Abstract This study proposes a watermarking method for authorization identification which aims to prevent hackers from using copyrighted images without authorization. The watermark is embedded in the log-polar (LP) coordinate system which is resilient against rotation, scaling and translation (RST). For watermark detection, only the watermark is required at the receiver site, and whether the image is watermarked can be realized. The diffusion phenomenon of the embedded watermark is explored and used to make it possible to correlate the original watermark and the embedded watermark in the LPM domain. Experimental results show that the proposed scheme is robust against several attacks, such as rotation, rotation with cropping, scaling, scaling with cropping, translation, translation with cropping and JPEG compression. 1. INTRODUCTION The Worldwide Web, digital networks and digital multimedia face an unprecedented challenge of copyright protection. Digitization facilitates piracy. Therefore, research into intellectual property protection has become important. Among many copyright protection methods, watermarking embeds secret information into multimedia material such that the embedded information is imperceptible to humans. Unauthorized persons may commit various attacks against digitally watermarked material. After successful attacks, the existence of watermarks cannot be verified, and thus the authorization of the owner cannot be declared. Then unauthorized persons can use the material without authorization. Among these attacks, geometrical attacks on digitally watermarked images, such as rotation, scaling and translation, are rather difficult to handle [1]. With respect to geometric attacks, watermark embedding methods can be separated into several categories. First, an auto-correlation function or periodic watermark enables geometric distortions to be detected by examining the distortion of the watermark. Kutter and Voloshynovskiy et al. [2, 3] proposed the usage of a periodic block allocation as the watermark. The periodic watermark is a regular grid, and the estimation of the watermark is key-independent. Since the watermark may be detected and destroyed [4, 5], its slight pre-distortion has been proposed to prevent destruction [6]. For example, the watermark of [6] is robust against local and non-linear geometrical distortions, such as random bending attacks. As for the second category, the watermark is embedded with a template designed based on the watermark. Geometric distortions are found by examining the embedded template, allowing geometric transformations to be reversed before the watermark is retrieved. All of these methods require information about the template to reverse the distortions before the watermark is extracted. They depend on the accurate retrieval of the template [7–9]. The basic concept of the third category is to embed the watermark in the geometrically invariant domain. The main disadvantage of such methods includes the theoretical and practical difficulties of constructing invariants. Ruanaidh et al. [8] were the first to propose a watermarking method in the Fourier–Mellin domain, in which watermarking can be robust to rotation, scaling and translation (RST). Thus the main contribution of [8] is the introduction of such a theoretically good watermarking domain. A strongly invariant transform was claimed to be important for inverting invariant signals back to the visual watermarked space. Notably, very severe implementation difficulties may be encountered [8]. Believing that the inverting of invariant signals is not necessary, Lin et al. [1] proposed a watermark extraction function which is sufficient for watermarking without invertibility of transforms required in [8]. In [1], the Fourier magnitudes of both the watermark and the un-watermarked image are transformed into the log-polar (LP) mapping (LPM) coordinates, and then mixed to be used for searching the corresponding watermarked version in the Fourier domain. Different kinds of difficult implementation issues in the Fourier–Mellin domain were discussed and solved delicately in [1], including difficulty of inverting LPM, dynamic range of the magnitudes, unreliability of extreme frequencies, high correlation between elements of extracted watermarks, interrelation between changes made in watermark elements and so on. Considering the possible high false positive rate caused by the summing and exhaustive search ideas in [1], Zheng et al. [10] proposed a phase-correlation-based approach to extracting watermark positions. Such a method suggested a simple and feasible implementation for RST-resilient watermarking in the Fourier–Mellin domain. The approximate inverse LPM (ILPM) was developed to eliminate the inaccurate ILPM, and then the watermark was embedded accurately in the Fourier magnitudes of the original image [10]. Phase correlation was used to locate the watermark without exhaustive searching. The effectiveness of phase correlation was based on the equal contribution of the phase difference for every frequency component. Zheng et al. [10] did a good job to compute the watermark locations based on correlating the watermarked image with the original image. The invariant transform in [8] and the summing along with the exhaustive searching in [1] were not required. However, for some watermarking applications, the existence of the watermark would be more important than the location of the watermark. Especially, for authorization