Geometric feature based vector map zero-watermarking method

Abstract

The application discloses a kind of vector map zero watermarking methods based on geometric features, first utilize the geometric invariability of Delaunay triangulation to construct vector map, through Delaunay triangulation, the circumscribed circle radius and the inradius of triangle are extracted as characteristic invariant, so that the stability of the constructed watermark is kept under rotation, scaling and translation and other geometric transformations, wherein, algorithm generates pseudo-random number sequence by the inradius of triangle, to determine the index position of watermark embedding, and introduce voting mechanism to determine the final value of each watermark bit, obtain zero watermark image by scrambling and exclusive-or operation and extract watermark image by anti-scrambling and exclusive-or operation.The application can keep geometric structure stability, and show significant robustness to vertex attack.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of map watermarking, and particularly relates to a vector map zero watermarking method based on geometric features. BACKGROUND

[0002] As an important part of geographic information systems, vector map data is widely used in military positioning, vehicle navigation, urban planning, forestry and other fields. With the development of space technology and information technology, and the construction of digital mapping system, the precision and efficiency of vector map production have been greatly improved. However, the developed network environment and portable hardware devices also make the spread of vector maps extremely easy, which can be easily stolen, illegally copied and spread by illegal persons, causing significant losses to the legal owner of the data. As a leading technology in the field of information security, digital watermarking plays a crucial role in the copyright protection of vector geographic data.

[0003] In the traditional field of digital watermarking technology, it is mainly divided into two categories: spatial domain and frequency domain. The spatial domain watermarking method directly modifies the coordinate values of the vector map to embed watermark information. This method is favored due to its intuitive and easy-to-operate nature. However, its robustness is generally weak, which is a key factor limiting its widespread application. In contrast, the frequency domain watermarking method adopts a more complex processing approach: first, perform frequency transformation on the coordinates of the vector map, and then adjust the frequency coefficients to embed the watermark. This scheme significantly improves the robustness and security of the watermark, but it comes with a large disturbance to the vector map, which is particularly unsuitable for vector maps that require high precision, such as high-precision mapping. It is worth noting that both spatial domain and frequency domain watermarking methods will have varying degrees of impact on the precision of the vector map. For low-precision vector maps, these minor changes can be ignored, but in fields such as military applications and road navigation systems that require high precision, such changes will directly lead to a significant decrease in data reliability. Given this, zero-watermarking technology, which is lossless, has increasingly attracted widespread attention from academia and practical application fields due to its ability to avoid any form of modification to the original data.

[0004] Zero-watermarking methods construct watermarks by exploiting feature information of vector maps, and no modification is made to the original data during the watermark construction process, which is very suitable for the high-precision use environment requirements of vector maps. Therefore, zero-watermarking methods do not have the problem of mutual restriction between watermark invisibility and robustness, and pursuing robustness of the method and uniqueness of the watermark becomes an important research direction for zero-watermarking.

[0005] Existing zero-watermarking schemes have certain research in the field of vector map security protection, such as:

[0006] Document [1] Zhang Z, Sun S, Wang Y, "Zero-watermarking method for two-dimensional vector digital map," Computer Engineering and Design, vol. 30, no. 6, pp. 1473-1475, 2009. It divides the vector map data into blocks and counts the number of vertices in each block, then performs XOR operation with the original watermark image using these vertex counts, thus constructing the publication right watermark image.

[0007] Document [2] X. XI, Y. HUA, Y. CHEN, "Zero-watermarking for vector maps combining spatial and frequency domain based on constrained delaunay triangulation network and discrete fourier transform" Entropy, vol. 25, no. 4, pp. 682, 2023. It uses spatial statistical information and frequency domain conversion method to construct a vector map zero watermarking scheme, which can recover the watermark image under common geometric attacks, cutting attacks and coordinate system transformation.

[0008] Document [3] Wang S, Zhang L, Li Y, "Zero-watermarking method for vector geographic data using singular value decomposition" Surveying and Mapping Science, vol. 47, no. 11, pp. 196-203, 2022. It divides the vector map into blocks and performs normalization and singular value decomposition on the divided data, meeting the copyright protection requirements of point, line and surface data, and having good robustness against scaling and cutting attacks.

