Design of optimal blind watermarking technique based on MOEA/D

IET Image ProcessingVolume 14, Issue 16 p. 4368-4375 Research ArticleFree Access Design of optimal blind watermarking technique based on MOEA/D Kwanghyok Mun, Corresponding Author Kwanghyok Mun mkh8594@yandex.com Applied Mathematics Faculty, Kim Chaek University of Technology, Pyongyang, Democratic People's Republic of KoreaSearch for more papers by this authorCholmin Son, Cholmin Son Applied Mathematics Faculty, Kim Chaek University of Technology, Pyongyang, Democratic People's Republic of KoreaSearch for more papers by this author Kwanghyok Mun, Corresponding Author Kwanghyok Mun mkh8594@yandex.com Applied Mathematics Faculty, Kim Chaek University of Technology, Pyongyang, Democratic People's Republic of KoreaSearch for more papers by this authorCholmin Son, Cholmin Son Applied Mathematics Faculty, Kim Chaek University of Technology, Pyongyang, Democratic People's Republic of KoreaSearch for more papers by this author First published: 23 February 2021 https://doi.org/10.1049/iet-ipr.2019.1551AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In image watermarking, the quality of the watermarked image and the watermark's robustness are the main indicators for evaluating the performance of the watermarking scheme, but they contradict each other, making it difficult to design a rational watermarking method. In this study, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is employed to solve the multi-objective optimisation problem to ensure the balance between contradictory objectives. The watermark is embedded by selecting the regions with the lowest human visual characteristics in the host image and modifying the frequency coefficients of the discrete cosine transform. At this time, the determination of the positions of embedding coefficients and parameters related to the modifications results in the multi-objective optimisation problem on the robustness and imperceptibility, and the optimal solution is determined by finding the approximate Pareto set. Simulation results for various attacks on watermarked images demonstrate the effectiveness of the proposed watermarking technique. 1 Introduction Digital watermarking originated from the steganography of the ancient Greeks to ensure confidentiality in communications. It has been introduced for the protection of multimedia contents that are rapidly spread through the internet from illegal acts. The application range of watermarking technology gets wider and wider, including the copyright protection of works of art such as paintings, music and movies, digital right management, transaction tracking, broadcast monitoring, content integrity, device control, copy protection and ownership authentication [[1]]. Recently, the most actively studied digital watermarking covers image watermarking, document watermarking, video watermarking, and voice watermarking and this paper focuses on image watermarking. Image watermarking can be divided into various categories according to representation, extraction way, and embedding domain. From the aspect of representation, digital watermarking can be classified into visible and invisible watermarking and invisible watermarking can be further classified into fragile, robust, and semi-fragile watermarking. There are three types of robust watermarking methods like blind, non-blind, and semi-blind watermarking depending on whether or not the original image is used in the watermarking extraction process. In addition, according to the embedding domain, watermarking methods can be classified into spatial and transform domain techniques [[2], [3]]. Spatial domain watermarking is a method of changing the values of the image pixels, which has low computational complexity and weakness in the attack. Transform domain watermarking is a method of embedding a watermark by changing the frequency coefficients of the image pixel values and having high stability. The most widely used transformations for transform domain watermarking include discrete wavelet transform (DWT), discrete cosine transform (DCT), discrete Fourier transform, discrete Hadamard transform and singular value decomposition (SVD) [[4]]. When designing a watermarking method, aspects of robustness, imperceptibility, capacity, security, and low complexity should be considered [[3]]. In particular, ensuring robustness and imperceptibility is the most essential problem in improving the performance of the watermarking algorithm. Robustness refers to how stably the watermark is reserved when intentional or accidental attacks such as image filtering, translation, enhancement, rotation, cropping, compression etc. are applied to the watermarked media and imperceptibility is an indicator that evaluates how similar the original and watermarked