Vector map watermarking method based on virtual vertex and ratio of dwt frequency coefficients

Abstract

The application discloses a vector map watermark embedding and extracting method based on virtual vertex and DWT frequency coefficient ratio, which is based on a DWT algorithm, converts a vector map from a spatial domain to a frequency domain, and designs the method to improve the robustness of the DWT watermark under vertex attack and geometric transformation, specifically, in order to enhance the robustness to vertex deletion attack, a virtual vertex is calculated from adjacent real vertices of the vector map, and a ratio of a DWT high-frequency coefficient calculated from an x coordinate of the virtual vertex to a coefficient calculated from a y coordinate is selected as an embedding domain, a watermark correction method is designed to ensure the consistency between the virtual vertex of the watermark and VVs newly calculated from the vector map with the watermark, finally, a quantization index modulation is adopted as a watermark embedding strategy, so that the watermark can be blindly extracted. The watermark technical scheme has excellent robustness when coping with vertex deletion, vertex addition and map clipping attacks.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vector map watermarking, and particularly relates to a vector map watermarking method based on virtual vertex and DWT frequency coefficient ratio. BACKGROUND

[0002] With the development of computer technology, vector maps, as a core component of geographic information systems, have been widely used in urban planning, navigation positioning, traffic management and other fields due to their high precision and ease of editing. Compared with traditional raster maps, vector maps have the advantages of good graphic display quality, small data volume, easy editing and analysis, and thus play a crucial role in the digital era. However, vector maps also face security risks such as illegal copying, tampering and redistribution. In order to protect the copyright and integrity of vector maps, digital watermarking technology has emerged.

[0003] As an effective means of copyright protection, digital watermarking technology can embed hidden watermark information in vector maps without significantly affecting their visual effects, achieving the functions of copyright authentication and authenticity identification. Traditional digital watermarking methods for vector maps are mainly divided into spatial domain and frequency domain. Spatial domain watermarking technology embeds watermarks by directly modifying the coordinates of the map, but this method has weak resistance to attacks such as vertex deletion and addition. Frequency domain watermarking technology embeds watermarks by converting the map to the frequency domain, such as algorithms based on discrete wavelet transform (DWT). Although these algorithms can effectively resist geometric attacks such as rotation and scaling, they have relatively weak robustness when the number of vertices changes, often failing to guarantee the robustness of the watermark, resulting in the loss or incorrect extraction of copyright information. This is because frequency domain watermarking usually relies on the global characteristics of the vector map, and once the number of vertices changes, the original frequency characteristics will be affected, thereby affecting the stability of the watermark. In order to enhance the robustness of the watermark, some research has proposed the method of introducing virtual vertices. However, the introduction of virtual vertices may cause consistency problems in the watermark embedding and extraction process, i.e., the calculation of virtual vertices may not be consistent between watermark extraction and embedding, resulting in a decrease in watermark extraction accuracy.

[0004] In the watermarking scheme of document [1] N. Ren, S. Guo, C. Zhu, and Y. Hu, “A zero-watermarking scheme based on spatial topological relations for vector dataset,” Expert Systems with Applications, vol. 226, pp. 120217, 2023., the watermark is embedded into the topological relations between polygons by slightly adjusting the measurement scale of spatial topological relations. These schemes utilize the geometric invariance of vector map structures to resist geometric attacks and often maintain high fidelity. However, the robustness of the watermark is influenced by the topological relations, which makes them still vulnerable to malicious attacks. In document [2] L. Zhang, D. Yan, S. Jiang, and T. Shi, “New robust watermarking algorithm for vector data,” Wuhan University Journal of Natural Sciences, vol. 15, no. 5, pp. 403-407, 2010., it is mentioned that the distance sequence between feature points and reference lines is subjected to DWT, and then the watermark is embedded by modulating these distances. However, these hidden watermarks are vulnerable to attacks involving map cropping, vertex deletion, and scaling. In document [3] C. Qu, X. Xi, J. Du, and T. Wu, “Robust watermarking scheme for vector geographic data based on the ratio invariance of DWT-CSVD coefficients,” ISPRS International Journal of Geo-Information, vol. 11, no. 12, pp. 583, 2022., it is mentioned that the feature point sequence is subjected to DWT processing, and then the transformed coefficients are decomposed using complex singular value decomposition (SVD). The extracted feature invariants are selected as the embedding domain of the watermark. This method has certain limitations in resisting vertex deletion and scaling attacks.

