Remote sensing image zero watermarking method based on depth features

Abstract

The invention discloses a remote sensing image zero-watermarking method based on depth features, relates to the field of digital watermarking, and aims to solve the problem of insufficient robustness during active feature design. The remote sensing image zero-watermarking method comprises the following steps: reading a remote sensing image, converting the remote sensing image into a gray scale, and normalizing the gray scale image; detecting feature points of the normalized image by using an SIFT algorithm, screening out feature points in a certain intensity interval, and constructing a Delaunay triangulation network according to a rule; calculating inscribed circles of triangles in the triangulation network one by one, constructing an inscribed circle mask set Masks, multiplying the mask set by the remote sensing image, and performing scale normalization processing on a result in order to facilitate feature extraction of the neural network; and inputting the feature domain into a trained U-Net neural network, and extracting robust features in the feature domain. According to the method, on the basis of good global stability and empty circle characteristics of the Delaunay triangulation network, each feature domain of the image exists independently, and good uniqueness of the watermark algorithm is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of digital watermarking, and specifically to a zero-watermark method for remote sensing images based on deep features. Background Art

[0002] In recent years, with the rapid development of aerospace technology and ground observation platforms, the accuracy of sensors has been continuously improved. Remote sensing images can record increasingly rich electromagnetic wave information, and the detection range has also been expanding day by day. They are widely used in fields such as disaster detection, land planning, and resource exploration. However, precisely because of the extremely high economic value contained in remote sensing images, the problems of illegal dissemination and copying of remote sensing images are serious, and the copyright trust problem is prominent, which has seriously damaged the healthy development of geographic information data. Therefore, there is an urgent need for a reliable copyright protection mechanism to ensure the data security of remote sensing images.

[0003] As a cutting-edge technology for information security protection, digital watermarking can embed copyright information into the carrier image without affecting the use value of the carrier image. Due to its unique action mechanism, digital watermarking provides a good solution strategy for the copyright problem of remote sensing images. However, all watermarks are embedded by modifying the pixel values of the carrier, and this process will inevitably cause different degrees of distortion of the carrier, which is not applicable to ultra-high-resolution or ultra-high-precision remote sensing images.

[0004] Different from traditional watermarks, zero-watermarks extract feature information from host data and generate watermarks through exclusive OR operations with copyright images, which can achieve copyright protection without modifying the original carrier data. However, current zero-watermark algorithms all focus on specific types of image data and rely more on artificially designed features, and it is difficult to meet the complex usage scenarios of remote sensing images in terms of security and robustness. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides a zero-watermark method for remote sensing images based on deep features, which solves the problem of insufficient robustness existing in the active design of features in the prior art.

[0006] To achieve the above objectives, the present invention is realized through the following technical solutions: A zero-watermark method for remote sensing images based on deep features, including the following steps:

[0007] S1 Zero-watermark generation, read the remote sensing image, convert it to grayscale, and at the same time, to improve the detection efficiency and accuracy of the SIFT algorithm, the grayscale image needs to be normalized. The specific rules are as follows:

[0008]

[0009] Wherein, I d is the input image, I' dis the output image, is image I d At the position of the pixel value, min(I d ) and max(I d ) respectively represent the minimum and maximum pixel values of the image;

[0010] S2 uses the SIFT algorithm to detect the feature points of the normalized image, filters out the feature points in a certain intensity range, and constructs a Delaunay triangulation network;

[0011] S3 calculates the inscribed circle of each triangle in the triangulation network one by one, sets the value inside the circle to 1 and the value in the area outside the circle to 0, thereby constructing the inscribed circle mask set Masks;

[0012] S4 multiplies the mask set by the remote sensing image, and at the same time, for the convenience of the neural network to extract features, the result is subjected to scale normalization processing;

[0013] S5 inputs the feature domain into the trained U-Net neural network to extract the robust features therein, assigns the corresponding area the value of 1 and the non-feature area the value of 0, thereby obtaining the robust feature set {L 1 L 2 , L 3 , …, L n};

[0014] S6 extracts the pixel positions with the value of "1" in the robust features as the set s, and uses the K-Means algorithm to cluster it into 2 categories. Taking the center μ max of the category with more samples as the starting point of the vector, and the other center μ min as the end point of the vector, thereby forming the vector

[0015] S7 calculates the included angle angle between the vector and the input correction vector , and normalizes the angle of the feature set {L 1 , L 2 , L 3 , …, L n} according to the formula, thereby obtaining the rotation-normalized feature set {L′ 1 , L′ 2 , L′ 3 , …, L′ n}, and the calculation formula is as follows:

[0016]

[0017] S8 takes {L′ 1 L′ 2 , L′ 3, …, L′ n} Superimpose to generate matrix F(x f , y f ), calculate the threshold, and binarize F(x f , y f ), finally obtain the feature matrix F′(x f , y f ). The threshold calculation formula is as follows:

[0018]

[0019]

[0020] S9 Scramble the original watermark w and the feature matrix F′(x f , y f ) respectively using different keys, so as to obtain the scrambled watermark w s and the feature matrix F′ s , and finally perform exclusive OR on the two to generate the zero-watermark copyright image w z .

