A vector map reversible watermarking method based on adaptive arithmetic coding

Abstract

The application discloses a vector map reversible watermarking method based on adaptive arithmetic coding and relates to the technical field of geographic information, wherein a local geometric structure formed by three adjacent vertices is used as a basic processing unit, a geometric invariant is constructed by using the length ratio of adjacent line segments as a watermark embedding domain, and the invariant is quantized and modulated to realize the geometric invariance of the embedding domain under translation, rotation and uniform scaling transformation. The embedding domain only depends on the local vertex relationship, avoids watermark failure caused by global feature change, reduces the probability of embedding domain repetition, realizes blind extraction without the original map, and has the robustness under geometric attacks and vertex editing attacks.

Description

Technical Field

[0001] This invention relates to the field of geographic information technology, specifically to a reversible watermarking method for vector maps based on adaptive arithmetic coding. Background Technology

[0002] With the rapid development of Geographic Information Systems (GIS), vector maps, as an important carrier of geospatial data, have been widely used in smart cities, autonomous driving, and military navigation. The digital nature of vector maps makes them susceptible to copying and tampering, leading to frequent copyright infringement issues and seriously damaging the legitimate rights and interests of data copyright holders. Digital watermarking technology, as a proactive information security measure, provides an effective solution for the copyright protection and integrity verification of vector maps by embedding copyright information into the carrier data.

[0003] Current research on reversible watermarking algorithms for vector maps focuses on three key indicators: robustness, invisibility, and watermark capacity. However, existing technologies struggle to achieve a balanced approach to all three. Among existing geometric feature-based technologies, some algorithms utilize polar coordinate invariance and virtual triangle feature domains to construct watermark embedding domains. While these methods offer some resistance to geometric attacks such as translation, rotation, and scaling, they suffer from insufficient watermark capacity and poor adaptability to different types of vector maps. Schemes combining data compression techniques can reduce the disturbance to the carrier caused by watermark embedding, but they often rely on fixed reference vertices, making them susceptible to vertex tampering and resulting in algorithm failure. Furthermore, they do not fully leverage geometrically invariant features, leaving room for improvement in robustness against geometric attacks.

[0004] Therefore, developing a reversible watermarking method for vector maps that balances large capacity, strong robustness, and low perturbation has become a pressing technical challenge. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a reversible watermarking method for vector maps based on adaptive arithmetic coding, which solves the problems mentioned in the background technology.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a reversible watermarking method for vector maps based on adaptive arithmetic coding, the method comprising: S1: Read the vector map and use three adjacent vertices in the vector map as the basic processing unit to construct the watermark embedding domain; S2: Read the watermark image data to be embedded, and after preprocessing it, obtain a decimal watermark sequence. The preprocessing includes performing binarization, iterative adaptive arithmetic coding, and decimal conversion. S3: Based on the decimal watermark sequence and watermark embedding field, the vertex coordinates are modulated to achieve watermark embedding in order to update the vector map; S4: Extract the watermark image data from the updated vector map to fully restore the original vector map, thus achieving the reversibility of the algorithm.

[0007] Preferably, the step of obtaining the basic processing unit includes: The spatial features in the vector map are analyzed, and the vertices in the vector map are traversed and extracted according to different types of spatial features to form a vertex sequence set; Based on spatial adjacency topology analysis, combined with spatial distance threshold determination method, the vertex sequence set is checked for continuity to remove broken or duplicate vertex coordinates, and the vertex sequence set is updated through adjacency relationship; Set the scanning window length, perform sliding window scanning on the updated vertex sequence set, construct basic processing units with three consecutive vertices as units, and form a three-vertex structure set.

[0008] Preferably, the step of constructing the watermark embedding field includes: Connect the first and last vertices of the three-vertex structure set with straight lines, calculate the midpoint of the corresponding line segment, take the midpoint of the line segment as the center of the circle, determine the diameter according to the length of the line segment connecting the first and last vertices, and construct the corresponding semicircular geometric structure. By connecting the midpoint of the line segment with the non-starting and end vertices, and extending the line segment to intersect the boundary of the semicircular geometric structure, we obtain the geometric auxiliary point; Record the spatial relationship data between geometric auxiliary points, the center of the circle, and the three vertices in the three-vertex structure set. The spatial relationship data includes the distance features from the center of the circle to the geometric auxiliary points and the distance features from the non-first and last vertices to the center of the circle. By using the ratio between the two distance features in the spatial relationship data as a geometric invariant, a watermark embedding domain is constructed.

[0009] Preferably, the watermark image data to be embedded is read and preprocessed to obtain a decimal watermark sequence, including: Read the watermark image data to be embedded, and perform binarization on the watermark image data to obtain a one-dimensional binary sequence. Group the sequence according to a preset encoding length to obtain a set of subsequences; the set of subsequences includes several groups of subsequences. Each subsequence is subjected to adaptive arithmetic coding. The subsequence is encoded by dividing the probability interval to generate the corresponding coding result. After iterative coding, the shortest coding result is selected as the final result. The compressed one-dimensional binary sequence is obtained by summarizing the results. The compressed one-dimensional binary sequence is regrouped according to the preset embedding strength to obtain several groups of binary subsequences. The binary subsequences are then converted to decimal values ​​to obtain decimal watermark sequences.

[0010] Preferably, based on the decimal watermark sequence and the watermark embedding domain, the vertex coordinates are modulated to achieve watermark embedding, so as to obtain a watermarked vector map, including: A proportional sequence is obtained based on the geometric invariants in each watermark embedding domain. By performing numerical transformation on the geometric invariants in the proportional sequence, a corresponding index sequence is obtained. The index sequence contains multiple sets of index values, which are used to determine the watermark data position corresponding to the corresponding basic processing unit. Based on the index sequence, the watermark value at the corresponding position in the decimal watermark sequence is matched. If the index value exceeds the length of the decimal watermark sequence, the index value is remapped using modulo operation to determine the valid position, and the watermark value corresponding to each basic processing unit is recorded to form a watermark matching sequence.

[0011] Preferably, based on the decimal watermark sequence and the watermark embedding domain, the vertex coordinates are modulated to achieve watermark embedding, so as to obtain a watermarked vector map, and the method further includes: S301: After watermark matching is completed, the watermark value is embedded into the geometric invariant to obtain the watermark ratio. The watermark ratio is used to reflect the relative proportion of the basic processing units after perturbation. S302: Based on the combination of each three-vertex structure set, calculate the movement direction of non-first and last vertices to obtain the direction unit vector. The direction unit vector represents the fixed unit direction along the center of the circle pointing to non-first and last vertices. S303: Based on the watermark ratio and combined with the direction unit vector, the coordinates of the non-first and last vertices are modulated in reverse to obtain the watermarked vertices. The watermarked vertices are used to ensure that the non-first and last vertices move in a fixed direction and reduce embedding disturbance. By progressively scanning all three-vertex structure sets and repeating steps S301 to S303 until all vertices have completed watermark embedding, the vector map is updated to obtain a watermarked vector map.