[0005] Specifically, documents [1]-[3] have been well applied in the copyright protection of vector maps. However, through experimental verification, there are still obvious defects. First, the vulnerability of vertex attack: documents [1] and [2] show weak robustness when facing vertex addition or map cropping attacks, which will change the vertex sequence of the vector map, thereby destroying the robustness and extractability of the watermark. Second, the limitation of frequency domain methods: although document [3] has certain resistance to geometric attacks, its performance will decrease significantly under the influence of vertex number change, scaling attack, etc. This is because these methods rely on fixed vertex coordinates, and the increase or decrease of vertices will directly affect the stability of the frequency coefficients. In addition, the current vector map digital watermark protection scheme still lacks an effective watermark correction mechanism: in the case of vertex inconsistency, existing technologies often lack effective watermark correction methods, resulting in reduced accuracy and reliability of watermark extraction. There is also a balance problem between watermark invisibility and robustness: in order to improve the concealment of the watermark, the existing algorithm may sacrifice its robustness, and vice versa. In actual application, it is difficult to find the best balance point between the two. Finally, the watermark algorithm lacks resistance to specific attack types: specific attacks, such as vertex noise attack and object deletion attack, pose a challenge to existing watermark algorithms, which can significantly change the characteristics of the vector map, making it difficult to accurately extract the embedded watermark information. SUMMARY

[0006] The technical problem to be solved by the present application is to provide a vector map watermarking method based on virtual vertices and DWT frequency coefficient ratios, which can effectively solve the vulnerability problem of vector map watermarking schemes under vertex attacks, and by introducing virtual vertices and using DWT frequency coefficient ratios to construct geometric feature invariants as stable watermark embedding domains, and through the newly designed watermark correction method, effectively solving the inconsistency problem caused by the introduction of virtual vertices, further improving the overall performance of the watermarking scheme.

[0007] To solve the above technical problems, the present application provides a vector map watermark embedding method based on virtual vertices and DWT frequency coefficient ratios, comprising the following steps:

[0008] Step 1, adding virtual vertices VVs to the original vector map G to obtain a vector map G containing virtual vertices VVs vv ;

[0009] Step 2, performing discrete wavelet transform DWT on the X coordinate set X vv and the Y coordinate set Y vv , respectively, to obtain high-frequency coefficients H xv and H yv ;

[0010] Step 3: Obtain the initial ratio sequence K by constructing the formula for the ratio-invariant domain and calculating it;

[0011] Step 4: First, enlarge the initial ratio sequence K, then embed the encrypted watermark image W. e The watermark information is then scaled down proportionally to obtain the watermarked ratio sequence K′;

[0012] Step 5: Based on the watermarking ratio sequence K′ and the high-frequency coefficient H yy Calculate the high frequency coefficient H of the watermark xv′ ;

[0013] Step 6: Adjust the high-frequency coefficient H of the watermark. xv′ By applying the inverse discrete wavelet transform (IDWT), the uncorrected X-coordinate set X containing the watermarked virtual vertices WVVs is obtained. vv′ ;

[0014] Step 7: Based on the coordinate set X vv′ Perform watermark correction and obtain the high-frequency coefficient H of the corrected watermark. xv″ Calculate the high-frequency coefficient H of the corrected watermark. xv″ With high frequency coefficient H yv The ratio K″ is used to calculate the correction ratio K. c ;

[0015] Step 8: Based on the correction ratio K c and high-frequency coefficient H yv Calculate and obtain the X coordinate set X for watermarking. vc ;

[0016] Step 10, use X vc Replace X vv To generate a vector map G containing watermarked virtual vertices WVVs vv′ Finally, remove WVVs to obtain the final watermarked vector map G′.