[0021] Preferably, the construction of the Delaunay triangulation network in S2 includes:

[0022] Detecting the feature points of the image part: To achieve the scale invariance of the algorithm, SIFT first needs to convolve the remote sensing image with Gaussian functions of different kernels, so as to generate multiple scale spaces. Taking the remote sensing image R(x r , y r ) as an example, its scale space L(x r , y r , σ ) is constructed as follows:

[0023] L(x r , y r , σ) = G(x r , y r , σ) * R(x r , y r )

[0024]

[0025] where (x r , y r ) is the pixel position, (x r , y r , σ) is the Gaussian function, * is the convolution calculation, σ is the spatial scale factor, and the smaller the value of σ, the less smooth the image;

[0026] Then use different scale factors (σ 1 , σ 2, …, σ n ) Generate different scale spaces, and construct the difference scale space between two adjacent scale spaces through the Difference of Gaussian (DOG) function. The specific formula is as follows:

[0027] D(x r , y r , σ) = (G(x r , y r , k σ ) - G(x r , y t , σ)) * R(x r , y r ) = L(x r , y r , kσ) - L(x r , y r , σ)

[0028] Among them, the difference scale space constructed by D(x r , y r , σ), and k is the scale factor.

[0029] Preferably, the Delaunay triangulation construction rule in S2 is as follows:

[0030] Construct a virtual auxiliary triangle to include all feature points;

[0031] Insert a new feature point P one by one, and find the triangle that contains this point according to the circumcircle of each triangle;

[0032] Interchange the diagonals to form a new triangle, and check whether there are other points in the new triangle until all points meet the condition of an empty circumcircle;

[0033] Loop steps 2 and 3 until all feature points are inserted, and finally complete the construction of the Delaunay triangulation.

[0034] Preferably, during the normalization process in S4, since the scaling interpolation of the feature domain will cause a certain degree of information loss, in order to ensure the stability of the extracted feature domain, the mask collection with too small a radius needs to be removed.

[0035] Preferably, during the training stage of the model in S5, the loss function needs to be used to calculate the difference between the true value and the predicted value, so as to guide the model to optimize the parameters and help the model quickly match the learned predicted value and the true value directly. The binary cross-entropy loss function is used, and the specific definition is as follows:

[0036]

[0037] Among them, N lis the number of training samples; y i is the true value of the sample; p i is the predicted value of the sample; δ(p i ) is the activation function.

[0038] Preferably, in S6, taking the data set s = {s 1 , s 2 , …, s m} as an example, the specific steps of K-Means clustering are as follows:

[0039] According to the number of divided categories k, randomly select k clustering centers in the data set s: μ = {μ 1 , μ 2 , …, μ k};

[0040] Taking the Euclidean distance as the metric, calculate the distance d i between each sample point s j and each clustering center μ i，j . When d i，j is the smallest, then s i is assigned to the corresponding category, thus forming a new clustering division: c = {c 1 , c 2 , …, c k}. The Euclidean distance calculation formula is as follows:

[0041]

[0042] where s i represents the i-th point in the data set s, and μ j represents the j-th clustering center;

[0043] According to all the points in the clustering c, recalculate the position of the clustering center. If the position does not change, then output c = {c 1 , c 2 , …, c k}, otherwise repeat steps S2 and S3. The calculation formula of the clustering center μk is as follows:

[0044]

[0045] where c k is the data point set of the k-th clustering, and |c k | is the number of data points in this set.

[0046] Preferably, the scrambling formula in S9 is:

[0047]

[0048] In the formula, N wis the side length of the input information matrix, mod(·) represents the modulo operation, k a , k b is a positive integer and is used as a key. n is the current scrambling times. (p x , p y ) and (p′ x , p′ y ) respectively represent the original position and the mapped position of a pixel in the matrix.