[0009] Although the zero watermarking schemes proposed in the above documents [1]-[3] have certain advancement in the field of vector map security protection, in the actual application environment, these schemes still have certain limitations. Specifically, document [1] constructs zero watermarking according to the relative storage order of elements, has strong robustness in precision reduction and projection transformation attack, however, in actual application, the number of vertices is often modified, and the watermarking construction scheme proposed in document [1] cannot cope with this situation. Document [2] uses the topological adjacent relationship existing in surface vector data to construct watermarking, but this method ignores the influence of element addition and deletion on the stability of watermarking. In addition, although the solution scheme for linear vector data is proposed in the document, the robustness in actual application is still unknown. Document [3] constructs zero watermarking on the basis of DFT transformation, but does not deeply explore its characteristics, and only uses the phase sequence, the addition and deletion of vertices will affect the extraction process of watermarking. In addition, the current zero watermarking protection scheme of vector map has certain deficiencies in coping with vertex addition and deletion, and in actual application, the addition and deletion of vertices are very common. SUMMARY

[0010] The technical problem to be solved by the present application is to provide a vector map zero watermarking method based on geometric features, which can maintain geometric structure stability and exhibit significant robustness to vertex attacks.

[0011] In order to solve the above technical problem, the present application provides a vector map zero watermarking embedding method based on geometric features, comprising the following steps:

[0012] Step 1: In the original vector map V, the vertex set P is extracted, and the feature point extraction is performed to obtain the feature point set P';

[0013] Step 2: For the feature point set P', a point-by-point insertion method is used to construct a Delaunay triangulation and obtain a point sequence DT;

[0014] Step 3: In the point sequence DT, read the three points constituting the triangle, calculate the circumradius R and the inradius r of each triangle, and generate a key key1 according to the average value of the circumradius R;

[0015] Step 4: Use the inradius r of the triangle as the seed of the pseudo-random number generator to generate uniformly distributed pseudo-random numbers, and generate a pseudo-random number sequence, and use the first number of the pseudo-random number sequence as the watermarking index;

[0016] Step 5: Calculate the watermark value of the corresponding watermarking index by the circumradius R of the corresponding triangle, and generate a feature sequence W index ;

[0017] Step 6: scrambling the original watermark image W and encrypting with the key key2 to obtain the scrambled watermark W', and converting it into a watermark sequence W i ;

[0018] Step 7: performing logical XOR operation between the generated feature sequence W' index and the watermark sequence W i to obtain the zero-watermark image W".

[0019] Further, in step 1, the vertex set P is {P = (x i , y i )|i = 0, 1, …, p-1}, where p is the number of vertices in the set, and the Douglas-Peucker method is used to extract feature points from the vertex set P to obtain the feature point set P'.

[0020] Further, in step 4, the Meissner rotation method is used to generate pseudo-random numbers, and the formula is as follows:

[0021]

[0022] Where X n represents the state of the nth pseudo-random number, represents the XOR operation, << represents the left shift operation, >> represents the right shift operation, n, m, s, t represent the shift step, shift mask and two bit shift parameters in the selected Meissner prime number respectively; Y n represents the twisted state, & represents the bitwise AND operation, u is an integer value for right shift operation, and d is a bit mask for changing the characteristics of the state, increasing the randomness of the pseudo-random number.

[0023] Further, the derivative version MT19937 of the Meissner rotation method is used to establish the pseudo-random number sequence, and the pseudo-random generator generates a set of pseudo-random number sequences using a seed. Different seeds generate different pseudo-random number sequences, and the same seed generates the same pseudo-random number sequence.

[0024] Further, the pseudo-random number is mapped to 0-L, L is the length of the watermark, and the watermark index value index is generated.

[0025] Further, in step 5, the voting mechanism is used to determine the final watermark value, and the rules are as follows: if the circumradius R of the corresponding triangle is greater than the average value Rm of all circumradii R, then the value of w(i) is increased by 1, otherwise the value of w(i) is decreased by 1. According to the final value of w(i), if it is greater than 0, the watermark value at this position will be recorded as 1, if it is less than 0, the watermark value at this position will be recorded as 0.