identification, the existence of the watermark is the major task, and the locations of the watermark in the watermarked data could be unnecessary. The advantage of such circumstances is that the receiver site needs to keep only watermarks, rather than original images or both the images and watermarks. Meanwhile, it would be a great relief to free from storing and updating the original images at the identification site. Thus, this work proposes a watermarking approach to authorization identification. It aims to embed the watermark in the RST-resilient LP domain, and to identify the existence of the watermark without the original image. The rest of this study is organized as follows. Section 2 elucidates the algorithms for the watermark embedding scheme and the watermark extraction process, as well as details of their implementation. Section 3 presents the experimental results concerning various RST distortions. Section 4 draws conclusions and makes recommendations for future work. 2. PROPOSED APPROACH 2.1. Preliminaries The RST-resilient property of the LPM of the Fourier magnitude is briefly described as follows [1, 8, 10]. For an image f(x,y) of size M×N , its discrete Fourier transform(DFT), F(u,v) , and the corresponding Fourier spectrum, ∣F(u,v)∣ , are given as follows. F(u,v)=1MN∑x=0M−1∑y=0N−1f(x,y)e−j2πuxM+vyN (1) ∣F(u,v)∣=[R2(x,y)+I2(x,y)]12 (2) where R(x,y) and I(x,y) are the real and imaginary parts of F(u,v) , respectively. The Cartesian coordinates (x,y) can be translated into LP coordinates (eρcosθ,eρsinθ) , where ρ and θ are computed as follows [10]: ρ=ln[(x−xc)2+(y−yc)2]12, (3) and θ=tan−1y−ycx−xc. (4) where (xc,yc) is the center of the LP sampling pattern. Now consider an original image io(x,y) . The corresponding distorted image is denoted as id(x,y) , which is a rotated, scaled and translated version of io(x,y) with parameters α , σ and (x0,y0) for rotation, scaling and translation, respectively. Then we have the following relation: id(x,y)=io(σ(xcosα+ysinα)−x0, σ(−xsinα+ycosα)−y0) (5) The corresponding Fourier magnitude, ∣Id(u,v)∣ , of id(x,y) is as follows: ∣Id(u,v)∣=∣σ∣−2∣Io(σ−1(ucosα+vsinα), σ−1(−usinα+vcosα)∣. (6) Note the translation invariance of the Fourier transform. Then, rewriting the magnitude using the LPM yields the LP coordinates as follows: u=eρcosθ (7) v=eρsinθ (8) ρ∈R2,0≤θ<2π . The Fourier magnitude can be written as follows: ∣Id(u,v)∣=∣σ∣−2∣Io(σ−1eρcos(θ−α),σ−1eρsin(θ−α))∣ (9) or ∣Id(u,v)∣=∣σ∣−2∣Io(ρ−lnσ,θ−α)∣. (10) And it can be found that image scaling causes a scaling ∣σ∣−2 of the LP spectrum and a translational shift lnσ along the log-radius ρ axis, while image rotation results in a cyclical shift of α along the angle θ axis. Notably, if correlation coefficients are used, the amplitude scaling of the spectrum is not an issue. From the above derivation, the RST-resilient property of the LPM of Fourier magnitudes can be found. Figure 1 shows an example of the scaling property of LPM. In Fig. 1, the circle is scaled up to Fig. 1c; the corresponding data line in Fig. 1b shifts downward as in Fig. 1d. When the circle in Fig. 1a is scaled down as in Fig. 1e, the corresponding data line in Fig. 1b shifts upward as in Fig. 1f. Figure 1. View largeDownload slide Example of scale attack: (a) original image (256 by 256). (b) LPM of original image. (c) Original image under scale attacks (scale up by factor of 1.2). (d) LPM of (c). (e) Original image under scale attacks (scale down by factor of 0.8). (f) LPM of (e). Figure 1. View largeDownload slide Example of scale attack: (a) original image (256 by 256). (b) LPM of original image. (c) Original image under scale attacks (scale up by factor of 1.2). (d) LPM of (c). (e) Original image under scale attacks (scale down by factor of 0.8). (f) LPM of (e). Figure 2 shows an example of the rotation property of LPM. The square in Fig. 2a is rotated into that in Fig. 2c; the corresponding data curve shifts leftward, as shown in Fig. 2d. Figure 2. View largeDownload slide Example of rotation attack: (a) original image (256 by 256). (b) LPM of original image. (c) Original image under rotation attacks. (d) LPM of (c). Figure 2. View largeDownload slide Example of rotation attack: (a) original image (256 by 256). (b) LPM of original image. (c) Original image under rotation attacks. (d) LPM of (c). 2.2. Watermark embedding The proposed watermark embedding process aims to achieve embedding a watermark sequence into the Fourier magnitudes of a cover image in the LPM domain. The basic idea is to take advantage of the RST-resilient property of the LPM. Figure 3 provides an overview of the proposed watermark embedding process. The process is briefly described as follows, and then some detailed descriptions and discussions can be found. Figure 3. View largeDownload slide Watermark embedding process. Figure 3. View largeDownload slide Watermark embedding process. First, a 1D watermark data sequence W0 is generated by a watermark generator. The sequence W0 is then represented in the LPM domain as a 2D watermark data WL . The approximative ILPM [10] is applied to transform WL from the LPM domain to the DFT domain, and the resulting watermark data WI are adjusted to be symmetric in the DFT domain, and denoted as W . Then, the watermark data W are embedded into the DFT magnitudes of the original image I0 via the embedder. Finally, the watermarked image IW is derived by applying the IDFT transform. In the watermark generator, the watermark data sequence W0 is generated