Accommodative extractor for QIM‐based watermarking schemes

IET Image ProcessingVolume 13, Issue 1 p. 89-97 Research ArticleFree Access Accommodative extractor for QIM-based watermarking schemes Zied Kricha, Corresponding Author Zied Kricha kricha.zied@gmail.com orcid.org/0000-0003-4237-1160 National School of Engineers of Sousse, University of Sousse, Sousse, Tunisia CSR Group with the Electronic and Microelectronic Laboratory, National School of Engineers of Monastir, University of Monastir, Monastir, TunisiaSearch for more papers by this authorAnis Kricha, Anis Kricha LATIS Laboratory, National School of Engineers of Sousse, University of Sousse, Sousse, Tunisia National School of Engineers of Monastir, University of Monastir, Monastir, TunisiaSearch for more papers by this authorAnis Sakly, Anis Sakly orcid.org/0000-0002-3608-0386 ESIR research Unit, National School of Engineers of Monastir, University of Monastir, Monastir, TunisiaSearch for more papers by this author Zied Kricha, Corresponding Author Zied Kricha kricha.zied@gmail.com orcid.org/0000-0003-4237-1160 National School of Engineers of Sousse, University of Sousse, Sousse, Tunisia CSR Group with the Electronic and Microelectronic Laboratory, National School of Engineers of Monastir, University of Monastir, Monastir, TunisiaSearch for more papers by this authorAnis Kricha, Anis Kricha LATIS Laboratory, National School of Engineers of Sousse, University of Sousse, Sousse, Tunisia National School of Engineers of Monastir, University of Monastir, Monastir, TunisiaSearch for more papers by this authorAnis Sakly, Anis Sakly orcid.org/0000-0002-3608-0386 ESIR research Unit, National School of Engineers of Monastir, University of Monastir, Monastir, TunisiaSearch for more papers by this author First published: 01 January 2019 https://doi.org/10.1049/iet-ipr.2018.5814Citations: 5AboutSectionsPDF 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 quantisation index modulation-based watermarking methods, each host coefficient is replaced by an adequate quantiser according to the embedded bit. However, after the attack, the distribution of the hosts does not remain the same, resulting in a failure to map coefficients to their correct bits. To maintain a good quality, many authors focused on improving the extraction, rather than playing on the embedding parameters. They used a reference message to define the parameters of the channel model after the attack. However, the available solutions were not effective, whereas the reference message cannot describe the channel alteration due to a shortage of samples, and the complexity of attacks modelling. To overcome these problems, the authors relied on a diversification technique, which allowed to enlarge and vary the samples. Then, based on quantisation embedding rules, they generated an accommodative detection model for each attack. At the extraction phase, the suitable detection model was identified by means of a reference message. To reinforce the security of their scheme, the watermark was initially shuffled, which prevents any unauthorised detection attempt. Both geometric and signal processing attacks were used in the validation of their method. The reduction of bit-error rate with respect to the conventional detection method reached up to 100%. 1 Introduction Throughout history, humans had not stopped evolving new techniques to prove their ownership of properties. Kings had minted coins with the symbols of their empires, stockmen had branded their livestock, and masters had tattooed their slaves. Although these techniques are effective in the real world, they are useless in the digital one. Thus, the watermark concept was initially introduced to handle the problem of digital copyright protection. Watermarking consists in embedding an extra-data within a digital object without altering the delivered information. The digital object can be a piece of hardware [1], a text of software [2], or a digital media (image [3], audio [4], or video [5]). According to the purpose of the watermark (insertion of metadata, fingerprints etc.), and the different attacks that the watermark should resist to, the embedding scheme can be classified as fragile [6], semi-fragile [7], or robust [8]. For example, in the case of digital rights management, the robustness of the watermark is critical while a fragile watermarking scheme is required for authentication purposes. In this work, we focus on the robust watermark for digital images, so in the rest of this paper, we denote by watermarking hiding a binary message in a digital image. For copyright protection, we distinguish two main embedding approaches: the spread spectrum, and the quantisation-based techniques known as the quantisation index modulation (QIM). Since it was introduced, the QIM was adopted