images are by the human visual system. As this robustness and imperceptibility are constrained to each other, constructing a rational watermarking method that guarantees them at the same time results in a multi-objective optimisation problem (MOP) in mathematics. The effective solution to this problem of watermarking is still challenging despite many discussions to date. 2 Related works As transform domain watermarking provides higher robustness than spatial domain watermarking, researches on robust watermarking methods in recent years have been mainly conducted in that direction. In particular, DWT, DCT and SVD have been widely used in watermarking embedding processes, and chaos and fractal theories have been introduced to increase the security of watermarking [[5]-[19]]. In the transform domain watermarking, the embedding process can be algebraic operation between the coefficients on the transform domain of the host image and the watermark in non-blind case. Otherwise, it can be algorithmic change operation of the coefficient of transform domain of only host image in blind case. For evaluation of the performance of the watermarking method, some indicators [(e.g. peak signal-to-noise ratio (PSNR) and normalised cross-correlation (NCC)] are established to assess the imperceptibility and robustness. Das et al. [[5]] proposed a blind watermarking method that extracts binary watermark by analysing of correlation between two DCT coefficients of neighbouring blocks in the same position and Roy and Pal [[6]] proposed colour multiple watermarking method based on the DCT and repetition code to protect copyright ownership and to verify the authenticity of various owners. Makbol et al. [[7]] selected the blocks with the smallest values as the best regions for the insertion of binary watermarks in the blocks using entropy and boundary entropy due to the characteristics of the human visual system for the robust watermarking. Bhowmik et al. [[8]] also thought that distortion of the watermarked image would not be noticed by the observer if watermark bits of lower and higher intensity were inserted in visual distinct and indistinct regions, respectively. Based on this idea, they proposed a novel robust image watermarking methodology with low-complexity. Liu et al. [[9]] doubly encrypted the watermark image in combination with fractal encoding to improve the security of the watermarking method based on the traditional DCT and Loan et al. [[10]] proposed a blind colour watermarking method based on chaotic encryption. Before inserting the original image, DCT was applied on the watermark and further chaos encryption was performed using Arnold Cat Map. Ernawan and Kabir [[11]] split the original image into 8 × 8 non-overlapping blocks and evaluated the human visual characteristics of each block using entropy. Then they selected blocks with the lowest characteristic value as watermark insertion position and six coefficients of the middle-frequency bands of these blocks were modified based on watermark bits under the human visual threshold. Also, Arnold Cat Map was applied to improve the security and the watermark was restored by comparing the coefficients of the middle frequency bands of the insertion position blocks. Lee et al. [[12]] proposed an adaptive watermarking scheme which was blindly extractable, imperceptible and robust to attack. Differently from the standard method which found first watermark insertion position, it used global space for finding suitable positions and distributed the multiple watermark data in all four lowest frequency sub-bands generated from the n-level Mallat two-dimensional DWT. With the introduction of the meta-heuristic optimisation imitating the intelligence of animals, new advances have been made in the digital watermarking theory. In the methods mentioned above, the empirical values were utilised to determine the parameters required in the watermark insertion and extraction process. For example, the DCT coefficients positions to be modified, thresholds, modification amounts, compensation parameters, scaling factors, and so on. The research works have been actively conducted from the idea that if we set the problem that these values are optimally calculated so that the watermarking method has high robustness and imperceptibility, the quality of the watermarking can be greatly improved [[13]-[19]]. Since increasing the imperceptibility of the watermark reduces the robustness, while increasing the robustness decreases the imperceptibility, the problem of determining parameters that improve both of these measures of watermarking quality at the same time results in a MOP mathematically. However, the process of determining the parameters of the watermarking method can be explained only schematically and not be represented