[0012] Preferably, the watermarked image data is extracted from the updated vector map to fully restore the original vector map, achieving the reversibility of the algorithm, including: Read the updated vector map and repeat step S1 to obtain the embedded vertex sequence set, the embedded spatial relationship data, and the embedded geometric invariants; By taking the modulo of the embedded geometric invariant with respect to the embedding period, the remainder of the embedded geometric invariant in the corresponding quantization interval is obtained. After normalization, the embedded watermark value is extracted, and the corresponding decimal watermark sequence is restored.

[0013] Preferably, extracting the watermarked image data from the updated vector map to fully restore the original vector map and achieve algorithm reversibility also includes: Based on the embedded watermark value, a quantization offset is obtained, and the corresponding quantization offset is subtracted from the embedded geometric invariant to restore the original geometric invariant. The quantization offset is to convert the watermark value into an embedded value that is adapted to the numerical magnitude of the geometric invariant. Using the restored original geometric invariants and the embedded vertex sequence set, the coordinates of the original non-first and last vertices are obtained by inversely calculating the geometric relationships. The original watermark image is restored by removing duplicates from the recovered decimal watermark sequence and converting it into a one-dimensional binary sequence, which is then restored by adaptive arithmetic decoding. Reconstruct all the recovered original vertices according to different spatial elements to obtain the complete original vector map.

[0014] The present invention has the following beneficial effects: (1) Using the local geometric structure formed by three adjacent vertices as the basic processing unit, a geometric invariant is constructed as the watermark embedding domain by the ratio of the lengths of adjacent line segments. This invariant is then quantized and modulated to achieve geometric invariance of the embedding domain under translation, rotation, and uniform scaling transformations. This embedding domain only depends on the local vertex relationships, avoiding watermark failure caused by global feature changes. It also reduces the probability of overlapping embedding domains, enabling the algorithm to perform blind extraction without the participation of the original map, and taking into account the robustness under geometric attacks and vertex editing attacks.

[0015] (2) To address the limited watermark capacity, adaptive arithmetic coding is introduced before watermark embedding to compress the original binary watermark information in multiple rounds, and the optimal coding result is selected as the final watermark representation. Furthermore, the amount of information per embedding is reduced through base conversion. Without significantly increasing the perturbation of vertex coordinates, the watermark carrying capacity per unit vertex is improved, and multi-position redundant embedding is achieved by shortening the watermark length, thereby enhancing the robustness of the algorithm against non-geometric attacks such as vertex addition and deletion, feature editing, and map clipping.

[0016] (3) In the process of watermark embedding and extraction, the geometric invariants are segmented and the vertex coordinates are modulated in reverse to realize the embedding and recovery of watermark information, ensuring that the vertices only undergo small and controllable displacements, effectively reducing the impact on the geometric accuracy and visual effect of the vector map. At the same time, through continuous polyline preprocessing, various types of vector data such as points, lines, and surfaces are uniformly converted into vertex sequences for processing, ensuring that the algorithm has good reversibility, invisibility and universality. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a diagram illustrating the geometric invariants constructed in this invention; Figure 3 This is a watermark encoding diagram for the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Example 1 Please see Figures 1 to 3 This invention provides a reversible watermarking method for vector maps based on adaptive arithmetic coding, the method comprising: S1: Read the vector map and use three adjacent vertices in the vector map as the basic processing unit to construct the watermark embedding domain; S2: Read the watermark image data to be embedded, and after preprocessing it, obtain a decimal watermark sequence. The preprocessing includes performing binarization, iterative adaptive arithmetic coding, and decimal conversion. The decimal watermark sequence is used to reduce the watermark length, increase the watermark capacity, and realize large-capacity watermark embedding with small information content. S3: Based on the decimal watermark sequence and watermark embedding domain, the coordinates of the vertex (excluding the first and last vertices) are modulated to achieve watermark embedding, while ensuring low perturbation in the embedding process, so as to update the vector map. S4: Extract the watermark image data from the updated vector map to fully restore the original vector map, thus achieving the reversibility of the algorithm.

[0020] In this embodiment, by constructing a watermark embedding domain with three adjacent vertices as basic units, and combining watermark data compression and low-perturbation coordinate modulation strategies, a comprehensive effect of high-capacity embedding, low geometric distortion, and reversible restoration of the original map is achieved. First, by performing binarization processing, iterative adaptive arithmetic coding, and decimal conversion on the watermark image, the length of the watermark data can be significantly compressed, reducing the amount of embedded data while maintaining information integrity, thereby improving the overall watermark capacity.

[0021] Secondly, in vector maps, the basic embedding unit is formed by three adjacent vertices. By embedding watermark information by modulating only the coordinates of the middle vertex (not the first and last vertices), the range of geometric disturbance can be effectively controlled, ensuring that the spatial shape of the map remains basically unchanged, and improving data concealment and robustness.

[0022] Finally, in the watermark extraction stage, watermark information can be extracted from the updated vector map according to the embedding rules, and vertex coordinates can be recovered in reverse, thereby achieving lossless restoration of the original vector map and meeting the application requirements with high spatial data integrity. The logic is to first efficiently compress the watermark information to reduce the embedding load, then use a geometrically stable vertex structure as the embedding carrier, embedding the information into the geometric parameters through reversible modulation, and finally recovering the original data through inverse operations during extraction. For example, when a 32×32 binary watermarked image needs to embed road vector data, the watermark sequence can first be compressed into a shorter decimal sequence through adaptive arithmetic coding, and then three consecutive vertices in the road polyline can be selected as embedding units. Watermark embedding can be completed by making only minor adjustments to the coordinates of the middle vertex. During extraction, the watermark information can be recovered by calculating the corresponding geometric parameters, while simultaneously restoring the original vertex coordinates, keeping the road vector shape consistent with that before embedding, thus achieving the effect of verifying copyright without affecting map accuracy.

[0023] Example 2 Please refer to Figure 1 Specifically, the steps for obtaining the basic processing unit include: The spatial features in the vector map are analyzed, and the vertices in the vector map are traversed and extracted according to different types of spatial features to form a vertex sequence set; Spatial elements include point elements, line elements, and polygon elements, and these elements are processed in a unified structure. A vertex is a geometric base point with unique geographic coordinates in a vector map. All point, line, and area elements are formed by vertices (coordinate points) through specific topological relationships (connection, closure, and adjacency).

[0024] Based on the spatial adjacency topology analysis method, combined with the spatial distance threshold judgment method, the continuity of the vertex sequence set is checked to remove broken or duplicate vertex coordinates. Then, the vertex connection order is reconstructed through adjacency relationship, and the vertex sequence set is updated so that all geometric elements in the vector map can be expressed as a continuous vertex sequence. Specifically, focusing on the spatial coordinate adjacency and topological connectivity of vertices, the vertex sequence is traversed to verify whether the spatial distance and connection order of adjacent vertices conform to the topological rules of the original geometric elements (e.g., the vertices of line elements must be adjacent in sequence, and the vertices of face elements must be closed adjacent). Next, continuity verification is achieved through broken vertex screening (if the spatial distance between adjacent vertices exceeds a threshold, it is determined to be a sequence break) and repeated vertex screening (if the coordinates of multiple vertices completely overlap or the distance is less than the precision threshold, it is determined to be a repetition).

