Hybrid secure and robust image watermarking scheme based on SVD and sharp frequency localized contourlet transform
Introduction
Nowadays, multimedia productions and their distributions are performed in digital form. One of the most important features of the digital data is their unlimited copying without any loss of quality. This advantage is not good for multimedia owners. Digital watermarking is developed to serve them to protect their products against unauthorized usages. The digital watermarking has applications like copy and copyright protections, ownership identification, authentication, secret communication and medical applications [1], [2], [3], [5]. The information related to the ownership is watermark and is embedded in the original data (cover work) without loss of quality of the data and resistant (robust) under some digital operations.
All digital watermarking procedures include two apart processes: the embedding process of the watermark and its detection process. The embedding process is done in the transmitter side and the detection process is implemented in the receiver part.
The important requirements of a watermarking scheme are robustness, capacity, imperceptibility and security. Robustness is the ability of the scheme in protecting the watermark under several attacks and is application-dependent [6], [18], [41]. This feature is measured by normalized correlation (NC) quantity which has an absolute value between 0 and 1. The second requirement is capacity and indicates the amount of all information which is embedded in the selected cover work [20]. Embedding the watermark changes the visual properties of the cover work. This reduction is imperceptibility feature of the scheme and is measured by peak signal-to-noise ratio (PSNR). A scheme is more imperceptible if this loss is low and then PSNR is high. For an image, generally the minimum acceptable value for the PSNR is 38 dB [21]. The security refers to ability of the watermarking scheme to resist intentional tampering [19].
Digital watermarking is classified into two categories: spatial domain techniques like least significant bits (LSB) [4] and transform domain techniques in which the most used transforms are discrete cosine transform (DCT) [7], [8], discrete Fourier transform (DFT) [9], and discrete wavelet transform (DWT) [11], [12], [13], [14], [15], [16]. Digital watermarking has been implemented widely with DWT which has good properties like multiresolution representation, superior human visual system modeling and time frequency localization. But in 2D, wavelets lack the directional property which is important in efficient computational image representation. This problem is solved using contourlet transform (CT) introduced by Do and Vetterli [22]. The contourlet is a non-separable 2D transform and a combination of the Laplacian pyramid [23] and the directional filter banks (DFB) [42].
CT captures the edges of the images in many directions and resolutions efficiently, but is not ideal in the frequency domain. Some waste components of frequency reduce the efficiency of contourlets in representing smooth contours of images. In [24] the authors represent sharp frequency localized contourlet transform (SFLCT) in which the non-localization problem is considerably decreased. In this study, the proposed watermarking scheme utilizes the useful properties of the SFLCT to enhance the watermarking requirements.
In most of the image processing applications researchers are considered the combination of two or more transforms to achieve the watermarking procedure goals [10], [12], [13], [14], [17], [25], [36]. Because of efficient properties, singular value decomposition (SVD) is used as a second transform in these hybrid watermarking systems. In this transform, image A is decomposed aswhere U and V are orthogonal matrices and Σ is a diagonal matrix. The diagonal entries of Σ are called singular values of A. These singular values are insensitive to small perturbations and the visual quality of the image changes very slightly under small variations of the singular values. Because of this special feature, SVD has been used in watermarking and the imperceptibility and robustness of SVD-based watermarking algorithms have been improved. However, considering SVD-based watermarking algorithms shows that these algorithms suffer from security requirement and are not resistant against ambiguity attacks introduced by Craver et al. [26]. In the lack of security, both the owner and attacker are able to extract their watermarks from the watermarked image, then neither can prove the ownership. This is the false positive problem which is a serious objection for the SVD-based watermarking techniques.
In this study a secure, robust and imperceptible image watermarking based on sharp frequency localized contourlet transform and SVD (SFLCT-SVD) is investigated and proposed. These two transforms have useful properties and we show that combining them increase the quality of the watermarking scheme. We solve the false positive problem of the SVD based schemes and resisting against ambiguity attacks by increasing the dependency of the embedding and detection processes on the watermark and it is possible due to variant downsampling rate d of the SFLCT. This preference also allows us to increase the watermark image size and choose it as same size as the original image. On the other hand, using SFLCT the useful properties of the SVD based algorithms (high PSNR and robustness) are protected. In the other words, these two transforms resolve the fault of each other and the advantages of each of them are preserved in the watermarking scheme. The host and the watermark images are both decomposed using SFLCT. Then the SVD transform are applied to some subbands of the host and watermark images.
