Copy‐for‐duplication forgery detection in colour images using QPCETMs and sub‐image approach

IET Image ProcessingVolume 13, Issue 9 p. 1437-1446 Research ArticleFree Access Copy-for-duplication forgery detection in colour images using QPCETMs and sub-image approach Khalid M. Hosny, Corresponding Author Khalid M. Hosny k_hosny@yahoo.com orcid.org/0000-0001-8065-8977 Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig, 44519 EgyptSearch for more papers by this authorHanaa M. Hamza, Hanaa M. Hamza Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig, 44519 EgyptSearch for more papers by this authorNabil A. Lashin, Nabil A. Lashin Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig, 44519 EgyptSearch for more papers by this author Khalid M. Hosny, Corresponding Author Khalid M. Hosny k_hosny@yahoo.com orcid.org/0000-0001-8065-8977 Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig, 44519 EgyptSearch for more papers by this authorHanaa M. Hamza, Hanaa M. Hamza Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig, 44519 EgyptSearch for more papers by this authorNabil A. Lashin, Nabil A. Lashin Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig, 44519 EgyptSearch for more papers by this author First published: 18 June 2019 https://doi.org/10.1049/iet-ipr.2018.5356Citations: 12AboutSectionsPDF 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 Most of the existing copy-move forgery detection (CMFD) methods utilised time-consuming overlapped block-based approach. Here, a novel sub-image approach is proposed for extremely fast and highly accurate detecting of the duplicated forged objects in colour images. The proposed approach consists of few steps. The input coloured images are converted into the hue-saturation-value (HSV) colour model. Then, the edges of all objects in the forged image are detected using the Sobel operator. Morphological opening operator and median filter are used in removing unnecessary small objects. The boundaries of the duplicated objects are accurately detected. A bounding rectangle is drawn around the detected object to form a sub-image. The features of this sub-image are extracted by using the quaternion polar complex exponential transform moments (QPCETMs) and their invariants to rotation, scaling, and translation. Finally, the duplicated regions are matched via calculating the Euclidian distances and the correlation between the feature vectors. Experiments are performed using different types of duplicated regions. The obtained results of the proposed method are much accurate when compared with the results of the existing methods. Also, the proposed method exhibits high robustness against different attacks such as additive white Gaussian noise, JPEG compression, scaling, and rotation. 1 Introduction The rapid development in digital cameras makes capturing of the digital images much easier. This development is supported by image-editing Software. With minimum experience, peoples can capture, edit, alter, and falsify the truth in the digital images. Therefore, there is a need to detect the changes in the digital images. As a result, digital image forgery detection becomes a very interesting research area. Digital image forgery detection techniques are classified into: active and passive [1]. The active techniques such as adding a watermark while creating the input image, which can be used to detect tampering if happen. The drawback of this methodology is that a watermark must be interleaved at the time of image acquisition. It limits this approach to specially equipped digital cameras. Moreover, there are millions of digital images uploaded to the Internet without watermarks or digital signatures. So, in such scenario, active approaches are not feasible to find the authenticity of these images [2]. In passive techniques, tampering includes data hiding or displaying incorrect information. Detection of these changes does not need any prior information about the image. It assumes that these forgeries leave no visual traces; it might alter the statistical properties of the image. Therefore, passive approaches try to detect tampered regions blindly without the support of an embedded security scheme [3, 4]. Copy-move forgery is one of the common passive forgery techniques for digital images. In such techniques, a specific part of an image is copied and shifted to another part of the same image so that forgers can hide or duplicate some part of the image [5]. Copy-move forgery is classified according to its purpose into two different categories, namely: copy for duplication and copy for hiding. Warif et al. [6] classified the types of copying regions into background, object, creature, and letter. Therefore, these types have been added to the copy for duplication category. The first category is considered the interest area of the proposed method. Three main steps constitute the skeleton of the most recent passive copy-move forgery detection (CMFD) methods. In