A new multiplicative watermark detector in the contourlet domain using t Location-Scale distribution
Introduction
One of the most challenging concerns of digital content providers is copyright protection. A common solution to this issue is digital watermarking, which entails embedment of secondary data into digital media (eg, audio, image, and video). Watermark embedding and extraction are 2 major steps in watermarking schemes. Data rate, perceptual transparency, and robustness are 3 requirements of watermarking schemes. Nonetheless, these requirements are of different priorities with respect to their application. Some digital watermarking applications include copyright protection, authentication, broadcast monitoring, and fingerprinting. Since copyright protection, which is the main application of digital watermarking, needs robustness against common watermarking attacks (signal processing and geometric attacks), some previous work [1], [2], [3], [4] have focused on robustness under specific attacks. In the present study, we examined the robustness of the proposed watermarking scheme under different signal processing and geometric attacks.
Watermark extraction methods are generally classified into 2 categories: watermark detection and decoding. Watermark detection determines if the received media includes a watermark. Watermark decoding refers to correct decoding of watermark bits from the received media. In this study, use of watermark detection for copyright protection was examined.
Watermark embedding techniques are based on either spread spectrum (SS) [5], [6] or quantization [7], [8], [9]. In the SS approach, the watermark is embedded generally in a transform domain, causing watermark robustness against different attacks. Image watermarking has been studied extensively in the transform domain, with transforms such as discrete cosine transform (DCT) [10], [11], discrete Fourier transform (DFT) [12], discrete wavelet transform (DWT) [13], [14], [15], [16], [17], contourlet transform (CT) [18], [19], [20], nonsubsampled contourlet transform (NSCT) [21], and ridgelet transform [22]. In several studies, contourlet-domain algorithms outperform other frequency-domain algorithms (eg, wavelets) against attacks [23], [24]. The contourlet transform has suitable features, such as spread property, ie, watermark bits spread in all subbands during watermarked image reconstruction if they are inserted in specific subbands [25]. In addition, the contourlet transform is effective in highlighting geometric structures and smooth contours and yield sparser coefficients [26].
The SS methods of embedding generally use additive and multiplicative techniques. The common multiplicative and additive embedding rules include:
- •
Additive watermarking:
- •
Multiplicative watermarking: .
For watermark detection, the correlation detector is commonly used in the frequency domain; however, this detector shows efficacy only if the data have a Gaussian distribution [28]. The contourlet coefficients have large peaks and are highly non-Gaussian; they also have heavier tails compared to a Gaussian probability density function (PDF) [29].
In the contourlet domain, watermark detection refers to the detection of a weak signal in noise. The log-likelihood ratio test (LLRT) is a well-accepted solution, which is asymptotically optimal if many data samples are available [12]. The LLRT accuracy depends on the precision of the statistical model for contourlet coefficients.
Considering the distribution for contourlet coefficient modeling, different watermark detectors can be obtained. In the literature [30], [31], generalized Gaussian distribution is used to model the contourlet coefficients. Moreover, in a previous study [32], univariate and bivariate alpha-stable distributions could be used to model the contourlet coefficients. Moreover, in the literature [13], a robust multiplicative detector in the contourlet domain was introduced, using k-form densities [4]. In some studies [33], [34], normal inverse Gaussian distribution was used for modeling the coefficients to design the contourlet domain watermark detectors.
In this paper, we propose a new multiplicative contourlet domain watermark detector, using t Location-Scale (tLS) distribution. It was revealed that this type of distribution closely fits the contourlet coefficient distribution. The histogram of coefficients and tLS PDF were also compared. We applied Kolmogorov-Smirnov (KS) test for quantifying the findings. We designed an LLRT-based watermark detector considering the tLS distribution. For theoretical analysis of the watermark detector, the receiver operating characteristics (ROC) analytically derives. Several experiments were performed to examine the detector performance, and comparisons were made with other available methods. The experimental results indicated the high efficiency of our method.
The main outcomes of this study include:
- (i)
Modeling the contourlet coefficients with respect to tLS distribution.
- (ii)
Developing an optimal LLRT detector for multiplicative watermarking in the contourlet domain with respect to tLS distribution and obtaining a closed form test statistic.
- (iii)
Theoretically deriving the ROC of watermark detector and examining the performance of the detector.
The rest of this paper is organized as follows. Modeling of contourlet coefficients is presented in Section 2. Section 3 presents the multiplicative watermarking method in the contourlet domain. In Section 4, performance of tLS detector is assessed. In Section 5, the simulation result of the proposed detector are compared with other detectors. Conclusions are finally presented in Section 6.
Section snippets
Statistical modeling
In this section, First, we analyzed the location-scale family distributions and reviewed the tLS distribution. Following, the Contourlet coefficient modeling was analyzed using tLS distribution.
Watermarking scheme
Watermark embedding and detection comprise a watermarking scheme. In this section, the proposed watermark embedding and detection are described.