[0025] Set the scanning window length, perform sliding window scanning on the updated vertex sequence set, construct basic processing units in units of three consecutive vertices, and arrange the basic processing units according to the vertex sequence order to form a three-vertex structure set, wherein the scanning window length is set to three; The steps to construct a watermark embedding field include: Connect the first and last vertices of the three-vertex structure set with straight lines, calculate the midpoint of the corresponding line segment, take the midpoint of the line segment as the center of the circle, determine the diameter according to the length of the line segment connecting the first and last vertices, and construct the corresponding semicircular geometric structure. By connecting the midpoint of the line segment with the non-starting and end vertices, and extending the line segment to intersect the boundary of the semicircular geometric structure, we obtain the geometric auxiliary point; Record the spatial relationship data between geometric auxiliary points, the center of the circle, and the three vertices in the three-vertex structure set. The spatial relationship data includes the distance features from the center of the circle to the geometric auxiliary points and the distance features from the non-first and last vertices to the center of the circle. By using the ratio between the two distance features in the spatial relationship data as a geometric invariant, a watermark embedding domain is constructed.

[0026] Non-first and non-last vertices refer to the middle vertex within a three-vertex structure set; Geometric auxiliary points are the intersection points between the extended lines and the semicircular boundary obtained by extending the lines. They reflect the regularized geometric mapping characteristics of the local geometric structure of the three vertices. They are regularized feature points obtained by transforming the irregular spatial relationship of the three vertices through the geometric transformation of the semicircle. The spatial position of this point is uniquely determined by the relative position of the three vertices and changes with the local geometric structure of the three vertices, but is independent of the global geometric transformations (translation / rotation / scaling) of the map. It is a unique mapping identifier of the local geometric structure.

[0027] Geometric invariants refer to geometric feature parameters of a vector map whose values ​​remain unchanged when subjected to geometric transformations such as translation, rotation, and uniform scaling (i.e., geometric attacks). They are extracted or constructed to address the insufficient robustness of vector map watermarks against geometric attacks. Their core function is to reflect the inherent and stable characteristics of the local geometric structure of the vector map, unaffected by external geometric transformations. They are the core identifiers of the geometric features of a vector map that do not change with geometric attacks. At the same time, as the carrier basis of watermark information, they provide a stable carrier resistant to geometric attacks for watermark embedding, ensuring that the watermark embedding position or carrier features do not become invalid when the map is subjected to common geometric tampering such as translation, rotation, and scaling, and the watermark can still be extracted normally afterwards.

[0028] A watermark embedding domain refers to a specific area, feature parameter, or data dimension within the carrier data (vector map) specifically selected to carry watermark information. It serves as the embedding carrier or storage space for the watermark information. It's important to note that the watermark embedding domain is not a physical space, but rather a feature dimension of the carrier data. In vector map watermarking, vertex coordinates, geometric feature parameters, topological relationships, etc., can be selected as the embedding domain.

[0029] Let the three vertices in the three-vertex structure set be, in order: , and The center of the circle is Geometric auxiliary points are Then the formula for calculating the distance characteristic from the center of the circle to the geometric auxiliary point is: The formula for calculating the distance feature from non-first and last vertices to the center of the circle is: For vertex index; The formula for calculating geometric invariants is: ; in, The distance feature from the center of the circle to the geometric auxiliary point is used to reflect the inherent scale feature of the local geometric structure of the three vertices. This distance is uniquely determined by the spatial position of the first and last vertices and is the core length parameter of the semicircular geometric structure. It is only related to the relative spatial span of the local three vertices and is independent of the absolute position, rotation angle, and scaling ratio of the map (after being constrained by semicircular geometry, it becomes a geometrically invariant length reference).

[0030] The distance feature from the non-first and last vertices to the center of the circle reflects the spatial offset and distance scale of the middle vertex relative to the midpoint of the line connecting the first and last vertices within a three-vertex structure. It is the most distinctive feature parameter in the local three-vertex geometry; this distance is correlated with... After the ratioization process, the influence of absolute scale is eliminated, and only the relative proportion is retained, becoming a geometrically invariant feature.

[0031] and These are the x and y coordinates of the center of the circle, respectively. and These are the x and y coordinates of the geometric auxiliary points, respectively. and These are the x and y coordinates of the non-first and non-last vertices, respectively. It is a geometric invariant.

[0032] In this embodiment, by performing structured parsing on the vertices of the vector map and constructing a basic processing unit with three consecutive vertices, and then combining the semi-circular geometric structure to construct geometric invariants as the watermark embedding domain, the technical effects of stable embedding position, strong geometric robustness and standardized data structure are achieved.

[0033] First, by performing unified structural processing on point, line, and surface elements and extracting vertex sequences through traversal, and then using spatial adjacency topology analysis and distance threshold determination to check the continuity of vertex sequences, broken vertices and duplicate vertices can be effectively eliminated, so that the geometric elements in the vector map are expressed as continuous vertex sequences in a standardized manner, ensuring the data reliability of subsequent watermarking processing.

[0034] Secondly, a three-vertex structure set is constructed using a sliding window method with three consecutive vertices, and a semi-circular geometric structure is constructed using the first and last vertices. By calculating the distance relationship between the center of the circle, the geometric auxiliary point, and the middle vertex, a geometric invariant is formed. This ratio only reflects the relative geometric relationship between the three vertices and is independent of the translation, rotation, and uniform scaling of the map. Therefore, it can serve as a stable watermark embedding carrier, improving the robustness of the watermark against common geometric attacks.

[0035] Meanwhile, modulating only the middle vertex in the three-vertex structure can reduce the impact on the overall map shape while ensuring embedding capacity. The logic is to first ensure the continuity and reliability of the vertex sequence through topological and distance constraints, and then transform the irregular three-vertex relationship into geometric features with stable proportional relationships through semicircular geometric mapping, thereby obtaining a stable watermark embedding domain. For example, in a road polyline with three adjacent vertices A, B, and C, a line segment is determined using A and C, and a semicircular structure is constructed to obtain the center M. Then, the distances from M to auxiliary points and the middle vertex B are calculated to form a ratio r. When the map is translated or scaled, although the positions of A, B, and C change, this distance ratio remains essentially unchanged. Therefore, the watermark information embedded in this ratio can still be correctly extracted. Furthermore, the original vertex coordinates can be recovered through the reverse process, allowing the vector map to maintain its original geometric shape.