by many researchers, and several improvements were proposed to achieve a better robustness. In fact, though its advantages regarding the capacity, imperceptibility, and robustness against some signal processing operations, the QIM remains vulnerable to other attacks. To obtain a better robustness, researcher's effort was focusing on either the embedding [9, 10] or the extraction phase [11-13]. However, the latter solutions had been given less attention than the former due to the complexity and variability of the channel characterisation. In fact, the existing adaptive detection methods for QIM embedding schemes are limited to some attacks and far from being optimal. In this paper, we bypass the need of a theoretical channel model by experimentally studying the effect of several attacks throughout a diversification technique. For each attack, we generate a new detection model that is able to decrease the detection error. In the extraction phase, we select the best detection model by means of a pre-embedded reference message. The rest of this paper is organised as follows. Section 2 provides an overview of state-of-the-art solutions targeting the extraction phase. Section 3 presents the new detection model generation's process. Section 4 reveals the proposed watermarking scheme including the embedding and detection phases. The computational complexity and the robustness performance of the proposed scheme are analysed in Sections 5 and 6, respectively. Finally, we draw the conclusions in Section 7. 2 Related works The QIM on its standard version [14] proved a good robustness against the additive white Gaussian noise (AWGN) and a high capacity of insertion as well as a favourable imperceptibility [15]. However, the common problem of the QIM is its sensibility to gain attacks [16]. In the literature, most of the schemes related to the QIM have sought to solve this issue by adopting one of two strategies. While the first targets the embedding side by creating an invariant domain to gain attack [8, 17] or utilising an adaptive quantisation step [18, 19]; the second focuses on the extraction side by estimating the attack effects through a known message or blindly, then adjusting the detection according to this estimation. Shterev and Lagendijk [20] put forward a statistical technique to exceed the use of the pilot signal. They first derived the probability density function (PDF) of the attacked and the watermarked signal, then they proposed an estimation of the scaling factor by a maximum-likelihood technique based on an exhaustive search. To reduce the complexity caused by exhaustive search, Dominguez-Conde et al. [21] suggested calculating the maximum likelihood by approximating the PDF of the received signal relying on several assumptions. In [22], Balado et al. presented a joint iterative decoding and estimation in combination with turbo-code error corrector to handle a channel with scaling and shift attacks. However, the main weakness of this method and iterative methods has generally been the initialisation issue. As mentioned before, the estimation of the channel distortion may also take place through a known message which is referred to in the literature as a reference watermark, informative watermark, template, or pilot signal. Regardless of the appellation, this message has to be transmitted to the watermark detector where it will serve in the search of the channel model's parameters. Eggers et al. [23] modelled the channel model as an AWGN prefixed by a constant amplitude scaling with a DC offset. To determine the parameters of the channel, they examined the histogram of the received reference message using the Fourier analysis. The reliability of the estimated channel was determined by the number of employed histogram bins (for the reference message and the key value), the reference message size, and the discrete Fourier transform length. In [9], the work of Shterev and Lagendijk [20] was extended by generalising more the channel model. The authors assumed that the watermarking channel was one with non-zero mean additive noise. Besides the estimation of the fading factor using [20], the impact of the noise's average in the detection was cancelled by shifting the decision zones to minimise the number of erroneous bits. In [24], Won claimed to tackle valumetric scaling and constant change attacks; he modelled the attacks as an affine transform (AT), then he modified the DC of the discrete cosine transform blocks using the QIM. For a better robustness against an AWGN attack, the parameters used on the AT model were exhaustively searched. 