CHAPTER 3 DIFFERENT DOMAINS OF WATERMARKING. domain. In spatial domain the watermark bits directly added to the pixels of the cover

Transcription

1 38 CHAPTER 3 DIFFERENT DOMAINS OF WATERMARKING Digital image watermarking can be done in both spatial domain and transform domain. In spatial domain the watermark bits directly added to the pixels of the cover image. Spatial domain methods can be easily modeled and analyzed mathematically. However the embedded watermark can be easily destroyed or removed by signal processing attacks such as filtering. The spatial domain technique makes use of human visual system, but sensitive to image scale so that same information must be embedded again and again in different locations of the host image. The least significant bit (LSB) method is an example of spatial domain method where the watermark is embedded into the least significant bits of the cover image. In this method, first the bit planes are extracted from the watermark and then shifted to the right. The shifted bit planes are added to the least significant bits of the cover image to get the watermarked image. The least significant bits are highly sensitive to noise, so that the watermark can easily be removed by image manipulations such as rotation and cropping. Thus, the LSB method provides high imperceptibility and less robustness. The correlation based method is another example of spatial domain techniques; in this method, the watermark is converted into Pseudo Noise sequence which is then weighted and added to the cover image bits. The watermarked image is compared with the cover image to detect the inserted watermark. The spatial domain methods are less complex compare to transform domain methods, however weak to different image attacks. The data hiding capacity of spatial domain techniques is higher than that of transform domain methods. Spatial domain techniques offer higher robustness to geometrical transformations.

2 DIGITAL IMAGE WATERMARKING IN FREQUENCY DOMAN The robustness and imperceptibility of the watermarked images can be improved by performing watermarking in frequency domain. Frequency domain techniques can provide better robustness against compression and filtering attacks, because the watermark coefficients spread throughout the cover image. In frequency domain, watermark embedding is done by modifying the image coefficients using image transforms. Masking techniques based on transform domain are more robust than least significant bit method with respect to cropping, compression and image processing. The main advantage of masking techniques is that they embed watermark coefficients in large areas of the host image. Many of the transform coefficients are small; hence even though they discarded during the process of compression the effect is negligible DIGITAL IMAGE WTERMARKING USING -D FOURIER TRANSFORMS The Discrete Cosine Transform (DCT), Discrete Laguerre Transform (DLT), Discrete Fractional Fourier Transform (DFRFT), Natural Preserve Transform (NPT) and Discrete Fourier Transform (DFT) are some of the two-dimensional image transforms available. DCT based watermarking can be done for an entire image or block-wise. In both of these methods, the image is transformed into its DCT coefficients and the watermark is added to these transformed coefficients based on frequency. The watermarking can be achieved by altering the transform coefficients of the image. Finally, the watermarked coefficients inverse transformed into the spatial domain and there by spreading the watermark throughout the image or blocks of the image. DCT takes the advantage of stastical dependency between color channels so that each color channel is then modified to embed the watermark. Two important issues should be considered with respect to DCT

3 40 based watermarking. The first one is the selection of coefficients, choosing the high frequency coefficients affect the imperceptibility and any filtering operation can remove the watermark from the image. The second issue is related to the amount of changes performed on DCT coefficients to embed the watermark. These changes made on coefficients influence the invisibility of the watermark and destroy the image to a large extent. Discrete Laguerre Transform (DLT) utilizes Laguerre functions, which constitute a set of orthogonal functions in the interval (0, ).Due to the exponential term present in the expansion, these functions are not polynomials. The drawback of DLT is the increase in computational complexity as the order of the DLT increases. The DLT based watermarking improves the quality of the watermarked image compared to DCT. The Discrete Fractional Fourier Transform (DFRFT) is the generalized form of classical Fourier transform and is a potential and powerful tool for non- stationary and time varying signal processing applications. Because of two additional degrees (watermark location and powers of DFRFT) of freedom DFRFT allows to embed more number of watermark bits than DCT and DFT. Natural Preserving Transform is used as an orthogonal transform which has some unusual properties to encode and reconstruct the data that is lost. The properties of NPT are similar to that of Hartley transform which achieves tradeoff between energy concentration feature and spreading feature. Thus, the NPT transform is capable to concentrate on energy of the image while preserving its original samples. This makes the NPT transform more capable to retrieve the original image from all parts of the