[0036] Example 3 Please refer to Figure 1 Specifically: the watermark image data to be embedded is read and preprocessed to obtain a decimal watermark sequence, including: Read the watermark image data to be embedded, and perform binarization processing on the watermark image data to obtain a one-dimensional binary sequence. Group the sequence according to a preset encoding length to obtain a set of subsequences; the set of subsequences includes several groups of subsequences. The watermark image data to be embedded refers to digital image files (such as company logos, copyright QR codes, custom logo images, etc.) that are used to embed into vector maps and have copyright identification or traceability functions. It is the physical carrier of watermark information and is a digital image file (common formats are BMP, PNG, JPG, etc.) that is pre-made by the copyright holder (such as designing a custom logo image or generating a traceability QR code image) or read from a specified storage medium (local file, database).

[0037] Binarization is the process of converting a color or grayscale watermark image (the watermark image data to be embedded) into a black and white image containing only 0 and 1 pixel values. The specific steps are as follows: First, read all the pixels of the watermark image, obtain the grayscale value of each pixel, and set a binarization threshold (128 is commonly used in the industry, and 128 is the middle value in the grayscale range of 0-255). Then, iterate through all the pixels. If the pixel grayscale value exceeds the binarization threshold, set its pixel value to 1, otherwise set it to 0. Finally, output a binary image containing only 0 and 1 pixel values ​​to complete the binarization process, so as to convert the pixel values ​​in the image into binary form. Specifically, the image pixels are linearly expanded according to row priority or column priority to convert the two-dimensional image structure into a one-dimensional binary sequence; After generating the one-dimensional sequence, the sequence length is calculated, and a sequence index structure is established so that each bit has a corresponding position number. This sequence serves as the basic representation of the watermark data and is used in subsequent compression processing.

[0038] Through formula The method involves grouping a one-dimensional binary sequence, determining the number of subsequences after grouping, and assigning an identifier to each subsequence. This splits a long one-dimensional binary sequence into fixed-length short subsequences, facilitating independent adaptive arithmetic coding for each subsequence and improving coding efficiency and compression performance. For a set of subsequences, For the first Subsequences after grouping For group numbering, This represents the total number of bits after the binary watermark image data is expanded (e.g., 64×64=4096 bits). The preset encoding length is the preset length of each subsequence. To perform the floor function, calculate the number of complete subsequences that can be divided from the total number of bits (e.g., ...). =4096、 =8, then =512 groups); Each group of subsequences is subjected to adaptive arithmetic coding. The subsequences are encoded by dividing the probability interval to generate corresponding coding results. After iterative coding processing, the shortest coding result is selected as the final result, and the compressed one-dimensional binary sequence is obtained. The encoding result is a decimal (or its binary representation) obtained by adaptive arithmetic encoding of a single subsequence. It is a compressed representation of the subsequence and is used to replace the original subsequence to reduce the data length.

[0039] The compressed one-dimensional binary sequence is the output sequence of each round of iterative encoding (such as the compressed sequence output in the first round of encoding, and the second round output is the sequence after further compression of the first round sequence), which is used as the input for the next round of iterative encoding or finally summarized into the compressed total sequence.

[0040] The mathematical expression for the compressed one-dimensional binary sequence is: ,in This is the compressed one-dimensional binary sequence, i.e., the compressed binary watermark sequence; For the compressed one-dimensional binary sequence, the first... 1 binary bit For each binary index in a one-dimensional binary sequence, This represents the total length of the compressed one-dimensional binary sequence. It is an abbreviation for binary. Adaptive arithmetic coding is a lossless data compression algorithm. Its core feature is adaptability, meaning that the probability of occurrence of symbols (0 or 1) is statistically analyzed in real time during the encoding process, without the need to pre-build a probability model. It has higher compression efficiency than traditional Huffman coding and is used to compress the length of binary watermark sequences, reducing geometric perturbations to the vector map during watermark embedding, while increasing the amount of watermark information that a unit vertex can carry (i.e., watermark capacity). The specific execution steps (combined with probability interval partitioning) are as follows: The first step is to initialize the encoding interval: set the initial probability interval to [0, 1), with the lower limit of the current interval being 0 and the upper limit being 1; The second step is to iterate through each bit (0 or 1) of a single subsequence: The probability P(0) and probability P(1) of 0 and 1 in the currently encoded bits are calculated in real time, where P(0) + P(1) = 1. The core of the adaptive method is to update the probability once for each bit encoded; P(0) and P(1) are the probability of 0 and 1 respectively. Probability interval division: Divide the current interval into two sub-intervals according to probability, namely, the interval corresponding to 0 is [Low, Low+(High-Low)×P(0)), and the interval corresponding to 1 is [Low+(High-Low)×P(0), High); where Low is the lower limit of the current interval and High is the upper limit; Shrinking interval: Based on the current encoded bit value (0 or 1), update Low and High to the upper and lower limits of the corresponding sub-intervals; The third step is to take any decimal number within the final interval [Low, High) as the encoding result of the subsequence (usually the midpoint of the interval). Fourth, repeat the above steps for all subsequences to complete the first round of encoding; Step 5, iterative encoding: Convert the first round of encoding results back into a binary sequence, repeat the above encoding process (multiple rounds of iteration), and finally select the shortest encoding result as the final encoding result of the subsequence; The sixth step is to summarize the final encoding results of all subsequences to obtain the compressed one-dimensional binary sequence.

[0041] The compressed one-dimensional binary sequence is regrouped according to the preset embedding strength to obtain several groups of binary subsequences. The binary subsequences are then converted to decimal values ​​to obtain decimal watermark sequences.

[0042] Embedding strength is a preset parameter, i.e., a set length; for example, if the embedding strength is 4, then every 4 bits form a group, i.e., a binary subsequence, which is the basic unit of decimal conversion.

[0043] Secondary compression is achieved by converting a fixed-length binary subsequence (e.g., 1011) into its corresponding decimal integer (e.g., 11). (A single decimal number can represent multiple binary bits.) The specific steps are as follows: The first step is to determine the length of the binary subsequence (i.e., the embedding strength s, such as s=3, the subsequence is 101). The second step is to assign weights to each bit of the binary subsequence: from left to right, the weight of the first bit is... The second one is ..., the s-th position is (For example, when s=3, the weights are as follows) =4、 =2、 =1); The third step is to iterate through each bit of the binary subsequence, multiply the bit value by the corresponding weight, and then sum them up. For example, if the binary subsequence is 101, calculate 1×4+0×2+1×1=5. The fourth step is to output the summation result, which is the decimal integer corresponding to the binary subsequence.

[0044] A decimal watermark sequence is a one-dimensional sequence set formed by arranging the decimal integers converted from all binary subsequences in their original order. ,in It is a decimal watermark sequence, which is the product of binary to decimal after two compressions; For the first A decimal integer derived from a binary subsequence. To limit the range of index values ​​for elements in the decimal watermark sequence, Embedding strength represents the number of binary bits separating each group when converting binary to decimal. It is the total number of elements in the decimal watermark sequence; This is the index value of the decimal watermark sequence; In this embodiment, by performing binarization, group adaptive arithmetic coding, and binary-to-decimal conversion on the image to be embedded with the watermark, the length of the watermark data can be significantly reduced, and the amount of information that a unit vector vertex can carry can be increased. This reduces the disturbance to the geometric structure of the vector map during the embedding process while ensuring the integrity of the watermark.