[0017] Furthermore, in step 1, for the original vector map G containing inherent real vertices RVs, virtual vertices VVs are added to each pair of real vertices. The process of adding virtual vertices VVs is as follows:

[0018]

[0019] After adding virtual vertices VVs, we obtain the X-coordinate sequence XV and the Y-coordinate sequence YV, thus obtaining the X-coordinate set X. vv and the Y coordinate set Y vv .

[0020] Furthermore, in step 4, Quantization Index Modulation (QIM) is used to embed the encrypted watermark image W. e .

[0021] Further, the embedding process is shown in the following equation:

[0022]

[0023] where M represents the amplification factor, τ is the step size of QIM, K' represents the ratio sequence after watermarking, N W represents the pixel count of the watermark.

[0024] Further, the encrypted watermark image W e in step 4 is obtained by using the original watermark image W org and the secret key K.

[0025] The calculation of Arnold transformation is as follows:

[0026]

[0027] where (b, d) and (b', d') represent the pixel positions of W org and W e respectively, N w represents the pixel count of the watermark; parameters m, n and N W are a secret key.

[0028] Further, in step 7, the coordinate set X' is obtained by deleting the watermark virtual vertex WVVs in the coordinate set X vv′ , and then the virtual vertex VVs is added to the coordinate set X' to obtain the coordinate set X vv″ , and then the coordinate set X vv″ is subjected to discrete wavelet transform DWT to obtain the corrected watermark high-frequency coefficient X xv″ .

[0029] The correction ratio K C is obtained by the following equation: where τ is the step size of QIM.

[0030] A vector map watermark extraction method based on virtual vertex and DWT frequency coefficient ratio, comprising the following steps:

[0031] Step 1, adding a virtual vertex VVs to the watermarked vector map G' to obtain a vector map G vv′ containing the virtual vertex VVs.

[0032] Step 2, performing discrete wavelet transform DWT on the X coordinate set V''' and the Y coordinate set V''' in the vector map G vv″ , to obtain high-frequency coefficients H x and H y respectively. xv″ yv″ ;​

[0033] Step 3, obtain the initial ratio sequence K''' by constructing the formula of the ratio-invariant field and calculation;

[0034] Step 4: magnify K''' by M times to obtain the magnified sequence K'' M ;

[0035] Step 5: calculate the watermark index Idx' according to the magnified sequence K'' M ;

[0036] Step 6: calculate and record the watermark bit and index set;

[0037] Step 7: determine the final watermark bit according to the recorded watermark bit and index set, and obtain the undecrypted watermark image W' e ;

[0038] Step 8: decrypt the watermark image W' using the inverse Arnold transformation e to obtain the final watermark image W'.

[0039] Further, the formula for calculating the watermark index Idx' is as follows:

[0040]

[0041] Further, the formula for calculating the watermark bit and index set is as follows:

[0042] N bt and N id represent the watermark bit and index set respectively, and all original element values are 0, used to record the watermark bit and index.

[0043] Further, the final watermark bit is determined by the following formula:

[0044] W′ e (i) represents the bit of the undecrypted watermark, and the index value is i.

[0045] The beneficial effects of the present application are:

[0046] (1) inserting virtual vertices between adjacent vertices of the vector map to enhance the robustness of the watermark against vertex attacks;

[0047] (2) improving the stability and attack resistance of the watermark scheme by calculating and using the ratio of DWT high-frequency coefficients as the watermark embedding field;

[0048] (3) optimizing the watermark embedding and extraction algorithm to ensure the concealment of the watermark information and the extractability under various attacks;

[0049] (4) By correcting the watermark, the inconsistency of virtual vertices is solved, and the accuracy of watermark extraction is improved.