the first step, the input image is divided into a number of small-size overlapped blocks. In the second step, image features with some invariant properties are extracted for each block and stored as a feature vector. In the third step, a matching method is applied to determine the similarity between the feature vectors. Additional post processing step is done to localise the forged region in the image and to check the accuracy of the CMFD method [7, 8]. Huang et al. [9] developed an improved discrete cosine transform (DCT)-based method for CMFD. In their method, the image is divided into fixed-size overlapped blocks and then, the features of each block are extracted by using the DCT. In order to reduce the execution times of sorting and matching, Huang and his co-authors further reduced the dimension of the features by truncation. Muhammad et al. [10] proposed a dyadic wavelet-based CMFD method. The input image is decomposed into approximated (LL1) and detailed (HH1) sub-bands. Then, the LL1 and HH1 sub-bands are divided into overlapping blocks where the similarity between blocks is calculated. Li [11] proposed another CMFD method. In this method, the image is divided into overlapping circular blocks. Features are extracted from these blocks using polar cosine transform (PCT). Potential copy-move pairs are then detected by identifying the blocks with similar features which is formulated as approximate nearest neighbour searching and accomplished by means of locality-sensitive hashing (LSH). Finally, post-verifications are performed on potential pairs to filter out false matches and improve the accuracy of forgery detection. Zhao and Guo [12] proposed a robust method based on DCT and SVD. Their method consists of three main steps. First, the input image is divided into fixed-size overlapped blocks where the DCT is applied to each block, and then the DCT coefficients are quantised by a quantisation matrix. Second, each quantised block is divided into non-overlapped sub-blocks and SVD is applied to each sub-block, then features are extracted to reduce the dimension of each block using its largest singular value. Third, the feature vectors are lexicographically sorted and duplicated image blocks are matched by predefined shift frequency threshold. Recently, Emam et al. [13] utilised the approximated polar complex exponential transform moments (PCETMs) to detect the copy-move forgery in grey-scale images. Evaluation of this method shows three main disadvantages. First, the method [13] is very time-consuming due to the implementation of the overlapped block-based approach in which the input image is divided into overlapped blocks. Second, the utilisation of approximated PCETMs results in inaccurate features which led to inaccurate forgery detection under geometric transforms. Third, Emam and his co-authors limit their work by grey-scale images. Wang et al. [14] utilised quaternion exponent moments (QEMs) to detect the copy-move forgery in colour images. They overcome the third disadvantage of [13] but unfortunately, encountered the first and second problem. In order to compute QEMs, Wang et al. [14] employed an approximated method which results in a set of inaccurate features. Wang et al. used overlapped circular block instead of the traditional Cartesian block-based approach which is very time-consuming. It is observed that, the common approach in most of existing CMFD methods is dividing the input digital images into overlapping square or circular blocks, and then extract the features from each block to form its feature vector. For a digital image of size , this step will produce blocks, where , is the size of divided blocks [9]. In most existing methods, small values of B are favourable to avoid any information loss. Such selection generates a very large number of blocks which results in a very time-consuming process. Also, these existing moments employed inaccurate feature in the similarity step which results in inaccurate similarity and inaccurate detection of duplicated objects. These fatal drawbacks motivate the authors to present the novel sub-image approach. Two major contributions are presented here. First, a novel sub-image approach is proposed for detecting the duplicated forged objects in colour images. In this approach, a simple pre-processing scheme including edge extraction and object detection is employed to accelerate the detection process. Second, highly accurate quaternion polar complex exponential transform moments (QPCETMs) are utilised to extract highly accurate features. These moments are invariants to rotation, scaling, and translation which meant that the extracted features are unchanged even with rotation of resize of the duplicated objects. The prosed sub-image approach is simple, highly accurate and very fast copy-move duplicate detection. Also, the proposed method shows a high robustness to different attacks such as additive white Gaussian noise, JPEG compression, rotation, and scaling. The remainder of the paper is structured as follows: QPCETMs and their invariants are briefly described in Section 2. In Section 3, the proposed sub-image approach for CMFD is presented. Different datasets are described in Section 4. In Section 5, a detailed description of the performed numerical experiments is presented. Also, the obtained results are discussed. Finally, a conclusion and future work are presented in Section 6. 