4 41 transformed image. The NPT transform provides high similarity between the original image and the watermarked image which is very much desirable in watermarking. Other -D transform used to perform image watermarking is DFT. An important property of DFT is that the shift of phase in spatial domain does not change the magnitude characteristics and watermark embedding is based on phase characteristics because phase is highly immune to noise. Adaptive phase modulation is also implemented to improve the fidelity of the watermarked image. Watermark embedding using DFT is invariant to rotation attack DIGITAL IMAFE WATERMARKING USING WAVELETS A wavelet is an oscillatory function of finite duration. The wavelet provides both spatial and frequency description details of the image. The temporal information is retained in this wavelet transformation process compared to other transforms like DCT and DFT. Haar, Daubechies, Complex, Balanced, Stationary, Morphological, Non-tensor, Berkley, Mexican- hat, Morlet, Shannon and Biorthogonal are the different wavelets used to perform image processing DISCRETE WAVELET TRANSFORM (DWT) The DWT is not effective to analyze non-stationary signals. Whereas short time Fourier Transform is an effective tool to do that operation, but the drawback is that it gives constant resolution at all frequencies. DWT provides both spatial and frequency description of an image with multiresolution. The multi-resolution property of the wavelet transform can be used to exploit the fact that the response of the human eye is different to high and low frequency components of the image. DWT can be applied to an

5 4 entire image without using block structure as used by the DCT, thereby reducing the blocking artifact. Wavelet is an oscillatory function of time or space that is periodic and of finite duration with zero average value. A family of wavelets can be generated by dilating and translating mother wavelet. Wavelet provides time- frequency representation of a signal and is used to analyze non- stationary signals. Multi-resolution technique is used in wavelet transform where different frequencies are analyzed with different resolutions. Big wavelets give an approximate value of a signal, while the smaller wavelets boost up the smaller details. DWT is computed either by using convolution based or lifting based procedures. In both the methods, the output sequence decomposed into low-pass and high-pass sub bands, where each sub bands constituting of half the number of samples of the original sequence. The DWT represents an NxN image by N coefficients. The DWT can be implemented through filter bank or lifting scheme. The DWT of an image is analyzed by allowing it to pass through an analysis filter bank followed by down sampling. The analysis filter bank consists of low-pass and highpass filters at decomposition stage. When an image passes through these filter banks, the image split into two sub bands. The low-pass filter performs averaging operation and extracts the coarse information of the image. Whereas the high-pass filter performs difference operation and extracts the details of the image. Then the output of the filtering operation is down sampled by two. This operation splits the image into four bands, namely, LL, LH, HL, and HH as shown in figure (3.1). The lowest resolution level LL consists of the approximation part of the original image and most of the energy is concentrated in this LL band. Hence modifications of this low

6 43 frequency subband would cost severe and unacceptable image degradation. So the watermark is not embedded in LL subband. The good areas for watermark embedding are high and middle frequency coefficients (vertical, horizontal and diagonal coefficients). Human visual system is insensitive to these high and middle frequency subbands and effective watermark embedding is achieved without being perceived by human visual system. LPF LL Band LPF W(x, y) HPF LH Band LPF HL Band HPF HPF HH Band Figure (3.1): Wavelet Decomposition using Sub-band coding The basic implementation of DWT for images is described as follows. First, an image decomposed into four parts of low, middle and high frequency sub components LL 1, LH 1, HL 1 and HH 1 by sampling horizontal and vertical channels using subband filters. The sub components LH 1, HL 1 and HH 1 represent the first level decomposition. To obtain the next level decomposition the sub component LL 1 is further decomposed as shown in figure (3.). This process of subsampling is repeated several times based on the requirement. In this work biorthogonal wavelets are used to perform watermark embedding and extraction. Biorthogonal wavelet generates two basis functions for decomposition and reconstruction.

