Image Copy-Rotation-Translation Forgery Detection Method Based on Gegenbauer Orthogonal Polynomials

Abstract

The present invention discloses an image copy-rotation-move forgery detection method based on Gegenbauer orthogonal polynomials. Two new sets of orthogonal polynomials are designed according to the parity of Gegenbauer polynomials, regularized and complex Fourier factors are added to obtain a new type of orthogonal moment. Then, using the phase shift property of orthogonal moments in the polar coordinate system, rotation invariant moments are designed, the image is divided into blocks and mapped to the feature space, and the multi-dimensional tree algorithm is used to establish a K-nearest neighbor index structure for the features to obtain the potential forgery regions of the image. Then, the regions that are accidentally similar due to spatial proximity and feature randomness during the image block division process are removed, and finally the forgery regions in the image are obtained. The present invention has effective detection and positioning functions for "copy-move" and "copy-rotation-move".

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and particularly relates to a method for detecting forgery of image copy-rotation-movement. Background Art

[0002] Facing the rapid development of digital image processing technology, digital images have the advantages of large amount of information, intuitiveness and concreteness, and have become one of the most important ways of digital information transmission. How to identify the originality and authenticity of a digital image has become an urgent problem in the academic community. We urgently need to technically achieve accurate and professional identification of the authenticity and integrity of images to enhance the credibility of digital images. Therefore, studying methods for detecting image forgery has important practical significance.

[0003] Currently, the forgery detection methods for digital images mainly include two major branches: active forensics technology and passive forensics technology. Generally, image tampering operations roughly include copy-movement, splicing, resampling, and JPEG (Joint Photographic Experts Group) compression, etc. Especially after the above operations, further processing is carried out through methods such as splicing, rotation, blurring, and compression mixing. Due to the advancement and complexity of image tampering operations, it is more difficult to visually distinguish whether an image has been modified. Among them, active forensics technology usually includes three steps: watermark encoder, transmission, and watermark decoder. This requires adding prior information to the picture in advance, with a huge workload. Passive forensics technology can be further divided into image source forensics and image content forensics. The former judges whether an image has been tampered with by detecting whether the image comes from the same imaging device. Obviously, this method is effective for splicing tampering of different images, but ineffective for copy-movement tampering of the same image; while the latter judges whether an image has been tampered with by relying on the features extracted from the digital image itself. This method has a wide application range, few limiting conditions, and significant effects on copy-movement tampering of the same image.

[0004] In terms of the selection of image feature descriptions, currently, there are many feature descriptors, such as Fourier descriptors, SIFT transforms, Histogram of Oriented Gradients (HOG), invariant moments, etc. Among many feature description methods, orthogonal moments have the advantages of being able to extract global features of targets, being easy to design, and having invariant features that are irrelevant to various geometric deformations and linear operations. Therefore, they are widely applied to the fields of pattern recognition and computer vision. Summary of the Invention

[0005] To overcome the deficiencies of the prior art, the present invention provides an image copy-rotation-move forgery detection method based on Gegenbauer orthogonal polynomials. Two new sets of orthogonal polynomials are designed according to the parity of Gegenbauer polynomials, regularized and complex Fourier factors are added to obtain a new type of orthogonal moment. Then, using the phase shift property of the orthogonal moment in the polar coordinate system, rotation-invariant moments are designed, the image is divided into blocks and mapped to the feature space, and a K-nearest neighbor index structure is established for the features using the multi-dimensional tree algorithm to obtain the potential forgery regions of the image. Then, the regions that are accidentally similar due to spatial proximity and feature randomness during the image block division process are removed, and finally the forgery regions in the image are obtained. The present invention has effective detection and positioning functions for "copy-move" and "copy-rotation-move".

[0006] The technical solutions adopted by the present invention to solve its technical problems include the following steps:

[0007] Step 1-1: Design orthogonal moments based on Gegenbauer polynomials, and the Gegenbauer polynomials are defined by the generating function:

[0008]

[0009] Among them, the coefficient polynomial is called the Gegenbauer polynomial of order n with parameter α. The Gegenbauer polynomial is an orthogonal polynomial defined on the interval (-1,1), and its orthogonality is mathematically expressed as follows:

[0010]

[0011] mn where Γ(α) represents the Gamma function, δ

[0012] Step 1-2: According to the parity of Gegenbauer polynomials, we get:

[0013]