[0026] w(i) represents the difference between the number of 1 and 0 in the i-th bit of the watermark.

[0027] Furthermore, in step 6, the watermark sequence is {W} i =0,1|i=0,1,…,L-1}, where L is the watermark length, calculated using the formula X k+1 =μX k (1-X k ), where X k ∈(0,1) represents the chaotic sequence generated by the k-th generation mapping, and μ∈[0,4] is the control parameter. The control parameter is used as the key and is denoted as key2.

[0028] A method for zero-watermark extraction from vector maps based on geometric features, for extracting the watermark embedded in the method described in any one of claims 1-8, includes the following steps:

[0029] A. Extract feature points from the vector map V and construct a Delaunay triangulation using the point-by-point insertion method to obtain the point sequence DT′. Based on the point sequence DT′, read the three points that constitute the triangles, calculate the circumcircle radius R′ and incircle radius r′ of each triangle, and then calculate the average value Rm′ of the circumcircle radius R′.

[0030] B. Compare the average value Rm′ with the key key1 to generate a scaling factor K, and scale the inscribed circle radius r′ accordingly based on the scaling factor K.

[0031] C. Using the incircle radius r′ of the scaled triangle as the seed for a pseudo-random number generator, generate uniformly distributed pseudo-random numbers and map them to the range 0-L to determine the watermark index value. Calculate the watermark value corresponding to the watermark index using the corresponding circumcircle radius R′, and generate the feature sequence W′. index ;

[0032] D. Regarding the zero-watermark image W″ and the feature sequence W′ index Perform an XOR operation to generate the watermark sequence W′. i ;

[0033] E. Use the Logistic method and key2 to process the watermark sequence W′. i The image is descrambled to obtain the extracted watermark image W″′, which is then compared and verified with the original watermark image W.

[0034] The beneficial effects of this invention are:

[0035] In view of the limitation of the existing zero watermark method in resisting vertex attack, the application provides a vector map zero watermark scheme based on Delaunay triangular net feature invariant and having robustness to vertex attack.

[0036] In the construction process of the zero watermark, the method skillfully uses the inradius and circumradius of the Delaunay triangle as key parameters to calculate the watermark index and watermark value. In order to ensure the uniform distribution and embedding strength of the watermark, the method introduces a Mason rotation operator to accurately control the embedding times of each watermark bit. In addition, the average value of the circumradius is used as an encryption key, which can significantly enhance the robustness of the Delaunay triangular net in resisting common geometric transformation attacks such as translation, rotation and scaling (RST), and provide a more comprehensive and effective solution for the copyright protection of vector map data. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is a watermark embedding flowchart of the application;

[0038] Figure 2 is a watermark extraction flowchart of the application;

[0039] Figure 3 is an experimental data graph of the application;

[0040] Figure 4 is a robustness experimental result line graph of the application. DETAILED DESCRIPTION

[0041] The application will be further described below in combination with the drawings and specific embodiments, so that those skilled in the art can better understand the application and implement it, but the embodiments are not limiting the application.

[0042] An embodiment of the vector map zero watermark method based on geometric features of the application is based on the zero watermark method of Delaunay triangular net feature invariant, and proposes to use the geometric invariance of Delaunay triangular net to construct the zero watermark technology of vector map. Through Delaunay triangulation, the circumradius and inradius of the triangle are extracted as feature invariants, so that the constructed watermark remains stable under geometric transformations such as rotation, scaling and translation.

[0043] Based on the application of pseudo-random number generation and voting mechanism, the method generates a pseudo-random number sequence by the radius of the incircle of a triangle to determine the index position of watermark embedding, and introduces a voting mechanism to determine the final value of each watermark bit. This method improves the stability and robustness of watermark information in the watermark embedding process.

[0044] Based on the high robustness to various attack forms, in order to cope with different situations in actual needs, the method is experimented on various data, and shows strong robustness in dealing with various vertex change related attacks such as rotation, scaling, translation, point addition, point deletion, precision reduction, etc., effectively overcoming the problem of insufficient robustness of traditional zero watermark method when the number of vertices changes.

