Average PSNR and correlation of proposed method and Y. Wang method [8].
1. Introduction
With the growth and advances in digital communication technologies, digital images have become easy to be delivered and exchanged. These forms of digital information can be easily copied and distributed through digital media. These concerns motivated significant researches in images watermarking [1]. New progress in digital technologies, such as compression techniques, has brought new challenges to watermarking. Various watermarking schemes that use different techniques have been proposed over the last few years [210]. To be effective, a watermark must be imperceptible within its host, easily extracted by the owner, and robust to intentional and unintentional distortions [7]. In specific, discrete wavelet transforms (DWT) has wide applications in the area of image watermarking. This is because it has many specifications that make the watermarking process robust. Some of these specifications are [4]: Spacefrequency localization, Multiresolution representation, Superior Human Visual system (HVS) modeling, and adaptively to the original image. A waveletbased watermarking technique for ownership verification is presented by Y. Wang [11]. It uses orthonormal filter banks that are generated randomly to decompose the host image and insert the watermark in it.
Another transform technique that is used extensively in image coding is the pyramid transform which was first introduced by Burt and Adelson [12]. It can provide high compression rates and at the same time low complexity encoding. Like the DWT, pyramid transform provides multiresolution representation of the images. These properties can be used in watermarking to establish a robust data hiding system.
In this chapter, our target is to develop an algorithm using optimal pyramid decomposition technique, and combine it with wavelet decompositions. The algorithm will be used for data hiding in digital images to meet the requirements of imperceptibility, robustness, storage requirements, security, and complexity.
2. Wavelet and Pyramid Transforms
The wavelet transform has the advantage of achieving both spatial and frequency localizations. Wavelet decomposition depends mainly on filter banks, typically the wavelet decomposition and reconstruction structures consist of filtering, decimation, and interpolation. Figure 1. shows twochannel wavelet structure [11].
Where
Special type of wavelet filters is the orthonormal filters. These filters can be constructed in such a way that they have large sidelobes. This makes it possible to embed more watermarks in the lower bands to avoid the effect of the different images processing techniques. These filter banks can be generated randomly depending on the generating polynomials. For twochannel orthonormal FIR real coefficient filter banks, the following relations shall be applied [11]:
If
Then it can be written as:
Depending on the factorization of the polynomials given in equation (7), analysis and synthesis filters can be generated. If
This decomposing structure is applied to King Saud University (KSU book) image of size 512×512 pixels shown in Figure 3. The resulting wavelet subbands are shown in Figure 4.
To have a good understanding of the DWT and its effects on the image, it is better to study this decomposition technique in the frequency domain. Frequency spectrum of the original KSU image (the book) is shown in Figure 5, and frequency responses of the four subbands that result from the first level decomposition are shown in Figure 6. The spectrums of the four bands show the effect of the filtering process, and the shapes of these filters. From these two figures it can be seen that the spectrum of subband
Pyramid transform was first introduced by Burt and Adelson [12]. It was used mainly for image compression. Like the DWT, pyramid transform provides the multiresolution structure. If
For decimation by a factor of 2, the image will be filtered using analysis lowpass filter
This process can be done for the higher levels and we will have the error images
Computational complexity depends on the number of operations (here multiplications) required to transform an image for a number of levels
For an image
The first part of equation (9) results from horizontal filtering and the second part is the number of multiplications needed for vertical filtering after decimated by
Then equation (9) can be applied for higher levels. In general, the total number of multiplications needed to get the decimated images
Where
The above analysis can be extended to the wavelet transform taking into account that there are four filters for each stage of decompositions and four filters for each stage of reconstructions, and the decimation factor is
Our algorithm performance will be measured in terms of peak signaltonoise ratio (PSNR) between the original image and the watermarked one, and the correlation between the original watermark and the extracted one. False alarm probability
The watermark extraction is similar to determining a signal in a noisy environment [11]; since the watermark is of size
Where
And
As the threshold value of the correlator increases, then the false alarm probability decreases which indicates more reliability. Accepted false alarm probability depends on the requirements, for example a
3. Proposed Watermarking Technique
In this section, we introduce our digital image watermarking technique. The technique consists of two stages: first stage is the pyramid transform and the second stage is the DWT. The watermark can be a logo image of size
Our proposed algorithm will use one of the error images resulting from the pyramid decomposition as a host image for the wavelet watermarking process. That is, the watermark will be inserted in one of the error images using wavelet decomposition. A method for wavelet image watermarking is proposed by Y. Wang [11]. It uses FIR, realcoefficients, randomly generated orthonormal filter banks. The watermark will replace the coefficients of one of the higher subbands. Then, the watermarked image will be reconstructed. However, a method for generating optimal pyramid transform filters has been introduced by F. Chin [14]. Therefore, The original image can be pyramidally decomposed using random analysis filters for three levels resulting in three error images
Method that depends on decomposing
4. Experimental Results
In this section we demonstrate the performance of our algorithm using our proposed method on grayscale test images of sizes 512×512 pixels, and compare it with method of Y. Wang [11]. The test images are Lena, Baboon, Peppers, Goldhill, and Barbara. The original and watermarked images of Lena are shown in figure 15. Our algorithm performance will be measured in terms of peak signaltonoise ratio (PSNR) between the original image and the watermarked one, and the correlation between the original watermark and the extracted one. For accepted false alarm probability