by mathematical analytical equations. Therefore, the existing optimisation methods based on the gradient of function cannot be applied. Therefore, the meta-heuristic optimisation has been applied to the watermarking theory in order to determine the parameters which optimise the imperceptibility and robust indicators of the watermarking scheme. Ali et al. [[13]] used the redistributed invariant wavelet transform to transform the original image into an invariant wavelet domain, subsequently dividing the low-frequency sub-bands of transform domain into non-overlapping blocks and then the visual system was used to select the most appropriate insertion blocks. The watermark bits were embedded by modifying the first column coefficients of the left matrix of the SVD using the threshold, and the distortion due to embedding was compensated by modifying the right matrix component using the compensation parameter. In this paper, the artificial bee colony (ABC) algorithm was used to determine the best threshold value and compensation parameters for imperceptibility and robustness. They minimised the weighted sum of differences from the ideal target values for good performance using ABC. Abdelhakim et al. [[14]] proposed an image watermarking method based on block-wise optimal embedding strength in DCT domain. In order to determine optimal embedding strength, they constructed objective function as a weighted sum of PSNR of watermarked image and bit correct ratio of extracted watermark under different attacks. They utilised the bee's algorithm to find an optimal solution for the objective function. Ansari and Pant [[15]] embedded watermark by mixing the principal components from the SVD on low-frequency sub-band coefficients which were obtained by three-level DWT on host image. The singular matrix corresponding to the host image was modified by adding multiplication by scaling factor and singular matrix of SVD on the low-frequency sub-band of the watermark by one-level DWT. At this time, the ABC algorithm was employed to optimise the scaling factor in terms of robustness and imperceptibility. The fitness function of the algorithm was set by the sum of the PSNR set as the imperceptibility evaluation index and the normalised correlation (NC) set as the robustness index. Abdelhakim et al. [[16]] set the objective function for determining embedding parameters as a single constrained objective optimisation problem to get the highest possible robustness under the predefined distortion limit and used the ABC algorithm. Takore et al. [[17]] utilised GA to optimise the visual quality and robustness of the method combining DWT, DCT, and SVD. Makbol et al. [[18]] presented an image watermarking method based on SVD using integer wavelet transforms and ant colony optimisation (ACO) to solve the false positive detection problem that often occurs when using singular value vectors as secret keys in the watermarking method using SVD. The additional security key was obtained from the watermarked image during the embedding process to enhance security, and the S and V matrices of the watermark were used as the secret key to completely overcome false positive detection. To increase the robustness while balancing the robustness and imperceptibility, the optimal scaling factor was determined by using the exponentially weighted sum of the difference between the ideal values and the indicator values as the objective function of the multi-objective ACO. Cui et al. [[19]] utilised the sum of the NC value of the original image and the watermarked image and the NC value of the original watermark and the extracted watermark as the objective function to obtain the best scaling factor. After converting the RGB colour image to the YIQ space more suitable for the human visual system, they performed three-level DWT on the illumination component Y to determine four different frequency sub-bands. Then they performed SVD on the three sub-bands, and scrambling and encrypting. Finally, the watermark images were mixed using DCT coefficients and a scaling factor. As seen above, the preceding methods of determining the watermarking parameters were mainly based on the converting MOP into a scalar optimisation problem by aggregating objective functions with the weights of the indices for the robustness and the imperceptibility, regardless of what meta-heuristic optimisation was utilised. They were very limited in finding the optimal solution of the MOP for determining the parameters required for watermarking. It was because that the solution of the MOP is generally not a single solution point but rather a set of candidate optimal solutions called Pareto set, and the uniquely determined solution with weights is only one candidate for some direction of the set and there is no guarantee that it is the best compared to other solutions [[20]]. The decomposition method has been introduced to solve these issues raised in the MOP [[20]]. In particular, since the problem of optimising the parameters required in watermarking cannot be solved by the method based on the gradient of a function, it is desirable to use a decomposition method based on the meta-heuristic optimisation. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been studied in [[20]-[24]]. Zhang and Li [[20]] first proposed the MOEA/D. Yuan et al. [[21]] adjusted the balance between convergence and diversity of colonies by searching the perpendicular distance from the weight vector to the solution to convergence in the evolutionary process. Li et al. [[22]] proposed a covariance matrix adaptation strategy (MOEA/D-CMA) to solve the balance problem between exploration and exploitation in search spaces. Wang et al. [[23]] presented the Pareto adaptive scalarising method (MOEA/D-PaS) which is based on the selection of appropriate norm spaces in order to increase the searching ability. Lin et al. [[24]] improved the effectiveness of the Pareto solution search by using multiple utopian reference points instead of one. Although the meta-heuristic optimisation method based on decomposition can solve the MOP effectively like that, to the best of our knowledge, there are no studies that have applied it to the watermarking theory. This paper presents a robust blind watermarking method based on DCT and MOEA/D. (In this paper, we consider the case embedding a binary watermark into the grey image.) The best embedding blocks are selected by dividing the image into non-overlapping blocks and calculating the human visual characteristic values for each block. DCT is then performed on the selected blocks and some AC coefficients are modified to embed the binary watermark bits. At this time, Arnold Cat Map is applied to the watermark bits to improve security, and the AC coefficients positions to be modified are selected optimally in the sense of imperceptibility and robustness by using MOEA/D. Then MOEA/D is utilised again to select the parameters for the modification of the coefficients and embed watermarking with the parameters for the determined AC coefficients positions and the modification. In order to demonstrate the effectiveness of the method, we apply the filtering and enhancing, geometric translation and compression attacks on a watermarked image and calculate the imperceptibility and robustness index values. The experimental results proved that the proposed watermarking method is not only visually imperceptible but also robust to different attacks. The novelty of this work may be emphasised as follows: (i) To overcome the drawback of the preceding researches which resolved the parameter optimisation problem by passing the MOP in terms of imperceptibility and robustness to the single objective optimisation problem using the unique weight coefficient vector defined by the user, this work applies the heuristic optimisation method based on decomposition to rationalise the balance between imperceptibility and robustness in the trade-off constraint. (ii) Unlike in [[11]], the positions of the AC coefficients of the DCT transform for embedding watermark bits are automatically and optimally found, not empirically. (iii) The parameters for modification balance and threshold values are determined not manually as in [[11]] but as a solution to the optimisation problem. Besides, the different values of parameters are used depending on the positions of coefficients to improve imperceptibility. The paper is organised as follows. Section 3 briefly provides the concepts to be used. In Section 4, the proposed watermarking method is described in detail. Experimental results of the method are analysed in Section 5 and the conclusion and future research directions are mentioned in Section 6. 3 Multi-objective evolutionary algorithm based on decomposition In general, the MOP is stated as follows: max F x x ∈ Ω (1) where Ω is the decision space, F x = ( f 1 x , f 2 x , … , f m x ) a T : Ω → R m consists of m real-valued objective functions and R m is objective space (Fig. 1). Fig. 1Open in figure viewerPowerPoint Algorithm 1: Framework of MOEA/D In many cases, since the objective functions in (1) contradict each other and the point of maximising all objective functions at the same time may not be in Ω, we introduce the concept of Pareto optimum to find a solution that balances them. Let υ , ν ∈ R m , υ is said to dominate ν if and only if υ i ≥ ν i for every i ∈ 1 , … , m and υ j > ν j for at least one index j ∈ 1 , … , m , a point x ∗ ∈ Ω is Pareto optimal to (1) if there is no point such that F(x) dominates F ( x ∗ ) and is called Pareto optimal vector. In other words, if the Pareto