using a pseudorandom number generator, in which the values are randomly sampled from the normal distribution and then rounded into integers. In order to satisfy the requirement of non-negative values of the DFT magnitudes, all the negative numbers are negated. Then the values are shifted by one in order to generate a watermark data sequence W0 of positive integers. The requirement of positive integers is prepared for watermark detection which is described in Section 2.3. Note that the length of W0 is N2 for an N×N original image I0 . Such a design is prepared for embedding the watermark in one row in the LPM domain and for the symmetry requirement in the DFT domain. For the LPM representation, one row in the LP domain is selected to put the watermark data sequence W0 . The row corresponds to a randomly selected ring in the middle frequencies. The basic idea here is that embedding data in the middle frequencies has been shown to achieve a compromise between robustness and fidelity [1], and to avoid embedding small data values into large DFT magnitudes at low frequencies [1]. To implement the idea, a ring shape represents the middle frequency area in the DFT is selected first, and then the corresponding band in the LPM domain can be derived. Then one row in the band is randomly selected, and the data values of W0 are placed one by one along the row. Figure 4a shows an example of WL , which is shown as an image in the LPM domain. It can be found that the watermark data occupy half of one row in the lower region of the LPM image. Figure 4. View largeDownload slide Illustrations generated during embedding process. (a) Example of WL in LPM domain. (b) Corresponding WI of (a) in DFT domain. (c) Corresponding symmetric W of WI in DFT domain. Figure 4. View largeDownload slide Illustrations generated during embedding process. (a) Example of WL in LPM domain. (b) Corresponding WI of (a) in DFT domain. (c) Corresponding symmetric W of WI in DFT domain. Then the approximative ILPM proposed by Zheng et al. [10] is used to transform the watermark data from the LPM domain to the DFT domain. The basic concept is to embed one watermark data number into each of the four magnitudes that are used by bilinear interpolation. The goal is to maintain the watermark data under bilinear interpolation. Figure 4b is an example of the result of the approximative ILPM, and it is the corresponding half-circle image WI of the half-line image WL in Fig. 4a. Because of the frequency symmetry, the transformed semicircular watermark WI is copied to symmetrical locations about the central point of the DFT magnitudes. Figure 4c shows an example of the result of symmetry adjust, and it is the corresponding circle image W of the half-circle image WI in Fig. 4b. Then, the DFT magnitudes D of the original image and the transformed watermark data W are added with the watermarking power a according to the following equation: D′=D+a×W, (11) where a>0 . The value of a is chosen to be larger than most magnitude values in the middle frequencies. According to the experimental experiences, a value of 104 is suggested. Such a selection of value for a is prepared for detecting watermark as described in Section 2.3. Finally, the watermarked image IW is derived by applying IDFT to the watermarked magnitudes D′ and the phase data P . 2.3. Watermark detection Figure 5 provides an overview of the proposed watermark detection process. Identify the presence of the watermark is the goal. The process is briefly given in the following three paragraphs, and the basic ideas, explanations of details and discussions follow. Figure 5. View largeDownload slide Watermark extraction process. Figure 5. View largeDownload slide Watermark extraction process. The whole detection process consists of two parts. As shown in Fig. 5, in the left part, first the received image IR is transformed into the DFT domain. Then the frequencies FR are filtered by the frequency filter. The remained frequencies FF are mapped into the LPM domain, and the corresponding magnitudes are denoted as DL . Then the two rows with the maximum numbers of the positive magnitudes of DL are chosen by the selector, and denoted as V1 and V2 . As for the right part, the original watermark W0 is represented in the LPM domain as the watermark data WL . Then WL is transformed into the DFT domain by using the approximative ILPM, and denoted as WI . The watermark data W which are the symmetric form of the WI in the DFT domain are derived by using the symmetry adjuster. Afterwards, the watermark W is transformed back into the LPM domain, and denoted as W′L . The two rows with the largest numbers of the positive magnitudes of W′L are found by the selector, and denoted as W1 and W2 . Then the correlation coefficients are computed as follows: Ci,j=ViWjT(ViViT)(WjWjT) (12) where i,j∈{1,2} . Note that all circularly shifted versions of Wj are tested for each Vi . Finally, if the maximum value of Ci,j exceeds a threshold, the existence of the watermark is confirmed. At the frequency filter, the frequencies in the high DFT frequencies and in the low DFT frequencies are filtered out since the watermark is embedded only in the middle frequencies. Those unwanted frequencies are marked as zeros. The corresponding magnitudes of the filtered frequencies, DL , are further transformed into the LPM domain. At the selector of the left part, the filtered frequencies FF are examined in the LPM domain, and the corresponding magnitude values which are