Watermark Decoding Research Articles

Color image watermarking using vector SNCM-HMT

An image watermarking scheme is typically evaluated using three main conflicting characteristics: imperceptibility, robustness, and capacity. Developing a good image watermarking method is challenging because it requires a trade-off between these three basic characteristics. In this paper, we proposed a statistical color image watermarking based on robust discrete nonseparable Shearlet transform (DNST)-fast quaternion generic polar complex exponential transform (FQGPCET) magnitude and vector skew-normal-Cauchy mixtures (SNCM)-hidden Markov tree (HMT). The proposed watermarking system consists of two main parts: watermark inserting and watermark extraction. In watermark inserting, we first perform DNST on R, G, and B components of color host image, respectively. We then compute block FQGPCET of DNST domain color components, and embed watermark signal in DNST-FQGPCET magnitudes using multiplicative approach. In watermark extraction, we first analyze the robustness and statistical characteristics of local DNST-FQGPCET magnitudes of color image. We then observe that, vector SNCM-HMT model can capture accurately the marginal distribution and multiple strong dependencies of local DNST-FQGPCET magnitudes. Meanwhile, vector SNCM-HMT parameters can be computed effectively using variational expectation–maximization (VEM) parameter estimation. Motivated by our modeling results, we finally develop a new statistical color image watermark decoder based on vector SNCM-HMT and maximum likelihood (ML) decision rule. Experimental results on extensive test images demonstrate that the proposed statistical color image watermarking provides a performance better than that of most of the state-of-the-art statistical methods and some deep learning approaches recently proposed in the literature.

Locally optimum watermark decoder based on fast quaternion generic polar complex exponential transform

Locally optimum watermark decoder based on fast quaternion generic polar complex exponential transform

Blind image watermark decoder in NSST-FPCET domain using Weibull Mixtures-HMT

Balancing imperceptibility, robustness, and data payload is a key topic in digital watermarking technology. Many contributions point to statistical modeling as an effective solution to this problem. On the basis of this, in this paper, we devise a hybrid domain image watermark decoder based on Weibull mixtures based hidden Markov tree (Weibull Mixtures-HMT) model. In the embedding phase, Otsu-Canny edge detection method is used to map the positions of high entropy blocks to the target subband obtained by non-subsampled shearlet transform (NSST), and fast polar complex exponential transform (FPCET) is computed in the target blocks to obtain the NSST-FPCET domain. The watermark signals are embedded into NSST-FPCET magnitudes by a linear method. In the extraction phase, NSST-FPCET magnitude coefficients are modeled by Weibull Mixtures-HMT model, which describes the distribution characteristics as well as the dependencies of NSST-FPCET magnitudes. The efficient variance reduced stochastic expectation maximization method is employed for estimating the parameters of Weibull Mixtures-HMT model. A statistical image watermark decoder in NSST-FPCET domain is finally achieved by the maximum likelihood decision. Massive experiments are performed so as to confirm the superiority of the designed scheme in trade-off among the data payload, imperceptibility, and robustness.

UDTCWT-PHFMs Domain Statistical Image Watermarking Using Vector BW-Type R Distribution

For any image watermarking algorithm, how to achieve the trade-off among robustness, imperceptibility, and watermark capacity is a challenging problem because of their mutually constrained relationship. In this paper, we design a statistical-based image watermarking system to solve the trade-off problem. In embedding process, consider the imperceptibility and the robustness, we inventively combine the undecimated dual tree complex Wavelet transform (UDTCWT) and the polar harmonic Fourier moments (PHFMs) to obtain the UDTCWT-PHFMs magnitudes as the watermark carriers, and we embed watermark signals in multiplicative manner. In modeling phase, by analyzing the statistical property and the multiple correlations of the UDTCWT-PHFMs magnitudes, we bound the magnitudes of different directions into the vector groups, and then we model them with the vector Roy type bivariate Weibull (BW-Type R) distribution so that we can capture accurately the marginal characteristics, the inter-scale dependencies, and the inter-orientation dependencies at the same time. Moreover, we obtain the model parameters with the double looped maximum likelihood estimation (double-looped MLE). Benefit from the reliable modeling result, we finally derive a novel specific image watermark decoder to blindly extract the hidden watermarks. Extensive experiment results declare the designed statistical image watermarking system achieves the better balance among imperceptibility, robustness, and payload.