[0049] Preferably, the inverse transformation formula for scrambling in S9 is:

[0050]

[0051] Finally, the scrambled feature matrix F′ s (x f , y f ) and the copyright image w s are subjected to an exclusive OR operation to generate a zero watermark. The specific calculation is as follows:

[0052] w z = xor(F′ s , w s )

[0053] where xor(·) is the exclusive OR function.

[0054] The present invention provides a zero watermark method for remote sensing images based on deep features. It has the following beneficial effects:

[0055] 1. To avoid the situation of repeated extraction in the feature domain, the present invention selects to bind the robust features and the feature domain. A Delaunay triangulation is constructed with the SIFT feature points of the remote sensing image, and the inscribed circle therein is extracted as the feature domain. Relying on the good global stability and empty circle property of the Delaunay triangulation, each feature domain of the image exists independently, ensuring the good uniqueness of the watermark algorithm.

[0056] 2. The present invention can obtain more accurate robust information in the feature domain. By introducing the U-Net network model and adding operations such as noise, filtering, and compression specifically in the training stage, the generalization ability of the network model is improved, ensuring the robustness of the extracted features.

[0057] 3. The present invention avoids the influence of geometric transformation on the robustness of the algorithm. By using the coordinate positions where the robust features are located as samples, the K-Means algorithm is used to perform binary classification on them. Taking the category center with more samples as the starting point of the vector and the other center as the end point of the vector, a vector is constructed to realize the rotation normalization of the robust features, ensuring the stability of the feature matrix to the greatest extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram for extracting the feature domain of remote sensing images in the embodiments of the present invention;

[0059] Figure 2 Schematic diagram of the U-Net network structure of the present invention;

[0060] Figure 3 Flowchart of training the U-Net neural network of the present invention and creating vectors using K-Means;

[0061] Figure 4 Test remote sensing image in the embodiments of the present invention;

[0062] Figure 5 Statistical chart of the results of the robustness experiment in the embodiments of the present invention. Detailed implementation manners

[0063] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0064] Please refer to the attached Figure 1 - attached Figure 5 , the embodiments of the present invention provide a zero-watermark method for remote sensing images based on deep features, including.

[0065] S1 Zero-watermark generation: Read the remote sensing image, convert it to grayscale. At the same time, to improve the detection efficiency and accuracy of the SIFT algorithm, the grayscale image needs to be normalized. The specific rules are as follows:

[0066]

[0067] Among them, I d is the input image, I' d is the output image, is the pixel value of the image I d at the position, and min(I d ) and max(I d ) respectively represent the minimum and maximum pixel values of the image.

[0068] S2 Use the SIFT algorithm to detect the feature points of the normalized image, screen out the feature points within a certain intensity range, and construct a Delaunay triangulation network;

[0069] (1) The SIFT construction rules are as follows. The specific steps are as shown in the attached Figure 1Part for detecting image feature points:

[0070] To achieve the scale invariance of the algorithm, SIFT first needs to convolve the remote sensing image with Gaussian functions of different kernels to generate multiple scale spaces. Taking the remote sensing image R(x r , y r ) as an example, its scale space L(x r , y r , σ) is constructed as follows:

[0071] L(x r , y r , σ) = G(x r , y r , σ) * R(x r , y r )

[0072]

[0073] where (x r , y r ) is the pixel position, (x r , y r , σ) is the Gaussian function, * is the convolution calculation, and σ is the spatial scale factor. The smaller the value of σ, the less smooth the image is;

[0074] Then, different scale factors (σ 1 , σ 2 , …, σ n ) are used to generate different scale spaces, and the difference scale space between two adjacent scale spaces is constructed through the Difference of Gaussian (DOG) function. The specific formula is as follows:

[0075] D(x r , y r , σ) = (G(x r , y r , kσ) - G(x r , y r , σ)) * R(x r , y r ) = L(x r , y r , kσ) - L(x r , y r , σ)

[0076] where the difference scale space constructed by D(x r , y r , σ), and k is the scale factor.

[0077] After obtaining the difference scale space D(x r , y r, after (σ), each pixel point therein needs to be compared with 8 adjacent points in the same scale space and 18 pixel points in the upper and lower differential scale spaces, so as to extract local maxima and local minima. These extreme points are also called candidate feature points. The construction process of the Difference of Gaussian scale space and the pixel neighborhood are as shown in the appendix Figure 1 Determine the candidate feature point part.

[0078] The Difference of Gaussian (DOG) function will produce strong edge effects (i.e., there will be a large principal curvature in the edge direction and a small principal curvature in the direction perpendicular to the edge), and these unstable points need to be removed from the candidate points. The principal curvature is obtained according to the Hessian matrix H at the candidate point:

[0079]

[0080] In the formula is the second-order derivative of the scale space image.

