Zero-Watermarking for Vector Maps Combining Spatial and Frequency Domain Based on Constrained Delaunay Triangulation Network and Discrete Fourier Transform

With its lossless properties, zero-watermarking has attracted a lot of attention in the field of copyright protection for vector maps. However, the common zero-watermarking algorithm puts too much emphasis on mining for global features, making it vulnerable to cropping attacks, and the robustness is not comprehensive enough. This study provides a vector map zero-watermarking scheme that utilizes spatial statistical information and frequency domain transformation methods in an effort to solve the aforementioned issue. In order to make the scheme more resistant to cropping and compression, it is constructed on the basis of feature point extraction and point constraint blocking of the original vector map. Within each sub-block, feature points are used to build constraint Delaunay triangulation networks (CDTN), and the angular values within the triangle networks are then extracted as spatial statistics. The angle value sequence is further transformed by discrete Fourier transform (DFT), and the binarized phase sequence is used as the final feature information to build a zero watermark by executing an exclusive disjunction operation with the encrypted copyright watermark image, both of which contribute to the scheme’s robustness and security. The results of the attack experiments show that the proposed vector map zero-watermarking can restore identifiable copyright images under common geometric attacks, cropping attacks, and coordinate system transformations, demonstrating a high level of robustness. The theoretical basis for the robustness of this watermarking scheme is the stability of CDTN and the geometric invariance of DFT coefficients, and both theory and experiment validate the method’s validity.


Introduction
With the characteristics of precise positioning, high accuracy, small storage capacity, and broad application, vector maps play a crucial and fundamental role in the construction of numerous fields, such as smart cities, national defense deployment, ecological protection, new agriculture, and disaster prevention and control, thereby establishing their extremely high commercial value [1][2][3]. Now more than ever, producers, legal owners, and consumers of vector maps are suffering enormous losses as a result of unlawful trafficking, dissemination, alteration, and unauthorized use of the data because of the ease with which electronic data may be transmitted. Therefore, there is a huge contradiction between the sharing and security of vector map data, and its security protection is highly valued by governments and scholars [4][5][6].
As the cutting-edge technique for copyright protection of digital products, digital watermarking provides technological support for the security protection of vector maps connect the disjoint points of the two triangles that share a side with v i and divide the two triangles that share a side into four triangles. The CDTN is formed after any vertex of the initial triangle is eliminated by regularizing the triangular dissection using the edge-swapping principle.
(2) Extraction of angle values. Generating triangle networks based on each block's feature points, extracting angle values with the inverse trigonometric function (Equation (2)) by calculating the distance between each triangle (Equation (1)), and composing a sequence of angle values A r (Equation (3)), ensuring that the length of the angle sequence A r within each block is greater than the length of the watermark sequence W in f .
A r = {α 1 , α 2 , α 3 , · · · · α n }, r = 1, 2, . . . , m In Equation (1), v x 1 , v x 2 , and v x 3 are the horizontal coordinate values of the first, second, and third points in  (2), α 1 ,α 2 , and α 3 are the three interior angle values within a triangle in Figure 1. The A r denotes the set of angle values of the r-th block, m demotes the total number of sub-blocks, and n denotes the total number of angles in Equation (3). The angle sequence A r is based on CDTN's invariance in the face of geometric attacks such as rotation, translation, and scaling. Based on this, we further processed A r to extract more robust information for the construction of zero-watermarking. (1) Construction of CDTN based on feature points. After the Douglas-Peuker simplification of the original vector map, obtain the discrete points set = { , , … , … }, and randomly sort each point. If the point is inside a triangle, connect it to the triangle's three vertices and divide the triangle into three triangles. If is on the side of a triangle, connect the disjoint points of the two triangles that share a side with and divide the two triangles that share a side into four triangles. The CDTN is formed after any vertex of the initial triangle is eliminated by regularizing the triangular dissection using the edgeswapping principle.
(2) Extraction of angle values. Generating triangle networks based on each block's feature points, extracting angle values with the inverse trigonometric function (Equation (2)) by calculating the distance between each triangle (Equation (1)), and composing a sequence of angle values (Equation (3)), ensuring that the length of the angle sequence within each block is greater than the length of the watermark sequence .
In Equation (1), , , and are the horizontal coordinate values of the first, second, and third points in Figure 1, respectively; , , and are the vertical coordinate values of the first, second, and third points in Figure 1, respectively; and , , and are the distances between different vertices, respectively. In Equation (2), , , and are the three interior angle values within a triangle in Figure 1. The denotes the set of angle values of the -th block, demotes the total number of sub-blocks, and denotes the total number of angles in Equation (3). The angle sequence is based on CDTN's invariance in the face of geometric attacks such as rotation, translation, and scaling. Based on this, we further processed to extract more robust information for the construction of zero-watermarking.