less than the watermarking power a are changed to be zeros. Those zero-valued magnitudes are not considered in the following correlation computation. The thoughts are as follows. First, the proposed watermark is a sequence of positive integers which means the smallest value is 1 . According to the watermark embedding formula (Equation (11)), a quantity of multiples of the watermarking power a , a×W , is added to the magnitude. Since the DFT magnitude D is non-negative, the watermarked magnitude D′ and the watermarking power a have the following relation: D′=D+a×W≥a×W≥a . That is, a watermarked magnitude smaller than a does not contain the watermark data. Hence, such magnitudes are marked as zeros to denote the impossibility of containing the watermark. Therefore, for a watermarked row in the LPM domain, the row should contain non-zero values along the whole row. Furthermore, considering computational imprecision due to the sampling process, the rows with maximum numbers of non-zero magnitudes are chosen to be candidates for the watermarked row. Although more row candidates may get a higher detection rate, we find that choosing two rows is adequate according to the experimental experiences. In the embedding process, the original watermark data sequence W0 is transformed into the watermark data W by using the LPM representation, the approximative ILPM and the symmetry adjuster. It is the watermark data W that are embedded, rather than the original watermark data sequence W0 . In the extraction process, the embedded watermark data W which are inside the received image IR goes through the LPM, and then the watermark matching happens. That is, both the approximative ILPM and the LPM are applied to the original watermark data sequence W before the extraction action. Unlike the DFT and the IDFT, which are the inverse functions of each other, the approximative ILPM and the LPM do not undo what each other does. Actually, after the approximative ILPM followed by the LPM, the watermark data WL′ are a diffusion version of the watermark data WL . An example of such diffusion phenomena is shown from left to right in Fig. 6. At the left of Fig. 6, the watermark data A=1 are marked as a red circle in the LPM domain. After applying the approximative ILPM, the value 1 is distributed to the four DFT magnitudes which are marked as the red circles in the middle of Fig. 6. Note that these four magnitudes surround the corresponding position of A in the DFT magnitudes. Then the LPM is applied again to transform the DFT magnitudes back to the LPM domain by using the bilinear interpolation. Besides getting the original value 1 at the position A , extra values appear at some of the neighboring positions of A . It is the diffusion phenomenon caused by applying the approximative ILPM and the LPM. Figure 6. View largeDownload slide Diffusion phenomenon caused by approximative ILPM and LPM. From left to right: the data A=1 are marked as a red circle in LPM domain. After approximative ILPM, the value 1 is distributed to four DFT magnitudes marked as red circles surrounding corresponding position of A in DFT magnitudes. Then after LPM, extra values appear at neighboring positions of A . Figure 6. View largeDownload slide Diffusion phenomenon caused by approximative ILPM and LPM. From left to right: the data A=1 are marked as a red circle in LPM domain. After approximative ILPM, the value 1 is distributed to four DFT magnitudes marked as red circles surrounding corresponding position of A in DFT magnitudes. Then after LPM, extra values appear at neighboring positions of A . Because of the above described diffusion phenomenon, it can be realized that the extracted watermark data at the receiver site is the result of applying the approximative ILPM and then the LPM to the original watermark, rather than the original watermark. So in the proposed watermark extraction process, the original watermark stored at the receiver site is arranged to go through the same process which the extracted watermark experiences, namely the process of the approximative ILPM and then the LPM before joining the correlation computation with the extracted watermark data. That is, the diffusion phenomenon is the reason why the original watermark in the LPM domain is transformed into the DFT domain and then transformed back into the LPM domain as shown in the right part of Fig. 5. The lack of a strongly invariant transform to invert watermarked signals from the LPM domain back to the visual space is the main difficulty of utilizing the RST-resilient properties for watermarking [8]. One alternative proposed in [1] is to watermark the condensed image signals in the LPM domain, and then to distribute the watermarking effect to the LP transform of the image. So the effect of inverse LPM transform can be reduced. Another alternative proposed in [10] is watermarking the host signals in the DFT domain with the watermark inverted from the LPM domain alone. Then the watermark data are retrieved in the LPM domain by transforming the original image into the LPM domain. In this paper, a new approach, which is different from the state of the art [1, 8, 10], is proposed. The diffusion phenomenon of the embedded watermark is explored, and then is used to facilitate the use of the original watermark to detect the existence of the embedded watermark in the LPM domain. Such an approach makes it possible to correlate the original watermark and the embedded watermark in the LPM domain. 