[0045] Specifically, the watermark image is first binarized and linearly expanded into a one-dimensional binary sequence, transforming the image information into a computationally processable bit sequence. Then, it is grouped according to a preset encoding length, and adaptive arithmetic coding is performed independently on each subsequence. During the encoding process, the interval is dynamically adjusted according to the real-time occurrence probability of 0 and 1, achieving lossless compression of the original binary data. The shortest encoding result is selected through multiple rounds of iteration, thereby further improving the compression efficiency. Finally, the compressed sequence is regrouped according to the embedding strength, and fixed-length binary subsequences are converted into decimal integers to form decimal watermark sequences. This allows multiple binary bits to be represented by a single integer, thereby reducing the amount of embedded data and improving watermark embedding efficiency and capacity. The logic is to first reduce the number of original watermark bits through adaptive arithmetic coding, and then achieve secondary information aggregation through binary-to-decimal conversion. This allows the same embedding space to carry more watermark information while reducing the number of modulation operations on vector vertex coordinates. For example, when a 32×32 binary watermark image is expanded to obtain a 1024-bit binary sequence, it is first grouped by length n=8 and adaptive arithmetic coding is performed, compressing the sequence into a shorter encoded result. Then, with an embedding strength s=4, the compressed sequence is regrouped by 4 bits. For example, the binary subsequence 1011 can be converted into the decimal number 11, thus compressing 4 bits of information into a single integer representation. In this way, when embedding watermarks in vector maps, only a small number of decimal numbers need to be embedded to represent the complete watermark information, which not only improves the embedding capacity but also effectively reduces the impact on the geometry of the original map.

[0046] Example 4 Please refer to Figure 1 Specifically: Based on the decimal watermark sequence and watermark embedding domain, the vertex coordinates are modulated to achieve watermark embedding, thereby obtaining a watermarked vector map, including: A proportional sequence is obtained based on the geometric invariants in each watermark embedding domain. By performing numerical transformation on the geometric invariants in the proportional sequence, a corresponding index sequence is obtained. The index sequence contains multiple sets of index values, which are used to determine the watermark data position corresponding to the corresponding basic processing unit. Based on the index sequence, the watermark value at the corresponding position in the decimal watermark sequence is matched. If the index value exceeds the length of the decimal watermark sequence, the index value is remapped using modulo operation to determine the valid position, and the watermark value corresponding to each basic processing unit is recorded to form a watermark matching sequence.

[0047] The effective position is the index range in the decimal watermark sequence. The position within is used to ensure that each basic processing unit (geometric unit) can match the actual watermark value in the decimal watermark sequence, avoiding watermark embedding failure due to index out-of-bounds.

[0048] Through formula Converting continuous geometric invariants (floating-point numbers) into integer index values ​​and forcibly constraining these index values ​​to fall within the valid index range of the decimal watermark sequence, thus achieving a precise mapping between geometric invariants and watermark sequence indices, is the core logic connecting the geometric carrier and the watermark data. The index value is an integer obtained by numerical transformation and modular operation of geometric invariants. It is a unique identifier connecting the geometric unit and the decimal watermark sequence. It is used to locate the watermark value at the corresponding position in the decimal watermark sequence, ensuring that each geometric unit can match a unique watermark value and realize the ordered embedding of the watermark; at the same time, it ensures that the index value is always within the length range of the watermark sequence to avoid matching failure.

[0049] It's a modulo operation, and its core function is to constrain... Within the effective range; The watermark value is the index of the decimal watermark sequence. The corresponding single decimal integer is the core value of the final embedded geometric invariant. As the smallest information unit of the copyright identifier, after being embedded in the geometric invariant, the watermark sequence can be restored by extracting this value to verify the map copyright or integrity. The method of obtaining it is: according to the index value, find the element at the corresponding position in the decimal watermark sequence, which is the watermark value matched by the current geometric unit.

[0050] The proportional sequence includes multiple sets of geometric invariants. The index calculation process for each geometric invariant involves converting each geometric invariant into a unique integer index value, achieving a one-to-one matching from the basic processing unit to the index, and then to the watermark value. The specific steps are as follows: The first step is to determine the core parameters for index calculation: preset scaling factor. The total length of the compressed one-dimensional binary sequence Embedding strength s; The second step is to iterate through each geometric invariant in the proportionality sequence and first calculate... and The product (scaling geometric invariants to a numerical range suitable for the watermark sequence length). The third step is... and The product result is executed Round down to the nearest integer to obtain the initial index value; The fourth step is to perform a modulo operation on the initial index value. (If the initial index exceeds the length of the watermark sequence, it will be remapped), and finally a unique index value corresponding to each geometric invariant will be obtained; The fifth step is to arrange the index values ​​of all basic processing units in order to construct a complete index sequence and complete the index calculation of all geometric invariants.

[0051] Assumption: , , If s=5, then calculate (Convert floating-point number to integer); then round down. Calculate the length of the decimal watermark sequence. This indicates that the sequence has a total of 372 watermark values, and then a modulo operation is performed. (45 < 372, keep directly); final ,match The 45th watermark value in the middle; The watermark data location refers to the specific index position in the decimal watermark sequence. The watermark data is the whole decimal watermark sequence carrying copyright or traceability information, as well as its individual elements. It is the final data form of the watermark information (obtained from the original watermark image after binarization, arithmetic encoding compression, and decimal conversion).

[0052] The watermark matching sequence is used to record the one-to-one correspondence between geometric units and watermark values, providing direct numerical input for subsequent calculation of watermark ratios and modulation of vertex coordinates.

[0053] S301: After watermark matching is completed, the watermark value is embedded into geometric invariants to obtain the watermark ratio, which reflects the relative proportion of the basic processing unit (three-vertex local geometry) after perturbation. The formula is as follows: ; in, As an intermediate parameter, it is The core benchmark identifier (the integer part of the geometric invariant after being split by a fixed step size, reducing the perturbation of the geometric invariant by the watermark embedding). This is the watermark ratio, used for vertex coordinate modulation. Step size, The perturbation amplitude used to control the watermark embedding is the minimum numerical step size for watermark embedding. The smaller the perturbation, the lower the level; Reference coefficients (coordinate system adaptation parameters, geographic coordinate system) =1, Projected coordinate system =0); a reference coefficient is defined based on the coordinate system type of the vector map to enhance the invisibility of the algorithm; To adapt the scaling factor to the coordinate system ( When =1, it is 10. =0 is 1, which adapts to the numerical range of different coordinate systems, that is, the reference coefficient raised to the power of 10, and the coordinate coefficient value is scaled by magnitude. The matched watermark value (decimal integer); s is the binary-to-decimal group length, which is also the disturbance control coefficient; , representing the embedding strength s raised to the power of 2, is the interval sub-cell division coefficient, reflecting the number of tiny sub-cells the algorithm divides for the baseline interval. The number of sub-cells is determined by the embedding strength; the larger s is, the more sub-cells there are, the smaller the value per unit sub-cell, and the lower the perturbation. It is used to scale the residual term proportionally, preserving the micro-features of the original geometric invariants while freeing up numerical space for watermark embedding.

