**1.3.1 Discrete Fourier transform**

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 magnitude of its coefficients.

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

$$F(\mathbf{u}, \mathbf{v}) = \frac{1}{\text{MN}} \sum\_{\mathbf{x}=\mathbf{0}}^{\text{M}-1} \sum\_{\mathbf{y}=\mathbf{0}}^{\text{N}-1} \mathbf{f}(\mathbf{x}, \mathbf{y}) \mathbf{e}^{\left(-j2\pi(\mathbf{u}\mathbf{x}/\mathbf{M} + \mathbf{v}\mathbf{y}/\mathbf{N})\right)}\tag{7}$$

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

The inverse DFT (IDFT) is given by:

$$\mathbf{F}(\mathbf{x}, \mathbf{y}) = \sum\_{\mathbf{u}=\mathbf{0}}^{\mathbf{M}-1} \sum\_{\mathbf{v}=\mathbf{0}}^{\mathbf{N}-1} \mathbf{F}(\mathbf{u}, \mathbf{v}) \mathbf{e}^{\left(j2\pi(\mathbf{u}\mathbf{x}/\mathbf{M} + \mathbf{v}\mathbf{y}/\mathbf{N})\right)} \tag{8}$$

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

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.

#### **1.3.2 The wavelets transform**

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

A DFT-DWT Domain Invisible Blind Watermarking

**1.5 Watermarking requirements** 

process, varies.

operation.

preserved.

this data is used to detect and conceal the block errors.

intended or non-intended any signal operations and capacity.

Techniques for Copyright Protection of Digital Images 521

There are also non-secure applications of digital watermarking. It can be used for indexing of videos, movies and news items where markers and comments can be inserted by search engines [8]. Another non-secure application of watermarking is detection and concealment of image/video transmission errors [11]. For block based coded images, a summarizing data of every block is extracted and hidden to another block by data hiding. At the decoder side,

The efficiency of a digital watermarking process is evaluated according to the properties of perceptual transparency, robustness, computational cost, bit rate of data embedding process, false positive rate, recovery of data with or without access to the original signal, the speed of embedding and retrieval process, the ability of the embedding and retrieval

Depending on the application, the properties, which are used mainly in the evaluation

The main requirements for copyright protection are imperceptibility and robustness to

The owner of the original data wants to prove his/her ownership in case the original data is copied, edited and used without permission of the owner. In the watermarking research world, this problem has been analyzed in a more detailed manner [13, 14, 15, 16, 17, 18].

The imperceptibility refers to the perceptual similarity between the original and watermarked data. The owner of the original data mostly does not tolerate any kind of degradations in his/her original data. Therefore, the original and watermarked data should be perceptually the same. Robustness to a signal processing operation refers to the ability to detect the watermark, after the watermarked data has passed through that signal processing

The robustness of a watermarking scheme can vary from one operation to another. Although it is possible for a watermarking scheme to be robust to any signal compression operations, it may not be robust to geometric distortions such as cropping, rotation, translation etc. The signal processing operations, for which the watermarking scheme should be robust, changes from application to application as well. While, for the broadcast monitoring application, only the robustness to the transmission of the data in a channel is sufficient, this is not the case for copyright protection application of digital watermarking. For such a case, it is totally unknown through which signal processing operations the watermarked data will pass. Hence, the watermarking scheme should be robust to any possible signal processing operations, as long as the quality of the watermarked data

The capacity requirement of the watermarking scheme refers to be able to verify and distinguish between different watermarks with a low probability of error as the number of differently watermarked versions of an image increases [17]. While the robustness of the watermarking method increases, the capacity also increases where the imperceptibility decreases. There is a trade off between these requirements and this trade off should be taken

into account while the watermarking method is being proposed.

module to integrate into standard encoding and decoding process etc. 7, 8, 9, 12, 13].

LL1, LH1, HL1 and HH1. The process can then be repeated to computes multiple "scale" wavelet decomposition, as in the 2 scale wavelet transform shown in Fig. 6.

One of the many advantages over the wavelet transform is that it is believed to more accurately model aspects of the HVS as compared to the FFT or DCT. This allows us to use higher energy watermarks in regions that the HVS is known to be less sensitive, such as the middle frequency bands (LH, HL) and high resolution band (HH). But watermark embedded in high resolution band can be easily be distorted by geometric transformation, compression and various signal processing operations.

Embedding watermarks in middle frequency regions allow us to increase the robustness of our watermark, at little to no additional impact on image quality [6].


Fig. 6. Scale 2 Dimensional DWT