3. EXPERIMENTAL RESULTS The images in the USC-SIPI Image Database are utilized in the experiments (website: http://sipi.usc.edu/database/). The watermark is generated, embedded and detected by using the proposed approach described in Section 2. 3.1. False positive rate A false positive detection means the incorrect conclusion of a watermark detected in an un-watermarked image. Here this probability is determined by applying the detector to 12 un-watermarked images to test each for 1000 randomly selected watermarks. Figure 7a presents the histograms of the 12 sets results. It is shown that most detection values fall between 0.18 and 0.3 , and the values are actually the maximum detection value 1024 correlation coefficients calculated by cyclical search. Thus, Fig. 7b represents the histogram of all the 1.024×106 correlation coefficients computed for each of the 12 un-watermarked images. From Fig. 7, it is shown that these detection distributions are quite reasonable. Figure 7. View largeDownload slide Detection values from searches for 1000 watermarks in 12 un-watermarked images. (a) Histogram of maximum detection values of searching 1000 watermarks for each of 12 un-watermarked images. (b) Histogram of a total of 1.024×106 correlation coefficients computed for each of 12 images. Figure 7. View largeDownload slide Detection values from searches for 1000 watermarks in 12 un-watermarked images. (a) Histogram of maximum detection values of searching 1000 watermarks for each of 12 un-watermarked images. (b) Histogram of a total of 1.024×106 correlation coefficients computed for each of 12 images. The predicted false positive rate is plotted as a dotted-starred line in Fig. 8a. A theoretical model [11] is used to compute the reference curve of the false positive rate. It can be known that the false positive rate of the proposed approach agrees with the theoretical estimates [11]. Figure 8. View largeDownload slide False positive rates measured when searching for 1000 watermarks in 12 un-watermarked images: (a) individual correlation coefficients; (b) final detection value. (Each solid curve corresponds to one of 12 images. Dotted lines represent theoretical estimates [11].) Figure 8. View largeDownload slide False positive rates measured when searching for 1000 watermarks in 12 un-watermarked images: (a) individual correlation coefficients; (b) final detection value. (Each solid curve corresponds to one of 12 images. Dotted lines represent theoretical estimates [11].) 3.2. Fidelity In the proposed approach, the watermark is embedded in the middle frequencies of the DFT magnitudes, and that is the main factor of fidelity. Furthermore, fidelity is controlled by the watermark strength parameter a as well. The value of a increases, the robustness of the watermarked image increases at the expense of reduced fidelity. Based on our experimental experiences, the value of a is suggested to be 10 000. In the experiments, a total of 108 images are tested, including all the images in the misc and the texture directories in the USC-SIPI. The images have varied content from smooth to heavily textured. A number of 100 watermarks are generated randomly. Each watermark is embedded in each image, and the average signal-to-noise ratio (PSNR) and the average structural similarity (SSIM) are computed for each image. Among these images, the worst average PSNR is 26.18 , and the original image, the watermarked image, the difference image and the histogram of the difference image scaled by factor 10 are given in Fig. 9. The best average PSNR is 46.65 , and the original image, the watermarked image, the difference image scaled by factor 50 and the histogram of the difference image are given in Fig. 10. It can be found that both the watermarked images are quite recognizable, and the differences between the corresponding watermarked and original images are small. Furthermore, how the watermarks are spread out in the spatial domain can be seen in Figs 9c and 10c, respectively. Figure 9. View largeDownload slide Image with minimum PSNR=26.18 : (a) original image. (b) Watermarked image. (c) Difference image scaled up by factor 10. (d) Histogram of difference image. Figure 9. View largeDownload slide Image with minimum PSNR=26.18 : (a) original image. (b) Watermarked image. (c) Difference image scaled up by factor 10. (d) Histogram of difference image. Figure 10. View largeDownload slide Image with maximum PSNR= 46.65 : (a) original image. (b) Watermarked image. (c) Difference image scaled up by factor 50. (d) Histogram of difference image. Figure 10. View largeDownload slide Image with maximum PSNR= 46.65 : (a) original image. (b) Watermarked image. (c) Difference image scaled up by factor 50. (d) Histogram of difference image. The box plots for the average PSNR and the average SSIM are shown in Figs 11 and 12, respectively. The heavily textured images get higher PSNR’s and SSIM’s compared with the smooth images. The average PSNR is around 38 dB. Note that about 85% of the images are with the SSIM values above 0.99 . Overall speaking, the fidelity of the proposed approach is quite acceptable. Figure 11. View largeDownload slide Box plot for PSNR based on 108 images having varied content ranged from smooth to highly textured. Figure 11. View largeDownload slide Box plot for PSNR based on 108 images having varied content ranged from smooth to highly textured. Figure 12. View largeDownload slide Box plot for SSIM based on 108 images having varied content ranged from smooth to highly textured. Figure 12. View largeDownload slide Box plot for SSIM based on 108 images having varied content ranged from smooth to highly textured. 