Zero watermarking method for vector map based on geometric features

Abstract

The invention discloses a vector map zero-watermarking method based on geometric features, which comprises the following steps of: firstly, constructing a vector map by utilizing geometric invariance of a Delaunay triangulation network, extracting a circumcircle radius and an inscribed circle radius of a triangle as feature invariants through Delaunay triangulation, and extracting the feature invariants through a Delaunay triangulation network; the algorithm generates a pseudo random number sequence through the radius of an inscribed circle of a triangle so as to determine the index position of watermark embedding, and introduces a voting mechanism to determine the final value of each watermark bit, so that the final value of each watermark bit is determined; a zero-watermark image is obtained through scrambling and exclusive-or operation, and a watermark image is extracted through inverse scrambling and exclusive-or operation. According to the method, the stability of the geometric structure can be kept, and remarkable robustness is shown for vertex attacks.

Description

Technical Field

[0001] The invention relates to the technical field of map watermarking, and in particular to a vector map zero watermarking method based on geometric features. Background Art

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

[0003] In the field of traditional digital watermarking technology, it is mainly divided into two categories: spatial domain and frequency domain. The spatial domain watermarking method embeds watermark information by directly modifying the coordinate values ​​of the vector map. This method is favored for its intuitiveness and ease of operation; however, its robustness is generally weak, which has become a key factor limiting its widespread application. In contrast, the frequency domain watermarking method adopts a more complex processing method: first, the coordinates of the vector map are frequency transformed, and then the watermark is embedded by adjusting the frequency coefficient. This scheme significantly improves the robustness and security of the watermark, but it is accompanied by a large disturbance to the vector map, which is particularly unsuitable for vector maps that require high accuracy (such as high-precision surveying and mapping). It is worth noting that both spatial domain and frequency domain watermarking methods will have different degrees of impact on the accuracy of the vector map. For vector maps with low precision requirements, these subtle changes may be negligible, but in fields with extremely high precision requirements such as military applications and road navigation systems, such changes will directly lead to a significant decrease in data reliability. In view of this, the lossless zero watermark technology has attracted increasing attention in academia and practical application fields because it can avoid any form of modification to the original data.

[0004] The zero watermark method constructs a watermark by mining the characteristic information of the vector map. The original data will not be modified during the watermark construction process, which is very suitable for the high-precision use environment of the vector map. Therefore, the zero watermark method does not have the problem of watermark invisibility and robustness constraining each other. Pursuing the robustness of the method and the uniqueness of the watermark has become an important research direction of zero watermark.

[0005] Existing zero watermark schemes have been studied in the field of vector map security protection, for example:

[0006] References [1] Zhang Zuoli, Sun Shusen, and Wang Yaming, “Zero watermark method for two-dimensional vector digital maps,” Computer Engineering and Design, vol. 30, no. 6, pp. 1473-1475, 2009. The vector map data is divided into blocks, and the number of vertices in each block is counted. Then, these vertex numbers are XORed with the original watermark image to construct a copyright watermark image.

[0007] Reference [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 transformation method to construct a vector map zero watermarking scheme, which can restore the watermarked image under common geometric attacks, shear attacks and coordinate system transformations.

[0008] Reference [3] Wang Shuai, Zhang Liming, and Li Yu, "Zero watermark 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 uses the block data for normalization and singular value decomposition, which meets the copyright protection requirements of point, line, and surface data and has good robustness against scaling and cropping attacks.

[0009] Although the zero watermark schemes proposed in the above-mentioned references [1]-[3] have certain advantages in the field of vector map security protection, these schemes still have certain limitations in practical application environments. Specifically, reference [1] constructs a zero watermark based on the relative storage order of elements, which is highly robust against precision reduction and projection transformation attacks. However, in practical applications, the number of vertices is often modified, and the watermark construction scheme proposed in reference [1] cannot cope with this situation. Reference [2] uses the topological adjacent relationship in planar vector data to construct a watermark, but this method ignores the impact of element addition and deletion on the stability of the watermark. In addition, although a solution for linear vector data is proposed in the paper, its robustness in practical application is still unknown. Although reference [3] constructs a zero watermark based on DFT transformation, it does not deeply explore its characteristics and only uses its phase sequence. The addition and deletion of vertices will affect the watermark extraction process. In addition, the current zero watermark protection scheme for vector maps has certain shortcomings in coping with vertex addition and deletion. In practical applications, vertex addition and deletion operations are extremely common. Summary of the invention

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

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

[0012] Step 1: In the original vector map V, extract the vertex set P and perform feature point extraction 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 network and obtain a point sequence DT;