[0054] Benchmark Item Intermediate parameters and baseline split step size The product of these values ​​represents the left boundary value of the reference interval where the original geometric invariant resides. It is also the core integer reference of the geometric invariant, reflecting its integer-level core geometric features. This fixed part of the geometric invariant remains unchanged regardless of watermark embedding, preserving its main proportional characteristics. By retaining the core geometric features of the original geometric invariant, the watermark ratio forms the basic framework, ensuring a high degree of consistency between the watermark ratio and the original geometric invariant in core values, with modifications only within a minor range.

[0055] Residual Item The difference between the original geometric invariant and the baseline term represents the decimal remainder of the original geometric invariant within the baseline interval (i.e., the portion of the geometric invariant that extends beyond the left boundary of the baseline interval). It reflects the fine decimal characteristics of the original geometric invariant within the baseline interval and is a micro-feature of the original geometric invariant, determining its precise value. By extracting the fine micro-features of the original geometric invariant, a foundation is provided for subsequent compensation term calculations, ensuring that these micro-features are preserved after watermark embedding, further reducing perturbations.

[0056] Compensation It is the quotient of the residual term divided by the embedding intensity factor, and is the compensation value of the micro-features of the original geometric invariant after being scaled proportionally. It reflects the residual value of the micro-features of the original geometric invariant after scaling. It is used to completely preserve the fine micro-features of the original geometric invariant, while scaling the residual term to a very small range to free up numerical space for the watermark embedding term. Moreover, the compensation term is an inherent feature of the original geometric invariant, which ensures the reversibility of the algorithm (the original residual term can be restored through the compensation term when extracting the watermark).

[0057] Watermark Embedded Item It converts the watermark value into an embedded value that fits the numerical order of geometric invariants, reflecting the numerical magnitude of the copyright information. It is a newly added watermark information component in the watermark ratio. Each watermark value corresponds to a unique embedded value, ensuring accurate extraction of the watermark information. It quantifies the copyright information (watermark value) into a tiny value that fits the numerical order of geometric invariants, and is the core carrier for integrating watermark information into geometric invariants; and the size of the embedded item is determined by… Control it to ensure it is at a minimum value to achieve low-disturbance embedding.

[0058] Specifically, the original geometric invariants are arranged according to... The basic step size is decomposed into integers to obtain the baseline integer, i.e., intermediate parameters. Essentially, this is to define an integer baseline interval for geometric invariants, so that watermark embedding only occurs within a small range of the interval, avoiding significant modifications to geometric invariants that could damage the geometric accuracy of the map. Next, the decomposed r is broken down into three parts: a baseline term, a watermark embedding term, and an original micro-feature compensation term. The watermark value is then incorporated into these parts through the watermark embedding term, and finally, they are concatenated to form the watermark ratio. When the baseline term, watermark embedding term, and original micro-feature compensation term are added together, the difference between the watermark ratio and the original geometric invariant is determined only by the watermark embedding term and the compensation term. Furthermore, through parameter constraints of step size and embedding strength, the difference is controlled within a certain range. The scale is reduced to achieve low-disturbance embedding; at the same time, the watermark ratio is still preserved. Its geometric invariance ensures resistance to translation, rotation, or scaling attacks.

[0059] The watermark ratio is a composite proportional parameter after fusing the watermark value with the original geometric invariants. It is a dual carrier of geometric features and copyright information. It completely preserves the translation, rotation, and scaling invariance of the original geometry and still accurately reflects the inherent features of the local geometric structure with the three adjacent vertices as the core, namely the proportional relationship between the distance from the center of the circle to the middle vertex and the distance from the center of the circle to the geometric auxiliary point. The only difference is that the watermark ratio is a tiny numerical adjustment to the original geometric invariants (the perturbation amplitude is within...). (at the order of magnitude), this adjustment only changes the slight value of the scale, does not destroy the relative spatial relationship of the local geometric structure, and does not cause any identifiable changes in the geometric shape and accuracy of the vector map. Therefore, the watermark ratio reflects both the original geometric features and the numerical state after controllable perturbation, ensuring the geometric accuracy of the map and providing a numerical carrier for watermark embedding.

[0060] A watermarked vertex is a new vertex obtained by slightly modulating the coordinates of the original middle vertex based on the watermark ratio. The coordinates of the first and last vertices remain unchanged, and only the middle vertex undergoes a slight displacement. This is to minimize the disturbance of the vector map's geometry caused by watermark embedding. It is used to ensure the watermark's invisibility and reversibility, and to support blind watermark extraction. Without the original map, the watermark value can be extracted simply by calculating the watermark ratio from the map composed of watermarked vertices, which is suitable for the needs of actual copyright verification scenarios.

[0061] S302: Based on the combination of each three-vertex structure set, calculate the movement direction of non-first and last vertices to obtain the direction unit vector. The direction unit vector represents the fixed unit direction along the center of the circle pointing to the non-first and last vertices, that is, the ray direction from the center of the circle pointing to the original middle vertex. S303: Based on the watermark ratio and combined with the direction unit vector, the coordinates of the non-first and last vertices are modulated in reverse to obtain the watermarked vertices. The watermarked vertices are used to ensure that the non-first and last vertices move in a fixed direction and reduce embedding disturbance. By progressively scanning all three-vertex structure sets and repeating steps S301 to S303 until all vertices have completed watermark embedding, the vector map is updated to obtain a watermarked vector map.

[0062] Through formula The watermarked vertices are obtained, and the coordinates of the intermediate vertices are modulated inversely by the watermark ratio. The watermark information is mapped from the ratio dimension to the vertex coordinate dimension, realizing the physical embedding of the watermark in the vector map. At the same time, it is ensured that the vertices only move slightly along a fixed direction, reducing the disturbance of embedding to the geometric accuracy of the map.

[0063] in and These are the horizontal and vertical coordinates of the watermarked vertices, i.e., the modulated coordinates of the non-first and last vertices; and These are the x and y coordinates of the non-first and non-last vertices, respectively. and These are the x and y coordinates of the center of the circle, respectively. The middle vertex relative to the center of the circle The axial unit vector is used to determine that a vertex can only move along the straight line from the center of the circle to the middle vertex, ensuring a fixed direction. The offset of the middle vertex relative to the center of the circle in the x-direction, divided by It normalizes the offset and converts it into a unit vector of direction. Let y be the unit vector of the middle vertex relative to the center of the circle. It is the new length after watermarking, which is calculated by multiplying by the unit direction. This yields the component of the new length in the x-direction. If multiplied by the unit direction Obtain the component of the new length in the y direction. ; Specifically, using the watermark ratio, the middle vertex is moved slightly from its original position along a fixed straight line from the center of the circle to the middle vertex to a new position, changing only the middle vertex and keeping the first and last points unchanged, thus minimizing the disturbance.