[0014] Equation (3) shows that all odd-order Gegenbauer orthogonal polynomials are mutually orthogonal; all even-order Gegenbauer orthogonal polynomials are mutually orthogonal. At the same time, the orthogonal interval is converted from (-1,1) to (0,1);

[0015] Step 1-3: Define the normalized Gegenbauer polynomial:

[0016]

[0017] The normalized Gegenbauer polynomial not only has orthogonality but also has regularity. The mathematical representation of its orthogonality is as follows:

[0018]

[0019] Steps 1 - 4: Use the radial Gegenbauer polynomial as the radial function and define the Fourier factor in the complex domain as the phase angle part. Its mathematical form is as follows:

[0020]

[0021] where V pq (r, θ) represents the basis function of the Gegenbauer - Fourier moment in the polar coordinate system, i is the imaginary unit, represents the normalized Gegenbauer polynomial of order p in the polar coordinate system, r ∈ (-1, 1) represents the radial distance in the polar coordinate system, θ ∈ [0, 2π] represents the polar axis in the polar coordinate system, and q represents the repetition rate of the Fourier factor;

[0022] Correspondingly, the Gegenbauer - Fourier moment h pq maps the image function to the basis function space defined in Equation (6):

[0023]

[0024] The "*" symbol represents taking the conjugate complex number, and f(r, θ) represents the original image function in the polar coordinate system;

[0025] Since the Gegenbauer - Fourier moment has orthogonality, the original image is reconstructed by a series of Gegenbauer - Fourier moments, that is:

[0026]

[0027] where, represents the reconstructed image in the polar coordinate system, and P max represents the maximum order of the polynomial used for reconstruction;

[0028] Step 2: Design rotation - invariant moments using the phase - angle division method;

[0029] Let represent the image of f(x, y) rotated by angle, represent the Gegenbauer - Fourier moment calculated for the image f(x, y); The phase - shift property is expressed as:

[0030]

[0031] Equation (9) indicates that the value of the Gegenbauer-Fourier moment of the rotated image differs from that of the original image only by an exponential term determined by the rotation angle; the modulus of the Gegenbauer-Fourier moment remains unchanged, and only the phase angle changes;

[0032] Therefore, rotation-invariant moments are designed using the phase-shift property:

[0033]

[0034] where h pq and h mn are Gegenbauer-Fourier moments of two different orders;

[0035] The image is divided into blocks and mapped to the feature space through rotation-invariant moments;

[0036] Step 3: Elements adjacent to each other in the image feature space are potential replication regions; using the multi-dimensional tree method as the implementation algorithm and the K-nearest neighbor retrieval method, find the similar features of the copy-rotation-move regions in the image feature space to determine the potential forgery regions;

[0037] Step 4: Determine the forgery regions;

[0038] For each feature in the image feature space, perform a nearest neighbor search using the method in Step 3 to obtain K matching points; whether these matching points correspond to replication regions requires excluding two types of situations:

[0039] First: Exclude the feature similarity caused by spatial proximity during the image block division process;

[0040] This feature similarity is caused by the spatial proximity during the image block division process, resulting in a large amount of the same information in two blocks, rather than being caused by artificial forgery or modification; if the image blocks B1(i,j) and B2(k,l) are adjacent in space, then their corresponding features are also similar. Exclude this misjudgment situation by calculating the Euclidean distance:

[0041]

[0042] where D min is the minimum distance threshold in the original space;

[0043] Second: Exclude the accidental similarity caused by the randomness of features;

[0044] If the features of the image blocks B1(i,j) and B2(k,l) are similar, then their features V B1 (i,j) and V B2(k, l) needs to satisfy the following formula:

[0045]

[0046] Among them, M max is the threshold of the maximum distance in the feature space;

[0047] After excluding the similar regions that meet the above two situations, the remaining feature-similar regions are the forged regions in the image to be found.