Performance analysis of the t Location-Scale detector
The watermark detector was examined regarding the probability of false alarm (Pfa) and probability of detection (Pdet) for an original image. We used receiver operating characteristic (ROC) as a plot of Pfa versus Pdet (distribution of LLRT (18)). Overall, LLRT is the sum of sufficient numbers of independent random variables. Considering the central limit theorem (CLT) [44], the Gaussian distribution can be used to estimate the LLRT distribution. The Pdet and Pfa can be measured as follows:
Simulation results
Using ROC curves, performance of tLS watermark detector was assessed regarding Pfa and . As described earlier, to determine the contourlet coefficients in the original image, the contourlet transform with PKVA filters (in multidirectional and multiscale decomposition) was applied. The watermark bits were embedded multiplicatively in the subband showing the greatest energy. The detector was assessed to determine if the image contains a watermark.
For investigating the efficiency of our
Conclusion
A detector was proposed for multiplicative watermarking in the contourlet domain, using tLS distribution before the contourlet coefficients. Based on the Neyman–Pearson criterion, for designing the watermark detector, LRT was optimal. The closed-form mean and variance of statistic were calculated, and ROC curves were used to evaluate the detector performance.
Performance of our watermark detector was examined based on several experiments and compared with BKF, NIG, and GG detectors in the
Sadegh Etemad received the B.S. Degree in Software Engineering from Shahrood University of Technology, Shahrood, Iran, in 2013, and the M.Sc. degree in Artificial Intelligence from Iran University of Science and Technology, Tehran, Iran, in 2015. He is currently pursuing the Ph.D. degree at the Department of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran, Iran. His research interests include Statistical Machine Learning and Statistical Image Modeling.
References (48)
- et al.
Digital image authentication and recovery: employing integer transform based information embedding and extraction
Inf. Sci.
(2010) - et al.
Blind image watermarking via exploitation of inter-block prediction and visibility threshold in DCT domain
J. Vis. Commun. Image Represent.
(2015) - et al.
A novel image watermarking scheme based on amplitude attack
Pattern Recognit.
(2007) - et al.
A novel robust scaling image watermarking scheme based on gaussian mixture model
Expert Syst. Appl.
(2015) Additive watermark detection in the wavelet domain using 2D-GARCH model
Inf. Sci.
(2016)- et al.
Wavelet-based image watermarking with visibility range estimation based on HVS and neural networks
Pattern Recognit.
(2011) - et al.
A new detector for contourlet domain multiplicative image watermarking using bessel k form distribution
J. Vis. Commun. Image Represent.
(2016) - et al.
A highly robust two-stage contourlet-based digital image watermarking method
Signal Process. Image Commun.
(2013) - et al.
A robust spread spectrum based image watermarking in ridgelet domain
AEU-Int. J Elecron. Comm.
(2012) - et al.
A new digital image watermarking algorithm resilient to desynchronization attacks
IEEE Trans. Inf. Forensics Secur.
(2007)
Robust signature-based geometric invariant copyright protection
IEEE International Conference on Image Process. (ICIP)
Geometrically invariant watermarking using feature points
IEEE Trans. Image Process.
A robust content-based watermarking technique
10th IEEE Workshop on Multimedia Signal Processing
Statistically robust detection of multiplicative spread-spectrum watermarks
IEEE Trans. Info Forensic Sec.
Secure spread spectrum watermarking for multimedia
IEEE Trans. Image Process.
Quantization index modulation: a class of provably good methods for digital watermarking and information embedding
IEEE Trans. Inf. Theory
Quantization index modulation-based image watermarking using digital holography
JOSA
An optimal detector structure for the fourier descriptors domain watermarking of 2d vector graphics
IEEE Trans. Vis. Comput Graph.
A new statistical detector for DWT-based additive image watermarking using the Gauss-Hermite expansion
IEEE Trans. Image Process.
Locally optimal detection of image watermarks in the wavelet domain using bessel k form distribution
IEEE Trans. Image process.
Additive watermark detector in contourlet domain using the t location-scale distribution
IEEE Interernational Conference on Signal Processing and Intelligent System (ICSPIS)
A novel color image watermarking scheme in nonsampled contourlet-domain
Expert Syst. App.
Enhancing robustness of digital image watermarks using contourlet transform
16th IEEE International Conference on Image Processing(ICIP)
Contourlet versus wavelet transform: a performance study for a robust image watermarking
2th International Conference on Applications of Digital Information and Web Technologies (ICADIWT)
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Sadegh Etemad received the B.S. Degree in Software Engineering from Shahrood University of Technology, Shahrood, Iran, in 2013, and the M.Sc. degree in Artificial Intelligence from Iran University of Science and Technology, Tehran, Iran, in 2015. He is currently pursuing the Ph.D. degree at the Department of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran, Iran. His research interests include Statistical Machine Learning and Statistical Image Modeling.
Maryam Amirmazlaghani received the B.S. degree in electrical engineering from the Iran University of Science and Technology, Tehran, Iran, in 2003, the M.S. degree in electrical engineering from the Sharif University of Technology, Tehran, in 2005, and the Ph.D. degree in electrical engineering from the Amirkabir University of Technology, Tehran, in 2009. She is currently a Faculty Member with the Department of Computer Engineering and Information Technology, Amirkabir University of Technology. Her research interests include statistical modeling and learning, image processing, and watermarking.