[0045] Specifically, the specific process of watermark embedding is as follows:

[0046] Referring to Figure 1 As shown in the figure, first, in the original vector map V, the vertex set P is extracted: {P=(x i , y i )|i=0,1,…,p-1}, where p is the number of vertices in the set, and the Douglas-Peucker method is used to extract feature points from the vertex set P to obtain the feature point set P'.

[0047] Then, the processed feature point set P' is used to construct a Delaunay triangular network by point-by-point insertion method and obtain a point sequence DT.

[0048] In the point sequence DT, read the three points that constitute a triangle, calculate the circumradius R and the inradius r of each triangle, and generate a key key1 according to the average value of the circumradius.

[0049] Then, use the inradius r of the triangle as the seed of the pseudo-random number generator to generate a pseudo-random number sequence, and use the first number of the pseudo-random sequence as the watermark index.

[0050] In order to establish the correspondence between the geometric features of the Delaunay triangular network and the watermark sequence, the method calculates the watermark index based on the inradius of the triangle. However, the radius of the incircle of the triangle is not uniformly distributed, in order to solve this problem, the method of Mason rotation is used to generate pseudo-random numbers. The method of Mason rotation is a high-quality pseudo-random number generation method, as shown in formula (1). After inputting the initial value, the pseudo-random number sequence with good statistical properties can be generated by means of linear shift register and nonlinear distortion function. As shown in formula (2).

[0051]

[0052] Where X n represents the state of the nth pseudo-random number, represents the exclusive or operation, << represents the left shift operation, >> represents the right shift operation, n, m, s, t represent the shift step, shift mask, two bit shift parameters in the selected Mersenne prime number respectively. Y n represents the twisted state, & represents the bitwise and operation, u is an integer value, used for right shift operation, d is a bit mask, used to change the characteristics of the state, increase the randomness of the pseudo-random number. Here, a derivative version of the Mersenne rotation method MT19937 is used to establish the pseudo-random number sequence. The pseudo-random generator generates a set of pseudo-random number sequences using a seed of a pseudo-random number. Different seeds will generate different pseudo-random number sequences, and the same seed will generate the same pseudo-random number sequence.

[0053] Since there is a difference between the value range of the pseudo-random number sequence and the watermark index value, the pseudo-random number M needs to be mapped to 0-L (L is the watermark length) according to formula (3) to generate the watermark index value index. It is used to calculate the corresponding relationship between the circumscribed circle radius R and the position of the watermark data.

[0054] index = mod (M, L) (3)

[0055] Then substitute the corresponding circumscribed circle radius R into formula (4) and formula (5) to calculate the watermark value corresponding to the watermark index. Combine the watermark value and the watermark index to generate the feature sequence W' index .

[0056] Since the watermark length and the number of inscribed circle radii r are basically impossible to be equal, in the above process, the watermark index value index generated by the inscribed circle radius r is a repeated positive integer with a value range of 0-L, that is, the triangular watermark indexes corresponding to multiple different inscribed circle radii r are the same. Therefore, a voting mechanism is used to determine the final watermark value. The rules are as follows: if the circumscribed circle radius R corresponding to the triangle is greater than the average value Rm of all circumscribed circle radii R, then the value of w(i) is increased by 1, otherwise the value of w(i) is decreased by 1, as shown in formula (4). Finally, the final result value is obtained by continuously increasing and decreasing, if the value of w(i) is greater than 0, the watermark value at this position will be recorded as 1, and if the value of w(i) is less than 0, the watermark value will be recorded as 0, as shown in formula (5).

[0057]

[0058] where w(i) represents the number difference between 1 and 0 in the i-th bit of the watermark, R j represents the circumscribed circle radius of the j-th triangle, Rm represents the average value of the circumscribed circle radii R of the triangles. W' index represents the generated feature sequence. The specific feature matrix construction process is shown in (b) of Figure 1 .

