Elsevier

Pattern Recognition

Volume 77, May 2018, Pages 99-112
Pattern Recognition

A new multiplicative watermark detector in the contourlet domain using t Location-Scale distribution

https://doi.org/10.1016/j.patcog.2017.12.006Get rights and content

Highlights

  • Modeling contourlet coefficients using t Location-Scale distribution.

  • Study adaptation between t Location-Scale distribution and contourlet coefficients.

  • Designing a contourlet domain multiplicative watermark detector using LRT.

  • Deriving ROC of the watermark detector theoretically and analyzing its performance.

Abstract

Digital watermarking is used to protect copyright information by embedding hidden data in digital media. In this study, a multiplicative watermarking scheme is proposed in the contourlet domain. Overall, selection of proper models is of great importance, as watermark detection processes can be replicated as decision rules. Accordingly, in this study, contourlet coefficients were modeled based on t-location scale distribution. Based on the Kolmogorov–Smirnov test, t Location-Scale distribution showed high efficiency in modeling the coefficients. We used the likelihood ratio decision rule and t-location scale distribution to design an optimal multiplicative watermark detector. Then, we derive the receiver operating characteristics (ROC) analytically. The detector showed higher efficiency than other watermarking schemes in the literature, based on the experimental results, and its robustness against different attacks was verified.

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: Y=X+αW

  • Multiplicative watermarking: Y=X+αXW.

where X, Y, and W refer to the original data, watermarked data, and watermark sequence, respectively. α is the weighting factor controlling the watermark strength. In copyright protection, multiplicative embedding is preferable to additive embedding, as it provides watermark dependent on the image content [27]. Therefore, in this study, multiplicative embedding was applied, while in our previous work [19], additive watermarking was used.

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: Pfa=

Simulation results

Using ROC curves, performance of tLS watermark detector was assessed regarding Pfa and Pdet. 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.

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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.

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