1. Introduction

Visual communication design mainly uses text, images, colors and other elements to convey information to the audience through visual media. Images, as a typical carrier of visual communication design, have been affected by the development of Internet technology in recent years, resulting in endless plagiarism and tampering of images. Especially with the popularity of image editing software, the threshold for plagiarism has been greatly reduced. After digital images have been tampered with by image editing software, the traces of tampering are difficult to discern with the naked eye, especially when used as a source of evidence, which greatly affects the public's judgment and creates great difficulties in the protection of intellectual property rights ^[1,2]. At the same time, the dispute caused by the tampering of digital images has caused the public trust crisis in multimedia data, and brought great challenges to digital security. Therefore, plagiarism and tampering detection of digital images has important legal significance. Currently common tampered image detection technologies include tampering detection based on non-overlapping sub-blocks and image features, image splicing detection based on bipolar signal interference, and image tampering detection based on illumination inconsistency. Among them, tampering based on non-overlapping sub-blocks and image features Detection is performed by comparing the pattern noise variance, signal-to-noise ratio, average energy gradient and information entropy of the original grayscale image. Image splicing detection based on bipolar signal interference uses phase features and bicoherent amplitude features. Detection; image tampering detection based on illumination inconsistency uses the difference in illumination models to detect. Although the above detection method can detect tampered images, its detection accuracy for tampered images processed by complex means is low, and it is difficult to resist the interference of original similar objects ^[3,4]. Therefore, in order to realize the accurate detection of tampered images and maintain digital security, a similar image detection model based on the improved KAZE algorithm and polar harmonic transformation is proposed. By checking the integrity and authenticity of digital images, it can effectively maintain the security of digital image information, ensure personal privacy and stabilize social order. Compared with the traditional detection method, the proposed image tampering detection method has the advantage of high detection accuracy, and can accurately locate the tampered area. This method innovatively improves the feature descriptor and similarity metric, expands the search radius of the algorithm, and implements the image plagiarism ensics with PHT.

The paper contains 4 parts. First, it is a literature review, which will briefly describe the related research on image tampering detection and KAZE algorithm; the second part will study the similar image detection model with the improved KAZE algorithm and PHT; the third part will study the similar image detection model with the improved KAZE algorithm. Test the similar image detection model with PHT and analyze its test results; the fourth part will summarize the research of the full text.

2. Related Works

Images are a typical carrier for transmitting information. With the rise and popularization of image processing software, more and more fake images have been processed and tampered with, making the authenticity of the information people receive questionable. Therefore, image tampering detecting a crucial task in the multimedia forensics. Yadav proposed an object tracking algorithm based on the improved vehicle detection, tracking and classification problem. The algorithm is tested on different video sequences and identifies objects in motion with minimal error rates compared to conventional frame difference methods ^[5]. Zhou and his team put forwards an image tampering detecting method with geometric correction and neural network to deal with the image manipulation detection. This algorithm performs geometric correction on the convolution feature map of the image through a spatial transformation network, and utilizes the residual feature map to capture the difference between the convolution feature map of each operation area and the geometrically corrected convolution feature map. This method can distinguish and locate areas with common tampering artifacts ^[6]. Yada evaluated the feasibility of emotion recognition by using principal component analysis, Gaussian mixed model, and support vector machine. The results show that the appearance confirmation has high rationality and feasibility in feasible applications such as monitoring and personal computer communication ^[7]. Karsh proposed a detection algorithm based on wavelet transform, discrete cosine transform and hash generated image mapping for the detection of tampered pictures. The algorithm first uses wavelet and discrete cosine transforming to construct a short hash, and then generates an image map through the hash to locate the tampered area. After testing, this algorithm can detect tampered areas, even if tampering and rotation-scaling-translation geometric transformation occur simultaneously ^[8]. Yadav et al. compared YOLO, SSD and R-CNN.result display. The R-CNN object detection technique outperformed the other methods in terms of accuracy, recall, accuracy, and loss ^[9].