Average PSNR  46.52  42.14 
Average correlation  0.992  0.986 
To see the robustness of our algorithm, the watermarked images were subjected to certain common attacks. These attacks are JPEG compression, median filters, histogram equalization, zero mean 100 variance Gaussian noise, and 1% saltandpepper noise. The average compression over the five test images is 0.328 bpp. Table 2 shows the average correlation values for the five test images with these attacks. It can be seen that our proposed algorithm provides higher values with two of the attacks. These attacks are the median filter and the JPEG compression. However, for the additive noise and the histogram equalization, it gives approximately the same average values. Importance of this result is that median filters and JPEG attacks are among the worst attacks in watermarking systems. They are able to destroy many watermarking systems without affecting the visual quality. Surviving them gives the used algorithm high robustness.
The other important advantage of our proposed algorithm is the savings in the computational complexity. Normally, DWT and pyramid transform use the fast Fourier transform (FFT). Computational complexity depends on the number of multiplications being performed [13]. Table 3 shows the number of multiplications and savings for our method and method of Y. Wang [11]. It can be shown that our method achieves a saving of 54%. This is due to the fact that the wavelet decomposition was performed on a smaller image






JPEG compression (average: 0.328 bpp)  0.602  0.562 
Median filter  0.909  0.430 
Histogram equalization  0.965  0.963 
Gaussian noise  0.967  0.974 
1% Saltandpepper noise  0.948  0.956 



Number of multiplications  16,687,104  36,347,904 
Savings in computational complexity (%)  54.09  0 
5. Application on Digital Color Images
The proposed PyramidBased Watermarking Technique can also be applied on the digital color images. In this section, we demonstrate the performance of our algorithm using the proposed method on standard RGB color test images of sizes 512×512 pixels and the watermark was inserted in the green component. The test images are Lena, Baboon, and Peppers. The original and watermarked images of Lena are shown in Figure 16. Table 4 shows the correlation values of the watermarking process for the images. To ensure the robustness of our method, it was subjected to attacks of Gaussian noise of zero mean and variance of 100, 1% saltandpepper noise, and JPEG compression. Tables 5 and 6 show the correlation values when adding the two types of noise. It can be seen that our proposed algorithm is robust to these kinds of noise. Table 7 shows the correlation values when our watermarked images were compressed using JPEG compression at quality factors of 50,60,70,80, and 90 to different bit rates. It can be seen that for an average bit rate of 1.67 bpp, the normalized correlation is 0.50. This value is above the threshold mentioned in reference [10] which is 0.23. So, our algorithm is robust against JPEG compression at quality factors greater than 50.


Lena  1 
Baboon  1 
Peppers  1 


Lena  0.90 
Baboon  0.98 
Peppers  0.77 


Lena  0.91 
Baboon  0.98 
Peppers  0.70 
Lena  50  0.74  0.29 
60  0.85  0.30  
70  1.03  0.41  
80  1.34  0.44  
90  2.11  0.74  
Baboon  50  1.54  0.50 
60  1.78  0.54  
70  2.13  0.65  
80  2.71  0.75  
90  4.06  0.91  
Peppers  50  0.80  0.23 
60  0.93  0.29  
70  1.13  0.35  
80  1.47  0.42  
90  2.45  0.67  
Average  1.67  0.50 
6. Conclusions
In this chapter, we proposed a pyramidwavelet watermarking technique. The technique uses the spatialfrequency properties of the pyramid and wavelet transforms to embed a watermark in digital images. From the results, the proposed algorithm achieved a tradeoff between the perceptual invisibility and the robustness. However, it enhanced the performance of the waveletbased watermarking algorithm of Y. Wang [11] in many aspects such as compression and median filter attacks. The security issues were addressed extensively in the design, where the filter banks being used are generated randomly. The owner has full control on the filter banks, the decomposition structure, and the band being used for embedding. On the other hand, the watermark can be also controlled by the owner; he can rotate and scramble it. The proposed algorithm provided savings in the computational complexity which is a significant aspect in watermarking systems design. The filters being used for pyramid and wavelet transform should be optimized for perfect reconstruction, and this will help in designing robust watermarking systems to get the best performance.
References
 1.
Langelaar G. C. Setyawan I. Lagendijk R. L. 2000 Watermarking digital image and video data. A stateoftheart overview  2.
Aboofazeli M. Thomas G. Moussavi Z. 2004 A wavelet transform based digital image watermarking scheme  3.
AlAsmari Awad Kh. AlEnizi Farhan A. 2006 A PyramidBased Watermarking Technique for Digital Images Ownership Verification First National Information Technology Symposium (NITS 2006), Feb. 57 King Saud University, Saudi Arabia  4.
Meerwald P. Uhl A. 2001 A survey of waveletdomain watermarking algorithms  5.
MongShu L. 2003 Image compression and watermarking by wavelet localization  6.
AlEnizi Farhan A. AlAsmari Awad Kh. 2006 A PyramidBased Watermarking Technique for Secure Fingerprint Images Exchange. The International Conference on Computer & Communication 2006 (ICCC06), International Islamic University Malaysia.  7.
Kundur D. Hatzinakos D. 1998 Digital watermarking using multiresolution wavelet decomposition  8.
Guzman V. H. Miyatake M. N. Meana H. M. P. 2004 Analysis of a waveletbased watermarking algorithm  9.
AlAsmari Awad Kh. AlEnizi Farhan A. 2009 Watermarking Technique for Digital Color Images Copyright Protection. International Conference of Computing in engineering, science and information 2009 (HPCNCS09) Florida, USA.  10.
ShihHao W. YuanPei L. 2004 Wavelet tree quantization for copyright protection watermarking  11.
Wang Y. Doherty J. F. Van Dyck R. E. 2002 A waveletbased watermarking algorithm for ownership verification of digital images  12.
Burt P. J. Adelson E. H. 1983 The Laplacian pyramid as a compact image code  13.
AlAsmari A. Kh. 1995 Optimum bit rate pyramid coding with low computational and memory requirements  14.
Chin F. Choi A. Luo Y. 1992 Optimal Generating Kernels for Image Pyramids by Piecewise Fitting