[0059] Next, the original watermark image W is scrambled and encrypted using the Logistic method to obtain the scrambled watermark W′, which is then converted into a watermark sequence W. i :{W i =0,1|i=0,1,...,L-1}. Its calculation formula is shown in (6).

[0060] X k+1 =μX k (1-X k (6)

[0061] In the formula, X k ∈(0,1) represents the chaotic sequence generated by the k-th generation mapping, and μ∈[0,4] is the control parameter. It is difficult to restore the watermark data without knowing μ. In the design process, the control parameter μ is used as the key, denoted as key2.

[0062] Finally, the generated feature sequence W′ is... index and watermark sequence W i Perform a logical XOR operation to obtain the zero-watermark image W″, thus completing the embedding. As shown in formula (7).

[0063]

[0064] The keys key1, key2, and the zero-watermark image W″ used in the above embedding process are all stored in a third-party organization and can be used directly during the extraction process.

[0065] Based on the above-embedded zero-watermark image W", the present invention also provides a watermark extraction method:

[0066] Reference Figure 2 As shown, the point sequence DT′ corresponding to the vector map V is obtained by using the embedding method. The three points that form a triangle are read, and the circumcircle radius R′ and incircle radius r′ of each triangle are calculated. Then, the average value Rm′ of the circumcircle radius R′ is calculated. The average value Rm′ is compared with the key key1 to generate a scaling factor K. The incircle radius r′ is scaled according to the scaling factor K.

[0067] Then, the inscribed radius r' of the scaled triangle is used as the seed for a pseudo-random number generator to generate uniformly distributed pseudo-random numbers. These pseudo-random numbers are then mapped to the range 0-L to determine the watermark index value. The watermark value corresponding to the watermark index is calculated using the corresponding circumscribed radius R', and a feature sequence W' is generated. index ;

[0068] For the zero-watermark image W″ and feature sequence W′ index Perform an XOR operation to generate the watermark sequence W′.i ; the water mark sequence W' is processed by the Logistic method and the key key2 to perform reverse shuffling to obtain an extracted water mark image W''' and finally compared with the original water mark image W to verify. i

[0069] To verify the performance of the method, the present application selects six groups of vector maps of different types and different regions as experimental data, as shown in Figure 3 Table 1 provides detailed information about these vector maps. The computer configuration for the experiment is: i7-13500H processor, RTX4060 graphics card, 16GB memory, window 11 operating system. The watermark image used in the experiment is a binary image with a size of 24x24 pixels. The schemes in documents [4] (S. Wang, L. Zhang, and Q. Zhang, “A zero-watermarking algorithm for vector geographic data based on feature invariants,” Earth Science Informatics, vol. 16, no. 1, pp. 1073-1089, 2023.); [5] (Q. Zhou, C. Zhu, and N. Ren, “Zero watermarking algorithm for vector geographic data based on the number of neighboring features,” Symmetry, vol. 13, no. 2, pp. 208, 2021.); [6] (L. Wenqing, Zhang Liming, “Vector geographic data zero watermarking method using DFT,” Acta Geodaetica et Cartographica Sinica, vol. 35, no. 1, pp. 94-98, 2018.) are selected as a comparison.

[0070] The experiment selects the normalized correlation coefficient (NC) to compare the similarity of two images, and sets the threshold value of NC to 0.8. If the NC value of the extracted watermark is higher than 0.8, it indicates that the watermark information extraction is successful, otherwise it indicates that the watermark information extraction fails. The calculation formula of NC is shown in formula (8).

[0071]

[0072] Table 1 provides detailed information about these vector maps. The computer configuration for the experiment is: i7-13500H processor, RTX4060 graphics card, 16GB memory, window 11 operating system. The watermark image used in the experiment is a binary image with a size of 24x24 pixels. The schemes in documents [4] (S. Wang, L. Zhang, and Q. Zhang, “A zero-watermarking algorithm for vector geographic data based on feature invariants,” Earth Science Informatics, vol. 16, no. 1, pp. 1073-1089, 2023.); [5] (Q. Zhou, C. Zhu, and N. Ren, “Zero watermarking algorithm for vector geographic data based on the number of neighboring features,” Symmetry, vol. 13, no. 2, pp. 208, 2021.); [6] (L. Wenqing, Zhang Liming, “Vector geographic data zero watermarking method using DFT,” Acta Geodaetica et Cartographica Sinica, vol. 35, no. 1, pp. 94-98, 2018.) are selected as a comparison.