3 Attack characterisation In this section, we start by revealing the limitation of the existing attack characterisation methods oriented to QIM watermarking schemes. Then, we present the implementation details of an accommodative detection model that is capable to ameliorate significantly the correct detection rate. 3.1 Overview of the problem The QIM, first introduced in Chen13s work [14], represents a class of robust watermark embedding methods. According to it, the insertion of a word w consists in modulating the host coefficient by an appropriate quantiser to generate a watermarked coefficient . For a further understanding, we consider a binary message to embed in the sub-band of the Lena image. Fig. 1 illustrates the different watermarking stages. The embedding phase involves the creation of two quantisers sets and for bits 1 and 0, respectively. We define (1) as the quantisation function generating these sets: , where h is the host coefficient and is the quantisation step which determines the distance between two adjacent quantisers belonging to the same set (i.e. and ) (1) (2) Fig. 1Open in figure viewerPowerPoint coefficients' distribution of the Lena image throughout watermarking life cycle, and median filter (3 × 3) impact on the extraction of the embedded watermark Under the influence of intentional or unintentional image processing operations, the watermarked host coefficient tend to move away from its respected quantisers, to become , yet the default detector (3) can still extract the correct inserted bit as long as (3)However, in most cases, the alteration surpasses that limit resulting in wrong extracted bits. To overcome this problem, researchers focus on the estimation of the alteration by considering the watermarking process as transmitting a watermarked image through a noisy channel, represented in [9] as (4)where is the fading of by a factor in conjunction with a non-zero mean additive noise . Some authors restricted the channel model to only a fading noise [10], and others went to a more general assumption when they considered the additive noise as AWGN [25] or a mixture of AWGN and Jitter [26]. However, the exact description of the channel is not available, and even if a model fits well with an attack it may fail with another. 3.2 Improved detector To overcome the limitations of the available solutions, we proposed to generate a specific detector for each attack by analysing the new distribution of the watermarked coefficients. In other words, for each received host coefficient , we assigned a watermark bit , which is not necessarily the same obtained from (3). We utilised a diversification technique to broaden and expand samples: we insert separately c random sequence in the sub-band of the original image, for each embedding, we recuperated the attacked coefficient, then sort them in ascending order. The role of a robust QIM detector is to assign a watermark bit to every range of values, referredto in this paper as a detection region (DR). To convert the samples into DRs andthen to a detection model capable to map any coefficient to the appropriate bit,we defined four steps derived from the quantisation embedding rules (Fig. 2): Step 1: According to the QIM principal, twodifferent bits cannot be represented by the same host value. Hence,in the first step, we got rid of the useless samples. Thesub-sampling process is described by the following algorithm. Fig. 2Open in figure viewerPowerPoint Generation steps of the accommodative detectionmodel Algorithm 1.Sub-samplingif & thenDelete Delete end if. Step 2: We clustered the samples into DR: Each group of sequenced samples carrying the same bit, where the distance between every consecutive couple does not exceed , will form an independent DR. Each DR is characterised by its lower and upper bounds, the unique bit affected to any coefficient belonging to that DR, and the number of samples within it. Step 3: Some created DRs did not really reflect the attack effect. Those DRs are distinguished by a limited number of samples . Hence, in step 3 we deleted those regions and merged the two adjacent DRs of the deleted one, as they represent the same bit. Step 4: The resulting detection model, which is a contiguity of different DR, should cover all the possible values of the host coefficients without any blind spot. In an attempt to achieve this, we proposed to stretch the maximum and minimum of each two adjacent regions to join in the middle of the non-covered zone. In Fig. 3, we represent a portion of the sub-band after median filter (3 × 3) attack. Although the inserted message was not a part of the training sequences, the generated DRs fit well with the samples. We should also note that the obtained DRs have a variable width, which was not considered in any prior work. Fig. 3Open in figure viewerPowerPoint Comparison between the default and accommodative detection models used to extract the embedded watermark after median filter (3 × 3) attack 4 Watermarking scheme We devote