[0050] (5) The watermark scheme proposed in the present application shows excellent robustness when dealing with vertex deletion, vertex addition and map clipping attacks. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is the watermark embedding flowchart of the present application;

[0052] Figure 2 is the watermark extraction flowchart of the present application;

[0053] Figure 3 is the six vector maps used in the verification process of the present application;

[0054] Figure 4 is the result comparison chart under different watermark correction times of the present application;

[0055] Figure 5 is the optimized mapping comparison chart under different watermark correction times of the present application;

[0056] Figure 6 is the robustness experiment result chart of the present application. DETAILED DESCRIPTION

[0057] The present application will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it, but the embodiments are not limiting to the present application.

[0058] The embodiment proposes a vector map watermarking scheme based on virtual vertices and DWT frequency coefficient ratio which is robust to vertex attacks. The core of the scheme is to improve the resistance to vertex addition or deletion attacks by inserting virtual vertices between adjacent vertices, and at the same time, to extract the ratio of DWT high frequency coefficients of x and y coordinate sequences by using DWT to decompose the sequence containing actual and virtual vertex coordinates, and to embed it as a watermark embedding domain to construct a geometric feature invariant with strong stability. Through this strategy of combining virtual vertices and DWT high frequency coefficient ratio, the stability of the watermark is significantly improved, and by maintaining the geometric invariance of the relative position between vertices, the stability of the watermark embedding domain is ensured when facing geometric transformation, further enhancing the overall robustness of the watermark scheme. To solve the inconsistency problem caused by the introduction of virtual vertices, the invention also designs a watermark correction method, which accurately adjusts the DWT high frequency coefficients by pre-extracting and comparing the watermark information, thereby improving the extraction accuracy and robustness of the vector map watermark. In addition, the invention optimizes the algorithm parameters and watermark embedding strategy to achieve the best balance between watermark invisibility and robustness, meeting the actual needs of copyright protection. Experimental results show that the watermarking scheme proposed in the invention has excellent robustness in dealing with vertex deletion, vertex addition and map clipping attacks.

[0059] Firstly, the basic idea, methodology, watermark embedding and extraction of the digital watermarking algorithm proposed in the invention are as follows: The overall scheme of the invention is based on DWT algorithm, which converts vector map from spatial domain to frequency domain, and designs methods to improve the robustness of DWT watermarking under vertex attacks and geometric transformation. For this problem, three strategies are proposed: 1. In order to enhance the robustness to vertex deletion attack, virtual vertices (VVs) are calculated from adjacent real vertices (RVs) of the vector map. In order to further resist geometric attacks, the ratio of DWT high frequency coefficients calculated from the x coordinates of VVs to the coefficients calculated from the y coordinates is selected as the embedding domain. 2. Quantization index modulation (QIM) is used as the watermark embedding strategy to enable blind extraction of the watermark. 3. Finally, before the embedding process is completed, the watermark virtual vertices (WVVs) are removed and not pre-stored, resulting in inconsistency between WVVs and newly calculated VVs from the watermarked vector map. This inconsistency weakens the robustness. In order to solve this inconsistency, a novel watermark correction method is designed.

[0060] For the problem of using virtual vertices to resist vertex deletion attack in DWT domain, according to the analysis, the change of vertex number will cause the instability of DWT coefficients. In order to solve this instability, it is proposed to use virtual vertices to enhance the stability of DWT coefficients. Before continuing, it is important to distinguish between two types of vertices in vector maps: real vertices (RVs) and virtual vertices (VVs). Real vertices (RVs) are inherent to vector maps, while virtual vertices (VVs) are generated using algorithms.

