In a watermarking system a simple video streaming authentication system is used as watermarking technique at the source principle rather than at channel or

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video delivery. The system is applicable for both unicast and multicasting application.

3. Discrete Wavelet Transform (DWT) The two-dimensional extension of DWT is essential for transformation of two- dimensional signals, such as a digital image.

A two-dimensional digital signal can be represented by a two-dimensional array [ ] with M rows and N columns, where M and N are nonnegative integers of 2D image array. The simple approach for two- dimensional implementation of the DWT is to perform the one-dimensional DWT row- wise to produce an intermediate result and then perform the same one-dimensional DWT column-wise on this intermediate result to produce the final result. This is shown in Fig. 3.. This is possible because the two-dimensional scaling functions can be expressed as separable functions which is the product of two-dimensional scaling function such as ( ) ( ) ( ).

The same is true for the wavelet function ( )as well. Applying the one-

dimensional transform in each row of image, two sub-bands are produced in each row.

When the low-frequency sub-bands of all the rows (L) are put together, it looks like a thin version (of size of the input signal as shown in Fig. 4(a). Similarly put together the high-frequency sub-bands of all the rows to produce the H sub-band of size , which contains mainly the high-frequency information around discontinuities (edges in an image) in the input signal. So that applying a one-dimensional DWT column- wise on these L and H sub-bands (intermediate result), four sub-bands LL, LH, HL, and HH of size are generated as shown in Fig.3 LL is a coarser version of the original input signal. LH, HL, and HH are the high frequency sub-band containing the detail information of the image. It is also possible to apply one- dimensional DWT column-wise first and then row-wise to achieve the same result.

Fig.4 comprehends the idea describe above.

Fig.3 Structure of wavelet decompositions

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Fig. 4 Extension of DWT in two - dimensional signals

The multi-resolution decomposition approach in the two-dimensional signal is demonstrated in Fig.4. After the first level of decomposition, it generates four sub-bands LL1, HL1, LH1, and HH1 as shown in Fig.

4. Considering the input signal is an image, the LL1 sub-band can be considered as a 2:

1 sub-sampled (both horizontally and vertically) version of image. The other three sub-bands HL1, LH1, and HH1 contain higher frequency detail information. These spatially oriented (horizontal, vertical or diagonal) sub-bands mostly contain information of local discontinuities in the image and the bulk of the energy in each of these three sub-bands is concentrated in the vicinity of areas corresponding to edge activities in the original image.

4. Discrete Cosine Transform (DCT)

In the last decade the advancement in data communication techniques were significant, during the explosive growth of the Internet the demand for using multimedia has increased. Video and Audio data streams require a huge bandwidth to be transferred in an uncompressed form. Several ways of compressing multimedia streams evolved, some of them use the Discrete Cosine Transform (DCT) and its inverse (IDCT) for transform coding. This report discusses different ways of implementing DCT hardware coders that could be used in a wide range of video and audio applications.

Formally, the discrete cosine transform is a linear, invertible function F : R^N -> R^N (where R denotes the set of real numbers, or equivalently an invertible N × N square matrix. There are several variants of the DCT [2, 16] with slightly modified definitions. The N real numbers x₀... x_N-1 are

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transformed into the N real numbers X0... XN- 1 according to one of the formulas:

DCT-I

( ( ) ) ∑ [

]

DCT-II

∑ [ ( ) ]

DCT-III

∑ [ ( )]

DCT-IV

∑ [ ( ) ( )]

Multidimensional DCT

∑ ( ∑ [ ( ) ]

)

[ ( ) ]

∑ ∑

[ ( ) ] [ ( ) ]

The mathematical model equation for a (8 x 8) point 2D DCT [7, 9] is shown below, in which the transformed outputs are represented as Y(k, m). Where k,m = 0,1,...,7, and the two dimensional input sequence, represents the image pixel values) by x(i, j), where i,j = 0,1,...,7.

( )

∑ ∑ ( ) [( )

]

[( ) ]

and C₀=1/2 else Ck, C_m =1. Using matrix notation, the (8 x 8) point 2D DCT [7] can be expressed as a matrix vector computation equation, where C represents the DCT coefficient matrix.