The robustness of the KAZE algorithm's features is significantly better than other features when facing information disappearing, noise interfering, compressing and reconstructing. Compared with linear scale space, boundary blurring and details disappearing do not arise in Nonlinear Scale Space (NSS), which is more stable. Therefore, it is widely used in various fields. Songlin and his team proposed a NSS based on the high frame rate and ultra-low latency A-KAZE matching structure to reduce the delay of human-computer interaction systems and increase the frame rate. Part of the system's NSS is moved forward in time and computed in the previous frame, thus reducing the latency. The matching system's average matching accuracy is higher than 95% ^[10]. Soni et al. proposed a CBIR technology based on KAZE feature extraction, tree and random projection index to solve the problem of retrieval accuracy of CBIR system. This technology combines indexing after feature extraction, which greatly reduces retrieval time and memory ^[11]. Gafour and his team proposed a classification algorithm based on the A-KAZE algorithm for image classification problems. This algorithm adopts the spatial pyramid matching method and introduces spatial information to enhance its robustness. Compared with other algorithms, this algorithm improves the image classifying accuracy ^[12]. Li et al. proposed a watermarking means with accelerated KAZE discrete cosine transforming to deal with the low security of medical image information. AKAZE-DCT is utilized to extract the medical image's feature vector, combing a perceptual hashing technology to get the image's feature sequence. And logistic chaos scrambling encryption is performed on the image. This approach maked watermarks being extracted when facing attacks ^[13]. Wang et al. put forwards an image splicing means with spatial gradient feature blocks to solve the problem of slow underwater terrain image splicing speed. This algorithm uses the spatial gradient fuzzy C-means algorithm to divide the image's feature blocks, which are combined using A-KAZE to match the reference and target images. This approach effectively improves the splicing speed and reduces the sensitivity to noise ^[14].

In summary, there have been many research results on image tampering and plagiarism detection, but there are few studies on image plagiarism detection for visual communication design. Due to its unique advantages, the KAZE algorithm is widely utilized in image processing and detection. Therefore, in order to realize image plagiarism detection and identification and evidence collection for visual communication design, this study proposes a similar image detection model based on improved KAZE and PHT, to provide strong support for the intellectual property protection of visual communication design.

3. Methods

As a field involving art, design, color composition, three-dimensional composition, software design, etc., visual communication design has become a major difficulty in determining whether it constitutes plagiarism. Therefore, in order to accurately identify plagiarism in visual communication design, an image plagiarism detection model based on the improved KAZE algorithm was proposed.

3.1. Image Feature Extraction and Plagiarism Detection Algorithm with Improved KAZE Algorithm

In the identification of image plagiarism, image feature extraction is a very important step. The similarity of its features determines whether the image constitutes plagiarism. To extract and identify image features, a detecting algorithm with KAZE was proposed. Different from traditional feature extraction algorithms, the KAZE algorithm extracts features in a nonlinear space, and during the feature extraction process, the resolution of the KAZE algorithm is always consistent with the image ^[15]. The image scale parameter calculation equation of the KAZE algorithm is shown in Eq. (1).

(1)

$ \sigma _{i} (o,s)=\sigma _{0} 2^{(o+s)/S},\quad o\!\in\! [0,~\cdots ,~O-1],\nonumber\\ \hskip 4pc s\!\in\! [0,~\cdots ,~S-1],~i\!\in\! [0,~\cdots ,~N] . $

$\sigma _{i} (o,s)$ refers to the image's scale parameter in Eq. (1); $o$ refers to the image's group number; $s$ represents the layer number of the layer where the image is located; $\sigma _{0} $ refers to the scale parameter's base value; $N$ represents the total number of images. Due to the use of anisotropic diffusion in the KAZE algorithm, the diffusion equation parameters are based on time, but the scale parameters in equation (1) are measured in pixels, so it is necessary to convert the scale parameters. The conversion equation is shown in Eq. (2).

(2)

$ t_{i} =\frac{1}{2} \sigma _{i}^{2} ,~i\in \{0,~\cdots ,~N\}. $

In Eq. (2), $t_{i} $ represents the parameter conversion time of the diffusion equation. After the scale parameter conversion is completed, the image in this scale space is obtained utlizing AOS. The image calculation method is shown in Eq. (3).