[0081] The eigenvalues of H are proportional to the principal curvature. Therefore, the ratio relationship between the second-order derivatives is used to avoid calculating the eigenvalues. Let λ max be the larger eigenvalue of H, and λ min be the smaller eigenvalue. Then the stability of the candidate point is obtained:

[0082]

[0083] where Tr(H) represents the trace of H, and Det(H) is the product of the determinants. Let the ratio of λ max and λ min be ρ. Then the above formula can be simplified:

[0084]

[0085] It can be seen from this that ρ is greater than or equal to 1, and the value of Stability increases as ρ increases, indicating that the larger the ratio of the two eigenvalues, that is, at this candidate point, the greater the difference between the two principal curvatures and the more obvious the edge effect. Therefore, only an upper limit κ m needs to be determined to remove the candidate feature points, that is:

[0086]

[0087] If the candidate feature point satisfies the above formula, then this point is a feature point. In this embodiment, ρ m is 10.

[0088] (2) The rules for constructing the Delaunay triangulation are as follows. The specific steps are as shown in the appendix Figure 1 Extract the feature domain part:

[0089] In this embodiment, the Delaunay triangulation is selected because of its properties: one is good global stability, that is, when several vertices are missing or added in the triangulation, only the several triangles around this point will be affected, which ensures the good stability of the constructed feature domain; the other is the empty circle property, that is, the circumcircle of any triangle in the triangulation does not contain any other points in the entire surface domain, so that the inscribed circle of each triangle exists independently, which avoids the problem of repeated extraction in directly constructing the feature domain and ensures the uniqueness of the watermark algorithm.

[0090] The process of constructing the Delaunay triangulation is as shown in the appendix Figure 1 and the specific steps are as follows:

[0091] 1) Construct a virtual auxiliary triangle that includes all feature points.

[0092] 2) Insert new feature points P one by one. According to the circumcircles of each triangle, find the triangle that contains this point.

[0093] 3) Swap the diagonals to form new triangles and check whether other points are included in the new triangles until all points meet the condition of an empty circumcircle.

[0094] 4) Loop steps 2 and 3 until all feature points are inserted, and finally complete the construction of the Delaunay triangulation.

[0095] S3 Calculate the inscribed circle of each triangle in the triangulation one by one, set the value inside the circle to 1 and the value in the area outside the circle to 0, so as to construct the inscribed circle mask set Masks.

[0096] S4 Multiply the mask set by the remote sensing image, and at the same time, for the convenience of the neural network to extract features, perform scale normalization on the result. In this process, due to the loss of a certain degree of information caused by the scaling and interpolation of the feature domain, in order to ensure the stability of the extracted feature domain, it is necessary to remove the mask set with too small a radius (in this embodiment, it is selected to remove the mask with a radius less than 40 pixels)

[0097] S5 Input the feature domain into the trained U-Net neural network to extract the robust features, assign the corresponding area the value of 1 and the non-feature area the value of 0, so as to obtain the robust feature set {L 1 ,L 2 ,L 3 ,…,L n}.

[0098] Traditional zero-watermark algorithms rely on humans to actively mine features and mainly design algorithms for specific types of images or specific application scenarios. The most powerful function of neural networks is their adaptive learning ability. They adjust according to the changes in training data and can better adapt to various complex watermark usage scenarios. Therefore, during the training of the network model, by specifically performing operations such as adding noise, filtering, and compressing on the training data, the generalization ability of the network model can be improved, and the accuracy of the features extracted by the model can be ensured.

[0099] U-Net is an end-to-end semantic segmentation model, consisting of an encoder and a decoder. The specific structure is as shown in the appendix. Figure 2 Among them, the encoder gradually reduces the data dimension and increases the depth of the input image through a series of convolutional layers and pooling layers, so as to extract the main semantic features. The decoder is mainly responsible for restoring the size and resolution of the image. It uses convolutional layers and transposed convolutional layers for upsampling step by step, maps the feature information in the network back to the corresponding positions of the original image, and thus gradually restores the spatial feature resolution lost during the encoding process and protects the segmented edge contours. U-Net also combines the feature maps in the encoder with the feature maps in the decoder through a concatenation operation. This design effectively retains the detailed information of the image. Therefore, U-Net can still achieve high-precision segmentation even with a very small training dataset, especially suitable for semantic segmentation of small targets. It highly coincides with the feature domain of the remote sensing images constructed above, making U-Net perform excellently when processing small-area remote sensing images, capable of effectively extracting and segmenting the target area, and enhancing the accuracy and reliability of the analysis.