Feature Information Construction Based on DFT
The DFT is a fundamental Fourier analysis technique that converts signals from the time domain to the frequency domain [38]. DFT plays an important role in vector map watermarking  (4) and (5), respectively.
where e denotes the natural logarithmic base, and i denotes the imaginary unit. The DFT is used to transform the angular values in CDTN and obtain the phase sequence as feature information, and the specific steps are shown as follows: by following the steps in Section 3.2 for obtaining the Angle values in the CDTN, the maximum and minimum values of each triangle Angle value are chosen to form the Angle sequence set A = {A 1 , A 2 , . . . , A m }.
A r = α min 1 , α max 1 , α min 2 , α max 2 · · · α min k , α min k (7) where α 1 i , α 2 i , and α 3 i are the three interior angles of the i-th triangle; α min i and α max i are the minimum and maximum values of these three angular values, respectively. A r is the sequence of angle values of the r-th block in Equation (7), and k is the number of triangles of the r-th block. The complex number A u r of the angle value is constructed by Equation (5). According to Equation (8), the discrete Fourier transform of complex sequence {A u r } was performed, and the Fourier coefficient {A v r } was obtained (Equation (9)). According to the property of Fourier coefficients, the amplitude sequence R v r and phase value sequence P v r of the r-th block can be obtained through Equations (10) and (11), in which P v r is represented by angle value.
A u r = (α min ) u + i·(α max ) u , (u = 0, 1, 2, 3 . . . k − 1) (8) A v r = k−1 ∑ u=0 A u r e −i2π/k uv , (v = 0, 1, 2, 3 . . . k − 1) (9) where u is the number of triangles in A r , and i is the imaginary unit of complex numbers in Equation (8); v is the DFT series in Equation (9); and R(A v r ) and I(A v r ) represent the real and imaginary parts of the Fourier coefficients A u r , respectively. Then, each angle value in the P v r is rounded down and converted into 8-bit binary form to form the feature sequence set P binary r . The lengths of each sequence in P binary r are compared with the watermark sequence W in f , and the supplementary bits strategy in Equation (12) is adopted to make P binary r equal to the length of the watermark information W in f . To improve watermarking security, W in f is scrambled, yielding the encrypted watermark information sequence W

Procedure of the Proposed Zero-Watermarking
Based on the aforementioned methods, the specific process of the proposed vector map zero-watermarking is depicted in Figure 2, with the following steps: .
Step 3: Equation (9) is used to build the complex sequence of angle values , and Equation (10) is used to obtain the sequence of phase values following DFT. To create the feature sequence set , each angle value in the sequence is rounded down and converted to an 8-bit binary representation.
is made equal length, with in accordance with the supplementary bits strategy in Equation (12).
Step 4: The binary image containing copyright content is taken as the initial watermark image , and the binary watermark sequence is read. The Arnold scrambling algorithm is employed to encrypt the watermark image, yielding the disordered watermark sequence .
Step 5: The Xor operation between and yields one zero-watermark for each block and distinct zero-watermark images in total. All zero-watermark images and the original watermark images are submitted to the intellectual property rights (IPR) center for preservation, and time stamps are added to resist interpretation attacks.  Step 1: Firstly, the Douglas-Peucker algorithm is used to compress the original vector map M by setting the compression threshold as ρ and obtaining the feature points set V f . The point-constrained blocking method is then used to block the feature point set V f , with the setting of the initial blocking area as a and the threshold number of points as t to divide the data into m sub-blocks, and each sub-block can obtain a feature point set V f r .
Step 2: Every sub-block can create a CDTN with feature points V f r and Equations (1) and (2) are used to calculate the angles of all triangles in the CDTNs. The maximum and minimum angles of each triangle are then selected to compose an angular sequence set A r .
Step 3: Equation (9) is used to build the complex sequence of angle values A v r , and Equation (10) is used to obtain the sequence of phase values P v r following DFT. To create the feature sequence set P binary r , each angle value in the sequence P v r is rounded down and converted to an 8-bit binary representation. P binary r is made equal length, with W in f in accordance with the supplementary bits strategy in Equation (12).
Step 4: The binary image containing copyright content is taken as the initial watermark image W, and the binary watermark sequence W in f is read. The Arnold scrambling algorithm is employed to encrypt the watermark image, yielding the disordered watermark sequence W ecy in f .
Step 5: The Xor operation between P binary r and W ecy in f yields one zero-watermark W zero r for each block and m distinct zero-watermark images in total. All zero-watermark images and the original watermark images are submitted to the intellectual property rights (IPR) center for preservation, and time stamps are added to resist interpretation attacks.