(3)

$ L^{t+i} =\left(1-(t_{i+1} -t_{i} )\sum _{i=1}^{m}A_{l} (L^{i} ) \right)^{-1} L^{i}. $

In Eq. (3), $L^{t+i} $ represents the image in the scale space $t+i$; $I$ represents the input image; $A_{l} $ represents the image conductivity matrix in each dimension. The schematic diagram of feature point detection of KAZE algorithm is shown in Fig. 1.

Fig. 1. Characteristic point detection.

From Fig. 1, the KAZE algorithm is implemented by finding the Hessian determinant's local extreme values after normalization at different scales. For example, the x feature point in Fig. 1 compares the 8 pixels around the same layer with the 9 pixels in adjacent layers. When it is greater than or less than all adjacent points, the point is an extreme point. The KAZE algorithm uses the Hessian determinant to find key points, and the strategy for finding local maxima is basically the same as SIFT. Firstly, the pixel is judged within the neighborhood of the current layer image. If the value of the pixel is larger than that of the surrounding 8 pixels, it is then compared with the corresponding image in the previous and next layers. If the maximum requirement is met, it is retained as a key point. Then, the Taylor expansion in SIFT is used for sub-pixel localization. Eq. (4) is the sub-pixel positioning equation.

(4)

$ \left\{\begin{aligned} L(x)=L+\frac{\partial L}{\partial x} +\frac{1}{2} x^{T} \frac{\partial ^{2} L}{\partial x^{2} } x,\\ \hat{x}=-\left(\frac{\partial ^{2} L}{\partial x^{2} } \right)^{-1} \frac{\partial L}{\partial x}. \end{aligned}\right. $

In Eq. (4), $L(x)$ means the Taylor expression; $L$ represents the image; $x$ represents the feature point; $\hat{x}$ refers to the feature point's sub-pixel coordinate. The construction idea of KAZE characteristic tachyons is the M-SURF idea, which is the same as SURF when determining the main direction of the feature point. Fig. 2 presents the schematic diagram of KAZE to determine the direction of feature points.

Fig. 2. A schematic illustration of determining the orientation of the feature points.

In Fig. 2, if the feature point's scale parameter is $\sigma _{i} $, then the searching radius is $6\sigma _{i} $. Create a 60? sector area in the circular area and count the sum of Haar wavelet features in the sector area; then rotate the sector area and count the sum of Haar wavelet features again. The direction with the largest sum of wavelet features is the main direction. Taking the main direction as the reference direction, select the surrounding $24\sigma _{i} \times 24\sigma _{i} $ area and divide it into 4*4 sub-areas. The size of each sub-area is $9\sigma _{i} \times 9\sigma _{i} $, and the overlap width of adjacent sub-areas is $2\sigma _{i} $ ^[16,17]. Each sub-region is weighted using a Gaussian kernel. At this time, the description vector of the sub-region is shown in Eq. (5).

(5)

$ d_{v} =\left(\sum L_{x} ,~\sum L_{y} ,~\left|\sum L_{x} \right| ,~\left|\sum L_{y} \right|\right). $

In Eq. (5), $d_{v} $ refers to the sub-region's description vector; $L_{x} $ refers to the wavelet response's horizontal direction; $L_{y} $ represents the vertical direction of the wavelet response. After feature extraction is completed, feature matching can be performed. When performing feature matching, the KAZE algorithm is implemented through the Euclidean distance and Ratio methods. The feature matching process is shown in Fig. 3.

Fig. 3. Feature-matching process.

As can be seen from Fig. 3, feature points are first detected on the standard image and the image to be matched, and corresponding descriptors are generated; then the Ratio ratio method is used for rough matching, and RANSAC is used for precise matching, and finally the matching map is obtained. Although the KAZE algorithm's performance is better than other feature extraction methods, its computational workload is huge. Therefore, the study reduces the computational workload of the KAZE algorithm by improving its feature descriptor and similarity measure. First, expand the rest of the search radius by 2 times and divide it into 5 annular sub-regions. At this time, the widths of the sub-regions and overlapping bands are $4\sigma _{i} $ and respectively $\sigma _{i} $. The improved sub-region description vector is shown in Eq. (6).