2 Quaternion polar complex exponential transform The quaternion was defined by Hamilton [15] as a generalisation of the complex number, where q has three imaginary and one real components as follows: (1)where , , and are imaginary units and a, b, c, and d are real numbers. A colour image, , can be represented by using pure quaternion as follows [16]: (2)where and represent the red, green, and blue components of the colour pixel, respectively. The right-side QPCETMs for the RGB colour image, , in polar coordinates are defined as follows: (3)where is called a unit pure quaternion. 3 Proposed method The proposed method has two major contributions. First, a new pre-processing approach called sub-image approach is proposed. In this approach, the conventional time-consuming overlapping block approach is completely ignored. The duplicated forged objects are detected and localised as sub-images. The invariant features are extracted for the sub-images. The extracted features are stored in a vector format. These vectors of features with different similarity distances are used in searching for similar objects. This novel approach significantly reduces the computational times. Second, utilising highly accurate QPCETMs and their rotation, scaling, and translation (RST) invariants achieves highly accurate detection results. It exhibits high robustness against various attacks such as additive white Gaussian noise, JPEG compression, rotation, and scaling. The proposed method consists of eight steps, these steps are explained in the following sub-sections. 3.1 Pre-processing The first main pre-processing step is the colour conversion. The input coloured image is converted into the hue-saturation-value (HSV) colour model. The hue (H) of a colour refers to which pure colour it resembles. All tints, tones, and shades of red have the same hue. Hues are described by a number from 0° to 360° degrees, starting at the red primary at 0°, passing through the green primary at 120° and the blue primary at 240°, and then enfolding back to red at 360°. The saturation (S) of a colour describes how white the colour is. A pure red is fully saturated, with a saturation of 1; tints of red have saturations <1; and white has a saturation of 0. The value (V) of a colour, also called its lightness, describes how dark the colour is. A value of 0 is black, with increasing lightness moving away from black [17]. Our experiments show that representation of the input colour image using the HSV's third plane gives better results than converting the input coloured image to the corresponding grey one. After getting HSV's third plane for the input image, auto-contrast adjustment operation is performed to increase the contrast of the input image by remapping the data values to fill the entire available intensity range. After these steps, the pre-processed input image is ready to detect the main edges. 3.2 Edge detection Sobel operator emphasises regions of high spatial frequency that corresponding to the edges in the image [18]. Typically, it is used to find the approximate absolute gradient magnitude at each point in an input grey-scale image. 3.3 Removing unnecessary small objects The unnecessary small noisy objects are removed using the following two consecutive sub-steps: 3.3.1 Morphological opening operation is performed This operator is employed to preserve foreground regions that have an area larger than a predefined value A, while eliminating all other regions of foreground areas smaller than A. Through the different experiments, the predefined value A is determined by 200 pixels. 3.3.2 Median filter usually does double jobs Preserving the useful details (edges) in the processed image is the first job, while removing noise is the second job. This filter is applied to improve the results of later processing steps. By completing this process, main objects in the input image are determined. 3.4 Determine boundaries of the detected objects The exterior boundary of each detected object is determined to precisely localised each object in the input image. To achieve this, we starting with any boundary points of the determined object and traced the exterior boundary in the clockwise direction using 8-connectivity. The stating point is used as initial point for the 8-connectivity process where the gradient is computed to find the next point on the exterior boundary of the object. The selected point is used as initial point for the next 8-connectivety. This process is repeated until we reached the starting point and then we determined a close exterior boundary of the determined object. The exterior boundary is highlighted by red colour. 