Watermark Detection
Watermark detection is the inverse process of watermark creation, and the settings of each execution step must be compatible with the parameters established during the construction process, the specific process is shown in Figure 3. The feature points set V is obtained by applying the same degree of Douglas-Peucker compression to the vector map to be detected, then performing a block operation on V with the same parameters as when constructing the zero watermark, and constructing a CDTN within each subblock, recording the maximum and minimum interior angles of each triangle to form a sequence of angle values A r . According to Equations (8) and (9), the complex sequence of angle values A u r of each sub-block A r are constructed, DFT is applied to acquire the Fourier coefficient sequence A v r , and then the phase value sequence P v r of each sub-block is obtained. The angular values in P v r are rounded down and converted to binary to form the feature sequence set P binary r . original watermark image for verification. Normalized Correlation (NC) is used to measure the similarity between images [3] (Equation (15) where , and , are original and extracted watermark bit information at the coordinates of (i, j), respectively. Bit error rate (BER) is used to evaluate the specific error size of the extracted watermarks [3] (Equation (16)).
where denotes the length of watermark information.  . The Xor operation is then applied to the successfully matched sequence to obtain multiple encrypted watermark images W ecy in f (Equation (14)).
The inverted Arnold scrambling is employed on an encrypted watermark image W ecy in f to obtain the decrypted watermark image W , and then W is compared with the original watermark image W for verification. Normalized Correlation (NC) is used to measure the similarity between images [3] (Equation (15)).
where W i,j and W i,j are original and extracted watermark bit information at the coordinates of (i, j), respectively. Bit error rate (BER) is used to evaluate the specific error size of the extracted watermarks [3] (Equation (16)).
where l denotes the length of watermark information.

Watermark Encryption
The watermark image utilized in this paper to create zero watermarks is a binary image with a size of 64 × 64 pixels (Figure 4a) that provides relevant copyright information 'SUST'. Arnold scrambling algorithm [39] is used to encrypt it to improve security. The scrambling period of the watermark image is 48 times when all parameters in the Arnold formula are set to 1 (See Reference [39] for the specific formula of the Arnold scrambling algorithm). Figure 5 shows the original watermark image and the status of the image at the 15th, 25th, 35th, and 48th perturbations, where the perturbed watermark image at the 15th, 25th, and 35th perturbations is similar to a random noise map that is difficult to identify and has good concealment and reverts to the original state at the 48th perturbation. We chose the 15th disrupted image as the encrypted state's watermark information and obtained its binary watermark sequence for the construction of zero watermarks.

Watermark Encryption
The watermark image utilized in this paper to create zero watermarks is a binary image with a size of 64 × 64 pixels (Figure 4a) that provides relevant copyright information 'SUST'. Arnold scrambling algorithm [39] is used to encrypt it to improve security. The scrambling period of the watermark image is 48 times when all parameters in the Arnold formula are set to 1 (See Reference [39] for the specific formula of the Arnold scrambling algorithm). Figure 5 shows the original watermark image and the status of the image at the 15th, 25th, 35th, and 48th perturbations, where the perturbed watermark image at the 15th, 25th, and 35th perturbations is similar to a random noise map that is difficult to identify and has good concealment and reverts to the original state at the 48th perturbation. We chose the 15th disrupted image as the encrypted state's watermark information and obtained its binary watermark sequence for the construction of zero watermarks.