[0073] Data name Data type Coordinate system Number of elements Number of vertices Map accuracy Administrative division Line BJ54 4712 90636 2.5 x 10 -6 ]]> Building Surface WGS84 23475 166717 2.5 x 10 -6 ]]> Railway Line WGS84 2303 178341 2.5 x 10 -6 ]]> Green land Line BJ54 8017 403328 2.5 x 10 -6 ]]> County boundary Surface BJ54 2591 902589 1 x 10 -5 ]]> Water system Line WGS84 7027 102643 2.5 x 10 -6 ]]> ​

[0074] Zero-watermark is not directly embedded in the vector map, but is constructed by using the characteristics of the vector map itself, therefore, the uniqueness of the watermark is one of the most important indicators to measure the zero-watermark method. A qualified zero-watermark method should have good uniqueness, which means that the zero-watermark images extracted from different vector maps will be very different. According to the selected six vector map data, the experimental results are shown in Table 2.

[0075] Table 2 is the zero-watermark uniqueness verification result

[0076]

[0077]

[0078] It can be seen that the zero-watermark NC value extracted from different vector maps is less than the threshold value 0.8. This is because the Delaunay triangulation constructed by different vector maps has uniqueness, which leads to different radii of the extracted triangles, and then the difference of the generated feature matrix is significant. Therefore, the zero-watermark method proposed in the present application shows unique uniqueness.

[0079] In order to verify the performance of the proposed method in robustness, the present application designs various types and intensities of attack scenes, aiming at comprehensively simulating various security threats that the vector map may encounter in actual application scenarios. Specifically, these attack scenes cover rotation, scaling, translation, point attack, point deletion attack, element increase attack, element deletion attack, reordering and precision reduction attack. These attack means adjust the vertex coordinate value, change the number of vertices and reduce the accuracy of the vertices from multiple dimensions, and systematically modify the vertex information of the vector map, aiming to deeply evaluate the performance stability of the method in dealing with the above-mentioned commonly existing attack situations.

[0080] Table 3 lists in detail the different types of attack methods and their specific attack target positions, providing a solid data basis for quantitatively evaluating the robustness of the method.

[0081] Table 3 is the attack method of robustness experiment:

[0082]

[0083]

[0084] In addition, Figure 4 Through intuitive graphical display, the differences between the present method and other comparative methods in experimental results are clearly presented, which facilitates intuitive understanding of the actual performance differences of each method in dealing with the above attacks.

[0085] The experimental results verify the performance of the vector map zero watermarking method based on the Delaunay triangulation feature invariant, and compared with the methods described in the documents [4-6], the method exhibits significantly enhanced robustness in the face of vertex deletion, vertex addition, precision reduction, translation, and reordering and other attack means. In particular, even in the face of vertex deletion and element deletion, the method proposed in the application can still extract complete watermark information, which embodies its high robustness. Compared with the prior art, the application has achieved more excellent performance in a number of key performance tests, which has proved the effectiveness and innovation of the application in the field of vector map copyright protection.

[0086] The above-described embodiments are only preferred embodiments for fully illustrating the present application, and the protection scope of the present application is not limited thereto. Any equivalent replacement or transformation made by those skilled in the art on the basis of the present application is within the protection scope of the present application.