3.5 Draw a bounding box around each detected object Each detected object with determined exterior boundary will be enclosed inside a rectangle. Each created rectangle is a sub-image. The positions of all pixel points on the exterior boundary of the object, , are sorted in ascending order where the two pixels with the greatest values of which we called, , , and the two pixels with the smallest values of which we called, , are used to determine the four corners, (, ), (, ), (, ) and, (, ) of a rectangle. For each detected object, the determined four corners are utilised to form a bounding box surrounding the detected object which constitute a sub-image. 3.6 Feature extraction For each coloured sub-image, the features of this sub-image are extracted by the low-order QPCETMs. We utilised the exact method of Hosny and Darwish [19] to compute the QPCETMs for orders from 0 to 15. Since the QPCETMs are defined in polar over a unit circle. The unit circle is divided into non-overlapped circular rings. Each of these circular rings is divided into a set of non-overlapped circular sectors of the same area where each sector is represented by one point in its centre. The right-hand side QPCETMs defined by (3) is rewritten in the following from: (4)Where the integration is performed with: (5) (6)The lower and upper limits of the definite integrals in (5) and (6) are expressed as follows: (7) (8)For the input image the radial distance of circular ring is , where and . The values of the angle can be created using the following pseudo-code. where The definite integrals in (5) and (6) are exactly computed for and as follows: (9) (10)where (11) (12)The interpolated function, , of the colour image could rewritten as follows: (13)The interpolated image functions , , and are deduced from the original colour image using the method of cubic interpolation [20]. Invariant to rotation, scaling, and translation are essential properties in CMFD. The QPCETMs are rotationally invariant where: (14)where represents the function of the rotated image and denotes the rotation angle. Both and are the QPCETMs of and f, respectively. Highly accurate scaling and translation QPCETMs invariants were derived in [19]. 3.7 Matching step (search for similar objects) In this step, the similarity between the feature vectors is measured using the Euclidian distance as defined by (15) and the correlation coefficient as defined by (16). The Euclidean distance (ED) is used to calculate the distance between the feature vectors. If the value of ED approaches zero, this means that the determined objects are very similar and then they are duplicated objects. Correlation coefficient is used to measure how strong a relationship is between the two feature vectors. If the calculated value is near to one, it refers to duplicated objects. (15) (16) 3.8 Post-processing Finally, robustness of the proposed method is tested against various post-processing attacks such as additive white Gaussian noise, JPEG compression, rotation, and scaling. 4 Dataset The proposed approach has been tested and evaluated using a dataset containing different types of tampered images, which have duplicated objects. This dataset contains 100 coloured images of size 512 × 512 and divided into two subsets. The first subset contains 50 original images that are selected from the dataset in [21] as displayed in Fig. 1. In the second subset, the authors collect 50 non-forged images and use the Adobe Photoshop CC 2015.5 to create a copy-move duplication with the three types, objects, creatures, and letters. The 50 forged images are displayed in Fig. 2. Fig. 1Open in figure viewerPowerPoint First set Fig. 2Open in figure viewerPowerPoint Second set 5 Results and discussion This section is divided into three sub-sections. Evaluation parameters are described in the first sub-section. Detailed description of the different experiments is presented in the second sub-section. The validity of the proposed method is proved and its accuracy in detecting the copy-move forgery from the coloured images is assessed. The experiments are performed in two fashions; pure copy-paste forgery detection and the duplicating forgery detection in presence of different attacks such as additive Gaussian noise, JPEG compression, scaling, and rotation. The performance of the proposed method is compared with the other existing methods [22-25]. Finally, the computational complexity and the computational times are reported in the third sub-section. 