this section to describe thoroughly the process of watermarking including both the embedding and the extraction processes. A full overview of the proposed scheme is presented in Fig. 4: a payload message is first secured through a key , then inserted in a cover image. In the meanwhile, different attacks are applied to the original image, and the corresponding detection models are obtained using the method described in Section 3.2. To select the adequate detection model, a key , generated during the watermarking process, is utilised by the extractor. Fig. 4Open in figure viewerPowerPoint General accommodative watermarking life cycle The embedding process is illustrated in Fig. 5 and described through steps 1–5: Step 1: The original image I is decomposed l times using the discrete wavelet transformation (DWT) to generate the host wavelet sub-band . is a matrix with a width and a height, where and are, respectively, the width and height of the original image. Fig. 5Open in figure viewerPowerPoint Schematic diagram of watermark embedding Step 2: To prevent any unauthorised extraction of , the Fisher–Yates [27] shuffling method is implementedas follows. Algorithm 2.Fisher–Yates to do such as swap ()end for where r is a random integer generated using a pseudo random number generator (PRNG) based on the secret key . Step 3: WK is composed of two independent watermarks: the shuffled form of the payload message , which is the message to recover after the attack; and a reference message , . RF will be used later in the detection phase to select the suitable watermark detector model. RF is constituted of an equal number of bits 1 and 0 that are spread over all bins of the histogram. For each bin containing m elements, n bits of are inserted in a way that preserves the same ratios: . Step 4: The watermark WK is embedded in using (1). Step 5: The original sub-band () is replaced by the watermarked one and the inverse DWT is applied l times to obtain the watermarked image I′. In the watermark extraction process, outlined in steps 6–9 (Fig. 6). It is likely that the watermarked image underwent an intentional or unintentional attack , resulting in an alteration of the hosts and of, respectively, and . Therefore, and will be received as and , respectively, resulting in errors in the extracted messages and . Note that the symbol is used to refer to an attacked signal. Fig. 6Open in figure viewerPowerPoint Schematic diagram of watermark extraction Step 6: The altered watermark's host matrix is extracted by performing a DWT to the attacked watermarked image. Step 7: The key is used to determine the host coefficients of both and . The message is a fixed message generated by an alternation between bits 1 and 0, thus it is known to the watermark detector. Step 8: The reference message is detected using all the available models. The suitable model is the one with the smallest number of wrong bits. The message is then extracted using the same model. Step 9: The extracted message, from step 6, is shuffled back using the key to obtain . 5 Computational complexity This section describes the computational complexity of the proposed approach, which is expressed in terms of big-Oh notation, where worst-case scenarios are considered. The proposed scheme in this paper is meant to reduce the number of erroneous extracted bits for a given watermarking scheme. Hence, in the following, only the additional complexity is analysed. Considering , the complexity of a given watermarking scheme, where and are, respectively, the height and width of the input image. The additional steps can be broken into six independent algorithms (Fig. 2), where the input variables of each step are defined by the previous one. The generation of the samples: involving watermarking, attack, and detection. Let be the complexity of the attack i. In the worst-case scenario, the complexities of all attacks are , where n is a constant representing the number of tested attacks and is the most computational attack. The complexity of the sorting algorithm is given by: . In the sub-sampling process (described by the first step in Section 1.2), the dimension of the input matrix is , in the worst case all elements are shifted (deleted) so the complexity is given by . In the clustering, fusion, and stretching algorithms, the time complexity is linear with the input dimension resulting from the sub-sampling phase, which is giving, in the worst case, by . In conclusion, the complexity of the watermarking scheme will be dominated by , , or according to the tested attacks and the embedding scheme. 