Zero Watermark Construction
The proposed watermarking scheme was performed using Python 3.10.4, Intel(R) Core(TM) i9-10900 CPU @ 2.80GHz, memory 32GB. Vector maps of buildings (Figure 5a), roads (Figure 5b), and water bodies (Figure 5c) were chosen as experimental data to test the dependability of the proposed watermarking scheme. Table 1 displays the detailed data information. The buildings, road, and water body maps each have 2708, 5115, and 844 elements, as well as 61,772, 86,367, and 422,764 vertices. The three maps generate 15,381, 21,237, and 15,294 feature points after Douglas-Peucker compression (all compression thresholds are set to 50 m), with compression ratios of 75.1 percent, 75.4 percent, and 96.4 percent, respectively. Point constraint blocking is performed on this basis. The initial block area parameter set is 1/4 of the entire area of the original data, and the coordinate point threshold is 5000. Finally, the building data yields 23 sub-blocks and zero watermarks, the road data yields 31 sub-blocks and zero watermarks, and the water map yields 22 sub-blocks and zero watermarks.

Watermark Encryption
The watermark image utilized in this paper to create zero watermarks is a binary image with a size of 64 × 64 pixels (Figure 4a) that provides relevant copyright information 'SUST'. Arnold scrambling algorithm [39] is used to encrypt it to improve security. The scrambling period of the watermark image is 48 times when all parameters in the Arnold formula are set to 1 (See Reference [39] for the specific formula of the Arnold scrambling algorithm). Figure 5 shows the original watermark image and the status of the image at the 15th, 25th, 35th, and 48th perturbations, where the perturbed watermark image at the 15th, 25th, and 35th perturbations is similar to a random noise map that is difficult to identify and has good concealment and reverts to the original state at the 48th perturbation. We chose the 15th disrupted image as the encrypted state's watermark information and obtained its binary watermark sequence for the construction of zero watermarks.   blocking is performed on this basis. The initial block area parameter set is 1/4 of the entire area of the original data, and the coordinate point threshold is 5000. Finally, the building data yields 23 sub-blocks and zero watermarks, the road data yields 31 sub-blocks and zero watermarks, and the water map yields 22 sub-blocks and zero watermarks.  blocking is performed on this basis. The initial block area parameter set is 1/4 of the entire area of the original data, and the coordinate point threshold is 5000. Finally, the building data yields 23 sub-blocks and zero watermarks, the road data yields 31 sub-blocks and zero watermarks, and the water map yields 22 sub-blocks and zero watermarks. Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.

Geometric Attacks
Translation, rotation, and scaling are examples of common geometric attacks. Watermark information is extracted from each sub-block of different data after various types and degrees of geometric attacks are performed on the experimental data. Table 2 lists the watermark images with the highest recognition degree extracted from different experimental data as well as different attack modes. It is evident that a watermark image with easily discernible copyright content can be extracted under all three geometric attack modes. Under both rotation and translation attacks, the extracted watermark images have NC values of 1, while under scaling attacks, the lowest NC value is 0.9821, and the highest is 1. Because of this, the proposed watermarking scheme can withstand attacks that use geometry. Because the CDTN architecture is both unique and invariant under rotation and translation attacks, the extracted spatial information remains unchanged after the DFT is calculated and remains consistent over time. In contrast, the experimental data produce a large change under the scaling attack, which has some effect on the feature points extraction. However, the CDTN possesses the characteristics of scaling invariance and overall invariance of local changes; the phase of DFT possesses scaling invariance; and, under the double insurance, the watermarking scheme also has strong robustness against the scaling attack.   The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. Table 3. Results of cropping attacks.

Cropping Attacks
The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks.

Cropping Attacks
The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. Table 3. Results of cropping attacks.

Cropping Attacks
The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. Table 3. Results of cropping attacks.

Cropping Attacks
The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. Table 3. Results of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. Table 3. Results of cropping attacks.

Cropping Attacks
The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. Table 3. Results of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. Table 3. Results of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks.

Cropping Attacks
The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks.

Cropping Attacks
The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks. The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks.