(6)

$ d=\Big(\sum L_{x} ,~\sum L_{y} ,~\sum \left|L_{x} \right| ,~\sum \left|L_{y} \right| ,~\sum L_{xx} ,~\sum L_{yy} ,\nonumber\\ \qquad \sum \left|L_{xx} \right| ,~\sum \left|L_{yy} \right| \Big) . $

In Eq. (6), $L_{xx} $ and $L_{yy} $represent $L$ the second-order differential of the filtered image respectively. When performing feature matching to ensure the matching accuracy, this study uses approximate Euclidean distance for matching. The approximate Euclidean distance calculation equation is shown in Eq. (7).

(7)

$ \left\{\begin{aligned} L_{2} =\alpha (L_{1} +L_{\infty } ),\\ L_{1} (x,y)=\sum _{i=1}^{n}\left|x_{i} -y_{i} \right|,\\ L_{\infty } (x,y)={\max_{1\le i\le n}} \{|x_{i} -y_{i} |\},\\ \alpha =\left\{\begin{aligned} \left|\frac{2^{n} (n)!!}{2^{\frac{n+1}{2} } \pi ^{\frac{n-1}{2} (n+1)!} } \right|^{\frac{1}{n} } ,&\text{$n$ is an odd number},\\ \left|\frac{2^{n} \left(\frac{n}{2} \right)!}{\pi ^{\frac{n}{2} } (n+1)!} \right|^{\frac{2}{n} } ,&\text{$n$ is an even number}. \end{aligned}\right. \end{aligned}\right. $

In Eq. (7), $L_{1} $ represents the distance of another block; $L_{2} $ refers to the approximate Euclidean distance; $L_{\infty } $ refers to the checkerboard distance; $\alpha $ refers to the real number related to the dimension; $n$ refers to the dimension of the vector; $x_{i} $ and $y_{i} $ indicate the different description vectors, respectively. After the feature matching is completed, the tampered area can be located. The study uses ZNCC to calculate the disparity map to find overlapping areas. The tampering positioning equation is shown in Eq. (8).

(8)

$ \left\{\begin{aligned}. ZNCC\left(p,d\right)\\ =\frac{\left(\begin{aligned}&\sum _{q\in N_{p} }(I(q)-I_{age} (p))\\ \quad \times (T(q-p)-T_{age} (p-d))\end{aligned}\right) }{\sqrt{\left(\begin{aligned}&\sum _{q\in N_{p} }(I(q)-I_{age} (p))^{2}\\ \quad \times (T(q-p)-T_{age} (p-d))^{2}\end{aligned}\right)} },\\ I_{age} (p)=\frac{1}{N} \sum _{q\in N_{p} }I(q). \end{aligned}\right. $

In Eq. (8), $p$ and $q$ represent the elements in the matching point set respectively; $I$ represent the original image; $I_{age} $ represents the average pixel value of the original image; $T_{age} $ represents the transformed pixel mean; represent $T$ the transformed image.

3.2. Image Plagiarism Forensic Algorithm Based on PHT

Although the above-mentioned image plagiarism detection algorithm with the improved KAZE algorithm can realize the identification of tampered pictures, when the original similar graphics present in the picture have a high misjudgment rate, it is easy to identify it as copy-paste tampering. Therefore, to avoid the interference of original similar objects, this study proposes an image plagiarism forensics method with PHT to improve the improved KAZE algorithm's accuracy. Now assume that there is an image with a $M\times N$ size of $P\times P$ The image will be divided into several blocks at this time, and each sub-block will be subjected to polar coordinate harmonic transformation to obtain the invariant moment. The PCET moment of the image block in polar coordinates is shown in Eq. (9).