[0064] The updated vector map is the watermarked vector map.

[0065] In this embodiment, by utilizing the index mapping relationship between geometric invariants and decimal watermark sequences, and combining proportional modulation and vertex micro-displacement strategies to achieve watermark embedding, a stable, concealed, and reversible watermark embedding effect can be achieved while ensuring that the geometric accuracy of the vector map remains basically unchanged.

[0066] Specifically, firstly, by performing numerical transformation and modulo operation through geometric invariants and scaling coefficients, continuous geometric features are mapped to discrete index values, thereby matching the corresponding watermark value in the decimal watermark sequence. This allows each three-vertex structural unit to be automatically associated with a watermark data, achieving a one-to-one correspondence between the geometric carrier and the watermark data.

[0067] Subsequently, the watermark value is embedded into the geometric invariant through quantization modulation to construct the watermark ratio. The baseline term and micro-feature compensation term of the original geometric invariant are retained, and the proportional relationship is changed only by the watermark embedding term within a very small range, thereby ensuring that the embedding perturbation is controlled within the micro-level.

[0068] Finally, the new vertex positions are calculated based on the watermark ratio. Only the non-first and last vertices are slightly displaced along a fixed direction from the center to the middle vertex, while the first and last vertices remain unchanged. This allows the watermark information to be mapped from the scale parameter to the actual coordinates, realizing the physical embedding of the watermark in the vector map, while minimizing the impact on the map shape.

[0069] Example 5 Please refer to Figure 1 Specifically: Extract watermarked image data from the updated vector map to fully restore the original vector map, achieving the reversibility of the algorithm, including: Read the updated vector map and repeat step S1 to obtain the embedded vertex sequence set, the embedded spatial relationship data, and the embedded geometric invariants; Specifically, the process of repeating step S1 is essentially the same as the steps described above, except that the object being processed has changed from the original vector map to a watermarked vector map, so it will not be described in detail here. By taking the modulo of the embedded geometric invariant with respect to the embedding period, the residual of the embedded geometric invariant in the corresponding quantization interval is obtained. After normalization, the embedded watermark value is extracted, and the corresponding decimal watermark sequence is recovered, which is the extracted watermark value. Store the index position corresponding to the decimal watermark sequence; The calculation formula is as follows: ,in This is the embedded watermark value; The geometric invariant after embedding is the watermark ratio. It should be noted that during embedding, the watermark modulation formula is used... The watermark ratio is constructed, and during extraction, the geometric ratio is recalculated from the watermark map. ,Should The watermarking ratio in the embedding stage is the same physical value, where and Distance features in the embedded spatial relationship data; For modulo operation, The embedding period, which is also the modulus of the modular operation (the length of the watermark interval), is determined by the embedding strength, step size, and coordinate system reference coefficient. It is used to limit the numerical range of the watermark information to ensure that the part corresponding to the watermark can be accurately extracted during extraction.

[0070] The remainder of the embedded geometric invariant in the corresponding quantization interval, i.e., the modulo operation result of the watermark ratio, is used to extract from... The data segment generated solely by the watermark is extracted, excluding the original geometric information.

[0071] The quantization interval is a numerical range of length 2ˢf×10ᶜ, meaning the watermark is embedded in the current... Within this interval; When restoring the original geometric invariants after extracting the embedded watermark value, since the watermark is embedded into the remainder of the original geometric invariants through quantization modulation during the embedding stage, the original geometric invariants need to be restored through the following calculation after extracting the embedded watermark value: Based on the embedded watermark value, a quantization offset is obtained, and the corresponding quantization offset is subtracted from the embedded geometric invariants to restore the original geometric invariants. The quantization offset is to convert the watermark value into an embedded value that is adapted to the numerical magnitude of the geometric invariants. Through formula The formula for restoring the original geometric invariants is the inverse operation performed during the watermark extraction stage to recover the original geometric invariants from the embedded geometric invariants. First, it removes the quantization interval reference and watermark offset from the watermark ratio, and then amplifies the geometric information compressed during embedding back (×). Finally, the interval reference is added back to fully restore the original geometric invariants; in Subtract the starting point of the quantization interval from the embedded geometric invariants Subtract the offset caused by the watermark. The original geometric margin obtained during the embedding stage is compressed. Its function is to strip away all the parts of the geometric invariants after embedding that do not belong to the original geometry, leaving only the compressed original information. It is the original geometric margin after compression multiplied by Its function is to reduce the size during embedding. The original geometric information is restored to its original size by a factor of 1.

[0072] Using the restored original geometric invariants and the embedded vertex sequence set, and through geometric relations, the coordinates of the original non-first and last vertices are calculated using the following formula: and ; in and These are the x and y coordinates of the non-first and last vertices, i.e., the original coordinates of the non-first and last vertices; For the embedded geometric invariants, and Distance features in the embedded spatial relationship data; and These are the x and y coordinates of the watermarked vertex, respectively. and The x and y coordinates of the center of the circle after embedding are given. The center of the circle before and after embedding, as well as the two vertices at the beginning and end, remain unchanged. This is because the reference of the geometric structure remains unchanged when restoring the original non-beginning and end vertices. The beginning and end vertices did not move at all during embedding. At this time, we only need to use the direction and proportion in the watermarked structure to revert the non-beginning and end vertices. The recovered decimal watermark sequence is deduplicated (taking the watermark value with the highest frequency of each index) and converted into a one-dimensional binary sequence. It is then restored to the original watermark image, i.e., the original watermark image data to be embedded, through adaptive arithmetic decoding. All the recovered original vertices are reconstructed according to different spatial elements to obtain a complete original vector map, thus achieving lossless restoration.

[0073] The vertices in the embedded vertex sequence set are watermarked vertices.

[0074] In this embodiment, by recalculating the geometric invariants in the watermarked vector map during the watermark extraction stage and utilizing the modulus operation and inverse quantization recovery mechanism, accurate extraction of watermark information and lossless recovery of the original vector map can be achieved, thereby ensuring that the algorithm has good reversibility and practicality.

[0075] Specifically, after reading the updated vector map, the embedded spatial relationship data and geometric invariants can be re-obtained through the same vertex resolution and ternary structure construction process as in the embedding stage. Subsequently, modulo operations are performed on the watermarked geometric invariants using the embedding period, and the embedded watermark value is obtained through normalization calculation, thereby gradually restoring the complete decimal watermark sequence.

[0076] Furthermore, based on the quantization and modulation rules of the watermark embedding stage, the original geometric invariants can be calculated inversely by subtracting the corresponding watermark offset from the watermarked geometric invariants and restoring the compressed geometric margin. Then, by combining spatial relationship data such as watermarked vertices, center points, and distance features, the original non-first and last vertex coordinates are calculated, achieving accurate restoration of vertex positions. Since the first and last vertices and geometric reference structure remain unchanged during the embedding process, only the intermediate vertices need to be inversely calculated during the restoration process to restore the original geometric structure.