Geometrical attacks resilient statistical watermark decoder using polar harmonic Fourier moments

This paper presents a new robust multiplicative watermark detector. Due to the strong robustness against various attacks, polar harmonic Fourier moment (PHFM) magnitudes are used as the employed watermark carrier. The distribution of PHFM magnitudes is highly non-Gaussian and can be properly modeled by a heavy-tailed probability density function (PDF). In this paper, we proved that Weibull distribution can suitably fit the distribution of PHFM magnitudes, and based on this, we presented a statistics-based watermark decoder by using the Weibull as a prior for the PHFM magnitudes. In watermark embedding, a multiplicative manner was used to embed watermark information in PHFM magnitudes of the highest entropy blocks to achieve better robustness and imperceptibility. In watermark detection, we developed a Weibull distribution-based statistical watermark decoder, which uses the maximum likelihood (ML) decision rule. Compared with Bessel K form (BKF), Cauchy, and generalized Gaussian (GG)-based decoders, the Weibull-based decoder demonstrates stronger robustness. In addition, the proposed watermark decoder is more robust against geometrical and common image processing attacks than existing statistical watermark decoders.

Image watermarking using DNST-PHFMs magnitude domain vector AGGM-HMT

Invisibility, robustness and payload are three indispensable and contradictory properties for any image watermarking systems. Therefore, in this paper a novel statistical image watermark decoder based on robust discrete nonseparable Shearlet transform (DNST)-polar harmonic Fourier moments (PHFMs) magnitude and effective vector anisotropic generalized Gaussian mixtures (AGGM)-hidden Markov tree (HMT). We begin with a detailed study on the robustness and statistical characteristics of local DNST- PHFMs magnitudes of natural images. This study reveals the excellent robustness, highly non-Gaussian marginal statistics and strong dependencies of local DNST-PHFMs magnitudes. We also find that conditioned on their generalized neighborhoods, the local DNST-PHFMs magnitudes can be approximately modeled as anisotropic generalized Gaussian variables. Based on these findings, we model local DNST-PHFMs magnitudes using a vector AGGM-HMT that can capture all interscale, interdirection, and interlocation dependencies. Meanwhile, model parameters can be estimated effectively by using localization clues guided expectation–maximization (LCGEM) approach. Finally, we develop a new statistical image watermark decoder using the vector AGGM-HMT and maximum likelihood (ML) decision rule. Extensive experimental results show the superiority of the proposed watermark decoder over several state-of-the-art statistical watermarking methods and some approaches based on convolutional neural networks.

Statistical image watermark decoder by modeling local NSST-PHFMs magnitudes with Morgenstern-type bivariate-generalized exponential distribution

Statistical image watermark decoder by modeling local NSST-PHFMs magnitudes with Morgenstern-type bivariate-generalized exponential distribution

Secure sparse watermarking on DWT-SVD for digital images

This paper suggests a sparse watermark image embedding scheme on the singular values of the pre-selected wavelet sub-band coefficients of the digital images. Dictionary learning (DL) method is used to make the watermark image sparse. Then a watermark decoder is designed based on the theory of compressed sensing (CS) in the framework of alternating direction method of multiplier (ADMM). The integration of DL and CS offers two benefits, firstly DL combined with singular value decomposition (SVD), enables protection against false positive detection (FPD) where the sparse watermark enhances embedding capacity at high imperceptibility of the hidden data. Simulation results show high visual quality for the watermarked images (PSNR = 60.45 dB, SSIM = 0.9997 and FSIM = 0.9979) and robustness (NCC value for the decoded watermark is ∼ 0.9) against various image processing operations including an unauthorized decoding - a typical value of 85% CS measurements lead to a watermarked image results in a FPD value of 0.42 that shows a visually indistinguishable watermark.

Statistical image watermark decoder by modeling local RDWT difference domain singular values with bivariate weighted Weibull distribution

Statistical image watermark decoder by modeling local RDWT difference domain singular values with bivariate weighted Weibull distribution

Statistical image watermark decoder using high-order difference coefficients and bounded generalized Gaussian mixtures-based HMT

Imperceptibility, robustness and data payload are three main requirements of any image watermarking systems to guarantee desired functionalities, but there is a tradeoff among them from the information-theoretic perspective. In order to achieve this balance, in this paper, we propose a new statistical image watermarking scheme in nonsubsampled Shearlet transform (NSST) domain, which is based on high-order difference coefficients and bounded generalized Gaussian mixture model (BGGMM) based hidden Markov tree (HMT). In embedding process, NSST is firstly performed on host image and NSST highpass subband is divided into no-overlapping blocks. Then high-order differences of NSST coefficient blocks are computed. And finally, watermark signal is inserted into robust high-order difference coefficients through non-linear multiplicative approach. In extraction phase, robust high-order difference coefficients are firstly modeled by employing BGGMM based HMT, which can capture accurately both marginal distributions and strong dependencies of high-order difference coefficients. Statistical model parameters are then estimated by combining the approach of minimizing the higher bound on data negative log-likelihood function and upward–downward algorithm. And finally, an image watermark decoder is developed using BGGMM based HMT and maximum likelihood decision. Experimental results on some test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed scheme.

