RT has excellent feature to transform the information from two-dimensional image into a string of one-dimensional projections which is computationally faster. It has the following advantages: It has the ability to detect line width and has good robustness for noisy images. RT produces a big matrix by computing projections of an image along specified direction. For this reason, there is very little effect of embedding watermark in RT domain, which provides high quality watermarked images as well as good robustness against various attacks.
Jordan decomposition also known as Jordan normal form or Jordan canonical form results from the conversion of a matrix into its diagonal form by a similarity transformation [ 13 ]. The Jordan matrix decomposition of a square matrix A can be represented by:. Here, the Jordan normal form J is the diagonal matrix of eigenvalues and the similarity transform matrix V contains the generalized eigenvectors as columns.
The use of similarity transform aims at reducing the complexity of the problem of evaluating the eigenvalues of a matrix. Indeed, if a given matrix could be transformed into a similar matrix in diagonal form, the computation of the eigenvalues would be easy. Moreover, the slight variations of eigenvalues in embedding watermark have little effect on the quality of the watermarked image.
For this reason, it provides high quality watermarked images as well as good robustness against various attacks. The proposed watermarking method is described in this section which can be divided into two parts i watermark embedding process and ii watermark extraction process. RT is applied on each block Ba of the color space Ib. After applying RT, transformed matrix Rb is obtained. This is because computational cost of JD is quite high and it takes long time to perform on a big matrix. The JD can be represented as follows:. Here, Jc is the Jordan normal form and Vc is the similarity transform matrix.
In order to guarantee the robustness and imperceptibility, the proposed algorithm embeds watermark bit into all coefficients of similarity transform matrix VC using a new quantization function.
Color Image Watermarking Based on Radon Transform and Jordan Decomposition
This ensures that the watermark is located at the most significant perceptual components of the image. Watermark data is embedded by using the following equation:. This can be expressed as follows:. In this section, we have evaluated the performance of our proposed method in terms of imperceptibility and robustness. We carried out several experiments and also compared with some recent methods.
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In this study, for simplicity the selected value for n and p are 16 and 2, respectively. Computational cost of JD is quite high and it takes long time to perform JD on a big matrix. For this reason, we have selected a small value for p. To test the imperceptibility of the proposed method, we have calculated peak signal-to-noise ratio PSNR and structural similarity index measurement SSIM watermarked images.
The watermarked images are shown in Figure 6. Watermarked images obtained in this experiment a airplane, b Lena, c house, and d baboon.
SSIM is an efficient method for measuring the similarity between two images and it can be expressed as:. Table 1 shows the PSNR comparison between the proposed scheme and two recent methods. This method has an average PSNR value of Al-Afandy et al. This is in contrast to the proposed method whose PSNR values ranges from Table 1 also shows the SSIM comparison between the proposed scheme and two recent methods. The more the SSIM value approaches to 1, the better the image quality is. Our proposed method provides SSIM values close to 1 which is excellent for a watermarked image.
Also, the proposed method shows higher SSIM values compared to the recent methods. Radon transform generates a large matrix from the given image matrix which is convenient for embedding watermark. For this reason, we have used a small portion of transformed matrix for watermark insertion. Hence, there is very little effect on embedding watermark into the host image and we obtained higher PSNR, SSIM values compared to the conventional methods. To assess the robustness, we have calculated normalized correlation NC which computes the difference between original watermark and the extracted watermark.
The equation of NC is given below:. To verify the robustness of our proposed method, we applied different malicious attacks such as noise addition, cropping, rotation, filtering, blurring, sharpening, JPEG compression etc. We can also observe the watermark image extracted from the attacked watermarked image in Figure 9. From this figures, we observed that our proposed method shows high robustness against various attacks. Tables 2 and 3 show the NC comparison between the proposed scheme and several recent methods against various attacks.
The method proposed by Ansari and Pant [ 4 ] show good robustness where NC values range from 0. But, this method cannot resist against cropping and rotation attack. The method proposed by Al-Afandy et al.
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Our proposed method shows higher NC values than these method against various attacks. This is because watermark is embedded into the similarity transform matrix of the RT coefficients obtained from b channel of the original host image using a new quantization equation. NC comparison between the proposed scheme and several methods against various noise and JPEG compression attacks. NC comparison between the proposed scheme and several methods against filtering, cropping, rotation, sharpening, and blurring attacks. In this chapter, we have introduced a color image watermarking method based on RT and JD.
Simulation results demonstrate that the proposed method is highly robust against different attacks such as noise addition, cropping, filtering, rotation, blurring, sharpening, and JPEG compression. Moreover, it outperforms state-of-the-art image watermarking methods in terms of imperceptibility and robustness. These results indicate that the proposed watermarking method can be used for image copyright protection.
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We are IntechOpen, the world's leading publisher of Open Access books. Papers People. The trade-off between the imperceptibility and robustness is one of the most difficult challenges in digital watermarking system. To solve the problem, an optimal algorithm for image watermarking is proposed. The algorithm embeds the The algorithm embeds the watermark by quantizing the wavelet packets coefficients of the image. In the proposed watermarking system, to protect the originality of the watermark image, a scrambled binary watermark embeds in the host image against intentional and unintentional attacks and each bit of the permuted Save to Library.
SVD-based robust watermarking using fractional cosine transform. In this paper, a robust watermarking technique based on fractional cosine transform and singular value decomposition is presented to improve the protection of the images. A meaningful gray scale image is used as watermark instead of A meaningful gray scale image is used as watermark instead of randomly generated Gaussian noise type Hiding a face in a fingerprint image.
Hiding Facial Information in Color Image.
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Our first scheme is an On the implementation of a information hiding design based on saliency map. Abstract In this paper, an adaptive spatial domain image watermarking scheme is proposed which embeds watermark information to the uneven bit depth salient image pixels. Watermarked image thus produced has better visual transparency with Watermarked image thus produced has better visual transparency with respect to human visual system HVS with high payload capacity. Experimental results reveal that proposed scheme has less perceptual error as well as improved A guide tour of video watermarking.
Robust Watermarking through Spatially Disjoint Transformations. An image watermarking scheme is introduced with an aim to satisfy the imperceptibility and robustness requirements. The image is divided into spatially disjoint areas. Multiple watermarks are simultaneously embedded in a single image in random order. Each area is selected sequentially and watermarked independently. The main advantage of this concurrent watermarking method is that it makes the watermark invariant to all the available frequency based attacks and geometric attacks.
The shortcomings of one transform based watermarking scheme are overcome by the other. DFT based watermarking is invariant to geometric attacks and watermark detection attacks but it is not best suited for frequency based attacks like filtering and noise addition. Its shortcomings are overcome by applying the DCT and DWT based method in other areas which are resilient to frequency based attacks but fail against geometric attacks.
Hence if any method fails against an attack the watermark can be efficiently extracted by the other implemented methods. Simulation results show that proposed method is able to withstand many image processing attacks.