6 Experimental results In this section, we experimentally evaluate the improvement of robustness achieved through the proposed detector. Nine standard grey-scale benchmark images, with a dimension of 512 × 512 pixels and 8 bits depth, were selected for the test purpose; for conciseness reasons, only the performance of some images (Lena, Baboon, Boat, and Peppers) were reported in this section. First, we compare our method with a state-of-the-art method [9], and then we test our method as a new extractor for other schemes. We depicted the imperceptibility of the watermark in terms of peak signal-to-noise ratio (PSNR) (5) and structural similarity index (SSIM), and the robustness after attacks in terms of bit-error rate (BER) and normalised correlation (NC) (5) (6)In the training phase, the parameters , , and are empirically chosen in a way that minimises the BER of the training sequence. To evaluate the robustness of the proposed scheme, we calculated the BER between the inserted watermark and the retrieved from the attacked image. First, the non-attacked image is tested, and then both signal processing and geometric attacks are considered in the experiments. The full list of these attacks and their abbreviations is given in Table 1. Table 1. List of used attacks Attack Parameters Abbreviation rotation ROT(−0.25) ROT(0.2) ROT(0.25) ROT(1) ROT(10) -> ROT(45) cropping 10% CROP(10) 20% CROP(20) 25% CROP(25) 50% CROP(50) translation resize vertical 10% TRV 512->256->512 RSZ horizontal 10% TRH vertical 10% TRV horizontal + vertical 10% TRHV median filter 3 × 3 MDF(3) 5 × 5 MDF(5) 7 × 7 MDF(7) 9 × 9 MDF(9) 11 × 11 MDF(11) histogram equalisation — HE low-pass filter — LPF sharpening 3 × 3 SHP salt and pepper 0.01 SP(0.01) 0.02 SP(0.02) 0.03 SP(0.03) 0.1 SP(0.1) 0.2 SP(0.2) Attack Parameters Abbreviation colour reduction 8–4 bits CR intensity scaling 255–32 grey level IS amplification × 1.5 AMP(1.5) × 1.8 AMP(1.8) × 2 AMP(2) DC intensity reduction −80 for each 8 × 8 block IDCC AWGN 0.0002 GN(0.0002) 0.02 GN(0.02) 0.03 GN(0.03) 0.04 GN(0.04) 0.05 GN(0.05) speckle noise mean = 0, variance = 0.01 SN mean filter 3 × 3 MF(3) 5 × 5 MF(5) 7 × 7 MF(7) 9 × 9 MF(9) gamma correction 1.2 GC(0.8) 0.8 GC(1.2) intensity variation + 20 IV + 20 −20 IV − 20 + 40 IV + 40 −40 IV − 40 Gaussian noise mean = 0, variance = 0.5 GN0/0.5 mean = 0, variance = 0.2 GN0/0.2 mean = 0.1, variance = 0.01 GN0.1/0.1 mean = 0.1, variance = 0.02 GN0.1/0.2 mean = 0.1, variance = 0.05 GN0.1/0.05 6.1 Comparison to similar work We embedded the watermark in the sub-band obtained after four levels of DWT using the bior4.4 filter. A higher level of transformation induced a lower capacity but a better robustness and vice versa. Embedding the watermark in the LL sub-band gave the best imperceptibility among the four available sub-bands (LL, HL, LH, and HH) but a lower robustness. The embedding capacity of the is 1024 bits divided as follows: 64 bits for the reference message and 960 bits for the payload message. The value of the quantisation step used at the embedding phase determines the embedding strength of the watermark. In our experiments, we selected manually in such a way as to generate a good quality of the watermarked image. The chosen and the obtained PSNR and SSIM for each image are depicted in Table 2. Table 2. Used quantisation step , and the resulting PSNR and SSIM values for different test images Image Proposed method [9] SSIM PSNR, dB PSNR, dB Lena 88 0.9978 43.57 43.5 Baboon 116 0.9989 41.21 41.1 Boat 100 0.9980 42.45 42.5 Peppers 98 0.9952 42.64 42.6 Besides these attacks, we tested the false-positive (FP) risks of our scheme, where the watermark extraction scheme was applied to a non-watermarked input image, and our scheme was FP free. The robustness results are summarised in Table 3, we compared the conventional detection method (1) presented in [14], which is still used in the literature today [28], with the proposed adaptive detector. Our extraction scheme showed an improvement of robustness in all studied attacks. However, the improvement rate was not the same for all attacks: the results indicated an improvement peak of 98% (average value) for the IDCC attack; the lowest result was obtained for the SN attack. As discussed in Section 2, the limitation of this scheme occurred when the training samples of bit one and zero are too close, which cannot be corrected. We compared the performance of our scheme with the results obtained in [9]. At the time of writing this paper, the work of Kang et al. [9] is the most generalised channel model used to adjust the QIM watermark detector according to the applied attack. Similar PSNR values are used at the embedding phase: Table 2 lists the resulting PSNR for the two embedding methods and Fig. 7 depicts the visual difference between the watermarked and the original images. Table 3. Experimental results in terms of BER (%) of the proposed accommodative detector and the default detector Attack Baboon Boat Lena Peppers Proposed Default detector Proposed