[0077] Finally, by performing deduplication, binary conversion, and adaptive arithmetic decoding on the extracted decimal watermark sequence, the original watermark image data can be recovered. Simultaneously, spatial features are reconstructed based on the recovered vertices, thus obtaining the complete original vector map. The effect is that even without relying on the original map data, it is possible to accurately extract the watermark and recover the original geometric structure from a watermarked map.

[0078] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A reversible watermarking method for vector maps based on adaptive arithmetic coding, characterized in that, The method includes: S1: Read the vector map and use three adjacent vertices in the vector map as the basic processing unit to construct the watermark embedding domain; S2: Read the watermark image data to be embedded, and after preprocessing it, obtain a decimal watermark sequence. The preprocessing includes performing binarization, iterative adaptive arithmetic coding, and decimal conversion. S3: Based on the decimal watermark sequence and watermark embedding field, the vertex coordinates are modulated to achieve watermark embedding in order to update the vector map; S4: Extract the watermark image data from the updated vector map to fully restore the original vector map, thus achieving the reversibility of the algorithm.

2. The reversible watermarking method for vector maps based on adaptive arithmetic coding according to claim 1, characterized in that, The steps for obtaining the basic processing unit include: The spatial features in the vector map are analyzed, and vertices in the vector map are extracted by traversing according to different types of spatial features to form a vertex sequence set; Based on spatial adjacency topology analysis, combined with spatial distance threshold determination method, the vertex sequence set is checked for continuity to remove broken or duplicate vertex coordinates, and the vertex sequence set is updated through adjacency relationship; Set the scanning window length, perform sliding window scanning on the updated vertex sequence set, construct basic processing units with three consecutive vertices as units, and form a three-vertex structure set.

3. The reversible watermarking method for vector maps based on adaptive arithmetic coding according to claim 2, characterized in that, The steps to construct a watermark embedding field include: Connect the first and last vertices of the three-vertex structure set with straight lines, calculate the midpoint of the corresponding line segment, take the midpoint of the line segment as the center of the circle, determine the diameter according to the length of the line segment connecting the first and last vertices, and construct the corresponding semicircular geometric structure. By connecting the midpoint of the line segment with the non-starting and end vertices, and extending the line segment to intersect the boundary of the semicircular geometric structure, we obtain the geometric auxiliary point; Record the spatial relationship data between geometric auxiliary points, the center of the circle, and the three vertices in the three-vertex structure set. The spatial relationship data includes the distance features from the center of the circle to the geometric auxiliary points and the distance features from the non-first and last vertices to the center of the circle. By using the ratio between the two distance features in the spatial relationship data as a geometric invariant, a watermark embedding domain is constructed.

4. The reversible watermarking method for vector maps based on adaptive arithmetic coding according to claim 3, characterized in that, The image data to be embedded with the watermark is read and preprocessed to obtain a decimal watermark sequence, including: Read the watermark image data to be embedded, and perform binarization processing on the watermark image data to obtain a one-dimensional binary sequence. Group the sequence according to a preset encoding length to obtain a set of subsequences; the set of subsequences includes several groups of subsequences. Each group of subsequences is subjected to adaptive arithmetic coding. The subsequences are encoded by dividing the probability interval to generate corresponding coding results. After iterative coding processing, the shortest coding result is selected as the final result, and the compressed one-dimensional binary sequence is obtained. The compressed one-dimensional binary sequence is regrouped according to the preset embedding strength to obtain several groups of binary subsequences. The binary subsequences are then converted to decimal values ​​to obtain decimal watermark sequences.

5. The reversible watermarking method for vector maps based on adaptive arithmetic coding according to claim 4, characterized in that, Based on the decimal watermark sequence and watermark embedding field, the vertex coordinates are modulated to achieve watermark embedding, resulting in a watermarked vector map, including: A proportional sequence is obtained based on the geometric invariants in each watermark embedding domain. By performing numerical transformation on the geometric invariants in the proportional sequence, a corresponding index sequence is obtained. The index sequence contains multiple sets of index values, which are used to determine the watermark data position corresponding to the corresponding basic processing unit. Based on the index sequence, the watermark value at the corresponding position in the decimal watermark sequence is matched. If the index value exceeds the length of the decimal watermark sequence, the index value is remapped using modulo operation to determine the valid position, and the watermark value corresponding to each basic processing unit is recorded to form a watermark matching sequence.

6. The reversible watermarking method for vector maps based on adaptive arithmetic coding according to claim 5, characterized in that, Based on the decimal watermark sequence and watermark embedding field, the vertex coordinates are modulated to achieve watermark embedding, so as to obtain a watermarked vector map, which also includes: S301: After watermark matching is completed, the watermark value is embedded into the geometric invariant to obtain the watermark ratio. The watermark ratio is used to reflect the relative proportion of the basic processing units after perturbation. S302: Based on the combination of each three-vertex structure set, calculate the movement direction of non-first and last vertices to obtain the direction unit vector. The direction unit vector represents the fixed unit direction along the center of the circle pointing to non-first and last vertices. S303: Based on the watermark ratio and combined with the direction unit vector, the coordinates of the non-first and last vertices are modulated in reverse to obtain the watermarked vertices. The watermarked vertices are used to ensure that the non-first and last vertices move in a fixed direction and reduce embedding disturbance. By progressively scanning all three-vertex structure sets and repeating steps S301 to S303 until all vertices have completed watermark embedding, the vector map is updated to obtain a watermarked vector map.

7. A reversible watermarking method for vector maps based on adaptive arithmetic coding according to claim 6, characterized in that, Extracting watermarked image data from the updated vector map to fully restore the original vector map, achieving algorithm reversibility, includes: Read the updated vector map and repeat step S1 to obtain the embedded vertex sequence set, the embedded spatial relationship data, and the embedded geometric invariants; By taking the modulo of the embedded geometric invariant with respect to the embedding period, the remainder of the embedded geometric invariant in the corresponding quantization interval is obtained. After normalization, the embedded watermark value is extracted, and the corresponding decimal watermark sequence is restored.

8. A reversible watermarking method for vector maps based on adaptive arithmetic coding according to claim 7, characterized in that, Extracting watermarked image data from the updated vector map to fully restore the original vector map, achieving algorithm reversibility, also includes: Based on the embedded watermark value, a quantization offset is obtained, and the corresponding quantization offset is subtracted from the embedded geometric invariant to restore the original geometric invariant. The quantization offset is to convert the watermark value into an embedded value that is adapted to the numerical magnitude of the geometric invariant. Using the restored original geometric invariants and the embedded vertex sequence set, the coordinates of the original non-first and last vertices are obtained by inversely calculating the geometric relationships. The original watermark image is restored by removing duplicates from the recovered decimal watermark sequence and converting it into a one-dimensional binary sequence, which is then restored by adaptive arithmetic decoding. Reconstruct all the recovered original vertices according to different spatial elements to obtain the complete original vector map.

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