7 44 Level- The Original Image Level-1 LL 1 HL 1 LH 1 HH 1 LL HL LH HH HL 1 LH 1 HH 1 Figure (3.): Discrete Wavelet Transformation BIORTHOGONAL WAVELETS Biorthogonal wavelets have the property of smoothness, exact reconstruction, symmetry and higher embedding capacity. Orthogonality and symmetry are conflict properties in the design of wavelets. Biorthogonal wavelets maintain linear phase constraint by relaxing orthogonality. Design of biorthogonal wavelets with symmetry gives good compression and reduces computational complexity. The Cohen-Daubechies- Feauveau (CDF) biorthogonal wavelet system is implemented in this work. The advantage of this system is that the scaling function and wavelet is symmetric and have similar lengths. The block diagram (109) of the two- band biorthogonal system is shown in figure (3.3). Analysis bank Synthesis bank X h h X g g Figure (3.3): Two-Band Biorthogonal Filter Bank

8 45 Let h and h denote a pair of dual lowpass filters of analysis and synthesis filters respectively (109). Where and denote a pair of dual highpass filters of analysis and synthesis filters respectively. The associated scaling functions and recursively defined as follows: ( ) h( ) ( ) (3.1) and ( ) h ( ) ( ). (3.) The associated biorthogonal filter bank wavelets and (109) are defined as ( ) ( ) h( ) ( ). (3.3) and ( ) ( ) h( ) ( ) (3.4) The set of four functions, { ( ), ( ) ( ), ( ) } form a two- band biorthogonal wavelet system. For perfect reconstruction, the following condition (109) must be satisfied. ( ) ( ) ( ) ( ). (3.5) Where ( ) h( ) and ( ) h ( ) respectively. 3. DIFFERENT TECHNIQUES TO OPTIMIZE WATERMARKING The performance of wavelet based watermarking algorithms has been improved by using different optimization techniques such as singular value decomposition, independent component analysis, the support vector machine, genetic algorithm, artificial neural network and fuzzy logic, etc.

9 46 Singular Value Decomposition (SVD) is the powerful numerical analysis tool used to analyze matrices, where the image matrix can be decomposed into three matrices that are of the same size as the original image matrix. SVD transformations preserve both oneway and non-symmetric properties, usually not available in DCT and DFT. The use of SVD in digital image watermarking has advantages like the size of the matrices not fixed and can be either rectangle or square. The advantage of Independent Component Analysis (ICA) is that each user can define their own ICA-based transformation. These transformations behave like private keys to blindly detect the watermark with a simple matched filter. Support Vector Machine (SVM) used as a tool to perform image watermarking in wavelet transform domain. Genetic Algorithm is a search heuristic used for optimization. In this work, the neural network and fuzzy logic are implemented to perform image watermarking in discrete wavelet transform domain. The discrete wavelet transform alone does not provide better robustness and imperceptibility. Back Propagation Neural Network (BPNN) has good nonlinear approximation ability, which makes it very useful in image processing applications. The BPNN is used to embed and extract the watermark, where the training process is completed before embedding watermark. Dynamic Fuzzy Expert System also known as The Dynamic Fuzzy Inference System (DFIS) is a computing framework which is widely accepted based on the well-known concepts of fuzzy set theory, fuzzy reasoning and fuzzy if-then rules. In this work Mamdani type DFIS is modeled using biorthogonal wavelets to improve watermark robustness and imperceptibility. The dynamic fuzzy inference system is recognized as a

10 47 powerful tool based on fuzzy mapping operations without using extensive mathematical operations. 3.3 CHAPTER SUMMARY In this chapter different domains of watermarking, discrete wavelet transform, biorthogonal wavelets and optimization techniques of watermarking are explained. Digital Image watermarking using back propagation is explained in the next chapter.