5.1 Performance evaluation Three measures are used to evaluate the performance of the proposed method and the existing methods: 5.1.1 Precision Denotes the proportion of predicted positive cases that are correctly real positives. (i.e. detect objects that are already forged) (17) 5.1.2 Recall Is the proportion of real positive cases that are correctly predicted positive. (i.e. the proportion of returned objects which are detected as forged from all the objects that are already forged) (18)Parameters used here are as follows [26]: True positive : indicates the number of blocks correctly classified as cloned in the detection map. False positive : indicates the number of blocks wrongly classified as cloned in the detection map. False negative : represents the number of cloned blocks, which are classified as authentic. 5.1.3 Score Is a compound measure for the accuracy of forgery detection. It considers both the precision p and the recall r. (19) 5.2 Numerical experiments Two series of experiments are performed to validate the proposed method at image-level and at pixel-level, respectively. Fig. 3 illustrates the proposed validation technique. First, we need to get a binary decision, or in other words, we need to generally decide if the input image is tampered or not. The process is performed using the input coloured image in the image-level. The steps from 3.1 to 3.5 of the proposed method are applied to the input coloured image till drawing a bounding box around each detected object. According to the size of the bounding box, it is easy to generally decide the input coloured image is tampered or not. Fig. 3Open in figure viewerPowerPoint Proposed validation technique Second, if the input colour image is tampered, it will go through the next test at the pixel-level to detect the duplicated object. In this phase, the steps from 3.6 to 3.8 are applied where the features of each sub-image are computed and then the similarity process is performed to detect the duplicated objects accurately and highlight them. 5.2.1 Detection results at image level We start the first test at image level on the two datasets of images. The first dataset consistsof 50 original images (un-tampered images), and the second set consists of50 tampered images. Subsequent experiments examine the effect of differentpost-processing attacks on the duplicated tempered objects. The experimentalresults at image level are shown in the following sub-sections. (A) Plain copy–move: In this sub-section, thefirst experiment (I) is performed. One sample image is selectedfrom the first set of the original images to show the accuracyof the proposed method in detecting if the input image iscopy-move tampered or not. The results of applying the fivesteps (from 3–1 to 3–5) are visualised and displayed inFig. 4. The experiments show that theproposed method can detect the original and the tampered imageswith Score equal 99.5%. Fig. 4Open in figure viewerPowerPoint Experiment (I): Proposed method in steps (B) Robustness to Gaussian noise: The proposedmethod is tested to validate its robustness to additive Gaussiannoise. We followed the same test method as in [27]. The image intensitiesare normalised between 0 and 1, where the zero-mean Gaussiannoise with standard deviations of 0.02, 0.04, 0.06, 0.08, and0.10 are added to the duplicated tampered objects. Theduplicated objects in the tested images are detected by usingthe proposed method and the other existing methods [22-25]. The obtained results for precision andrecall are plotted and displayed in Figs. 5a and b,respectively. It is clear that, the proposed method achieves thebest performance where both precision and recall percentagesapproach the maximum. On the other side, the existing methods[22-25] are sensitive to thedifferent level of noises. Fig. 5Open in figure viewerPowerPoint Robustness to Gaussian noise and robustness to JPEG atimage level (a), (b) Robustness to Gaussiannoise at image level, (c), (d)Robustness to JPEG at image level (C) Robustness to JPEG compression: We testedthe robustness of the proposed algorithm against JPEGcompression at nine different quality levels 100, 90, 80, 70,60, 50, 40, 30, and 20%. Figs. 5c and d show theprecision and the recall percentages. The proposed method provesits robustness to JPEG against and better performance than theother existing methods [22-25] forall the quality levels. (D) Scale-invariance: The proposed method istested under resizing effect. In this experiment, the duplicatedobject is rescaled at different levels. Its size is reduced bythe following percentages 91, 93, 95, 97, and 99% and magnifiedby the following percentages 120%, 200% Figs. 6a andb show precision and recall results,respectively. It is obvious that the proposed method achievedthe scale invariance with all the percentages reduction andmagnification with consistent results. On the other side, allother existing methods [22-25] failedto achieve the scale invariance for most reduction andmagnification. Fig. 6Open in figure viewerPowerPoint Scale-invariance and rotation-invariance at imagelevel (a), (b) Scale-invariance at imagelevel, (c), (d)Rotation-invariance at image level (E) Rotation-invariance: In the last experiment,the rotation invariance is tested. The duplicated object isrotated by an angle ranging between 2° and 10°, in steps of 2°,and with three larger rotation angles, 20°, 60° and 180°.Precision and recall percentages are shown in Figs. 6c andd, respectively. The proposed method showsthe highest level of precision and recall results. All othermethods [22-25] show bad results exceptthe method [22] whichshows good results. 