[ ] [ ] [ ]

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With the help of row column decomposition, the algorithm can be rewritten using two, 1D DCTs and a matrix transpose, as shown in Equation.

[ ] [ ] [ ] [ ]

With row column decomposition, the 8 point 1D DCT is applied to each row of the input matrix, and each (8 x 8) block of "semi-transformed" values is transposed and has a further 1D DCT applied to it. The expanded matrix representation for the 8 point 1D DCT is given below.

Here C_x = cos (x/ 16). In the implementation of the above equation, there is the requirement of 64 multiplications and 56 additions. With the help of symmetrical approach, the above can be rewritten, which reduces computations and the hardware in terms of multiplications, which are 32 and 8 additions and subtractors.

.

The simplifications of the above can be done as following with the assumption of

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Where,

C₁= ⁄ = 0.9808 K1 = x(0) + x(7) C2 = ⁄ = 0.9239 K2 = x(1) + x(6) C3 = ⁄ = 0.8315 K3 = x(2) + x(5) C₄= ⁄ = 0.7071 K4 = x(3) + x(4) C₅= ⁄ = 0.5556 K₅= x(0) - x(7) C₆= ⁄ = 0.3827 K6 = x(1) - x(6) C7 = ⁄ = 0.1951 K7 = x(2) - x(5) K8 = x(3) - x(4)

After solving the above matrix the output equations can be written in simplified form Y(0) = C4 ( K1 + K2 +K3 +K4)

Y(2) = C₂ ( K₁ – K₄ ) + C₆(K₂ –K₃) Y(4) = C4 [ ( K1 + K4 ) – ( K2 +K3) ] Y(6) = C6 ( K1 – K4 ) – C2 (K2 –K3) Y(1) = C₁K₅ + C₃K_{6 +} C₅K_{7 +} C₇K₈ Y(3) = (C3K5 – C7K6 ) – (C1K7 + C5K8)

Y(5) = (C5K5 – C1K6 ) + (C7K7 + C1K8) Y(7) = (C₇K₅ + C₃K₇ ) – (C₅K₆ + C₅K₈)

5. Results and Discussion

The MATLAB simulation is carried out in MATLAB 2013 with the help of MATLAB image processing tool. Figure 5 to 7 shows the input image with key and extracted

watermark as output. The images are extracted from the MATLAB software directly. Fig. 5 and fig. 6 shows the processing of HAAR DWT and fig. 7 and fig. 8 shows the processing for DCT and image under region of interest (ROIs).

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Fig. 5 (a) original image (b) Image after one level HAAR DWT

Fig. 6(a) original Image (b) watermark image

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Fig. 6 (c) Watermarked image using DWT (d) extracted watermark

Fig. 7(a) original Image (b) watermark image

Fig. 7 (c) Watermarked image using DCT (d) extracted watermark

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Fig. 8(a) original Image (b) ROI image

Fig. 8 (c) Watermarked image using DCT (d) extracted watermark

6. Conclusion

Digital watermarks provide an efficient cost effective means of a digital image which may be used for copyright protection. In watermarking technology, the watermark key is unique and exhibits a one-to-one correspondence with every watermark. In the paper the MATLAB simulation is carried out for digital watermarking using both DCT and DWT algorithms. It is noticed that the simulation time for the DCT is 1.48 seconds and for DWT it is 0.9 seconds for the same size of image. It is tested on 10

images. So , it can be estimated that DWT is much faster than DCT. The size of watermark key is also very important. The key is private and known to only authorized parties, eliminating the possibility of illegal usage of digital content.

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BIOGRAPHIES

Arisudan Tiwari, M. Tech Scholar, Department of Computer Science

& Engineering, Maharishi Ved Vyas Engineering College ,

Jagadhri Yamuna Nagar, India. I

Completed my B.Tech

(Information Technology) in 2011. I am having good Interest in image processing and analysis.

Shubham Shukla working as a Assistant Professor in the Department of Computer Science

& Engineering, Neelkanth Institute of Technology, Meerut, India. He has good knowledge in Digital Image Processing and published various papers.