[0100] Expanding the dataset through data augmentation is a common method in neural networks to prevent overfitting. In this embodiment, considering various attacks that the images may encounter during use and also to improve the generalization ability of the network model, during the data augmentation process, in addition to performing conventional inversion, rotation, and stretching on the training dataset, certain operations of adding noise, filtering, and compressing are also carried out on it.

[0101] During the training stage of the model, the loss function is needed to calculate the difference between the true value and the predicted value, so as to guide the model to optimize the parameters and help the model quickly match the learned predicted value and the true value directly. The binary cross-entropy loss function used in this embodiment is specifically defined as follows:

[0102]

[0103] Where N l is the number of training samples; y i is the true value of the sample; p i is the predicted value of the sample; δ(p i ) is the activation function.

[0104] According to the loss function, the gradients of the parameters are then calculated through the backpropagation algorithm, and then the network parameters are updated. In this embodiment, the Adaptive-Moment-Estimation (Adam) algorithm is used to optimize the parameters of the neural network. Adam dynamically adjusts the learning rate of each parameter using the first-order moment estimate (mean-of-gradient) and second-order moment estimate (variance-of-the-gradient) of the gradient. The main point is that after bias correction, there is a definite range for the learning rate in each iteration, making the parameters relatively stable. The specific update steps are as follows:

[0105] 1) Calculate the gradient \(g\) at time step \(t\) t :

[0106]

[0107] where represents the gradient of the loss function Loss with respect to the parameter \(\theta\) t-1 ;

[0108] 2) Using the idea of the momentum algorithm, comprehensively consider the first-order moment estimate \(m\) of the gradients at previous time steps t-1 , and thus calculate the first-order moment estimate \(m\) of the gradient at the current step t :

[0109] \(m\) t =\(\beta\) 1 \(m\) t-1 +(1 - \(\beta\) 1 )\(\beta\) 1 \(g\) t

[0110] where \(\beta\) 1 is the decay coefficient of the first-order moment estimate, responsible for controlling the weight distribution, with a default value of 0.9; when \(t = 0\), the value of \(m\) 0 is 0;

[0111] 3) Similarly, combine the previous second-order moment estimate to calculate the second-order moment estimate \(v\) of the gradient at the current time step t :

[0112]

[0113] where \(\beta\) 2 is the decay coefficient of the second-order moment estimate, which can control the influence of the previous gradient variance, with a default value of 0.999; when \(t = 0\), the value of \(v\) 0 is 0

[0114] 4) Since \(m\) 0 and \(v\) 0The initial value of is 0, which will cause m in the initial training stage t and v t to be biased towards 0. Therefore, it is necessary to correct the bias of m t and v t :

[0115]

[0116] 5) Adjust the parameter θ adaptively according to the first-order moment estimation and the second-order moment estimation : t :

[0117]

[0118] where α is the learning rate, which is set to 0.001 in this embodiment; ∈ = 10^(-8) to avoid division by zero.

[0119] S6 Extract the pixel positions with the robust feature median of "1" as the set s, and use the K-Means algorithm to cluster them into 2 categories. Take the category center μ max with more samples as the starting point of the vector, and the other center μ min as the end point of the vector, thus forming the vector

[0120] In the process of using remote sensing images, operations such as coordinate transformation and geometric correction are often involved, and the direction of the feature domain will also change to a certain extent. Therefore, the robust features extracted by U-Net cannot directly construct a feature matrix. For this reason, the present invention selects the pixel positions where the robust features are located as the sample data set, and uses K-Means clustering to quickly generate clustering centers, thereby constructing a vector to correct the robust features and improve the robustness of the algorithm. K-Means is a classic unsupervised learning method. Without any prior knowledge, it quickly partitions the data set to generate multiple clustering centers; taking the data set s = {s 1 , s 2 , …, s m} as an example, the specific steps of K-Means clustering are as follows:

[0121] 1) According to the number of partition categories k, randomly select k clustering centers in the data set s: μ = {μ 1 , μ 2 , …, μ k};

[0122] 2) Using the Euclidean distance as the metric, calculate the distance d i between each sample point s j and each clustering center μ i，j , and when d i，jWhen it is the smallest, s is i assigned to the corresponding category, thus forming a new clustering division: c = {c 1 , c 2 , …, c k}. The Euclidean distance calculation formula is as follows:

[0123]

[0124] where s i represents the i-th point in the dataset s, and μ j represents the j-th cluster center;

[0125] 3) According to all the points in the cluster c, recalculate the position of the cluster center. If the position does not change, output c = {c 1 , c 2 , …, c k}. Otherwise, repeat steps S2 and S3. The calculation formula for the cluster center μ k is as follows:

[0126]

[0127] where c k is the set of data points of the k-th cluster, and |c k | is the number of data points in this set.