5.2.2 Results of detection at pixel level In this sub-section, the accuracy of the features is calculated at the pixel level which mean that these experiments are performed to evaluate how a duplicated object can be detected accurately. Instead of classifying the image as tampered or not, we focused on the images which are determined to be tempered. Here, the second level of the proposed method is presented to determine accurately the duplicated object location in the tampered coloured images. The experimental results at pixel level are shown in the following sub-sections. Plain copy–move: Experiments are performed to assess the accuracy of the proposed method in the plain cop-move at which no post-processing operations are applied on the duplicated tempered objects. Another experiment is performed and visualised step by step in Detection Results at Image Level We start the first test at image level on the two datasets of images. The first dataset consists of 50 original images (un-tampered images), and the second set consists of 50 tampered images. Subsequent experiments examine the effect of different post-processing attacks on the duplicated tempered objects. The experimental results at image level are shown in the following sub-sections. Plain copy–move: In this sub-section, the first experiment (I) is performed. One sample image is selected from the first set of the original images to show the accuracy of the proposed method in detecting if the input image is copy-move tampered or not. The results of applying the five steps (from 3–1 to 3–5) are visualised and displayed in Fig. 4. The experiments show that the proposed method can detect the original and the tampered images with F1 Score equal 99.5%. Robustness to Gaussian noise (F) The proposed method is tested to validate its robustness to additive Gaussian noise. We followed the same test method as in [27]. The image intensities are normalised between 0 and 1, where the zero-mean Gaussian noise with standard deviations of 0.02, 0.04, 0.06, 0.08, and 0.10 are added to the duplicated tampered objects. The duplicated objects in the tested images are detected by using the proposed method and the other existing methods [22-25]. The obtained results for precision and recall are plotted and displayed in Figs. 5a and b, respectively. It is clear that, the proposed method achieves the best performance where both precision and recall percentages approach the maximum. On the other side, the existing methods [22-25] are sensitive to the different level of noises. Robustness to JPEG compression We tested the robustness of the proposed algorithm against JPEG compression at nine different quality levels 100, 90, 80, 70, 60, 50, 40, 30, and 20%. Figs. 5c and d show the precision and the recall percentages. The proposed method proves its robustness to JPEG against and better performance than the other existing methods [22-25] for all the quality levels. Scale-invariance: The proposed method is tested under resizing effect. In this experiment the duplicated object is rescaled at different levels. Its size is reduced by the following percentages 91, 93, 95, 97, and 99% and magnified by the following percentages 120%, 200% Figs. 6a and b show precision and recall results, respectively. It is obvious that the proposed method achieved the scale invariance with all the percentages reduction and magnification with consistent results. On the other side, all other existing methods [22-25] failed to achieve the scale invariance for most reduction and magnification. Fig. 7. The experiments show that the proposed method can detect the duplicated tampered objects in images with Score equal 99.5%. Additional experiments are performed to evaluate the accuracy of the proposed method in detecting the duplicated tempered objects in different cases of post-processing attacks. Fig. 7Open in figure viewerPowerPoint Experiment (II): Proposed method in steps Robustness to Gaussian noise: In the experiment, the image intensities are normalised between 0 and 1 and a zero-mean Gaussian noise with standard deviations of 0.02, 0.04, 0.06, 0.08, and 0.10 is added to the duplicated tampered objects. The resulted values of the precision and recall are displayed in Figs. 8a and b, respectively. These results show that the proposed method achieve the highest precision and recall when compared with the other existing methods [22-25]. Fig. 8Open in figure viewerPowerPoint Robustness to Gaussian noise and robustness to JPEG at pixel level (a), (b) Robustness to Gaussian noise at pixel level, (c), (d) Robustness