optimal point is improved in one objective function component, at least one other objective function component is deteriorated [[20]]. The MOEA/D for solving the MOP was first presented by Zhang and Li [[20]]. The starting point of the decomposition is that under some conditions, the Pareto optimal solution of the MOP can be the optimal solution of the scalar optimisation problem, in which objective is an aggregation of all the objective functions. In scalar optimisation, all the solutions are compared with each other based on the objective function value to find one optimal solution. However, in multi-objective optimisation, as the solutions cannot be sorted as in scalar optimisation in the object space, it aims to create as many Pareto optimal solutions as possible in order to represent the entire Pareto set. The MOEA/D method minimises all N objective functions simultaneously in one run by decomposing the MOP into several scalar optimisation sub-problems and solving them by evolving the solution population. In every generation, the population includes the best solutions up to the time of each sub-problem. Let λ 1 , … , λ N be the set of evenly spread weight vectors and z ∗ be the reference point, the approximation problem of the Pareto solutions of (1) can be decomposed into N scalar optimisation sub-problems by Tchebycheff method [[21]] and the objective function of the jth sub-problem is expressed as follows: g x | λ j , z ∗ = max 1 ≤ i ≤ m λ i j f i x − z i ∗ (2) where λ j = λ 1 j , … , λ 1 j T . The framework of MOEA/D is described in Algorithm 1 [[20]]. 4 Proposed watermarking method This section describes the proposed watermarking scheme and a parameter optimisation method for robustness and imperceptibility using MOEA/D. 4.1 Watermarking embedding and extraction The proposed watermarking method is based on the recent technique presented in [[11]]. The method first divides the original image into non-overlapping blocks and selects the blocks to embed the binary watermark bits by using the human visual characteristics of every block. For the watermark image, Arnold Cat Map is performed in order to improve security. A binary watermark bit is embedded by performing the DCT on each selected block and adjusting six coefficients of its middle-frequency band. When extracting, the watermark is reconstructed by comparing the coefficients of the middle frequency bands of the embedding position blocks. The proposed modified embedding process involves solving two optimisation problems. One is to find the position of the DCT coefficients to embed a binary watermark bit at selected blocks. Instead of the middle frequency band coefficients in [[11]], six coefficients positions are determined as a solution to the optimisation problem to ensure robustness and imperceptibility at the same time. Next is to determine the optimal parameters to be used for the modification of coefficients. Since the watermark bit is embedded by comparing the values of even and odd positions among the six coefficients, we introduce parameters to determine the absolute difference between coefficients and to adjust the modification ratio of the two coefficients. In [[11]], an experimental threshold value was used to ensure the absolute difference of coefficients to be compared, and the values of the odd or even positions of the six DCT coefficients were changed by the threshold. If the modification amount of every coefficient which is changed in the embedding process is reduced as much as possible while maintaining robustness, watermarking can be more imperceptible. From this idea, we introduce parameters for the modification amount and the ratio and determine the values as the solution to the optimisation problem, changing the odd-numbered and even-numbered coefficients simultaneously. In this way, the absolute difference between the coefficients to be compared is obtained optimally to ensure the robustness, while the correction amount of the coefficients to be modified is reduced as much as possible to increase the imperceptibility. 4.1.1 Embedding Watermark embedding process of the proposed scheme is described in Algorithm 2 (Fig. 2). Fig. 2Open in figure viewerPowerPoint Algorithm 2: Watermark embedding process 4.2 Extraction Th watermark extraction process is described in Algorithm 3 (Fig. 3). Fig. 3Open in figure viewerPowerPoint Algorithm 3: Watermark extraction process 4.3 Application of MOEA/D in finding optimal parameters As seen in the watermarking process, the six-dimensional position parameters and the six-dimensional modification parameters are required to be found. The problem is to determine the optimal parameters that ensure robustness and imperceptibility at the same time. To express this problem mathematically, suitable indicators need to be