[0014] Step 3: Read the three points that form the triangle in the point sequence DT, calculate the circumscribed circle radius R and the inscribed circle radius r of each triangle, and generate the key key1 based on the average value of the circumscribed circle radius R;

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

[0016] Step 5: Calculate the watermark value of the corresponding watermark index through the circumscribed circle radius R of the corresponding triangle, and generate the feature sequence W index ;

[0017] Step 6: Scramble the original watermark image W and encrypt the key key2 to obtain the scrambled watermark W′, and convert it into the watermark sequence W i ;

[0018] Step 7: Generate the feature sequence W′ index and watermark sequence W i Perform a logical XOR operation to obtain the zero watermark image W".

[0019] Furthermore, 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. The Douglas-Peucker method is used to extract feature points from the vertex set P to obtain a set of feature points P′.

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

[0021]

[0022] Among them, X n Represents the state of the nth pseudo-random number, represents an XOR operation, <<< represents a left shift operation, >>> represents a right shift operation, n, m, s, t represent the shift step size, shift mask, and two shift parameters in the selected Mersenne prime number respectively; Y n Represents the distorted state, & represents the bitwise AND operation, u is an integer value used for right shift operation, and d is a bit mask used to change the characteristics of the state and increase the randomness of the pseudo-random number.

[0023] Furthermore, a derivative version of the Mersenne Twister method, MT19937, is used to establish a pseudo-random number sequence. The pseudo-random generator generates a set of pseudo-random number sequences using a seed. Different seeds generate different pseudo-random number sequences. The same pseudo-random number sequence is obtained by inputting the same seed.

[0024] Furthermore, the pseudo-random number is mapped to a range between 0 and L, where L is the watermark length, to generate a watermark index value index.

[0025] Furthermore, in step 5, a voting mechanism is used to determine the final watermark value, and the rules are as follows: if the circumscribed circle radius R of the corresponding 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. According to the final value of w(i), if it is greater than 0, the watermark value of the position will be recorded as 1, and if it is less than 0, the watermark value of the position will be recorded as 0;

[0026] w(i) represents the difference between the number of 1s and 0s 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}, L is the watermark length, and its calculation formula is X k+1 =μX k (1-X k ), where X k ∈(0, 1) represents the chaotic sequence generated by the k-th generation mapping, μ∈[0, 4] is the control parameter, and the control parameter is used as the key, denoted as key2.

[0028] A method for extracting zero watermark from a vector map based on geometric features, for extracting the watermark embedded in the method according to any one of claims 1 to 8, comprising the following steps:

[0029] A. Extract feature points from the vector map V and construct a Delaunay triangulation network using the point-by-point insertion method to obtain a point sequence DT′. According to the point sequence DT′, read the three points that constitute the triangle, calculate the circumscribed circle radius R′ and the inscribed circle radius r′ of each triangle, and then calculate the average value Rm′ of the circumscribed circle 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 according to the scaling factor K;

[0031] C. Use the radius r' of the inscribed circle of the scaled triangle as the seed of the pseudo-random number generator to generate uniformly distributed pseudo-random numbers, and map the pseudo-random numbers to between 0 and L to determine the watermark index value index; calculate the watermark value corresponding to the watermark index by the corresponding circumscribed circle radius R', and generate the feature sequence W' index ;

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

[0033] E. Use the Logistic method and key key2 to watermark the sequence W′ i After reverse scrambling, the extracted watermark image W″′ is obtained, and finally compared with the original watermark image W for verification.

[0034] Beneficial effects of the present invention:

[0035] In view of the limitations of existing zero-watermarking methods in resisting vertex attacks, this paper proposes a vector map zero-watermarking scheme based on Delaunay triangulation feature invariants that is robust to vertex attacks. It is based on Delaunay triangulation feature invariants and exhibits significant robustness to vertex attacks. Specifically, the method first uses the Douglas-Peucker method to accurately extract feature points, and then constructs a Delaunay triangulation based on these feature points. This combined strategy effectively overcomes the problem that traditional Delaunay triangulation is difficult to maintain geometric structure stability when facing point addition or deletion attacks.