[0048] Furthermore, in the K-nearest neighbor retrieval method, K is a parameter set in advance. When any sample X to be classified needs to be classified, this method calculates the feature distance between X and the training samples, so as to select the K training samples corresponding to the nearest distances, and determines the category of X according to the classification situations of these training samples;

[0049] In the process of comparing the sample X to be classified with the training samples, the corresponding distance is adopted for the measurement between features:

[0050]

[0051] Among them, X and Y are vectors containing N elements; p is a constant. When p = 1, d(X, Y) is the Manhattan distance; when p = 2, d(X, Y) is the Euclidean distance;

[0052] The multi-dimensional tree method is adopted as the implementation algorithm of the K-nearest neighbor retrieval method; the process of the multi-dimensional tree method is: first, a dimension is selected to divide the space, and then the space is divided into two parts with this dimension; the entire space is divided into two sub-spaces by a hyperplane; and so on, until each sample point in the data set is processed; finally, the K-dimensional space is divided into multiple sub-spaces by the hyperplanes passing through all sample points in the data set, and a tree structure is established; the multi-dimensional tree transforms the data set of N elements into a binary tree structure with logN layers, and on this basis, similar features are searched to determine potential forged regions.

[0053] The beneficial effects of the present invention are as follows:

[0054] 1. As the features of the image, Gegenbauer-Fourier moments have good image representation ability. This can be clearly seen from the reconstruction results of Gegenbauer-Fourier moments for the original image.

[0055] 2. The Gegenbauer polynomial, which is the basis function of the orthogonal moment designed in the present invention, is an orthogonal polynomial. Each type of orthogonal polynomial supports calculation through a recurrence formula, which makes the calculation of rotation-invariant moments very convenient. Secondly, mapping the target image to the orthogonal basis further reduces the information redundancy between orthogonal moments of different orders. This is extremely beneficial for the design of features.

[0056] 3. The present invention realizes an image automatic forgery detection technology, which has effective detection and positioning functions for "copy-move" and "copy-rotate-move". BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 The original image cameraman for reconstruction in the embodiment of the present invention.

[0058] Figure 2 This is a comparison chart of image reconstruction results of different orthogonal moments in the embodiment of the present invention. The maximum orders of the reconstructed images from left to right in the figure are 16, 36, 56, and 76 orders respectively.

[0059] Figure 3 The artificial image lena randomly rotated in the embodiment of the present invention.

[0060] Figure 4 The Gegenbauer-Fourier invariant moment values of the artificial image lena in the embodiment of the present invention.

[0061] Figure 5 This is a forged detection result chart of "copy-rotate-move" for the artificial image Hermite in the embodiment of the present invention.

[0062] Figure 6 This is a forged detection result chart of "copy-rotate-move" for the artificial image cameraman in the embodiment of the present invention.

[0063] Figure 7 This is a forged detection result chart of "copy-rotate-move" for the images in the CMFD dataset in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0064] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0065] An image copy-rotate-move forgery detection method based on Gegenbauer orthogonal polynomials includes the following steps:

[0066] Step 1: Design of orthogonal moments;

[0067] Step 1-1: The present invention designs orthogonal moments based on Gegenbauer polynomials, and the Gegenbauer polynomials can be defined by a generating function:

[0068]

[0069] Coefficient polynomial It is called the Gegenbauer polynomial of order n with parameter α. Obviously, the Gegenbauer polynomial is an orthogonal polynomial, defined on the interval (-1, 1), and its orthogonality is mathematically expressed as follows:

[0070]

[0071] where Γ(α) represents the Gamma function, and δ mn represents the Kronecker function.

[0072] Step 1-2: According to the parity of the Gegenbauer polynomial, we can obtain:

[0073]

[0074] The above formula shows that all odd-order Gegenbauer orthogonal polynomials are mutually orthogonal; all even-order Gegenbauer orthogonal polynomials are mutually orthogonal. At the same time, the orthogonal interval is converted from (-1, 1) to (0, 1).

[0075] Step 1-3: When using orthogonal moment design for feature description, the common practice for basis functions is to regularize them, that is, to define the regularized Gegenbauer polynomial:

[0076]

[0077] The regularized Gegenbauer polynomial not only has orthogonality but also has regularity, and the orthogonality is maintained and strengthened. Its orthogonality is mathematically expressed as follows:

[0078]

[0079] Step 1-4: Use the radial Gegenbauer polynomial as the radial function and define the Fourier factor in the complex domain as the phase angle part. Its mathematical form is as follows:

[0080]

[0081] where i is the imaginary unit. Correspondingly, the Gegenbauer-Fourier moment maps the image function to the basis function space defined by the above formula:

[0082]

[0083] The "*" symbol represents taking the conjugate complex number. Since the Gegenbauer-Fourier moments are orthogonal, the original image can be reconstructed by a series of Gegenbauer-Fourier moments, that is:

[0084]