[0128] In this embodiment, K-Means is used to establish the direction vector. Considering the efficiency of the watermarking algorithm, the sample data is only clustered into two categories: using the category center μ max with more samples as the starting point of the vector, and the other center μ min as the end point of the vector, thus forming the vector Calculate the angle angle between and the correction vector . The specific calculation formula is as follows:

[0129]

[0130] where sign(·) is the sign function, represents the modulus of the vector.

[0131] After obtaining the rotation angle, use affine transformation for central rotation to achieve the rotation normalization of the robust feature. There is the following relationship between the robust feature L(x f , y f ) and the normalized feature L′(x f , y f ):

[0132]

[0133] where x f and y f are the horizontal and vertical axis coordinate positions of the image respectively, and are the central abscissa and central ordinate positions of the image respectively.

[0134] S7 calculates the included angle angle between the vector and the input correction vector , and performs angle normalization on the feature set {L 1 , L 2 , L 3 , …, L n} according to the formula, so as to obtain the rotation-normalized feature set {L′ 1 , L′ 2 , L′ 3 , …, L′ n}, and the calculation formula is as follows:

[0135]

[0136] S8 superimposes {L′ 1 , L′ 2 , L′ 3 , …, L′ n} to generate the matrix F(x f , y f ), calculates the threshold, binarizes F(x f , y f ), and finally obtains the feature matrix F′(x f , y f ), and the threshold calculation formula is as follows:

[0137]

[0138] S9 scrambles the original watermark w and the feature matrix F′(x f , y f ) respectively using different keys, so as to obtain the scrambled watermark w s and the feature matrix F′ s , and finally performs exclusive OR on the two to generate the zero-watermark copyright image w z .

[0139] Before generating the zero watermark, it is usually necessary to scramble the feature matrix and the watermark using a scrambling algorithm. One is to improve the security of the generated watermark; the other is that the energy of the feature matrix is concentrated in the circular domain, and using the scrambling algorithm can disperse the energy, further ensuring the good uniqueness of the generated zero watermark. The scrambling formula is:

[0140]

[0141] In the formula, N w is the side length of the input information matrix, mod(·) represents the modulo operation, k a , k b is a positive integer and is used as the key, n is the current scrambling times, (p x , p y ) and (p′ x , p′ y ) respectively represent the original position and the mapped position of a pixel in the matrix. The inverse transformation formula of Arnold scrambling is:

[0142]

[0143] Finally, the scrambled feature matrix F′ s (x f , y f ) and the copyright image w s are XOR-operated to generate the zero watermark. The specific calculation is as follows:

[0144] w z = xor(F′ s , w s )

[0145] where xor(·) is the XOR function.

[0146] Uniqueness verification:

[0147] The experiment was carried out on a computer with configuration parameters of Windows11, AMD5800H CPU, 3070 GPU and 32GB RAM.

[0148] An important feature of the zero watermark is uniqueness, that is, the zero watermarks constructed in different remote sensing images should have significant differences. Even in the case of extremely similar ground object features, each image can still correspond to a unique watermark. To verify this, this embodiment selects 3 groups of remote sensing images with similar ground object characteristics as experimental data ( Figure 4 a - f in). At the same time, to verify the generalization of the zero watermark algorithm, four additional remote sensing images with different precisions and different types are added in this experiment ( Figure 4 g - j), and the specific information is shown in Table 1. Finally, this embodiment uses a binary image as the watermark image, and the original watermark and the scrambled watermark are as shown in Figure 4 (k) and (l) in.

[0149] Table 1 - Details of remote sensing image data

[0150]

[0151] In the uniqueness verification, this embodiment tested the similarity of zero watermarks generated from three groups of remote sensing images with similar ground objects. The verification results are shown in Table 2. It can be seen that for the zero watermarks generated by the algorithm proposed in this embodiment, the maximum NC value between each watermark is 0.568, indicating that the similarity between the generated watermarks is extremely small, and it can well distinguish extremely similar images. This is mainly due to three reasons: First, the algorithm uses a U-Net neural network with extremely high precision to extract robust features of remote sensing images, which ensures that unique features are extracted from different remote sensing images. Second, in the robust feature rotation correction stage, the algorithm generates the centroid position through the K-Means clustering method to determine the direction of the features. At the same time, in this embodiment, different direction vectors are input for each remote sensing image, which ensures that a unique feature matrix will be generated for each remote sensing image. Third, in this embodiment, different scrambling keys are used each time the watermark is scrambled. Different feature matrices can better ensure the uniqueness of the watermark algorithm after being scrambled with different keys.