Cropping Attacks
The three sets of experimental data are attacked with different degrees of cropping. The cropping scale is about 20%, 25%, 50%, and 75% of the original area of the map. Based on this, the watermark images are extracted and restored, and the number of watermark images that can be restored in each set of data is counted. Table 3 displays the results, showing that all three data sets preserve a substantial number of complete sub-blocks and can extract a full watermark image at the 20%, 25%, and 50% crop stages, respectively. When the cropping scale hits 75%, there are just a handful of sub-blocks left from which to extract the watermark, whereas data (a) keeps the entire sub-block and extracts the watermark in its entirety so that it can be restored in full. Data (b) and data (c) both have NC values above 0.95 of extracted watermark images, indicating that the watermark images are recognized with a high degree of accuracy, despite the fact that a fully restored watermark image is not possible in these cases. Based on the experimental results, it is clear that the watermarking algorithm proposed in this paper is highly resistant to cropping attack. This excellent performance is mainly attributable to the strategy of blocking and watermarking supplementary bits in the data preprocessing stage, which builds multiple zero watermarks and can effectively resist a large degree of cropping attacks.

Points Attacks
The coordinate point attack consists of three parts: adding or removing points at random and data compression. As the experiment progresses, we subject the experimental data to a range of data adding, deletions, and compression, all the while trying to extract the optimal watermark images and recording the resulting BER values. The points-adding attack is to add random coordinate points to the line elements of the experimental data, with the intensity of the incremental points increasing gradually by 10% of the number of vertices in the original experimental data, up to double the original data. The experimental outcomes are illustrated in Figure 6. At 20% strength of the points-adding attack, watermark images with low BER values can typically be retrieved from the data, and we believe that copyright identification is attained. When the attack intensity exceeds 20% (data (c) is larger than 30%), the BER values of the retrieved watermark image are typically greater than 15%, making it difficult to recognize legitimate copyright content and impossible to validate copyright. The points-adding attack affects feature point extraction, which in turn contributes to CDTN's shaky building blocks. Experimental results show that the proposed zero-watermarking approach is still usable under the incremental point attack with an intensity level of up to 20%. The points-adding attack influences feature point extraction, which in turn leads to inconsistencies between the original and rebuilt CDTN. Experiments show that the proposed zero-watermarking scheme is reliable even when facing point-adding attacks with an intensity of 20% or less.