[0061] Since DWT can effectively capture local features and is insensitive to local modifications, it is often used in vector map watermark design. DWT uses a specified filter to decompose the input vector map to obtain low and high frequency coefficients. Various filters can be used to obtain DWT coefficients, with Haar filter being the simplest and most commonly used. Let G represent a vector map, where G = (V, E). Here, V = {v i |v i =(x i ,y i ), i = 1, 2, …, n} is the vertex set, and E is the edge set. Using the Haar filter, the DWT process of the vector map is as follows, taking the x-coordinate of the vector map as an example:

[0062]

[0063] where L and H represent low and high frequency coefficients, respectively. DWT-based watermarking embeds watermark by modifying L or H, so their stability is crucial for the robustness of the watermark. Since vertex deletion does not change the coordinate values of the remaining vertices, the stability of L and H depends on the order of the vertices. Since (1) and (2) show that both L and H are determined by pairs of adjacent vertices, the behavior of these vertices when deletion occurs, each element of H is a multiple of the difference between two adjacent x-coordinates, which can be geometrically represented as the horizontal distance between vertices.

[0064] Specifically, for a pair of real adjacent vertices VV, the calculation formula of its virtual vertices {(x i , y i ), (x i+1 , y i+1 )} is as follows:

[0065]

[0066] The vertex sequence of the vector map with virtual vertices is represented as V', where:

[0067]

[0068] The addition process of vertices is shown in (4):

[0069]

[0070] Taking the x-coordinate as an example, the sequence of x-coordinates XVobtained after adding the virtual vertex VVs is represented as:

[0071]

[0072] One-dimensional discrete wavelet transform (DWT) is performed on XVto obtain low-frequency coefficients L xv and high-frequency coefficients H xv :

[0073]

[0074] Regarding the embedding strategy of the quantization index modulation (QIM), the quantization index modulation (QIM) can use a quantizer to classify the host data into different index intervals according to the watermark information. In the watermark detection stage, the watermark information can be identified according to the quantization index interval of the modulated data.

[0075] The formula for embedding the watermark w into the host data h using QIM is as follows, s represents the data embedded with the watermark:

[0076]

[0077] The process of extracting the watermark using QIM involves calculating the interval in which the data s containing the watermark is located, which is as follows:

[0078]

[0079] Suppose the watermark is a binary watermark, and the number of pixels with values of 0 and 1 in the watermark is equal, that is, the watermark w satisfies the following condition:

[0080]

[0081] where P(·) represents the probability of event · occurring. Since the host data h and Q are independent, the following holds:

[0082]

[0083] The watermark coefficient is defined as M, and embedding the watermark information through QIM can be simplified as the superposition of the host data and the watermark coefficient:

[0084]

[0085] The virtual vertex has inconsistency problems. The inconsistency of the virtual vertex VVs refers to the difference between the watermark virtual vertex WVVs and the virtual vertex calculated from the real vertex WRVs after watermarking.

[0086] First, the watermark information is embedded into the high-frequency coefficients Hxv The middle can be expressed as follows:

[0087] H' xv (i) = H xv (i) + M(i), i e {1, 2,..., n} (13)

[0088] where H' xv represents the watermark high frequency coefficient of the discrete wavelet transform (DWT).

[0089] In order to obtain the watermarked x coordinate sequence XV', the inverse DWT is performed on the watermark high frequency coefficient and the original low frequency coefficient. The value of XV' is expressed as follows:

[0090]

[0091] where XV(2i) represents a watermarked real vertex WRV, and XV'(2i) is a watermarked virtual vertex WVV.

[0092] The CVVs are calculated by calculating the average value between adjacent WRVs, as follows:

[0093]

[0094] where Value cvv represents the coordinate value of a CVV.

[0095] Next, the influence of the inconsistency of the virtual vertex on watermark extraction is studied. Since the virtual vertex used in watermark extraction is CVV rather than WVV, the DWT high frequency coefficient H" xv in the watermark extraction stage can be obtained by substituting Value cvv into (2) and calculating as follows:

[0096]

[0097] According to (16), H" xv (i) is obtained by shifting H' xv (i) along unit. The relationship between H" xv (i) and the quantization index modulation (QIM) interval in which H' xv (i) is located has only two cases: one is in the same interval, and the other is in adjacent intervals. When H" xv (i) and H' xv (i) are located in the same interval, the inconsistency of the virtual vertex is negative, and vice versa.