to JPEG at pixel level Robustness to JPEG compression: The robustness of the proposed method against JPEG compression at different quality levels varied between 100% and 20 in steps of 10. The proposed method achieves a high precision and recall rates at all quality levels as displayed in Figs. 8c and d. Scale-invariance: In this experiment, the duplicated object is rescaled with scaling ratios. In addition to aggressive scaling with percentages, 50, 80, 120, and 200% from original size, slight scaling with the percentage between 91 and 109% with step of 2%. The obtained results of the precision and recall are displayed in Figs. 9a and b, respectively. Fig. 9Open in figure viewerPowerPoint Scale-invariance and rotation-invariance at pixel level (a), (b) Scale-invariance at pixel level, (c), (d) Rotation-invariance at pixel level The proposed method achieves high accuracy at all scaling percentages. It shows stable behaviour even with the extreme scaling percentages 50 and 200%. On the other side, the results of the other existing methods [22-25] are extremely bad for aggressive and slight scaling. Rotation-invariance: In the last experiment, the rotation invariance of the proposed method and the other existing methods [22-25] is tested. The duplicated object is rotated in the counter clockwise direction with angles between 2° to 10°, in steps of 2° in addition to three larger rotation angles, 20°, 60° and 180°. The precision and recall percentages are displayed in Figs. 9c and d. The proposed method shows the best performance for all rotation angles. 5.3 Computational times Complexity analysis and the computational execution times for the proposed method and the other existing [22-25] methods are reported in this subsection. Since the existing methods utilise the overlapped block-based approach to detect the duplicated regions, counting the total number of blocks in entire computational process is imperative. On the other side, the proposed method utilised the novel sub-image approach, in which the objects are enclosed within bounding boxes with different size. Therefore, we determined the size accurately as discussed in step (3.5). Three experiments are performed with non-forged colour image and two forged colour images using the proposed method and the other existing methods [22-25]. The number of sub images in the proposed method depends on the content of the image, while the number of blocks in the existing methods is predefined by the user, so, different block size is used for more clarification as shown in Table 1. Table 1. No. of blocks processed by using the existing previous method [22-25] vs. the proposed method The existing methods [22-25] The proposed method Block size No. of blocks Block size No. of Sub images Experiment (I): original image. 16 × 16 247,009 92 × 10944 × 7768 × 71 3 24 × 24 239,121 32 × 32 231,361 64 × 64 201,601 Experiment (II): Tampered image. 16 × 16 247,009 71 × 10474 × 10747 × 10819 × 2235 × 55 5 24 × 24 239,121 32 × 32 231,361 64 × 64 201,601 The underlined block size values correspond to the duplicated tempered sub-images. Table 1 shows that for the existing block-based methods [22-25], the smallest number of blocks in one image is 201,601. The features are extracted from each one of these bocks. Also, the similarity is tested between these blocks. This process is extremely time-consuming. On the other side, for the same image, the proposed method detects three sub-images. The features are extracted for these three sub-images. The size of the detected sub-images is very close to the size of the blocks in the block-based approach. It is easy to see the huge different in the execution times of the proposed sub-image method and the block-based existing methods. Similar results are obtained for the other two images. Table 2 shows the execution times for these three experiments. The programs of the proposed method and the other existing methods [22-25] are coded using Matlab 2013 and executed by Core i5 Sony Vaio machine operated with Window 8. Table 2. Computation time in seconds: these values belong to Experiment (II) Method Computation time, seconds proposed QPCETMs sub-image approach 14.45 PCET [13] 129,364.02 QEM [14] 1,006,756.48 zernike [22] 26,399.92 hu [23] 123,182.54 DCT [24] 122,278.50 DWT [25] 122,445.77 For image size = 128*128, block size = 16* 16, and #of blocks = 12769. 6 Conclusion Copy-move forgery is one of the common forgery techniques. A new method for detecting duplicated objects from the coloured images is presented. This method is based on detecting the main objects in the input coloured image constituting sub-images, extract QPCETMs features, and then match their values to detect the duplicated tampered objects. The proposed method has been verified by experimental results using 100 test images through two series of experiments. First, the proposed method is tested for its ability to distinguish tampered images from the original ones. Second, if the input image is determined to be tampered the experimental results show that the proposed method can detect the duplicated objects in the tampered image efficiently. The proposed method is much faster than the other similar existing methods with more accuracy rates. Future work will concentrate on comparing the proposed method accuracy by feature-based methods like scale invariant feature transform (SIFT). 