The rest of the paper is organized as follows: In Section 2 the methodology and related work are stated and a brief review of the transforms used in the scheme are given. In Section 3 the proposed watermarking scheme (i.e., the embedding and detection processes) is explained in details. Section 4 describes the requirements of a watermarking procedure and Section 5 includes the experimental implementations and obtained results of the suggested procedure. In Section 6 the introduced scheme in this paper is compared to some recent schemes and finally in Section 7 the conclusions of the paper are stated.
Section snippets
Methodology and related work
When we consider the SVD-based image watermarking schemes, we see that the reason of the false positive problem is concerned with low dependency of schemes on the watermark in both embedding and detection processes. Indeed, by reviewing these algorithms, the most of them act as follows:In this equation Σ is the singular values of a frequency subband of original image, w is the watermark or a subband of its transform and α is the strength factor. The singular values Σ are modified
The proposed SFLCT-SVD scheme
In this section the suggested SFLCT-SVD watermarking scheme is described in details. The scheme has two important parts: the embedding and the detection processes. In the embedding process the watermark image is embedded in the host image and the result is the watermarked image. The watermarked image may be attacked by image processing or geometrical manipulations during the transfer operation and in the receiver part the attacked watermarked image is considered by detection process to extract
Requirements of a watermarking system
In this section the requirements which are needed for any watermarking algorithm are considered. The most important criteria are capacity, security, imperceptibility and robustness under different attacks. The offered scheme is compared to some available schemes with respect to these principles.
Capacity is the amount of the data which is embedded in the image. Security and robustness principles are neighboring concepts, which are hardly perceived as different. The intentionality behind the
Experimental implementation and results
The simulation of the suggested scheme has been performed in MATLAB. We have implemented our scheme on about twenty test images and the results for the known test images Lena of size 512 × 512 and Cameraman of size 512 × 512 have been reported as host and watermark images, respectively, due to comparisons with the other methods.
Comparative analysis of the proposed scheme
In this section the comparison of the SFLCT-SVD procedure with the schemes of Makbol et al. [14], Ansari et al. [36] and Lagzian et al. [12] is considered. In all of the schemes the Lena and Cameraman images are selected as host and watermark images, respectively. The comparison examination is based on the four requirements of the watermarking schemes security, robustness, imperceptibility and capacity. About the security, in our proposed scheme the false positive problem is solved without
Conclusion
In this paper, a combination of the sharp frequency localized contourlet transform (SFLCT) and SVD is used to construct a secure watermarking algorithm. The useful properties of these two transforms lead to enhancing the quality of the proposed watermarking scheme in terms of the watermarking requirements. The different downsampling rates of SFLCT caused to achieve high capacity of the watermarking procedure and using SVD to the details subbands increased the imperceptibility and moreover, the
Esmaeil Najafi received his Ph.D. degree in Applied Mathematics - Numerical Analysis from Iran University of Science and Technology, Tehran, Iran in 2012, M.Sc. degree in Applied Mathematics from Iran University of Science and Technology, Tehran, Iran in 2008 and B.Sc. degree in Applied Mathematics from Payame Noor University, Tabriz, Iran in 2006. He is currently an assistant professor in Faculty of Science, Department of Mathematics at Urmia University, Urmia, Iran. His research interest is
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Esmaeil Najafi received his Ph.D. degree in Applied Mathematics - Numerical Analysis from Iran University of Science and Technology, Tehran, Iran in 2012, M.Sc. degree in Applied Mathematics from Iran University of Science and Technology, Tehran, Iran in 2008 and B.Sc. degree in Applied Mathematics from Payame Noor University, Tabriz, Iran in 2006. He is currently an assistant professor in Faculty of Science, Department of Mathematics at Urmia University, Urmia, Iran. His research interest is in the area of image processing and image watermarking.
Khaled Loukhaoukha received Doctorate (Ph.D.) degree in electrical engineering from Laval University, Quebec, Canada in 2010, the Electronics Engineer degree and Master’s degree in electrical engineering from Saad Dahlab University, Blida, Algeria in 1999 and 2002, respectively. He has pursuing his Ph.D. degree research project in digital watermarking and image encryption field at the Department of Electrical and Computer Engineering of Laval University. He has pursuing his master’s degree research project in speech coding field at the Division of Architecture and Multimedia Systems of the Center for Development of Advanced Technologies (CDTA), Algiers. He is the author or co-author of more than 20 journal and conference papers. His research interests include information security, digital watermarking, cryptography, image processing, information theory, telecommunication and optimization methods.