[0098] Therefore, although there can still be inconsistency of virtual vertexes after correction, the increase of the probability of negative inconsistency indicates that watermark correction theoretically enhances the robustness of the watermark algorithm. To further improve the robustness of the watermark algorithm, the watermark correction process can be repeated multiple times on the vector map with watermark, until the optimal watermark is extracted from the corrected vector map.

[0099] Regarding the correction strategy of the watermark, the purpose of watermark correction is to reduce the probability of positive virtual vertex inconsistency. The basic idea is to pre-extract the watermark w' from the coefficients in the vector map with watermark. Then compare w' with the original watermark w in the watermark embedding process. If they are inconsistent, use the correction method to modify the coefficients at the inconsistent points to ensure that the correct watermark information can be extracted.

[0100] Inconsistency between CVVs and WVVs can cause differences between H" xv and H' xv , resulting in potential errors in watermark extraction. Since the watermark information corresponding to the quantization interval where H' xv is located is the correct watermark information, the most direct watermark correction method can be to modify the value of H" xv so that it falls within the same quantization interval as H' xv . The watermark correction model is represented by the following formula:

[0101]

[0102] where H" c represents the corrected discrete wavelet transform (DWT) high frequency coefficient, and represents the floor function. Similar to equation (12), the watermark correction process can be simplified to the formula:

[0103] H" c = H" xv + C (18)

[0104] where C represents the correction coefficient. Although there is still inconsistency of virtual vertexes after watermark correction, the increase of the probability of negative inconsistency indicates that watermark correction theoretically enhances the robustness of the watermark algorithm. To further improve the robustness of the watermark algorithm, the watermark correction process can be repeated multiple times on the vector map with watermark, until the optimal watermark is extracted from the corrected vector map.

[0105] With respect to the ratio domain embedding, in order to enhance the algorithm's resistance to geometric attacks, a new watermark embedding domain, called the scale-invariant domain, is proposed. The present invention performs a discrete wavelet transform (DWT) on the X and Y coordinates, and extracts their corresponding high-frequency coefficients. Subsequently, the ratios of these coefficients are calculated to establish a watermark embedding domain that remains stable under geometric operations. The formula for constructing the scale-invariant domain is shown below:

[0106] When the vector map is translated by a units along the X-axis and β units along the Y-axis, the ratio R α，β of the corresponding coefficients can be expressed as:

[0107]

[0108] When the vector map is scaled by a scale factor η (η ≠ 0), the ratio R η of the corresponding coefficients can be expressed as:

[0109]

[0110] By integrating (19) and (21), it can be inferred that by embedding the watermark information into the coefficient ratios, the algorithm's resistance to geometric attacks, particularly translation and scaling, has been theoretically enhanced.

[0111] Based on the above basic ideas, methodologies, specific steps for watermark embedding and extraction, detailed explanations are as follows:

[0112] Referring to Figure 1 , a flowchart of watermark embedding is shown, which includes the following steps:

[0113] First, add a virtual vertex VVs to the original vector map G to obtain a vector map G vv containing a virtual vertex VVs; add a virtual vertex VVs to the inherent real vertex RVs in the original vector map G, and the addition of the virtual vertex VVs is according to formula (4); after adding the virtual vertex VVs, the X coordinate sequence XV and the Y coordinate sequence YV can be obtained, i.e., the X coordinate set X vv and the Y coordinate set Y vv are obtained.