(9)

$ \left\{\begin{aligned} H_{nl} ft(r,\theta)=R_{n} (r)e^{il\theta } =e^{i2\pi nr^{2} } e^{il\theta }, \\ M_{nl} =\frac{1}{\pi } \int _{0}^{2\pi }\int _{0}^{1}\left[H_{nl} ft(r,\theta)\right]^{*} fft(r,\theta)rdrd\theta. \end{aligned}\right. $

In Eq. (9), $H_{nl} ft(r,\theta)$ represents the basis function; $n$ and $l$ are both integers, representing the order and degree of repetition respectively; $R_{n} (r)$ represents the pixel's radius in polar coordinates; $e^{il\theta } $ represents the pixel's angle in polar coordinates $M_{nl} $; represents the PCET moment of the image block; $fft(r,\theta)$ represents the image. The PCET moment does not change when scaling, so only the pixels within the unit circle domain are needed to calculate the PCET moment. The PCET moment calculation equation of digital images is shown in Eq. (10).

(10)

$ M_{nl} =\frac{1}{\pi MN} \sum _{x=0}^{M-1}\sum _{y=1}^{N-1}\left[H_{nl} (x,y)\right]^{*} f(x,y). $

In Eq. (10), $M\times N$ refers to the image size; $f(x,y)$ represents a digital image, namely, the pixel coordinates of the image. After obtaining the invariant moment, it is necessary to find similar blocks to achieve matching and positioning of the copy and paste area. In order to improve the search speed of similar blocks, research uses efficient block matching algorithms for search. The search process of the efficient block matching algorithm is shown in Fig. 4.

Fig. 4. The search process of the efficient block matching algorithm.

In Fig. 4, this efficient block matching method is divided into three steps, namely the initialization process, the propagation process and the search process. During the initialization process, the nearest neighbor will be initialized by random assignment, that is, a legal random value is assigned to the offset value in the nearest neighbor, and the mapping relationship of the image is randomly established. Banding is then performed to improve the nearest neighbor results. Each iteration scans the image in all directions to check for offsets and performs random search and propagation crossover operations. In the propagation process, a hierarchical prediction method is adopted, and in order to ensure non-deformation and propagation accuracy, the study increases the number of adjacent block offset values of the meta-block matching algorithm, and uses the adjacent block offset values to Correct the offset value of the target block. When scanning the image, the scheme of scanning from the lower right corner for odd numbers of times and the upper left corner for even numbers is adopted ^[18-20]. During the search process, to improve the search efficiency, this search strategy using two-dimensional Gaussian distribution is studied, that is, the closer the image block is to the target block, the higher the probability of being selected. The calculation equation of the probability of an image block being selected is shown in Eq. (11).

(11)

$ P_{z} =\frac{1}{2\pi \sigma ^{2} } e^{-(x^{2} +y^{2} )/(2\sigma ^{2} )},~x,~y\in [-u_{i} ,~u_{i} ],~x,~y\ne 0. $

In Eq. (11), $P_{z} $ represents the probability of the image block being selected; $u_{i} $ represents the search radius; $(x,y)$ represents the image block's coordinates. After completing the calculation of the offset domain, the offset domain needs to be normalized. The fitting equation of the offset domain is shown in Eq. (12).

(12)

$ \hat{\delta }(s_{i} )=As_{i} ,~i=1,~\cdots ,~N . $

In Eq. (12), $\hat{\delta }(s_{i} )$ represents the fitting bias domain; $A$ represents the transformation parameter; $s_{i} $ represents the neighborhood; $N$ represents the number of domains. The calculation equation of the sum of square errors and its minimization is shown in Eq. (13).