3.3. Effectiveness For watermarking approach, the effectiveness [1] means the probability of detection of the watermark when there are not any distortions applied after watermark embedding. Figure 13 shows the measured effectiveness of the current scheme based on 12 images. The red curve is the distribution of the detection scores of the un-attacked watermarked images. A total of 6000 randomly generated watermarks are tested to generate one red curve. Note that different sets of 6000 watermarks are used for different red curves. So these red curves are quite similar but not exactly the same. The blue curve represents the distribution of the detection scores of the attacked images. As shown in Fig. 13, the attacks include (a) rotation without cropping, (b) rotation with cropping, (c) scaling up without cropping, (d) scaling up with cropping, (e) scaling down, (f) translation without cropping and (g) translation with cropping [1]. An illustration of the attacks can be found in Fig. 14. For one specific parameter set of the attack, for example, a rotation of 5 degrees, a total of 6000 watermarks are tested. Figure 13. View largeDownload slide Illustration of effectiveness. Red and blue curves represent distributions of detection scores of un-attacked watermarked images and attacked images. Attacks include: (a) rotation without cropping, (b) rotation with cropping, (c) scaling up without cropping, (d) scaling up with cropping, (e) scaling down, (f) translation without cropping and (g) translation with cropping. Figure 13. View largeDownload slide Illustration of effectiveness. Red and blue curves represent distributions of detection scores of un-attacked watermarked images and attacked images. Attacks include: (a) rotation without cropping, (b) rotation with cropping, (c) scaling up without cropping, (d) scaling up with cropping, (e) scaling down, (f) translation without cropping and (g) translation with cropping. Figure 14. View largeDownload slide Examples of RST attacks: (a) padding original image. (b) Rotating image without cropping. (c) Scaling image up. (d) Translating image. (e) Original image. (f) Rotating image with cropping. (g) Scaling image up with cropping. (h) Scaling image down. (i) Translating the image with cropping. Figure 14. View largeDownload slide Examples of RST attacks: (a) padding original image. (b) Rotating image without cropping. (c) Scaling image up. (d) Translating image. (e) Original image. (f) Rotating image with cropping. (g) Scaling image up with cropping. (h) Scaling image down. (i) Translating the image with cropping. As shown in Fig. 13, the mode of effectiveness occurs at a score higher than 0.9 with a probability around 0.5 in all cases, and the shape of the distribution is peak-like. It can be said that the proposed watermark extraction method is effective. Furthermore, compared with the blue curves of the attacked images, the red curves of un-attacked images are narrower and higher, and located at larger scores. That is, the attacks distort the embedded watermarks, especially for the attacks of rotation with cropping and scaling up. The attacks of translation have the least effect. However, most areas of all the blue curves still located above the score of 0.8 . It again indicates that the proposed watermark extraction method is effective. 3.4. Robustness Seven kinds of geometric distortion attacks [1] related to rotation, scaling and translation are studied. The examples of these attacks can be found in Fig. 14. 3.4.1. Rotation Experiments were conducted to test the robustness of the watermark against rotation. The first involves distortion by rotation without cropping, and the second is the more realistic distortion of rotation with cropping. The first experiment involved 12 images and 1000 watermarks, rotations from 5° to 360° with a step size of 5°. Accordingly, a total of 72 angles were utilized for each pair of one image and one watermark. Figure 15a represents the distributions of the detection scores of the average, the best and the worst results among the 12 tested images. These three cases distribute similarly, and it means that the proposed approach performs consistently for different host images under rotation attacks. Most detection values are between 0.81 and 0.98. In Fig. 15b, the average curve of the attacked watermarked cases and the average curve of the attacked un-watermarked cases are shown to be separated by a large gap. The gap indicates that the area can be used to set the threshold for classifying the attacked watermarked images from the attacked un-watermarked images, for example, the midpoint of the area. That is, the proposed approach is robust to rotation attack. Figure 15. View largeDownload slide Illustration of robustness to rotation. (a) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of rotation without cropping, respectively. (b) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. (c) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of rotation with cropping, respectively. (d) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. Figure 15. View largeDownload slide Illustration of robustness to rotation. (a) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of rotation without cropping, respectively. (b) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. (c) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of