[0152] Table 2 - Uniqueness Evaluation

[0153]

[0154]

[0155] Robustness Analysis:

[0156] In this embodiment, according to the scenarios encountered by remote sensing images in actual use, geometric attacks, noise attacks, compression attacks, filtering, affine transformation, and cropping were respectively performed on the remote sensing images, and the robustness of the algorithm was verified on this basis. To verify the feasibility of the watermark algorithm proposed in this embodiment, two zero watermarks (Xing et al.

[15] , Xu et al.

[39] ) and three embedded robust watermark algorithms (Yuan and Guan.

[40] , Xu et al. [5], Zhang et al.

[41] ) were respectively selected for comparison;

[0157] To facilitate the quantitative evaluation of the performance of the watermark algorithm, in this embodiment, the peak signal-to-noise ratio (PSNR) value between the original image and the attacked image is used to reflect the attack intensity, and the robustness of the algorithm against different attacks is measured by the normalized correlation coefficient (NC) between the extracted watermark and the original watermark. The calculation formula of PSNR is as follows:

[0158]

[0159] Where, R max is the maximum pixel value in the remote sensing image, M r and N r are the length and width of the remote sensing image respectively, P(x r , y r) and R′(x r ,y r ) are the pixel values of the original image and the post - attack image at the position (x r ,y r ) respectively; the larger the PSNR value, the lower the attack intensity on the attacked remote - sensing image, and the easier it is to extract the complete watermark information. Conversely, the smaller the PSNR value, the more difficult it is to extract the complete watermark. The calculation method of NC is as follows:

[0160]

[0161] where C(i c ,j c ) and C′(i c ,k c ) are the pixel values of the original copyright watermark and the extracted copyright watermark at the position (i c ,k c ) respectively, M w and N w represent the row width and column width of the watermark respectively; the closer the NC value is to 1, the higher the similarity between the two watermarks, and the stronger the robustness of the corresponding algorithm. The final measured experimental data are shown in Table 3 below, and the data statistical chart sorted according to Table 3 is shown in Appendix Figure 5 as follows:

[0162] Table 3 - Attack Modes of Robustness Experiment

[0163]

[0164] As shown in Appendix Figure 5 and Table 3, the experimental results show that the present invention can extract watermarks with NC close to 1 in all 11 attack modes listed in Table 3, indicating that the present invention has very strong robustness against common attacks.

[0165] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A remote sensing image zero watermarking method based on deep features, characterized in that: The following steps are involved: S1 zero watermark generation, read remote sensing images, convert them into grayscale, and in order to improve the detection efficiency and accuracy of the SIFT algorithm, the grayscale image needs to be normalized. The specific rules are as follows: Among them, I d is the input image, I′ d is the output image, For image I d exist The pixel value of the position, min(I d ) and max(I d ) represent the minimum and maximum pixel values ​​of the image respectively; S2 uses the SIFT algorithm to detect the feature points of the normalized image, screens out the feature points in a certain intensity range, and constructs a Delaunay triangulation network; S3 calculates the inscribed circle of each triangle in the triangulated network one by one, sets the value inside the circle to 1, and the value outside the circle to 0, thereby constructing an inscribed circle mask set Masks; S4 multiplies the mask set with the remote sensing image, and normalizes the result to facilitate feature extraction by the neural network; S5 inputs the feature domain into the trained U-Net neural network, extracts the robust features, assigns the corresponding area a value of 1, and assigns the non-feature area a value of 0, thereby obtaining the robust feature set {L1, L2, L3, ..., L n }; S6 extracts the pixel positions with the median value of "1" as a set s of robust features, and uses the K-Means algorithm to cluster them into two categories, with the category center μ containing more samples. max As the starting point of the vector, the other center μ min Then it is the end point of the vector, thus forming the vector S7 calculates the vector The correction vector with the input The angle angle, and the feature set {L1, L2, L3, ..., L n }According to the formula, the angle normalization is performed to obtain the rotation normalized feature set {L′1, L′2, L′3, …, L′ n }, the calculation formula is as follows: S8 will {L′1, L′2, L′3,…,L′ n }Superposition generates the matrix F(x f ,y f ), calculate the threshold, and then convert F(x f ,y f ) is binarized, and finally the feature matrix F′(x f ,y f ), the threshold calculation formula is as follows: S9 combines the original watermark w and the feature matrix F′(x f ,y f ) use different keys to scramble, so as to obtain the scrambled watermark w s and the feature matrix F′ s Finally, the two are XORed to generate the zero-watermark copyright image w z .