(13)

$ \left\{\begin{aligned} \varepsilon ^{2} (s)=\sum _{i=1}^{N}\left\| \delta \left(s_{i} \right)-\hat{\delta }\left(s_{i} \right)\right\| ^{2},\\ a^{opt} ={\mathop{\arg \min }\limits_{a}} \left\| \delta -Sa\right\| ^{2}.\ \end{aligned}\right. $

In Eq. (13), $\varepsilon ^{2} (s)$ represents the sum of squares error; $\delta \left(s_{i} \right)$ represents the real data of the neighborhood; $a^{opt} $ represents the minimized sum of squares error; $a$ refers to the parameter vector of the affine transformation; $\delta $ refers to the offset vector set; $S$ represents the homogeneous coordinate matrix of the neighborhood pixels. Since $a=\left[a_{0} ,a_{1} ,a_{2} \right]^{T} $, substitute the N * 3 matrix of homogeneous coordinates (13) to rewrite the fitting formula of the offset domain to formula (14).

(14)

$ \hat{\delta }(s_{i} )=a_{0} +a_{1} s_{i1} +a_{2} s_{i2} ,~i=1,~\cdots ,~N. $

In Eq. (14), $a_{0} $, $a_{1} $, and are $a_{2} $ all elements of the parameter vector of affine transformation. At this time, the sum of square errors is shown in Eq. (15).

(15)

$ \varepsilon ^{2} (s)=\left\| \delta -S(S^{T} S)^{-1} S^{T} \delta \right\| ^{2} =\left\| (1-H)\delta \right\| ^{2}\nonumber\\ =\delta ^{T} (1-H)\delta . $

In Eq. (15), $H=S(S^{T} S)^{-1} S^{T} $ and has idempotence and symmetry. If the neighborhood has a fixed shape, it $H$ has nothing to do with $s$. While the computational cost can be further reduced by splitting the $H$ matrix with rank 3. At this time, $H$ the calculation equation of the matrix and sum of square errors is shown in Eq. (16).

(16)

$ \left\{\begin{aligned} H=QQ^{T} ,~Q=\left[q_{1} ,~q_{2} ,~q_{3} \right],\\ \varepsilon ^{2} (s)=(\delta ^{T} \delta )-(\delta ^{T} q_{1} )^{2} -(\delta ^{T} q_{2} )^{2} -(\delta ^{T} q_{3} )^{2}. \end{aligned}\right. $

In Eq. (16), $q_{j} $ represents a column vector of length $N$. By introducing $q_{j} $, the number of filtering and product operations of the sum of square errors can be reduced. The algorithm flow of the KAZE-PHT similar image detection model is shown in Fig. 5.

Fig. 5. Algorithm flow of the similar image detection model.

In Fig. 5, the similar image detection method first performs feature point detection and feature point description on the standard image and the image to be detected respectively; then uses the ratio algorithm to perform rough matching, and uses the RANSCA algorithm to perform precise matching to obtain the matching image. Then perform polar harmonic transformation on the image and perform block matching; finally, post-processing is performed to obtain the output result.

4. Results and Discussion

To verify the performance of KAZE-PHT and whether the evaluation area can achieve accurate detection and localization of altered images, it was tested in this study and compared with FCM-EPO-BFM ^[21] and SR-KM ^[22]. The experimental environment is Inter Core i3-2350M CUP @2.3 GHZ 4.0 GB RAM, and the programming environment is Visual Studio 2010 and MATLAB R2014b. The experimental databases are Coverage and CoMoFoD. Coverage The database has 100 tampered images and 100 real images, including 16 simple translation operations, 16 zoom operations, 16 rotation operations and 16 arbitrary deformation, 16 light transformations and 20 integrated operations. Picture format is TIFF, color picture type, 458 * 158 ${\sim}$ 752 * 472. The JPEG compression factor of the CoMoFoD database is $[20$, $30$, $40$, $50$, $60$, $70$, $80$, $90$, $100]$, The mapping range of the luminance transform is $[(0.01$, $0.95)$, $(0.01$, $0.9)$, $(0.01$, $0.8)]$, the mean filter size is $[3\times 3$, $5\times 5$, $7\times 7]$, and the intensity level of each color channel is $[32$, $64$, $128]$. The evaluation index of the experiment are the detection accuracy and false detection speed, that is, the time required to identify the tampered picture. Table 1 is the number of characteristic points for the different algorithms.