rotation with cropping, respectively. (d) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. The second experiment involved the same conditions as the first, but with rotation with cropping. The experimental results are shown in Fig. 15c and d, cropping shifts all curves to the left a little bit. However, the overall performance of the two experiments is very similar. That is, the proposed approach works consistently and robustly under the attack of rotation with cropping as well. 3.4.2. Scaling Three experiments were performed to test robustness against scaling. The first and the second experiments elucidate the effects of scaling up with and without cropping, respectively, and the third elucidates the effects of scaling down. In the first experiment, the first steps were the first rotation steps, but with scaling up of the image. The first experiment involved 12 images and 1000 watermarks with up-scalings of the original image by 5%, 10%, 15% and 20%, yielding the results that are shown in Fig. 16a and b. Figure 16. View largeDownload slide Illustration of robustness to scaling. (a) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of scaling up without cropping, respectively. (b) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. (c) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of scaling up with cropping, respectively. (d) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. (e) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of scaling down, respectively. (f) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. Figure 16. View largeDownload slide Illustration of robustness to scaling. (a) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of scaling up without cropping, respectively. (b) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. (c) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of scaling up with cropping, respectively. (d) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. (e) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of scaling down, respectively. (f) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. The second experiment was the same as the first, except that no padding was used before scaling, so the image was cropped off after scaling. The experiment was performed under the same conditions as the first experiment, yielding the results in Fig. 16c and d. The third experiment involved a scale-down attack. The experiment involved 12 images and 1000 watermarks with scaling down of the original image by 5%, 10%, 15% and 20%, yielding the results in Fig. 16e and f. The results of scaling-up in Fig. 16b show that the detection values were in the range between 0.78 and 0.94, with two peaks at approximately 0.98 and 0.89. In Fig. 16d and f, most detection values both are between 0.89 and 0.98. Therefore, the scaling up without cropping yields the worst results, but the detection values remain in a reasonable range. These results are quite similar to those of the rotation attack discussed in Section 3.4.1. The figures represent similar distributions of the average, the best and the worst cases. That is, the proposed approach performs consistently under scaling attacks. Furthermore, large gaps still can be found between the average curves of the attacked watermarked cases and the average curves of the attacked un-watermarked cases. It indicates that classifying the attacked watermarked images from the attacked un-watermarked images can be easily done by setting the thresholds. So the proposed approach is robust to scaling attack. 3.4.3. Translation Two experiments were conducted to evaluate robustness against translation. The first experiment was similar to the first parts of the experiments with rotation and scaling, and then the tested image was translated by cropping some gray parts off the bottom and the right, before padding the top and left parts with gray. The experiment involved 12 images and 1000 watermarks with translations by 4–20% of the original image size with a step size of 2%. Figure 17a and b presents the results. Figure 17. View largeDownload slide Illustration of robustness to translation. (a) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of translation without cropping, respectively. (b) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. (c) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of translation with cropping, respectively. (d) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. Figure 17. View largeDownload slide Illustration of robustness to translation. (a) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of translation without cropping, respectively. (b) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. (c) Red, green and blue curves represent average, worst and best distributions of detection scores after attack of translation with cropping, respectively. (d) Large gap exists between curves of attacked un-watermarked images on the left and curves of attacked watermarked images on the right. The second experiment did not involve padding before the translation, so part of the watermark pattern was cropped during translation. The experiment was carried out under the same conditions as the first. Figure 17c and d shows the results. The results of these two experiments indicate that cropping slightly shifts the curves leftward and expands their separation, but the detection values remain above 0.93. These results are quite similar to those of the rotation attack and