7 Acknowledgments The authors would like to thank Dr. Mohamed M. Darwish for his helpful comments on this manuscript. The authors would also like to thank the anonymous reviewers for their constructive comments and suggestions for raising the value of the paper. 8 References 1Singh R., and Kaur M.: 'Copy move tampering detection techniques: a review', Int. J. Appl. Eng. Res., 2016, 11, (5), pp. 3610– 3615 2Nandini A.M.S.C.: 'Investigational study of image forensic applications, techniques and research directions', Int. J. Emerg. Technol. Adv. Eng., 2014, 4, (8), pp. 2250– 2259 3Gupta A., Saxena N., and Vasistha S.: 'Detecting copy move forgery using DCT', Int. J. Sci. Res. Publ., 2013, 3, (5), pp. 3– 6 4Redi J., Taktak W., and Dugelay J.-L.: 'Digital image forensics: a booklet for beginners', Multimedia Tools Appl., 2011, 51, (1), pp. 133– 162 5Kaur G., and Kumar M.: 'Study of various copy move forgery attack detection techniques in digital images', Int. J. Res. Comput. Appl. Robot., 2015, 3, (9), pp. 30– 34 6Warif N.B.A. et al: 'Copy-move forgery detection: survey, challenges and future directions', J. Netw. Comput. Appl., 2016, 75, pp. 259– 278 7Deoli M., and Joshi J.: 'A fast and robust approach to detect copy-move forgery in digital images', Int. J. Comput. Appl., 2016, 137, (5), pp. 29– 33 8Sekhar R., and Chithra A.: 'Recent block-based methods of copy-move forgery detection in digital images', Int. J. Comput. Appl., 2014, 89, (8), pp. 28– 33 9Huang Y. et al: 'Improved DCT-based detection of copy-move forgery in images', Forensic Sci. Int., 2011, 206, (1), pp. 178– 184 10Muhammad G., Hussain M., and Bebis G.: 'Passive copy move image forgery detection using undecimated dyadic wavelet transform', Digital Invest., 2012, 9, (1), pp. 49– 57 11Li Y.: 'Image copy-move forgery detection based on polar cosine transform and approximate nearest neighbour searching', Forensic Sci. Int., 2013, 224, (1), pp. 59– 67 12Zhao J., and Guo J.: 'Passive forensics for copy-move image forgery using a method based on DCT and SVD', Forensic Sci. Int., 2013, 233, (1), pp. 158– 166 13Emam M., Han Q., and Niu X.: 'PCET based copy-move forgery detection in images under geometric transforms', Multimedia Tools Appl., 2016, 75, (18), pp. 11513– 11527 14Wang X.Y., Liu Y.N., and Xu H. et al: 'Robust copy–move forgery detection using quaternion exponent moments', Pattern Anal. Appl., 2018, 21, (2), pp. 451– 467 15Hamilton W.R.: ' Elements of quaternions' ( Longmans, Green, & Company, London, 1866) 16Hosny K.M., and Darwish M.M.: 'Accurate computation of quaternion polar complex exponential transform for colour images in different coordinate systems', J. Electron. Imaging, 2017, 26, (2), pp. 1– 17 17Agoston M.K.: ' Computer graphics and geometric modeling' ( Springer-Verlag London, London, 2005) 18Gonzalez R.C., and Woods R.E.: ' Digital image processing' ( Addison-Wesley, Pearson, 2007, 3rd edition), ISBN-13: 978-0131687288 19Hosny K.M., and Darwish M.M.: 'Highly accurate and numerically stable higher order QPCET moments for colour image representation', Pattern Recognit. Lett., 2017, 97, pp. 29– 36 20Hosny K.M., Shouman M.A., and Salam H.M.A.: 'Fast computation of orthogonal Fourier–mellin moments in polar coordinates', J. Real-Time Image Process., 2011, 6, (2), pp. 73– 80 21Ardizzone E., Bruno A., and Mazzola G.: 'Copy–move forgery detection by matching triangles of keypoints', IEEE Trans. Inf. Forensics Sec., 2015, 10, (10), pp. 2084– 2094 22Ryu S.-J., Kirchner M., and Lee M. et al: 'Rotation invariant localization of duplicated image regions based on zernike moments', IEEE Trans. Inf. Forensics Sec., 2013, 8, (8), pp. 1355– 1370 23Wang J., Lui G., and Zhang Z. et al: 'Fast and robust forensics for image region-duplication forgery', Acta Autom. Sin., 2009, 35, (12), pp. 1488– 1495 24Fridrich A.J., Soukal B.D., and Lukáš A.J.: ' Detection of copy-move forgery in digital images'. in Proc. of Digital Forensic Research Workshop, 2003, Citeseer 25Bashar M. K., Noda K., and Ohnishi N. et al: 'Exploring duplicated regions in natural images', IEEE Trans. Image Process., 2010, 1, pp. 1– 40 26Powers D.M.: 'Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation', Int. J. Mach. Learn. Technol., 2011, 2, (1), pp. 37– 63 27Christlein V., Riess C., and Jordan J. et al: 'An evaluation of popular copy-move forgery detection approaches', IEEE Trans. Inf. Forensics Sec., 2012, 7, (6), pp. 1841– 1854 Citing Literature Volume13, Issue9July 2019Pages 1437-1446 FiguresReferencesRelatedInformation