Default detector Proposed Default detector Proposed Default detector MDF(3) 6.063 21.74 0.979 5.208 0.188 2.057 0.438 0.615 MDF(5) 15.854 34.083 9.604 19.479 4.521 10.599 2.75 6.026 MDF(7) 23.375 40.115 16.958 25.333 8.958 15.266 8.583 13.76 MDF(9) 28.833 41.599 22.521 28.953 15.688 21.99 15.042 20.51 MF(3) 1.542 4.224 0.292 2.781 0.354 3.042 1.667 3.422 MF(5) 1.542 3.198 3.958 7.646 2.333 8.917 2.771 8.104 MF(7) 4.458 7.203 10.688 15.396 11.958 22.906 10.979 23.385 MF(9) 14.167 17.729 18.542 29.156 23.125 38.833 23.813 34.557 HE 14.458 49.026 26.521 48.958 17.292 52.146 25.688 50.047 SP(0.01) 3.75 4.818 5.604 8.724 9.208 13.01 6.979 12.932 SP(0.03) 21.208 26.781 28.604 34.453 33.792 42.073 30.063 43.807 AMP(1.5) 15.813 49.771 8.646 50.198 10.521 50.328 7.833 53.401 AMP(1.8) 29.854 50.323 31.875 51.839 25.083 49.656 20.729 48.615 AMP(2) 34.875 51.526 38.333 50.005 30.021 49.453 25.625 49.109 CR 0 48.844 2.542 53.307 10.75 49.797 5.521 50.823 IS 0 50.089 0 47.906 0 50.969 0 49.688 GC(1.2) 0.146 26.922 1.625 75.781 2.25 45.141 5.146 67.714 GC(0.8) 0.083 67.662 1.375 42.307 2.208 61.693 6.083 50.396 IDCC 0 100 0 100 0.2 98.542 1.625 96.771 GN(0.02) 38.167 39.479 45.313 46.313 46.771 47.943 46.063 47.396 GN(0.05) 46.938 48.88 47.375 49.63 48.438 50.474 47.771 50.229 SN(0.01) 2.771 3.339 6.25 6.766 8.375 9.047 4.146 4.964 IDCC + IS 0 49.255 0 48.083 0.292 48.745 2.271 50.354 JPEG + MDF(3) 7.583 16.25 2.458 4.599 0.771 0.979 0.542 0.698 JPEG + MF(3) 2.688 4.25 0.958 2.578 1.146 3.016 2.146 3.51 ROT( − 0.25) 15.604 16.328 15.083 20.682 16.396 23.016 17.417 22.672 ROT(0.2) 10.417 12.375 10.917 14.422 11.729 17.292 15.063 22.214 ROT(0.25) 15.875 16.453 15.229 20.255 16.917 22.729 17.5 24.802 TRH 0.292 3.693 0.333 2.172 0.208 2.771 0.333 2.969 TRV 0 1.818 0.229 2.479 0.75 4.229 0.208 2.646 TRHV 1.271 8.146 1.458 7.938 0.813 8.5 1.229 7.849 CROP(10) 3.938 21.74 5.396 21.37 4.708 20.75 4.583 20.583 CROP(20) 8.188 25.807 9.208 25.599 6.688 24.792 7.833 22.318 CROP(25) 10.313 24.453 10.75 26.156 10.125 24.099 10.021 22.016 CROP(50) 19.75 32.896 21.958 33.776 19.667 33.802 19.354 28.146 Fig. 7Open in figure viewerPowerPoint Visual quality of the watermarked images using the insertion parameters in Table 2 (a) Watermarked Lena, (b) Watermarked Baboon, (c) Watermarked Boat, (d) Watermarked Peppers, (e) Original Lena, (f) Original Baboon, (g) Original Boat, (h) Original Peppers Kang et al. of [9] used 128 coefficients from the available 1024 of the sub-bands to embed the reference message, which leaves 896 coefficients for the payload message against 960 in our scheme. From Fig. 8, we noted that in comparison with the work of [9], our scheme achieved a reduction of the BER. For the Baboon image, we were able to extract the watermark after CR, IS, GC(1.2), GC(0.8), and IDCC + IS attacks with fewer than two wrong bits in the worst case, and a mean value of BER 0.0005; unlike [9] where the mean of the BER was 0.01 with 80 bits wrongly detected. For the Pepper image, the average of the BER drops from 0.17 to 0.05 for MDF(3) and MDF(5) attacks. Similar results were obtained in the rest of the test images. Fig. 8Open in figure viewerPowerPoint Robustness comparison between different extraction models (a) Baboon, (b) Boat, (c) Lena, (d) Peppers 6.2 Robustness improvement of existing schemes The proposed method is not intended to substitute a watermarking scheme. However, to be combined with a well-established method that uses the classic QIM or one of its derivatives (progressive QIM, angle QIM etc.) at the embedding phase to improve the robustness. To further evaluate the efficiency of our method, we implement our method into four QIM-based schemes. In the four methods, the watermark was embedded in different domains such as the difference of two DCT coefficients [12], the DC of a DCT block [29], or the q_DWT domain as in [13]; or using a variant QIM such as the logarithmic QIM (LQIM) [11]. In the four cases, the watermark size is fixed to 4096 bits, where 256 bits were dedicated to the reference message. The robustness with and without the use of the accommodative extractor for the Lena image is tabulated in Tables 4–7 for [11, 12, 13, 29], respectively. We can conclude from these results that our scheme has improved the robustness of different QIM-based schemes, whether implemented in the DWT or DCT domain to watermark a single coefficient or a relation between coefficients (difference) using a uniform or a non-uniform quantisation step (LQIM). Table 4. Comparison between the BER using the default detector and the proposed one for Hu et al.'s watermarking scheme [12] Quality SSIM = 0.913 SSIM = 0.964 Detection method Default Proposed Default Proposed JPEG(10) 0.439 0.258 0.637 0.379 JPEG(20) 0.000 0 0.327 0.231 JPEG(30) 0 0 0.028 0.021 JPEG(40) 0 0 0.000 0