Points Attacks
The coordinate point attack consists of three parts: adding or removing points at random and data compression. As the experiment progresses, we subject the experimental data to a range of data adding, deletions, and compression, all the while trying to extract the optimal watermark images and recording the resulting BER values. The points-adding attack is to add random coordinate points to the line elements of the experimental data, with the intensity of the incremental points increasing gradually by 10% of the number of vertices in the original experimental data, up to double the original data. The experimental outcomes are illustrated in Figure 6. At 20% strength of the points-adding attack, watermark images with low BER values can typically be retrieved from the data, and we believe that copyright identification is attained. When the attack intensity exceeds 20% (data (c) is larger than 30%), the BER values of the retrieved watermark image are typically greater than 15%, making it difficult to recognize legitimate copyright content and impossible to validate copyright. The points-adding attack affects feature point extraction, which in turn contributes to CDTN's shaky building blocks. Experimental results show that the proposed zero-watermarking approach is still usable under the incremental point attack with an intensity level of up to 20%. The points-adding attack influences feature point extraction, which in turn leads to inconsistencies between the original and rebuilt CDTN. Experiments show that the proposed zero-watermarking scheme is reliable even when facing point-adding attacks with an intensity of 20% or less. The points-deletion attack is to randomly delete the vertices in the line elements, and the intensity of the deletion increases in the order of 5% of the number of vertices in the original data, up to 50% of the total number of vertices. Figure 7 displays the statistical outcomes of the points-deletion attacks. When the attack intensity is less than 50%, the BER values of the restored watermark images in different data are generally less than 10%. For example, in data (a) under a 45% density of points-deletion attack, the BER value of the extracted watermark image is 9.63%, and the NC value is 0.9425, allowing for clear identification of the copyright content. The results of the experiments show that the proposed watermarking scheme is highly resistant to the points-deletion attack. This is primarily because of the consistency of the feature points and the fact that local changes to the CDTN do not affect the whole. Furthermore, the majority of the deleted points are The points-deletion attack is to randomly delete the vertices in the line elements, and the intensity of the deletion increases in the order of 5% of the number of vertices in the original data, up to 50% of the total number of vertices. Figure 7 displays the statistical outcomes of the points-deletion attacks. When the attack intensity is less than 50%, the BER values of the restored watermark images in different data are generally less than 10%. For example, in data (a) under a 45% density of points-deletion attack, the BER value of the extracted watermark image is 9.63%, and the NC value is 0.9425, allowing for clear identification of the copyright content. The results of the experiments show that the proposed watermarking scheme is highly resistant to the points-deletion attack. This is primarily because of the consistency of the feature points and the fact that local changes to the CDTN do not affect the whole. Furthermore, the majority of the deleted points are non-feature points, which have less of an effect on the reconstruction of the CDTN within some sub-blocks.  Data compression is a unique form of point attack that simplifies the vector map's line elements. Figure 8 displays the BER values of the ideal watermark pictures that may be retrieved from three sets of experimental data at varying degrees of Douglas-Peucker compression. Evidently, it is always possible to extract watermark pictures with a BER of 0 as long as the compression ratio during data preprocessing is not exceeded. Additionally, even if the compression attack surpasses its original compression ratio by a small proportion, it can still be resisted well and remain robust. As depicted in Figure 8, when the compression ratio hits 80%, which slightly exceeds the predetermined compression ratio of 75% for data (a) and data (b), watermark images with high recognition can still be spotted. Since the proposed zero-watermarking is constructed based on feature points and the compression ratio is set to a high value, it retains a high level of robustness despite a relatively heavy compression attack.  Data compression is a unique form of point attack that simplifies the vector map's line elements. Figure 8 displays the BER values of the ideal watermark pictures that may be retrieved from three sets of experimental data at varying degrees of Douglas-Peucker compression. Evidently, it is always possible to extract watermark pictures with a BER of 0 as long as the compression ratio during data preprocessing is not exceeded. Additionally, even if the compression attack surpasses its original compression ratio by a small proportion, it can still be resisted well and remain robust. As depicted in Figure 8, when the compression ratio hits 80%, which slightly exceeds the predetermined compression ratio of 75% for data (a) and data (b), watermark images with high recognition can still be spotted. Since the proposed zero-watermarking is constructed based on feature points and the compression ratio is set to a high value, it retains a high level of robustness despite a relatively heavy compression attack.
non-feature points, which have less of an effect on the reconstruction of the CDTN within some sub-blocks. Data compression is a unique form of point attack that simplifies the vector map's line elements. Figure 8 displays the BER values of the ideal watermark pictures that may be retrieved from three sets of experimental data at varying degrees of Douglas-Peucker compression. Evidently, it is always possible to extract watermark pictures with a BER of 0 as long as the compression ratio during data preprocessing is not exceeded. Additionally, even if the compression attack surpasses its original compression ratio by a small proportion, it can still be resisted well and remain robust. As depicted in Figure 8, when the compression ratio hits 80%, which slightly exceeds the predetermined compression ratio of 75% for data (a) and data (b), watermark images with high recognition can still be spotted. Since the proposed zero-watermarking is constructed based on feature points and the compression ratio is set to a high value, it retains a high level of robustness despite a relatively heavy compression attack.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Coordinate System Transformation Attacks
When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Attack$$$Mode NCmax/$$$(a) W′ Count/(a) NCmax/$$$(b) W′ Count/(b) NCmax/$$$(c) W′ Count/(c)
Geodetic coordinate system transformation When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Attack$$$Mode NCmax/$$$(a) W′ Count/(a) NCmax/$$$(b) W′ Count/(b) NCmax/$$$(c) W′ Count/(c)
Geodetic coordinate system transformation When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Attack$$$Mode NCmax/$$$(a) W′ Count/(a) NCmax/$$$(b) W′ Count/(b) NCmax/$$$(c) W′ Count/(c)
Geodetic coordinate system transformation When working with vector maps, coordinate system transformation is a common data editing technique that is also a highly specialized form of data processing due to its inherent geographical characteristics. Coordinate system transformation is one of the most common data editing methods encountered in the use of vector maps, and it is also a very specialized way of data processing with geographical characteristics. Vector map coordinate systems are broadly classified as geodetic and projection coordinate systems, with the WGS1984-UTM projection coordinate system being used for the experimental data in this paper. The effectiveness of the proposed watermarking is tested by converting each set of experimental data into a different geodetic and projection coordinate system, then extracting the watermark images and tallying the number of watermarks that can be read from each set of data. During the experiments, the experimental data are transformed into the WGS1972 and WGS1984 geodetic coordinate systems, as well as the WGS1972 UTM Zone49 projection coordinate system. Additionally, the experimental data are modified from the original 49th sub-band to the 50th sub-band to test the robustness of the projection attack under malicious attack. In Table 4 below, we can see that under different transformations, highly discriminative watermark images can be extracted in all three sets of experimental data. For example, when shifting to the geodetic coordinate system of WGS1984 and two different transformations of the projection coordinate system, we can extract a complete watermark image with an NC value of 1. Although the recoverable watermark images are on the small side after transformation to the WGS1972 geodetic coordinate system, the NC values are maintained at or above 0.97 in every case. Together, the coordinate system transformation robustness of the watermarking algorithm proposed is very high. Table 4. Results of coordinate system transformation attacks.