[0114] Subsequently, the coordinate set X vv and the coordinate set Y vv are subjected to a discrete wavelet transform DWT, and high-frequency coefficients H xv and H yv are obtained, respectively;

[0115] The scale-invariant domain is constructed by formula (19) and the initial ratio sequence K is calculated;

[0116] Then, the encrypted watermark image We encrypted watermark image W e using the original watermark image W org obtained by scrambling through Arnold transformation; the calculation of Arnold transformation is as follows:

[0117]

[0118] where (b, d) and (b', d') represent the pixel positions of W org and W e respectively, and N W represents the pixel count of the watermark; the parameters m, n and N w are represented as a secret key.

[0119] Then the initial ratio sequence K is enlarged, the watermark information of the encrypted watermark image W e is embedded, and then it is scaled down to obtain the watermarked ratio sequence K'; the encrypted watermark image W e is embedded using the quantization index modulation QIM, and the embedding process is shown in the following formula:

[0120]

[0121] where M represents the enlargement factor, τ is the step of QIM, K' represents the watermarked ratio sequence, and N W represents the pixel count of the watermark.

[0122] The watermark high-frequency coefficient H yv ′ is obtained according to the watermarked ratio sequence K' and the high-frequency coefficient H xv ; the calculation formula is: H xv ′(i) = H yv (i) x K'(i).

[0123] Then the inverse discrete wavelet transform IDWT is applied to the watermark high-frequency coefficient H xv ′ to obtain the X coordinate set X vv ′ of the uncorrected watermark virtual vertex WVs; the watermark is corrected according to the coordinate set X vv ′ to obtain the corrected watermark high-frequency coefficient H xv "; specifically, the coordinate set X' is obtained by deleting the watermark virtual vertex WVs in the coordinate set X vv ′, then the above-mentioned added virtual vertex VVs is added to the coordinate set X' to obtain the coordinate set X vv ", and then the discrete wavelet transform DWT is performed on the coordinate set X vv " to obtain the corrected watermark high-frequency coefficient H xv "; the corrected watermark high-frequency coefficient H xv " and the high-frequency coefficient Hyv The ratio K″ is used to calculate the correction ratio K. c ;

[0124] Correction ratio K c Obtained from the following formula: Where τ is the step size of QIM.

[0125] As needed, according to the latest calculated correction ratio K c The watermark high-frequency coefficient H is obtained by replacing the watermark ratio sequence K′. xv And calculate the new correction ratio K step by step. c The final correction ratio K is obtained by repeated calculations. c Correction ratio K c and high frequency coefficient H yv Reverse calculation to obtain the watermarked X coordinate set X vc ;

[0126] Using the X coordinate set X vc The X coordinate set X obtained after replacing the original vector map G and adding virtual vertices VVs vv To generate a vector map G containing watermarked virtual vertices WVVs vv Finally, remove the WVVs to obtain the final watermarked vector map G′. Watermark embedding is now complete.

[0127] The watermark extraction process also involves adding virtual vertices (VVs) and constructing wavelet domain ratio invariance, which is the same as the watermark embedding process. For example... Figure 2 As shown, the extraction steps are as follows:

[0128] First, add virtual vertices VVs to the watermarked vector map G′ to obtain a vector map G containing the virtual vertices VVs. vv ′;For vector map G vv The X coordinate set V″′ in "" x and Y coordinate set V″′ y Perform Discrete Wavelet Transform (DWT) to obtain the high-frequency coefficients H. xv "and H yv ";The initial ratio sequence K″′ is obtained by constructing the formula for the ratio invariant domain and calculating it; this process can refer to the corresponding steps during embedding, and the two are the same, so it will not be described in detail.

[0129] Then, K″′ is amplified by M times to obtain the amplified sequence k″′. M ;

[0130] According to the amplification sequence K″′ M Calculate the watermark index Idx′; the formula for calculating the watermark index Idx′ is as follows:

[0131]

[0132] The watermark bits and the index set are calculated and recorded according to the following formula, and the index set is updated:

[0133] N bt and N id respectively represent the watermark bits and the index set, all original element values are 0, and are used to record the watermark bits and the index. First, the watermark is repeatedly embedded, for example, the value of the 50th watermark bit is 1, and it is embedded for 20 times. In the extraction stage, only 18 times of the result are 1 and 2 times of the result are 0 in the 20 times. At this time, the voting mechanism is used to determine whether the result of the 50th watermark bit is 0 or 1. Obviously, 18 times of 1 and 2 times of 0 are extracted, and the result should be 1.