[0085] Step 2: Design of rotation invariant moments

[0086] The present invention uses the phase angle division method to design rotation invariant moments. denotes the image after rotating the image f(x, y) by angle, denotes the Gegenbauer-Fourier moment calculated for the image f(x, y). The phase shift property can be expressed as:

[0087]

[0088] The above formula shows that the value of the Gegenbauer-Fourier moment of the rotated image and the value of the original image only differ by an exponential term determined by the rotation angle. The modulus of the Gegenbauer-Fourier moment does not change, only the phase angle changes. Therefore, using the phase shift property, we can design rotation invariants:

[0089]

[0090] where h pq and h mn are two Gegenbauer-Fourier moments of different orders. The rotation invariant moment features designed in this way not only achieve rotation invariance but also retain the phase angle information of the moments in the invariants, enhancing the discrimination ability of the invariants.

[0091] Step 3: K-nearest neighbor retrieval

[0092] The image is mapped in the feature space, and the features in the "copy-rotate-move" area are highly similar. Therefore, the K-nearest neighbor (KNN) retrieval method is used to find similar features and determine potential forgery areas.

[0093] In the K-NN algorithm, K is a parameter set in advance. When any sample X needs to be classified, the algorithm calculates the feature distance between X and the training samples, selects the nearest K training samples corresponding to the distances, and determines the category of X according to the classification of these training samples.

[0094] During the comparison process between the sample X to be classified and the training samples, the corresponding distance, such as the Minkowski distance or the Euclidean distance, is used as the metric between the features.

[0095]

[0096] Among them, X and Y are vectors containing N elements. p is a constant. For example, when p = 1, the Minkowski distance is the Manhattan distance; p = 2 corresponds to the Euclidean distance.

[0097] In the present invention, the K-NN algorithm is not used for classification. The main purpose of using this algorithm is to find potential neighboring elements, and these elements that are adjacent to each other in the feature space are potential replication regions. Therefore, the present invention uses this algorithm to search for and locate potential replication regions.

[0098] The present invention adopts the multi-dimensional tree method as the implementation algorithm of K-NN. The process of the multi-dimensional tree algorithm is as follows: In the division of the space, first select a certain dimension, and then divide it into two parts with this dimension. The entire space is divided into two sub-spaces by a hyperplane at a certain value of this dimension. And so on, until each sample point in the data set is processed. Finally, the K-dimensional space is divided into multiple sub-spaces by the hyperplanes passing through all sample points in the data set, and a tree structure is established. The multi-dimensional tree transforms the data set of N elements into a binary tree structure with logN layers. On this basis, the search range is greatly reduced, and the search efficiency is improved. We can quickly search for similar features through this structure and determine potential forgery regions.

[0099] Step 4: Determination of forgery regions

[0100] After the index structure of the image feature space is established, for each feature therein, a nearest neighbor search in the space is performed to obtain K matching points. Whether these matching points correspond to replication regions still needs to exclude two types of situations.

[0101] First, the feature similarity caused by spatial proximity during the image block division can be excluded. This feature similarity is caused by the spatial proximity during the image block division, which in turn causes a large amount of the same information in two blocks, rather than being caused by deliberate forgery or modification. Obviously, if the image blocks B1(i,j) and B2(k,l) are adjacent in space, then their corresponding features also have great similarity. We can exclude this misjudgment situation by calculating the Euclidean distance:

[0102]

[0103] Among them, D min As the threshold of the minimum distance in the original space.

[0104] Second, the accidental similarity caused by the randomness of features also needs to be excluded. Different functions are mapped to a finite invariant moment feature space, and there is a certain probability that two features are similar. If the features of image blocks B1(i,j) and B2(k,l) are similar, then their features and need to satisfy the following formula:

[0105]

[0106] where M max is the threshold of the maximum distance in the feature space.

[0107] After excluding the similar regions in the above two cases, the remaining similar feature regions are the forged regions in the image we are looking for. Specific embodiments:

[0109] Embodiment 1: The Gegenbauer-Fourier moments of the present invention have good image representation ability, which can be illustrated by the image reconstruction method. Image reconstruction is a classic method for detecting the image representation ability of moments and orthogonal moments. All along, before selecting orthogonal moments as the feature description method, reconstruction based on orthogonal moments can be adopted, and the difference between the target image and the reconstructed image is compared to evaluate the image representation ability of the orthogonal moments. In this embodiment, the image reconstruction based on Gegenbauer-Fourier moments is used to evaluate the image representation ability of the selected features. The quality of the reconstructed image is measured by the Normalized Mean Square Error (NMSE). The definition of NMSE is as follows:

[0110]

[0111] where H and W respectively represent the height and width of the image in pixels, I represents the original image, and I P represents the reconstructed image generated when the maximum order is P.