According to Table 1, in the detection of different images, the KAZE-PHT algorithm has higher feature points than FCM-EPO-BFM and SR-KM algorithms. The feature points for tree detection are the highest, with the feature points for the three algorithms being 7254, 7179, and 7163, respectively. KAZE-PHT has higher accuracy in detecting images. The matching accuracy and matching time of different algorithms are shown in Fig. 6.

Fig. 6. Matching accuracy and matching time of different algorithms.

In Fig. 6(a), KAZE-PHT, FCM-EPO-BFM, and SR-KM algorithms' matching accuracy is highest at 98.6%, 82.8%, and 89.5%, respectively, and lowest at 97.5%, 91.6%, and 88.7%, respectively. The average accuracy is 98.1%, 92.5%, and 89.1%, respectively. The matching accuracy of KAZE-PHT is much higher than other algorithms. In Fig. 6(b), the three algorithms require 1.5 minutes, 2.3 minutes, and 2.6 minutes to match 10 images, and 14.6 minutes, 22.9 minutes, and 25.8 minutes to match 100 images, respectively. The average matching time for each image is 8.76 seconds, 13.74 seconds, and 15.48 seconds, respectively. From this, the image matching speed of KAZE-PHT is faster than other methods. The detection results of the blurred images by the KAZE-PHT algorithm are shown in Fig. 7.

Fig. 7. Detection results of the blurred images.

From Fig. 7, Fig. 7(a) is the original image, and Fig. 7(b) is the image obtained after blur processing. Fig. 7(b) is only blurred without any transformation. From Fig. 7(c), KAZE-PHT accurately identifies the tampered part of the image and locates its location. The above results show that the KAZE-PHT algorithm can accurately identify blurred images. This is because the study expanded the search radius of the KAZE algorithm by l2 times and divided it into five annular subregions, and ZNCC to perform the parallax map. The recognition accuracy and recognition speed of the KAZE-PHT algorithm and other algorithms on the CoMoFoD data set are shown in Fig. 8.

Fig. 8. Identification accuracy and speed of each algorithm on the CoMoFoD dataset.

From Fig. 8(a), the highest accuracy rates of KAZE-PHT, FCM-EPO-BFM and SR-KM are 99.3%, 89.3% and 86.7% respectively, and the lowest accuracy rates are 97.1%, 87.6% and 85.2% respectively, the average accuracy rates are 98.1%, 88.5% and 86.0% respectively. The accuracy of KAZE-PHT is much higher than other algorithms. From Fig. 8(b), KAZE-PHT, FCM-EPO-BFM and SR-KM require 1.8 min, 2.6 min and 2.9 min respectively when identifying 10 pictures, and 18.1 min when identifying 100 pictures respectively. min, 25.7 min and 28.8 min, the average recognition time of each picture is 10.86 s, 15.42 s and 17.28 s respectively. The image recognition speed of KAZE-PHT is faster than other methods. The above results show that in the CoMoFoD data set, the KAZE-PHT algorithm can quickly and accurately identify plagiarized images. This is because polar harmonic transformation has the characteristics of rotational invariance and orthogonality, and is also insensitive to conventional signal processing. Efficient block matching algorithms can obtain offset domain distributions, effectively improving recognition efficiency. The detection results of the KAZE-PHT algorithm on background tampered images in the Coverage database are shown in Fig. 9.

Fig. 9. Detection results of background tampered images.

Fig. 9(a) is the original picture. Fig. 9(b) is the picture after the background has been tampered with. Compared with the original picture, the background in Fig. 9(b) changes from day to night. From Fig. 9(c), KAZE-PHT accurately identifies the tampered background and locates its location. The above results show that the KAZE-PHT algorithm can accurately identify images with tampered backgrounds. This is because the polar harmonic transformation of each pixel block, adopts the efficient block matching algorithm, and adopts the search strategy of two-dimensional Gaussian distribution to improve the search efficiency. Fig. 10 is the detection results of real similar objects by KAZE-PHT.

Fig. 10. Detection results of real similar objects.