2. The remote sensing image zero watermark method based on depth features according to claim 1 is characterized in that: The Delaunay triangulation constructed in S2 includes: Detection of image feature points: To achieve scale invariance of the algorithm, SIFT first needs to convolve the remote sensing image with Gaussian functions of different kernels to generate multiple scale spaces. r ,y r ) as an example, its scale space L(x r ,y r ,σ) is constructed as follows: L(x r ,y r ,σ)=G(x r ,y r ,σ*R(x r ,y r ) Where (x r ,y r ) is the pixel position, (x r ,y r ,σ) is the Gaussian function, * is the convolution calculation, σ is the spatial scale factor, the smaller the σ value is, the smaller the smoothness of the image is; Then, different scaling factors (σ1, σ2, ..., σ n ) to generate different scale spaces, and construct the differential scale space of two adjacent scale spaces through the Gaussian difference (DOG) function. The specific formula is as follows: D(x r ,y r ,σ)=(G(x r ,y r ,kσ)-G(x r ,y r ,σ))*R(x r ,y r )=L(x r ,y r ,kσ)-L(x r ,y r ,σ) Where D(x r ,y r ,σ) to construct the differential scale space, k is the scale factor.

3. The remote sensing image zero watermark method based on depth features according to claim 1 is characterized in that: The Delaunay triangulation construction rules in S2 are as follows: Construct a virtual auxiliary triangle to include all feature points; Insert new feature points P one by one, and find the triangle containing this point based on the circumscribed circles of each triangle; Swap the diagonals to form a new triangle and check whether the new triangle contains other points until all points satisfy the empty circumcircle condition; Repeat steps 2 and 3 until all feature points are inserted, and finally complete the construction of the Delaunay triangulation.

4. The remote sensing image zero watermark method based on depth features according to claim 1 is characterized in that: During the normalization process in S4, since the scaling interpolation of the feature domain will cause a certain degree of information loss, in order to ensure the stability of the extracted feature domain, the mask collection with a radius too small needs to be removed.

5. The remote sensing image zero watermark method based on depth features according to claim 1 is characterized in that: In the training phase of the model in S5, the difference between the true value and the predicted value needs to be calculated through a loss function, so as to guide the model to optimize parameters and help the model to quickly match the learned predicted value and the true value directly. The binary cross entropy loss function is used, which is specifically defined as follows: Where N l is the number of training samples; y i is the true value of the sample; p i is the predicted value of the sample; δ(p i ) is the activation function.

6. The remote sensing image zero watermark method based on depth features according to claim 1 is characterized in that: In S6, the data set s={s1,s2,…,s m } as an example, the specific steps of K-Means clustering are as follows: According to the number of classification categories k, k cluster centers are randomly selected in the data set s: μ = {μ1, μ2, …, μ k }; Using Euclidean distance as the metric, calculate each sample point s i and each cluster center μ j The distance d i，j , when d i，j When s is the minimum i into the corresponding categories, thus forming a new cluster division: c = {c1, c2, ..., c k }, the Euclidean distance calculation formula is as follows: where s i represents the i-th point in the data set s, μ j represents the jth cluster center; According to all the points in cluster c, recalculate the cluster center position. If the position has not changed, output c = {c1, c2, ..., c k }, otherwise repeat steps S2 and S3. Cluster center μ k The calculation formula is as follows: where c k is the set of data points of the kth cluster, |c k | is the number of data points in the set.

7. The remote sensing image zero watermark method based on depth features according to claim 1 is characterized in that: The scrambling formula in S9 is: Where N w is the side length of the input information matrix, mod(·) represents the modulus operation, k a , k b is a positive integer that can be used as a key, n is the number of times the scrambling is currently performed, (p x , p y ) and (p′ x , p′ y ) represent the original position and the mapped position of a pixel in the matrix respectively.

8. The remote sensing image zero watermark method based on depth features according to claim 1 is characterized in that: The inverse transformation formula of the scrambling in S9 is: Finally, the scrambled feature matrix F′ s (x f ,y f ) and copyright image w s Perform XOR operation to generate zero watermark. The specific calculation is as follows: w z =xor(F′ s ,w s ) Where xor(·) is the exclusive OR function.

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