[0112] Figure 1 The gray image cameraman with a size of 256*256 is used as the test image this time. Theoretically, the stronger the feature description ability, the closer the reconstructed image is to the original image, and the smaller the NMSE value; the greater the difference between the reconstructed image and the original image, the larger the NMSE value, indicating the worse the feature description ability.

[0113] Figure 2 Figure shows the comparison of the image reconstruction results of different orthogonal moments. The maximum orders of the reconstructed images from left to right in the figure are 16, 36, 56, and 76 orders respectively.

[0114] Visually, the images reconstructed by Gegenbauer-Fourier moments have the best effect among all orthogonal moments and are closest to the original images, and the corresponding NMSE values also support this fact. The error values and the quality of the reconstructed images together indicate that Gegenbauer-Fourier moments have the best image representation ability, and this kind of orthogonal moment meets the primary condition for being a feature.

[0115] Example 2: Verification of rotational invariance.

[0116] In this example, the designed rotation-invariant feature was tested and verified. First, a 256*256 grayscale image lena was subjected to a rotation transformation. The original image and the rotated images are as Figure 3 shown. The original image was randomly rotated under a unified background to obtain 8 test images. Figure 4 shows the values of 6 invariant moments corresponding to these 9 images. It can be seen that Figure 4 all the curves of [the invariant moments] almost become straight lines, indicating that each invariant moment has almost the same value for different rotated images. Thus, it shows that the Gegenbauer-Fourier moments designed by the present invention have rotational invariance.

[0117] Example 3: Results of image anti-counterfeiting detection.

[0118] Artificial images were tested using the most common test images in the field of image processing, namely the two grayscale images Hermite and cameraman. The size of these images is 256*256 pixels and the resolution is 8 bits.

[0119] The process of establishing a forged image is as follows: (1) Select an original image and arbitrarily select a circular area on the original image. (2) Rotate the selected circular area by an arbitrary angle. (3) Paste the result at an arbitrary position on the original image. The above is the production process of a "copy-rotate-move" forgery. Figure 5 and Figure 6 show the artificial images with forged areas and the detection results.

[0120] In the test of the image anti-counterfeiting public dataset, the "CMFDBenchmark Data" image forgery detection dataset of Friedrich-Alexander-Universität Erlangen-Nürnberg is selected. This dataset contains different types of forged images and corresponding original images. For example, the suffix "O" represents the original image, "F" represents the forged image, "B" represents the binary filtering operation, "JC" represents the JPEG compression, "IB" represents the use of blurring, "CR" represents the color weakening, "CA" represents the contrast adjustment, "BC" represents the brightness change, etc. The present invention mainly aims at the forgery form of "copy-rotate-move". This kind of forgery mainly corresponds to the images with the suffix "F". Finally, it is statistically found that the CMFD dataset contains a total of 40 images of this type of forgery. These images are tested and evaluated in this embodiment. From Figure 7 It can be seen that this embodiment can accurately detect the copied area. Considering the actual situation where the forgery type is unknown, in this case, a circular area is used for feature extraction so as to be able to detect the "copy-rotate-move" forgery area in the image at the same time. Therefore, the detected copied areas are all in the form of superposition of arc-shaped edges.