Claims

1. A geometric feature-based vector map zero-watermark embedding method, characterized in that, Comprising the following steps: Step 1: In the vector map , a set of vertices is extracted , and feature point extraction is performed to obtain a set of feature points ; Step 2: to the feature point set , using the point-by-point insertion method to construct the Delaunay triangulation and get the point sequence ; Step 3: In the point sequence three points constituting a triangle are read, the circumradius R and the inradius r of each triangle are calculated, and a key key1 is generated according to the average of the circumradii R; Step 4: using the radius r of the inscribed circle of the triangle as the seed of the pseudo-random number generator, generating a uniformly distributed pseudo-random number, and generating a pseudo-random number sequence, using the first number of the pseudo-random number sequence as the watermark index; Step 5: Calculate the watermark value of the corresponding watermark index by the circumradius R of the corresponding triangle, and generate the feature sequence ; Step 6: Original watermark image is scrambled and encrypted with key key2 to get scrambled watermark Step 7: The scrambled watermark is converted to watermark sequence Step 8: The watermark sequence is converted to watermark image ; Step 7: The generated feature sequence and the watermark sequence are logically XORed to obtain a zero-watermark image .

2. The geometry-feature-based vector map zero-watermark embedding method of claim 1, wherein, In step 1, the vertex set is wherein is the number of vertices in the set, the vertex set is subjected to feature point extraction using the Douglas-Peucker method to obtain a set of feature points .

3. The geometry-feature-based vector map zero-watermark embedding method of claim 1, wherein, In step 4, the pseudo-random number is generated by using the mersenne twist method, and the formula is as follows: ； ； wherein, represents the state of the nth pseudo-random number, represents the XOR operation, represents the left shift operation, represents the right shift operation, n, m, s, t represent the shift step, shift mask and two bit shift parameters in the selected Mersenne prime number, respectively; represents the twisted state, represents the bitwise AND operation, is an integer value for the right shift operation, is a bit mask for changing the characteristics of the state, increasing the randomness of the pseudo-random number.

4. The geometry-feature-based vector map zero-watermark embedding method of claim 3, wherein, A derivative version of the mersenne twist method, MT19937, is used to establish the pseudo-random number sequence, and the pseudo-random number generator generates a set of pseudo-random number sequences using a seed, different seeds generate different pseudo-random number sequences, and the same seed is input to obtain the same pseudo-random number sequence.

5. The geometry-feature-based vector map zero-watermark embedding method of claim 3, wherein, mapping the pseudo-random number to 0 L between, L for the watermark length, generating a watermark index value .

6. The geometry-feature-based vector map zero-watermark embedding method of claim 5, wherein, In step 5, the final watermark value is determined by a voting mechanism, the rules are as follows: if the circumradius R of the corresponding triangle is greater than the average value Rm of all circumradii R, then the value of the corresponding triangle is increased by 1, otherwise the value of the corresponding triangle is decreased by 1, according to the final value, if greater than 0, the watermark value of the position will be recorded as 1, if less than 0, the watermark value of the position will be recorded as 0; represents the difference between the number of 1's and 0's counted in the i-th bit of the watermark.

7. The geometry-feature-based vector map zero-watermark embedding method of claim 1, wherein, In step 6, the watermark sequence is , L is the watermark length, and the calculation formula is , wherein represents the chaotic sequence generated by the kth generation mapping, is a control parameter, and the control parameter is used as a key, denoted as key2.

8. A vector map zero-watermark extraction method based on geometric features, characterized in that, The watermark embedded by the method of any one of claims 1-7 is extracted, comprising the following steps: A, to the vector map Feature point extraction is performed and a Delaunay triangulation is constructed using a point-by-point insertion method to obtain a point sequence According to the point sequence , three points constituting a triangle are read, the circumradius R' and the inradius r' of each triangle are calculated, and then the average value Rm' of the circumradius R' is calculated; B. Compare the average value Rm' with the key key1 to generate a scaling factor K, and scale the inscribed circle radius r' according to the scaling factor K; C. The radius r' of the inscribed circle of the scaled triangle is taken as the seed of the pseudo-random number generator to generate a uniformly distributed pseudo-random number, and the pseudo-random number is mapped to 0- L between to determine the watermark index value ; the watermark value corresponding to the watermark index is calculated by the corresponding circumscribed circle radius R', and the feature sequence is generated; D. zero-watermark image and feature sequence performing XOR operation to generate watermark sequence ; E. The watermarked sequence is inverted using the logistic method and key key2 The watermarked image is extracted by inverting the sequence The extracted watermarked image is compared to the original watermarked image to verify the extraction.

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