**1. Introduction**

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The great success of Internet and digital multimedia technology have made the fast communication of digital data, easy editing in any part of the digital content, capability to copy a digital content without any loss in quality of the content and many other advantages.

The great explosion in this technology has also brought some problems beside its advantages. The great facility in copying a digital content rapidly, perfectly and without limitations on the number of copies has resulted the problem of copyright protection. Digital watermarking is proposed as a solution to prove the ownership of digital data. A watermark, a secret imperceptible signal, is embedded into the original data in such a way that it remains present as long as the perceptible quality of the content is at an acceptable level. The owner of the original data proves his/her ownership by extracting the watermark from the watermarked content in case of multiple ownership claims

In general, any watermarking scheme (algorithm) consists of three parts.


Each owner has a unique watermark or an owner can also put different watermarks in different objects the marking algorithm incorporates the watermark into the object. The verification algorithm authenticates the object determining both the owner and the integrity of the object [1].

### **1.1 Embedding process**

Let us denote an image by *I*, a signature by *S =s1, s2, …* and the watermarked image by I′. E is an encoder function, it takes an image *I* and a signature *S*, and it generates new image which is called watermarked image *I′*, mathematically,

$$\mathbf{I} \to \begin{pmatrix} \mathbf{I} \ \mathbf{S} \end{pmatrix} = \mathbf{I}' \tag{1}$$

It should be noted that the signature S may be dependent on image *I*. In such cases, the encoding process described by (1) still holds. The figure 1 illustrates the encoding process [1].

#### **1.2 Extraction process**

A decoder function *D* takes an image *J* (*J* can be a watermarked or un-watermarked. image, and possibly corrupted) whose ownership is to be determined and recovers a signature S from the image [1].

In this process an additional image *I* can also be included which is often the original and unwatermarked version of J. This is due to the fact that some encoding schemes may make use of the original images in the watermarking process to provide extra robustness against intentional and unintentional corruption of pixels. Mathematically,

$$\mathbf{D} \text{ (J, I)} = \mathbf{S}' \tag{2}$$

A DFT-DWT Domain Invisible Blind Watermarking

Fig. 2. Decoder

Fig. 3. Comparator

Ratio) and *AR* (Accuracy rate)

Techniques for Copyright Protection of Digital Images 517

other cases, we can detect only whether a specific given watermarking signal is present in an image, a procedure we call watermark detection. It should be noted that watermark extraction can prove ownership whereas watermark detection can only verify ownership.

The quality of extracted watermark can also be measured by: *PSNR* (Peak Signal-to-Noise

*PSNR* is provided only to give us a rough approximation of the quality of the watermark.

<sup>Z</sup> <sup>255</sup> PSNR log dB

Where *MSE* is mean square error of an image with H × W pixels is defined as:

Where ij a is the original pixel value and ij a is the processed pixel value.

i j MSE a a HXW 

1 1

MSE

10 <sup>10</sup> (4)

<sup>1</sup> (5)

 H W ij ij

2

The proposed technique extract watermark to prove ownership.

In proposed algorithm, original image is not used while extracting watermark from watermarked image and we provide robustness by using some keys.

The extracted signature *S* will then be compared with the owner signature sequence by a comparator function *Cδ* and a binary output decision generated. It is 1 if there is match and 0 otherwise, which can be represented as follows.

$$\mathbf{C}\_3(\mathbf{S'}, \mathbf{S}) = \begin{cases} 1. \; \mathbf{c} \le \delta \\ 0. \; \text{Otherwise} \end{cases} \tag{3}$$

Where *C* is the correlator, x= c3(S,S'). *C* is the correlation of two signatures and *δ* is certain threshold. Without loss of generality, watermarking scheme can be treated as a three-tupple (*E, D, Cδ*). Following figure 2 & figure 3 demonstrate the decoder and the comparator respectively.