Claims

1. An image copy-rotation-move forgery detection method based on Gegenbauer orthogonal polynomials, characterized in that It includes the following steps: Step 1-1: Design orthogonal moments based on Gegenbauer polynomials, and the Gegenbauer polynomials are defined by the generating function: Among them, the coefficient polynomial is called the nth-order Gegenbauer polynomial with parameter α. The Gegenbauer polynomial is an orthogonal polynomial defined on the interval (-1, 1), and its orthogonality is mathematically expressed as follows: where Γ(α) represents the Gamma function, δ mn represents the Kronecker function, and m represents the order of the Gegenbauer polynomial;; Step 1-2: Obtain according to the parity of Gegenbauer polynomials: Equation (3) shows that all odd-order Gegenbauer orthogonal polynomials are mutually orthogonal; all even-order Gegenbauer orthogonal polynomials are mutually orthogonal. At the same time, the orthogonal interval is converted from (-1, 1) to (0, 1); Step 1-3: Define the normalized Gegenbauer polynomials: The normalized Gegenbauer polynomials not only have orthogonality but also regularity, and the mathematical representation of its orthogonality is as follows: Step 1-4: Use the radial Gegenbauer polynomials as the radial function and define the Fourier factor in the complex domain as the phase angle part, and its mathematical form is as follows: Among them, V pq (r, θ) represents the basis function of Gegenbauer-Fourier moments in the polar coordinate system, i is the imaginary unit, represents the p-th normalized Gegenbauer polynomial in the polar coordinate system, r ∈ (-1, 1) represents the radial distance in the polar coordinate system, θ ∈ [0, 2π] represents the polar axis in the polar coordinate system, and q represents the repetition rate of the Fourier factor; Accordingly, the Gegenbauer-Fourier moment h pq maps the image function to the basis function space defined by Equation (6): The "*" symbol represents taking the conjugate complex number, and f(r, θ) represents the original image function in the polar coordinate system; Due to the orthogonality of Gegenbauer-Fourier moments, the original image is reconstructed by a series of Gegenbauer-Fourier moments, that is: Among them, represents the reconstructed image in the polar coordinate system, and P max represents the maximum order of the polynomial used for reconstruction; Step 2: Design rotation-invariant moments by using the phase angle division method; Let denote the image after rotating the image f(x, y) by angle, denote the Gegenbauer-Fourier moments calculated for the image f(x, y); the phase-shift property is expressed as: Equation (9) shows that the value of the Gegenbauer-Fourier moment of the rotated image and the value of the original image only differ by an exponential term determined by the rotation angle; the modulus of the Gegenbauer-Fourier moment remains unchanged, and only the phase angle changes; Therefore, use the phase shift property to design rotation-invariant moments: where h pq and h mn are two Gegenbauer-Fourier moments of different orders; The image is divided into blocks and mapped to the feature space through rotation-invariant moments; Step 3: The elements adjacent to each other in the image feature space are potential replication regions; use the multi-dimensional tree method as the implementation algorithm and adopt the K-nearest neighbor retrieval method to find the similar features of the replication-rotation-movement regions in the image feature space and determine the potential forgery regions; Step 4: Determine the forgery regions; For each feature in the image feature space, use the method in Step 3 to perform nearest neighbor search to obtain K matching points; and whether these matching points correspond to the replication regions needs to exclude two types of situations: First: Exclude the feature similarity caused by spatial proximity during the image block division process; This feature similarity is caused by the spatial proximity during the image block division process, resulting in a large amount of the same information in two blocks, not caused by artificial forgery or modification; if the image blocks B1(i, j) and B2(k, l) are spatially adjacent, then their corresponding features are also similar, and this misjudgment situation is eliminated by calculating the Euclidean distance: Among them, D min is the minimum distance threshold of the original space; Second: Exclude the accidental similarity caused by the randomness of features; If the features of the image blocks B1(i,j) and B2(k,l) are similar, then their features and need to satisfy the following formula: Among them, M max is the threshold of the maximum distance in the feature space; After excluding the similar regions that meet the above two situations, the remaining feature similar regions are the forgery regions in the image to be found.

2. The method for detecting image copy-rotation-move forgery based on Gegenbauer orthogonal polynomials according to claim 1, wherein, In the K-nearest neighbor retrieval method, K is a parameter set in advance. When any sample X to be classified needs to be classified, the method calculates the feature distance between X and the training samples, selects the K nearest training samples corresponding to the distances, and determines the category of X according to the classification of these training samples; In the process of comparing the sample X to be classified with the training samples, the corresponding distance is adopted for the measurement between features: where X and Y are vectors containing N elements; p is a constant. When p = 1, d(X, Y) is the Manhattan distance; when p = 2, d(X, Y) is the Euclidean distance; The multi-dimensional tree method is adopted as the implementation algorithm of the K-nearest neighbor retrieval method; the process of the multi-dimensional tree method is as follows: First, a dimension is selected to divide the space, and then the space is divided into two parts by this dimension; the whole space is divided into two sub-spaces by a hyperplane; and so on until every sample point in the data set is processed; finally, the K-dimensional space is divided into multiple sub-spaces by the hyperplane passing through all the sample points in the data set, and a tree structure is established; the multi-dimensional tree transforms the data set of N elements into a binary tree structure with logN layers. On this basis, similar features are searched to determine the potential forgery area.

Images