Multiplicative Watermarking Method with the Visual Saliency Model Using Contourlet Transform

We have proposed an image adaptive watermarking method by using contourlet transform. Firstly, we have selected high-energy image blocks as the watermark embedding space through segmenting the original image into nonoverlapping blocks and designed a watermark embedded strength factor by taking advantage of the human visual saliency model. To achieve dynamic adjustability of the multiplicative watermark embedding parameter, the relationship between watermark embedded strength factor and watermarked image quality is developed through experiments with the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM), respectively. Secondly, to detect the watermark information, the generalized Gaussian distribution (GGD) has been utilized to model the contourlet coefficients. Furthermore, positions of the blocks selected, watermark embedding factor, and watermark size have been used as side information for watermark decoding. Finally, several experiments have been conducted on eight images, and the results prove the effectiveness of the proposed watermarking approach. Concretely, our watermarking method has good imperceptibility and strong robustness when against Gaussian noise, JPEG compression, scaling, rotation, median filtering, and Gaussian filtering attack.

Statistical image watermark decoder based on local frequency-domain Exponent-Fourier moments modeling

There are three indispensable, yet contrasting requirements for a watermarking scheme: perceptual transparency, watermark capacity, and robustness against attacks. Therefore, a watermarking scheme should provide a trade-off among these requirements from the information-theoretic perspective. In this paper, we propose a statistical image watermark decoder based on the local frequency-domain Exponent-Fourier moments modeling, which can achieve the tradeoff among imperceptibility, robustness and data payload. The frequency-domain EFMs magnitudes are first generated by combining stationary wavelet transform (SWT) and Exponent-Fourier moments (EFMs). We divide the target region to select local frequency-domain EFMs magnitudes, which are planned to embed watermarks, statistical modeling, and extract watermarks. In order to achieve an accurate modeling process, we conduct the comprehensive statistical analyses of local frequency-domain EFMs magnitudes and establish the powerful Beta Generalized Weibull mixtures-based hidden Markov tree (BGW-HMT) model, which can take into account the non-Gaussian distribution characteristic and the interscale dependency at the same time. The Expectation/Conditional Maximisation Either (ECME) algorithm and upward–downward algorithm are successfully applied to estimate the parameters of BGW-HMT model. At the receiver, the BGW-HMT model is used in the design process of watermark decoder. The decoder structure is developed by using the maximum likelihood decision. In order to prove the effectiveness of proposed watermarking scheme, multi-angle performance tests are performed, including imperceptibility, robustness, watermark capacity and time complexity. The corresponding experimental results from the above four perspectives are inspiring. Compared with the state-of-the-art schemes, our statistical decoder is significantly superior to other statistical decoders.

Statistical image watermarking using local RHFMs magnitudes and beta exponential distribution

The imperceptibility, robustness and data payload are widely considered as the three main properties vital for any image watermarking systems. They are complimentary to each other and hence challenging to attain the right balance between them. The statistical model-based multiplicative watermarking is an effective way to achieve the tradeoff among imperceptibility, robustness and data payload. Radial harmonic Fourier moments (RHFMs) is a strong tool in image processing, which has many advantages, such as lower noise sensitivity, powerful image description ability and geometric invariance feature. In this paper, we propose a new statistical image watermarking scheme using local RHFMs magnitudes and Beta exponential distribution model. Our image watermarking scheme consists of two parts, namely, embedding and extraction. In the embedding process, we divide the host image into no-overlapping blocks and compute the local RHFMs of image blocks, then insert the watermark signal into the robust local RHFMs magnitudes through multiplicative approach. In the extraction phase, robust local RHFMs magnitudes are firstly modeled by employing the Beta exponential distribution, where the statistical properties of local RHFMs magnitudes are captured accurately. Then the modified maximum likelihood parameter estimation (MMLE) approach is introduced to estimate the statistical parameters of Beta exponential distribution model. And finally an image watermark decoder for multiplicative watermarking is developed using Beta exponential distribution and maximum likelihood decision criterion. Experimental results on some test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed statistical image watermarking.