Attack$$$Mode NCmax/$$$(a) W′ Count/(a) NCmax/$$$(b) W′ Count/(b) NCmax/$$$(c) W′ Count/(c)
Geodetic coordinate system transformation  Table 5 displays the comparative findings between the proposed watermarking scheme and the zero-watermarking schemes for vector maps that have proven strong robustness against multiple attacks in recent years. Among them, the reference [34] is our previous similar study, which agrees with the construction of CDTN but extracts different feature information. In the table, ' √ ' means that retrieving a valid watermarked image is possible, while '×' means that doing so is impossible. In comparison to these representative studies, the present watermarking is only incapable of extracting the watermark image in larger scale points-adding attacks, whereas it is capable of extracting a valid watermark image in other attack patterns of varying degrees, demonstrating stronger robustness. In particular, most watermarking algorithms, such as [31,32,40], fail to extract watermark information in the face of larger-scale points-deletion and cropping attacks, while the proposed watermarking scheme shows a very strong robustness advantage. Due to the stability of the feature points and the geometric invariance of the CDTN, the proposed watermarking scheme can extract and verify the watermark with a small quantity of data, and this is also the primary reason why the proposed watermarking can extract the watermark image under the condition of different forms of coordinate points reduction. The algorithm described in [34] has a similar theoretical foundation to the proposed technique, notably with respect to the use of CDTN to extract feature information, and hence exhibits a very similar robustness performance in the comparison findings. However, Ref. [34] is unable to withstand the transformation of the projection coordinate system, whereas the technique presented in this study has been enhanced in this regard. The algorithm in [23] also mines the spatial angle values of vector maps as feature information based on feature points, which can complete the construction of zero watermark with a small amount of data. The results show that the method has very comprehensive robustness, especially in terms of coordinate point attacks, which is better than the algorithm in this paper. However, the scheme is difficult to resist coordinate system changes, while the proposed algorithm is greater in this regard. In general, the proposed zero-watermarking algorithm offers a more comprehensive performance in terms of robustness than the majority of current studies. coefficients, a robust zero-watermarking scheme for vector maps is presented in this study. In spatial domain information mining, feature points are used to build a CDTN, and the angle values in the CDTN are used to obtain the initial set of features. The extracted angle value sequence is changed using DFT, and the zero watermarks are made using the binary conversion of the phase sequence of DFT as the feature information. The uniqueness of CDTN, the fact that local alterations have no effect globally, and the geometric invariance of DFT transform coefficients provide a solid foundation of robustness for the proposed zerowatermarking scheme. Experimental results demonstrate that the proposed watermarking scheme has good performance against common geometric attacks, clipping attacks, and point attacks, making it a potential technical reference solution for copyright protection of vector maps. The proposed algorithm needs computational efficiency improvements. Zerowatermark construction takes roughly half an hour for data (b) with little information and around 20 h for data (c) with much information, which affects the algorithm's practicability.

Comparative Analysis
In future work, we will concentrate on the computational efficiency and interpretive threats in the zero-watermarking technique for vector maps. For instance, we may choose a language that runs faster than Python or simplifies code and combine the blockchain method to ensure that the zero-watermark key and protected data can be traced, hence enhancing the algorithm's practical utility.
Author Contributions: X.X. and Y.H. conceived and designed the experiments; X.X. wrote the original draft; Y.C. and Y.H. reviewed and edited the paper; Q.Z. contributed framing, ideas, context, and wordsmithing. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Natural Science Foundation of China (grant no. 42101420).

Data Availability Statement:
The data used in this study can be accessible by request to the corresponding author.