It can be seen from Fig. 10 that Fig. 10(a) is a real picture without any tampering, and contains two real objects with high similarity. Fig. 10(b) shows the detection result of SIFT feature matching. It can be seen that there are 4 similar points in the picture, and it was finally determined that the picture was tampered with. Fig. 10(c) presents the detection results of KAZE-PHT. The detection results are sparse noise points. After processing, they will not be judged as tampered images, but will be recognized as real images. In summary, KAZE-PHT can effectively combat the detection of real similar objects and reduce the false positive rate. The reason why the KAZE-PHT algorithm has high detection accuracy for similar objects is that it utilizes the advantage of the invariance of polar harmonic transformation moments, and combined with the proposed improved and efficient block matching method, it can effectively solve the problem of copying, pasting, and tampering detection of real similar objects. The recognition accuracy and recognition speed of the KAZE-PHT algorithm and other algorithms on the Coverage database are shown in Fig. 11.

Fig. 11. Identification accuracy and speed of each algorithm on the coverage database.

From Fig. 11(a), the highest accuracy rates of KAZE-PHT, FCM-EPO-BFM and SR-KM are 91.2%, 82.4% and 79.6% respectively, and the lowest accuracy rates are 89.5%, 81.1% and 78.3% respectively, the average accuracy rates are 90.3%, 81.7% and 79.0% respectively. The accuracy of KAZE-PHT is much higher than other algorithms. From Fig. 11(b), KAZE-PHT, FCM-EPO-BFM and SR-KM require 1.9 min, 2.8 min and 3.1 min respectively when identifying 10 pictures, and 19.1 min when identifying 100 pictures respectively. min, 27.5 min and 30.1 min, the average recognition time of each picture is 11.5 s, 16.5 s and 18.1 s respectively. The image recognition speed of KAZE-PHT is faster than other methods. In summary, KAZE-PHT can quickly and accurately identify plagiarized images in the Coverage database. In order to further explore the performance of the proposed KAZE-PHT algorithm in the study, it was compared with the recent Convnext-Upernet algorithm and the improved Faster R-CNN model to explore the proportion of correct matching key points of the three, and the comparison results are shown in Fig. 12.

Fig. 12. The proportion of correctly matching key points for each algorithm.

From Fig. 12, compared with improved Faster R-CNN and Convnext-Upernet, the KAZE-PHT algorithm is always higher than the other algorithms. Taking the pillow picture as an example, the proportion of correctly matching key points for KAZE-PHT, improved Faster R-CNN, and Convnext-Upernet were 0.51,0.42, and 0.44, respectively, with KAZE-PHT being at least 15.9% higher than other algorithms. The above results show that the KAZE-PHT algorithm can better detect the tampered images.

5. Conclusion

In visual communication design, images are an important way of expression. However, with the development and improvement of image processing software, the threshold for image tampering and plagiarism is getting lower and lower, posing a serious threat to the protection of intellectual property rights. The issue of image plagiarism identification has received widespread attention. Therefore, in order to realize the identification and evidence collection of tampered images, an image plagiarism identification model based on the improved KAZE algorithm and PHT was proposed and tested. Experimental results show that in the CoMoFoD database, the KAZE-PHT algorithm can accurately detect and locate the wear part of images modified by copy and paste, brightness tampering, and blur processing. Compared with the FCM-EPO-BFM algorithm and the SR-KM algorithm, the average accuracy and image recognition speed of the KAZE-PHT algorithm are 98.1% and 10.86 s/image respectively, which are better than other algorithms. In the Coverage database, the KAZE-PHT algorithm can accurately identify and locate images with background tampering, and can effectively resist interference from real similar objects. Compared with other algorithms, the KAZE-PHT algorithm has an average accuracy of 90.3% and an average recognition time of each picture of 11.5 s, both of which are better than other algorithms. The above results show that the KAZE-PHT algorithm proposed in the study can quickly and accurately identify tampered images and accurately locate the tampered parts. However, because the study only considers a single tampering method, the image detection effect of multiple tampering methods is poor. Therefore, future research will focus on developing detection algorithms that can counter hybrid post-processing operations.