[0036] In the process of constructing the zero watermark, the method cleverly uses the incircle radius and circumcircle radius of the Delaunay triangle as key parameters to calculate the watermark index and watermark value. To ensure the uniform distribution and embedding strength of the watermark, the method introduces the Mersenne rotation operator to accurately control the number of embeddings of each watermark bit. In addition, the average value of the circumcircle radius is used as the encryption key, which can significantly enhance the robustness of the Delaunay triangulation network in dealing with common geometric transformation attacks such as translation, rotation, and scaling (RST), providing a more comprehensive and effective solution strategy for the copyright protection of vector map data. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a watermark embedding flow chart of the present invention;

[0038] Figure 2 It is a watermark extraction flow chart of the present invention;

[0039] Figure 3 It is an experimental data diagram of the present invention;

[0040] Figure 4 It is a line graph of the robustness experimental results of the present invention. DETAILED DESCRIPTION

[0041] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0042] An embodiment of the zero watermark method for vector maps based on geometric features of the present invention is a zero watermark method based on the feature invariant of the Delaunay triangulation, and proposes a zero watermark technology for constructing vector maps by using the geometric invariance of the Delaunay triangulation. Through Delaunay triangulation, the circumscribed circle radius and the inscribed circle radius of the triangle are extracted as feature invariants, so that the constructed watermark maintains stability 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 through the radius of the inscribed circle of the triangle to determine the index position of watermark embedding, and introduces a voting mechanism to determine the final value of each watermark position. This method improves the stability and robustness of watermark information during the watermark embedding process.

[0044] Based on its high robustness to various forms of attacks, in order to cope with different situations in actual needs, this method experiments on a variety of data and shows strong robustness in dealing with various vertex change-related attacks such as rotation, scaling, translation, adding points, deleting points, and precision reduction. It effectively overcomes the problem of insufficient robustness of traditional zero-watermark methods when the number of vertices changes.

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

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

[0047] Then, the processed feature point set P′ is used to construct the Delaunay triangulation and obtain the point sequence DT.

[0048] In the point sequence DT, the three points constituting the triangle are read, the circumscribed circle radius R and the inscribed circle radius r of each triangle are calculated, and the key key1 is generated according to the average value of the circumscribed circle radius.

[0049] Then, the radius r of the inscribed circle of the triangle is used as the seed of the pseudo-random number generator to generate a pseudo-random number sequence, and the first number of the pseudo-random sequence is used as the watermark index.

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

[0051]

[0052] Among them, X n Represents the state of the nth pseudo-random number, represents an XOR operation, <<< represents a left shift operation, >>> represents a right shift operation, and n, m, s, and t represent the shift step size, shift mask, and two shift parameters in the selected Mersenne prime number, respectively. n Represents the distorted state, & represents the bitwise AND operation, u is an integer value used for right shift operation, and d is a bit mask used to change the characteristics of the state and increase the randomness of the pseudo-random number. Here, a derivative version of the Mersenne rotation method, MT19937, is used to establish a pseudo-random number sequence. The pseudo-random generator uses a pseudo-random number seed to generate a set of pseudo-random number sequences. Different seeds will generate different pseudo-random number sequences. The same pseudo-random number sequence can be obtained by inputting the same seed.

[0053] Since there is a difference between the value range of the pseudo-random number sequence and the watermark index value, it is necessary to map the pseudo-random number M 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 radius R of the circumscribed circle and the number 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 of the corresponding watermark index. Combine the watermark value and 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, the watermark index value index generated by the inscribed circle radius r in the above process is a repeated positive integer in the range of 0-L, that is, the watermark indexes corresponding to multiple triangles with different inscribed circle radii r are the same. Therefore, a voting mechanism is used to determine the final watermark value. The rule is as follows: If the circumscribed circle radius R of the corresponding triangle is greater than the average value Rm of all circumscribed circle radii R, 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 continuous increase and decrease. 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 difference between the number of 1s and 0s in the i-th bit of the watermark, R j W′ represents the radius of the circumscribed circle of the jth triangle, and Rm represents the average value of the circumscribed circle radius R of the triangle. index Represents the generated feature sequence. The specific feature matrix construction process is as follows Figure 1 As shown in (b).

[0059] Then, the original watermark image W is encrypted by scrambling the watermark information using the Logistic method to obtain the scrambled watermark W′, which is then converted into the 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 kth generation mapping, μ∈[0,4] is the control parameter, and it is difficult to restore the watermark data without knowing μ. In the design process, the control parameter μ is used as a key, denoted as key2.

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

[0063]

[0064] The key key1, key key2, and zero watermark image W″ in the above embedding process are all stored in a third-party organization and can be directly used in 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 the embedding method, the three points constituting the triangle are read, the circumscribed circle radius R' and the inscribed circle radius r' of each triangle are calculated, and then the average value Rm' of the circumscribed circle radius R' is calculated; the average value Rm' is compared with the key key1 to generate the scaling factor K, and the inscribed circle radius r' is scaled by the corresponding ratio according to the scaling factor K;

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

[0068] For zero watermark image W″ and feature sequence W′ index Perform XOR operation to generate watermark sequence W′i ; Use the Logistic method and key key2 to watermark the sequence W′ i After reverse scrambling, the extracted watermark image W″′ is obtained, and finally compared with the original watermark image W for verification.