A watermark must be detectable or extractable to be useful. Depending on the way the watermark is inserted and depending on the nature of the watermarking algorithm, the method used can involve very distinct approaches. In some watermarking schemes, a watermark can be extracted in its exact form, a procedure we call watermark extraction. In

Fig. 2. Decoder

It should be noted that the signature S may be dependent on image *I*. In such cases, the encoding process described by (1) still holds. The figure 1 illustrates the encoding process

A decoder function *D* takes an image *J* (*J* can be a watermarked or un-watermarked. image, and possibly corrupted) whose ownership is to be determined and recovers a signature S

In this process an additional image *I* can also be included which is often the original and unwatermarked version of J. This is due to the fact that some encoding schemes may make use of the original images in the watermarking process to provide extra robustness against

In proposed algorithm, original image is not used while extracting watermark from

comparator function *Cδ* and a binary output decision generated. It is 1 if there is match and 0

Where *C* is the correlator, x= c3(S,S'). *C* is the correlation of two signatures and *δ* is certain threshold. Without loss of generality, watermarking scheme can be treated as a three-tupple (*E, D, Cδ*). Following figure 2 & figure 3 demonstrate the decoder and the comparator

A watermark must be detectable or extractable to be useful. Depending on the way the watermark is inserted and depending on the nature of the watermarking algorithm, the method used can involve very distinct approaches. In some watermarking schemes, a watermark can be extracted in its exact form, a procedure we call watermark extraction. In

<sup>3</sup> 1. c C S', S . Otherwise 

D J, I S' (2)

<sup>0</sup> (3)

will then be compared with the owner signature sequence by a

intentional and unintentional corruption of pixels. Mathematically,

watermarked image and we provide robustness by using some keys.

otherwise, which can be represented as follows.

[1].

Fig. 1. Encoder

**1.2 Extraction process** 

The extracted signature *S*

respectively.

from the image [1].

Fig. 3. Comparator

other cases, we can detect only whether a specific given watermarking signal is present in an image, a procedure we call watermark detection. It should be noted that watermark extraction can prove ownership whereas watermark detection can only verify ownership.

The proposed technique extract watermark to prove ownership.

The quality of extracted watermark can also be measured by: *PSNR* (Peak Signal-to-Noise Ratio) and *AR* (Accuracy rate)

*PSNR* is provided only to give us a rough approximation of the quality of the watermark.

$$\text{PSNR} = 10 \log\_{10} \left( \frac{255^Z}{\text{MSE}} \right) \text{dB} \tag{4}$$

Where *MSE* is mean square error of an image with H × W pixels is defined as:

$$\text{MSE} = \frac{1}{\text{HXW}} \sum\_{i=1}^{\text{H}} \sum\_{j=1}^{\text{W}} \left( \mathbf{a}\_{\text{ij}} - \overline{\mathbf{a}}\_{\text{ij}} \right)^{2} \tag{5}$$

Where ij a is the original pixel value and ij a is the processed pixel value.

Besides, we utilized the accuracy rate *AR* to evaluate the robustness of a copyright protection scheme for a specific attack. The formula for *AR* is shown below:

$$\text{AR} = \frac{\text{CP}}{\text{NP}} \tag{6}$$

A DFT-DWT Domain Invisible Blind Watermarking

Fig. 5. Types of watermarking techniques

**1.3.1 Discrete Fourier transform** 

Given a two-dimensional signal f(x, y), the DFT is defined

For u = 0, 1, 2…, M-1, v = 0, 1, 2 ,., N-1 and j=√-1

where, (M, N) are the dimensions of the image.

The inverse DFT (IDFT) is given by:

**1.3.2 The wavelets transform** 

magnitude of its coefficients.

Techniques for Copyright Protection of Digital Images 519

Commonly used frequency-domain transforms include the Discrete Wavelet Transform (DWT), the Discrete Cosine Transform (DCT) and Discrete Fourier Transform (DFT). The host signal is transformed into a different domain and the watermark is embedded in

The Discrete Fourier Transformation (DFT) controls the frequency of the host signal. Energy of watermarking message can be distributed averagly in space domain after the signal is implemented DFT. It enables the schemes further to embed the watermark with the

M N <sup>j</sup> ux M vy <sup>N</sup>

M N <sup>j</sup> ux M vy <sup>N</sup>

The DFT is useful for watermarking purposes because it helps in selecting the adequate parts of the image for embedding, in order to achieve the highest invisibility and robustness.

Wavelet transform decomposes an image into a set of band limited components which can be reassembled to reconstruct the original image without error. The DWT (Discrete Wavelet Transform) divide the input image into four non-overlapping multi-resolution sub-bands

1 1 <sup>2</sup>

1 1 <sup>2</sup>

<sup>1</sup> (7)

(8)

x y F u,v f x,y e MN

u v F x,y F u,v e

 

0 0

 

0 0

selective coefficients. Here we have described DFT and DWT domain techniques.

Where *NP* is the number of pixels of the watermark image and *CP* is the number of correct pixels in the extracted watermark image.