introduced to quantitatively express robustness and imperceptibility. Among the widely used indicators, we use the NCC as the robustness indicator and the PSNR as the invisible indicator. The method in the paper is not limited by the choice of indicators and can be used for other indicators. For original image matrix I, watermarked image matrix I ∗ , original watermark matrix W, assuming Q possible attack types and letting reconstructed watermark matrix after applying ith attack on the watermarked image be W i ∗ i = 1 , Q ¯ , the imperceptibility is F imperceptibility = PSNR I , I ∗ = 10 lo g 10 255 2 1 M N ∑ i = 1 M ∑ j = 1 N I i , j − I i , j ∗ 2 (3) and the robustness on Q attacks is evaluated as follows: F robustness = 1 Q ∑ k = 1 Q NCC W , W k ∗ = 1 Q ∑ k = 1 Q ∑ i = 1 M ∑ j = 1 N ⁡ W i , j W i , j ∗ ∑ i = 1 M ∑ j = 1 N ⁡ W i , j 2 ∑ i = 1 M ∑ j = 1 N ⁡ W i , j ∗ 2 (4) Therefore, the problem of determining the optimal parameters in watermarking results in the following MOP: max F x x ∈ Ω where Ω is the decision space, F x = F 1 x , F 2 x T : Ω → R 2 consists of two real-values objective functions and F 1 x = F imperceptibility F 2 x = F robustness Most of the preceding researches solved this problem by assigning the appropriate weights to the two objective functions and aggregating objective functions to convert into a scalar optimisation problem. The solution is nothing more than a solution in one direction of the Pareto solution set of the MOP, and it is difficult to secure the optimality. The proposed method solves this problem by using MOEA/D instead of the user-defined weight vector-based algorithms to determine the approximation of the total Pareto solution set of MOPs. The proposed scheme requires position parameters P 1 , P 2 , P 3 , P 4 , P 5 , P 6 and modification parameters T 1 , T 2 , T 3 , R 1 , R 2 , R 3 . It is difficult to find them all at the same time, so we first set the level number of modification of coefficients and then optimise the position parameters based on it. After that, the modification parameters are optimised using the predetermined position parameters. The algorithm for optimising the position parameters is described in Algorithm 4 (Fig. 4) and the algorithm for optimising the modification parameters using the optimised position parameters is described in Algorithm 5 (Fig. 5). Fig. 4Open in figure viewerPowerPoint Algorithm 4: Position parameter optimisation Fig. 5Open in figure viewerPowerPoint Algorithm 5: Modification parameter optimisation 5 Experimental results In this section, we examine the effectiveness of the proposed method through simulations. In the experiment, nine 512 × 512 greyscale images are used as the host images, and 32 × 32 binary image is embedded as the watermark logo. Since the presented method divides the host image into 8 × 8 non-overlapping blocks and inserts a watermark, 64 × 64 watermark can be embedded into a 512 × 512 image. The watermark logo is scrambled by using Arnold Cat Map to increase security. Fig. 6 shows nine host images used in the experiment, and the original watermark and the scrambled watermark by Arnold Cat Map are shown in Fig. 7. Fig. 6Open in figure viewerPowerPoint Host images Fig. 7Open in figure viewerPowerPoint Watermark and scrambled watermark Unlike many of the previous methods, the experiments do not use user-defined weights or threshold for robustness and imperceptibility and use MOEA/D to obtain approximate Pareto set on parameters. The level number of modification parameters to determine position parameters is set to 10. The effectiveness of the proposed method is evaluated by comparing imperceptibility and robustness of existing schemes under the different image processing, geometrical transform and compression attacks. 5.1 Imperceptibility analysis In this experiment, the PSNR is utilised to evaluate the imperceptibility of the watermarked image. PSNR is the most widely used as the metric in imperceptibility measurement and calculated by (3). PSNR value indicates the similarity between host and watermarked images and it is presented in decibel (dB). The watermark is inserted into nine host images, and the PSNRs with the original images are calculated and compared with the results of existing methods [[5], [10], [11], [17]]. PSNR values of the proposed scheme for nine host images are shown Fig. 8. As seen in Fig. 8, all PSNR values are above 46. In the light of the fact that if the PSNR between two images is >30, the human's eye cannot easily identify the differences, it can be concluded that the presented method ensures the high visual quality of watermarked images. Fig. 8Open in figure viewerPowerPoint Host images, watermarked image and their PSNR values The comparison results between proposed and existing methods in imperceptibility a