[0069] In order to verify the performance of the method, the present invention selected six sets of vector maps of different types and regions as experimental data, such as Figure 3 As shown in the figure, they are administrative divisions, buildings, railways, green spaces, county boundaries and water systems. Table 1 provides detailed information on these vector maps. The computer configuration of the experiment is: i7-13500H processor, RTX4060 graphics card, 16GB memory, window11 operating system. The watermark image used in the experiment is a binary image with a size of 24×24 pixels. The schemes in literature [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.); literature [5](Q.ZHOU,C.ZHU,and N.REN,“Zerowatermarking algorithm for vector geographic data based on the number ofneighboring features,”Symmetry,vol.13,no.2,pp.208,2021.); literature [6](Lv Wenqing,Zhang Liming,“Zero watermarking method for vector geographic data based on DFT,”Journal of Surveying and Mapping Science and Technology,vol.35,no.1,pp.94-98,2018.) are selected for comparison.

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

[0071]

[0072] Table 1 shows the detailed information of the vector map:

[0073] Data name Data Types Coordinate system Number of elements Number of vertices Map accuracy Administrative divisions Wire BJ54 4712 90636 <![CDATA[2.5×10 -6 ]]> building noodle WGS84 23475 166717 <![CDATA[2.5×10 -6 ]]> railway Wire WGS84 2303 178341 <![CDATA[2.5×10 -6 ]]> Greenland Wire BJ54 8017 403328 <![CDATA[2.5×10 -6 ]]> County Boundaries noodle BJ54 2591 902589 <![CDATA[1×10 -5 ]]> Water system Wire WGS84 7027 102643 <![CDATA[2.5×10 -6 ]]>

[0074] Zero watermark is not directly embedded into 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 for measuring 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. This paper conducts experiments based on the selected six vector map data, and the results are shown in Table 2.

[0075] Table 2 shows the zero watermark uniqueness verification results

[0076]

[0077]

[0078] It can be seen that the zero watermark NC values ​​extracted from different vector maps are all less than the threshold value of 0.8. This is because the Delaunay triangulation constructed by different vector maps is unique, resulting in different extracted triangle radii, and thus significantly different feature matrices. Therefore, the zero watermark method proposed in the present invention exhibits unique uniqueness.

[0079] In order to verify the robustness of the proposed method, the present invention designs attack scenarios of various types and intensities, aiming to fully simulate various security threats that vector maps may encounter in actual application scenarios. Specifically, these attack scenarios cover rotation, scaling, translation, point addition attack, point deletion attack, element addition attack, element deletion attack, reordering, and precision reduction attack. These attack methods systematically modify the vertex information of the vector map from multiple dimensions such as vertex coordinate value adjustment, vertex number change, and vertex precision reduction, aiming to deeply evaluate the performance stability of the method in dealing with the above-mentioned common attack scenarios.

[0080] Table 3 lists in detail the different types of attack methods and their specific attack target locations, providing a solid data foundation for the robustness of the quantitative evaluation method.

[0081] Table 3 shows the attack methods of the robustness experiment:

[0082]

[0083]

[0084] also, Figure 4 Through intuitive graphical display, the differences in experimental results between this method and other comparison methods are clearly presented, making it easier to intuitively grasp the actual performance differences of each method in dealing with the above-mentioned attacks.

[0085] The experimental results verify the performance of the vector map zero watermark method based on Delaunay triangulation feature invariants proposed in this invention. Compared with the methods described in references [4-6], this method shows significantly enhanced robustness in the face of various attack methods such as vertex deletion, vertex addition, precision reduction, translation, and reordering. In particular, even in the extreme case of vertex deletion and feature deletion, the method proposed in this invention can still extract complete watermark information, reflecting its high robustness. Compared with the prior art, the present invention has achieved better performance in multiple key performance tests, which strongly proves its effectiveness and innovation in the field of vector map copyright protection.