the scaling attack discussed in Sections 3.4.1 and 3.4.2 . That is, the similar distributions of the average, the best and the worst cases in the figures show the proposed approach performs consistently under translation. Besides, large gaps between the average curves of the attacked watermarked cases and the average curves of the attacked un-watermarked cases imply that setting thresholds to classify the attacked watermarked images from the attacked un-watermarked images is possible. That is, the detection of the watermark still performs consistently and robustly even after translation attack. Note that the ROC curves of the RST attacks from Figs 13 through 19 in Lin et al. [1] show that the true positive rates approach 100% with a relatively low false positive rate, for example, 10−3 . The comparable results can also be found in the proposed approach. Remember the gap between the curves of the attacked un-watermarked images and the attacked watermarked images from Figs 15 to 17. The gap indicates that the true positive rates are 100% if the false positive rates are larger than zero. Similarly, from Table I to Table IV in Zheng et al. [10], a large gap can also be found between the correlation coefficients of the attacked un-watermarked images and the attacked watermarked images. 3.4.4. JPEG compression JPEG compression is a common watermarking attack. Hence, a test of robustness against JPEG compression was also conducted. After the embedding stage, the watermarked images were compressed by JPEG at quality factors of 90, 80, 70, 60 and 50 using Equilibrium Debabelizer Pro [1]. The test was performed on 12 images with 1000 watermarks. Figure 18 reveals that the results are very good, because the embedding of watermarks in mid-range frequencies provides robustness against JPEG compression. Figure 18. View largeDownload slide Good visibility shows robustness against JPEG compression. The images are JPEG-compressed at quality factors of 100 (the original), 90, 80, 70, 60 and 50 from (a) to (f), respectively. Figure 18. View largeDownload slide Good visibility shows robustness against JPEG compression. The images are JPEG-compressed at quality factors of 100 (the original), 90, 80, 70, 60 and 50 from (a) to (f), respectively. 4. CONCLUSION AND FUTURE WORK Many watermarking methods are most vulnerable to geometric attacks. This work proposes an approach to authentication identification that applies LPM and ILPM to not only the DFT magnitude spectrum of a watermarked image but also the watermark, reducing the inherent instability cased by LPM. The experimental results reveal that the method is robust against rotations with or without cropping, scale changes with or without cropping, translations with or without cropping, and JPEG compression. The future work is suggested to improve the peak signal-to-noise ratio (PSNR) of the watermarked image. REFERENCES 1 Lin , C. , Wu , M. , Bloom , J. , Cox , I. , Miller , M. and Lui , Y. ( 2001 ) Rotation, scale, and translation resilient watermarking for images . IEEE Trans. Image Process. , 10 , 767 – 782 . Google Scholar Crossref Search ADS PubMed 2 Kutter , M. ( 1998 ) Watermarking Resistance to Translation, Rotation, and Scaling. In Proc. SPIE: Multimedia Systems Applications, Vol. 3528, pp. 423–431. 3 Voloshynovskiy , S. , Deguillaume , F. and Pun , T. ( 2000 ) Content Adaptive Watermarking Based on a Stochastic Multiresolution Image Modeling. In Proc. 10th European Signal Processing Conf. (EUSIPCO’2000), Tampere, Finland. 4 Shim , H.J. and Jeon , B. ( 2002 ) Rotation, Scaling, and Translation Robust Image Watermarking Using Gabor Kernels. In Proc. SPIE: Security and Watermarking of Multimedia Contents IV, San Jose, CA, Vol. 4675, pp. 563–571. 5 Voloshynovskiy , S. , Pereira , S. , Herrigel , A. , Baumgartner , N. and Pun , T. ( 2000 ) Generalized Watermark Attack Based on Watermark Estimation and Perceptual Remodulation. In Proc. SPIE: Electronic Imaging 2000, Security and Watermarking of Multimedia Content II, Vol. 3971. 6 Voloshynovskiy , S. , Deguillaume , F. and Pun , T. ( 2001 ) Multibit Digital Watermarking Robust Against Local Nonlinear Geometrical Distortions. In Proc. IEEE Int. Conf. Image Processing, Thessaloniki, Greece, Vol. 3, pp. 999–1002. 7 Kang , X. , Huang , J. , Shi , Y.Q. and Lin , Y. ( 2003 ) A dwt-dft composite watermarking scheme robust to both affine transform and jpeg compression . IEEE Trans. Circuits Syst. Video Technol. , 13 , 776 – 786 . Google Scholar Crossref Search ADS 8 Ruanaidh , J.J.K.O. and Pereira , S. ( 1998 ) A Secure Robust Digital Image Watermark. In SPIE Proc. Electronic Imaging: Processing, Printing and Publishing in Color, pp. 150–163. 9 Cox , I.J. , Kilian , J. , Leighton , F.T. and Shamoon , T. ( 1997 ) Secure spread spectrum watermarking for multimedia . IEEE Trans. Image Process. , 6 , 1673 – 1687 . Google Scholar Crossref Search ADS PubMed 10 Zheng , D. , Zhao , J. and Saddik , A. ( 2003 ) Rst-invariant digital image watermarking based on log-polar mapping and phase correlation . IEEE Trans. Circuits Syst. Video Technol. , 13 , 753 – 765 . Google Scholar Crossref Search ADS 11 Miller , M.L. and Bloom , J.A. ( 1999 ) Computing the Probability of False Watermark Detection. In Proc. 3rd Int. Workshop Information Hiding. © The British Computer Society 2018. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
The Computer Journal – Oxford University Press
Published: Nov 1, 2018
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