Locally optimum watermark decoder in NSST domain using RSS-based Cauchy distribution

It is important to consider the tradeoff between imperceptibility and robustness requirements in developing an image-watermarking technique, some statistical model-based image watermarking schemes have been designed in the past decade. The effectiveness of a statistical watermark decoder depends highly on the modeling of the transform-domain coefficients and the use of hypothesis testing. In this study, a multiplicative image watermarking scheme is proposed in the nonsubsampled Shearlet transform (NSST) domain, where NSST coefficients are modeled by ranked set sample (RSS) based Cauchy statistical distribution and locally most powerful (LMP) test criterion is applied. Digital image watermarking technique consists of two parts, namely, embedding and extracting. In the embedding process, to achieve relatively good imperceptibility and robustness, watermark data is inserted into the significant NSST directional subband that has the highest energy value, by modifying nonlinearly the significant NSST coefficients. In the extracting phase, a scheme is proposed for designing a blind NSST domain watermark decoder incorporating the RSS based Cauchy statistical distribution and LMP test criterion. Here, the RSS method is used to estimate the location parameter and shape parameter of Cauchy statistical distribution instead of traditional maximum-likelihood (ML) method, which can provide the Cauchy model with higher precision parameters. Experimental results on a set of standard test images show significant improvements in imperceptibility and robustness using the proposed method compared with the best known state-of-the-art approaches.

Contourlet domain locally optimum image watermark decoder using Cauchy mixtures based vector HMT model

Digital image watermarking has become a necessity in many applications such as data authentication, broadcast monitoring on the Internet and ownership identification. Various watermarking schemes have been proposed to protect the copyright information. There are three indispensable, yet contrasting requirements for a watermarking scheme: imperceptibility, robustness and payload. Therefore, a watermarking scheme should provide a trade-off among these requirements from the information-theoretic perspective. Generally, in order to enhance the imperceptibility, robustness and payload simultaneously, the human visual system (HVS) and the statistical properties of the image signal should be fully taken into account. The statistical model-based transform domain multiplicative watermarking scheme embodies the above ideas, and therefore the detection and extraction of the multiplicative watermarks have received a great deal of attention. The performance of a statistical model-based watermark detector or decoder is highly influenced by the accuracy of the statistical model itself and the applicability of decision rule. In this paper, we firstly propose a new hidden Markov trees (HMT) statistical model in Contourlet domain, namely Cauchy mixtures-based vector HMT (vector CMM–HMT), by describing the marginal distribution with Cauchy mixture model (CMM) and grouping Contourlet coefficients into a vector, which can capture both the subband marginal distributions and the strong dependencies across scales and orientations of the Contourlet coefficients. Then, by modeling the Contourlet coefficients with vector CMM–HMT and employing locally most powerful (LMP) test, we develop a locally optimum image watermark decoder in Contourlet domain. We conduct extensive experiments to evaluate the performance of the proposed blind watermark decoder, in which encouraging results validate the effectiveness of the proposed technique, in comparison with the state-of-the-art approaches recently proposed in the literature.

Color image watermark decoder by modeling quaternion polar harmonic transform with BKF distribution

It still remains a challenging problem to improve both of the imperceptibility and robustness for the digital image watermarking task. In this study, a color image watermarking scheme is proposed based on quaternion polar harmonic transform (QPHT) with maximum likelihood decoder, which better balances imperceptibility and robustness in a novel fashion. Thanks to the strong robustness of QPHT, the digital watermark is embedded into the QPHT magnitudes using a multiplicative approach. At the receiver, the watermark decoder can be formulated as a problem of weak signal detection, as the QPHT magnitudes are highly non-Gaussian. In view of this, selection of proper models is of great importance to construct a suitable watermark decoder. Further, we validate that the probability density function of Bessel K form suitably models the heavy tail behavior of QPHT magnitudes, and thus the maximum likelihood decoder is developed by modeling QPHT magnitudes with Bessel K form distribution. Experimental results on standard benchmarks demonstrate that the proposed approach provides better imperceptibility and robustness against various kinds of attacks compared to previous state-of-the-art methods.