[0086] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or change made by a person skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A vector map zero watermark embedding method based on geometric features, characterized in that: The following steps are involved: Step 1: In the vector map v, extract the vertex set P and perform feature point extraction to obtain the feature point set P′; Step 2: For the feature point set P′, a point-by-point insertion method is used to construct a Delaunay triangulation network and obtain a point sequence DT; Step 3: Read the three points that form the triangle in the point sequence DT, calculate the circumscribed circle radius R and the inscribed circle radius r of each triangle, and generate the key key1 based on the average value of the circumscribed circle radius R; Step 4: Use the radius r of the inscribed circle of the triangle as the seed of the pseudo-random number generator to generate uniformly distributed pseudo-random numbers and a pseudo-random number sequence, and use the first number of the pseudo-random number sequence as the watermark index; Step 5: Calculate the watermark value of the corresponding watermark index through the radius R of the circumscribed circle of the corresponding triangle, and generate the feature sequence W′ index ; Step 6: Scramble the original watermark image W and encrypt the key key2 to obtain the scrambled watermark W′, and convert it into the watermark sequence W i ; Step 7: Generate the feature sequence W′ index and watermark sequence W i Perform a logical XOR operation to obtain the zero watermark image W″.

2. The vector map zero watermark embedding method based on geometric features as claimed in claim 1 is characterized in that: 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. The Douglas-Peucker method is used to extract feature points from the vertex set P to obtain a set of feature points P′.

3. The vector map zero watermark embedding method based on geometric features as claimed in claim 1 is characterized in that: In step 4, the Mersenne rotation method is used to generate pseudo-random numbers. The formula is as follows: Among them, X n Represents the state of the nth pseudo-random number, represents an XOR operation, <<< represents a left shift operation, >>> represents a right shift operation, n, m, s, t represent the shift step, shift mask and two shift parameters in the selected Mersenne prime number respectively; Y n Represents the distorted state, & represents the bitwise AND operation, u is an integer value used for right shift operation, and d is a bit mask used to change the characteristics of the state and increase the randomness of the pseudo-random number.

4. The vector map zero watermark embedding method based on geometric features as claimed in claim 3 is characterized in that: A derivative version of the Mersenne Twister method, MT19937, is used to establish a pseudo-random number sequence. The pseudo-random generator uses a seed to generate a set of pseudo-random number sequences. Different seeds generate different pseudo-random number sequences. The same pseudo-random number sequence is obtained by inputting the same seed.

5. The vector map zero watermark embedding method based on geometric features as claimed in claim 3 is characterized in that: Map the pseudo-random number to between 0 and L, where L is the watermark length, and generate the watermark index value index.

6. The vector map zero watermark embedding method based on geometric features as claimed in claim 5, characterized in that: In step 5, a voting mechanism is used to determine the final watermark value. The rules are as follows: if the circumscribed circle radius R of the corresponding 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. According to the final value of w(i), if it is greater than 0, the watermark value of this position will be recorded as 1, and if it is less than 0, the watermark value of this position will be recorded as 0. w(i) represents the difference between the number of 1s and 0s in the i-th bit of the watermark.

7. The vector map zero watermark embedding method based on geometric features as claimed in claim 1 is characterized in that: In step 6, the watermark sequence is {W i =0.1|i=0, 1, ..., L-1}, L is the watermark length, and its calculation formula is X k+1 =μX k (1-X k ), where X k ∈(0, 1) represents the chaotic sequence generated by the k-th generation mapping, μ∈[0, 4] is the control parameter, and the control parameter is used as the key, denoted as key2.

8. A method for extracting zero watermark from vector maps based on geometric features, characterized in that: Extracting the watermark embedded in the method according to any one of claims 1 to 8 comprises the following steps: A. Extract feature points from the vector map V and construct a Delaunay triangulation network using the point-by-point insertion method to obtain a point sequence DT'. According to the point sequence DT', read the three points that constitute the triangle, calculate the circumscribed circle radius R' and the inscribed circle radius r' of each triangle, and then calculate the average value Rm' of the circumscribed circle radius R'; B. Compare the average value Rm' with the key key1 to generate a scaling factor K, and scale the inscribed circle radius r' accordingly according to the scaling factor K; C. Use the radius r' of the inscribed circle of the scaled triangle as the seed of the pseudo-random number generator to generate uniformly distributed pseudo-random numbers, and map the pseudo-random numbers to between 0 and L to determine the watermark index value index; calculate the watermark value corresponding to the watermark index through the corresponding circumscribed circle radius R', and generate the feature sequence W' index ; D. Zero watermark image W″ and feature sequence W′ index Perform XOR operation to generate watermark sequence W′ i ; E. Use the Logistic method and key key2 to watermark the sequence W′ i After reverse scrambling, the extracted watermark image W″′ is obtained, and finally compared with the original watermark image W for verification.

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