A new watermark decoder in DNST domain using singular values and gaussian-cauchy mixture-based vector HMT

There are three indispensable, yet contrasting requirements for a watermarking scheme: imperceptibility, robustness, and payload. Therefore, it is a challenge to obtain a tradeoff among above requirements in image watermark detection. In this paper, we propose a new statistical watermark decoder in discrete non-separable Shearlet transform (DNST) domain using singular values and Gaussian-Cauchy mixture-based vector hidden Markov tree (HMT). Our method can obtain great performance in imperceptibility, robustness and payload, and it is necessary for image copyright protection. We first perform DNST on the host image, and apply singular value decomposition (SVD) to the significant DNST domain high entropy blocks. We then embed the digital watermark into the DNST high entropy blocks by modifying the robust singular values. At the receiver, by combining the Gaussian-Cauchy mixture-based vector HMT and maximum likelihood (ML) decision, we propose a new blind image watermark decoder in DNST domain. Here, robust DNST domain singular values are firstly modeled by using Gaussian-Cauchy mixture-based vector HMT, where the Gaussian-Cauchy mixture marginal distribution and various strong dependencies of DNST domain singular values are incorporated. Then the statistical model parameters of Gaussian-Cauchy mixture-based vector HMT are estimated using parameter-expanded expectation–maximization (PXEM) approach. And finally, a blind image watermark decoder is developed using Gaussian-Cauchy mixture-based vector HMT and ML decision rule. The major contribution of this paper is the use of singular value, Gaussian-Cauchy mixture-based vector HMT and PXEM algorithms, which enhances the performance of watermarking scheme. Experimental results on some test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed method.

A blind watermark algorithm in SWT domain using bivariate generalized Gaussian distributions

Imperceptibility, robustness, and payload are three main requirements of any audio watermarking systems to guarantee desired functionalities, but there is a tradeoff among them from the information-theoretic perspective. Generally, in order to enhance the imperceptibility, robustness, and payload simultaneously, the human auditory system and the statistical properties of the audio signal should be fully taken into account. The statistical model based transform domain multiplicative watermarking scheme embodies the above ideas, and therefore the detection and extraction of the multiplicative watermarks have received a great deal of attention. Although much effort has been made in recent years, improving the ability of imperceptibility, watermark capacity, and robustness at the same time remains a challenge within the audio watermarking community. In this paper, we propose a blind audio watermark decoder in stationary wavelet transform domain based on bivariate generalized Gaussian distributions, wherein both the local statistical properties and inter-scale dependencies of the stationary wavelet transform coefficients of digital audio are taken into account, and also the adaptive nonlinear watermark embedding strength functions are designed. The results of our tests with different host audios, digital watermarks, and various attacks, we experimentally confirm that the proposed approach performs well compared to the state-of-the-art audio watermarking methods.

Blind Image Watermark Decoder in UDTCWT Domain Using Weibull Mixtures-Based Vector HMT

As one promising solution, digital watermarking has been proposed to resolve image copyright protection and content authentication, and has been applied successfully in many fields. Owing to their excellent description capability and invariance property, statistical models have become a popular tool for the image watermarking resulting in favorable trade-offs among imperceptibility, robustness and data payload. By modeling the robust undecimated dual tree complex Wavelet transform (UDTCWT) coefficient magnitudes with the Weibull mixtures based vector hidden Markov trees (HMT) and employing maximum likelihood (ML) test criterion, we propose a new image watermarking approach in UDTCWT domain in this paper. Our image watermarking approach consists of two parts, namely, embedding and extracting. In the embedding process, we compute the robust UDTCWT coefficient magnitudes with UDTCWT domain real/imaginary parts, and insert the digital watermark into the significant UDTCWT coefficient magnitude subband. In the extracting phase, robust UDTCWT coefficient magnitudes are firstly modeled by employing the Weibull mixture-based vector HMT, where the statistical properties of UDTCWT magnitudes are captured accurately. Then the expectation/conditional maximization (ECM) approach is introduced to estimate the statistical model parameters. Finally, an image watermark decoder for multiplicative watermarking is developed using the Weibull mixtures based vector HMT and ML test. The experiments show that the proposed method not only improves the imperceptibility, but also increases the robustness performance and outperforms state-of-the-art methods on a set of standard test images.

Complex Wavelet-Based Image Watermarking with the Human Visual Saliency Model

Imperceptibility and robustness are the two complementary, but fundamental requirements of any digital image watermarking method. To improve the invisibility and robustness of multiplicative image watermarking, a complex wavelet based watermarking algorithm is proposed by using the human visual texture masking and visual saliency model. First, image blocks with high entropy are selected as the watermark embedding space to achieve imperceptibility. Then, an adaptive multiplicative watermark embedding strength factor is designed by utilizing texture masking and visual saliency to enhance robustness. Furthermore, the complex wavelet coefficients of the low frequency sub-band are modeled by a Gaussian distribution, and a watermark decoding method is proposed based on the maximum likelihood criterion. Finally, the effectiveness of the watermarking is validated by using the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM) through experiments. Simulation results demonstrate the invisibility of the proposed method and its strong robustness against various attacks, including additive noise, image filtering, JPEG compression, amplitude scaling, rotation attack, and combinational attack.