[0134] The final watermark bit is determined according to the recorded watermark bit and the index set, and the undecrypted watermark image W′ e is obtained. The final watermark bit is determined by the following formula:

[0135] W′ e (i) represents the bit of the undecrypted watermark, and the index value is i.

[0136] Finally, the watermark image W′ e is decrypted using the inverse Arnold transformation to obtain the final watermark image W′. As follows:

[0137]

[0138] where (b, d) and (b′, d′) represent the pixel positions of W′ and W′ e respectively. The extraction of the watermark is completed.

[0139] The embedding and extraction method of the present application is compared with the existing method through experiments, as follows:

[0140] The invisibility and robustness of the present application are verified in a computer with the configuration parameters of Windows 10, AMD 4800U GPU and 16GB RAM. In order to evaluate the performance of the proposed watermarking scheme, six vector maps are selected as experimental data. These maps are respectively called coastline map, river map, building map, green land map, road map and waterway map, as shown in Figure 3The coastline map and the river map are both in China Geodetic Coordinate System 2000 (CGCS2000), which can be downloaded from the China Geographical Information Catalogue Service website (https: / / www.webmap.cn). The building map, the green land map and the road map are in local coordinate system, which are provided by a surveying and mapping institute in China. The waterway map can be obtained from the OpenStreetMap website (http: / / download.geofabrik.de).

[0141] Table 1 provides detailed information of these vector maps:

[0142]

[0143] and T. Wu, “Robust watermarking scheme for vector geographic data based on the ratio invariance of DWT-CSVD coefficients,” ISPRS International Journal of Geo-Information, vol. 11, no. 12, pp. 583, 2022.); [4] N. Wang, H. Zhang, and C. Men, “A high-capacity reversible data hiding method for 2D vector maps based on virtual coordinates,” Computer-Aided Design, vol. 47, pp. 108-117, 2014.; [5] X. Xi, X. Zhang, J. Bao, and Z. Zhang, “An improved DFT and QR code vector map digital watermarking algorithm,” Surveying and Mapping Sciences, vol. 47, no. 10, pp. 190-197, 2022, doi: 10.16251 / j.cnki.1009-2307.2022.10.025.; [6] Y. Li, L. Zhang, X. Wang, X. Zhang, and Q. Zhang, “A novel invariant based commutative encryption and watermarking algorithm for vector maps,” ISPRS International Journal of Geo-Information, vol. 10, no. 11, pp. 718, 2021.; and [7] Z. Lin, F. Peng, and M. Long, “A low-distortion reversible watermarking for 2D engineering graphics based on region nesting,” IEEE Transactions on Information Forensics and Security, vol. 13, no. 9, pp. 2372-2382, 2018.

[0144] To evaluate the imperceptibility of the proposed scheme, the maximum error (E max ) and the average error (E avg ) between the watermarked and the host vector maps were used as evaluation metrics. These metrics are defined as follows:

[0145]

[0146] where max(·) denotes the function that computes the maximum value, (x i , y i ) and (x′ i , y′ i ) represent the coordinate values of the i-th vertex in the original and watermarked vector maps, respectively.

[0147] In addition, two metrics of the schemes in [3], [4], [5], [6] and [7] were also computed for comparison. The error statistics are recorded in Tables 2 and 3. From these two tables, it is clear that the E max and E avg of the proposed scheme are both lower than the map accuracy and close to zero. The schemes [3], [5] and [6] also achieve high imperceptibility by setting a very small embedding strength, resulting in error statistics close to zero. [4] and [7] control the error by the embedding parameter related to the map accuracy, so their schemes also achieve good imperceptibility. In addition, the E avg in the proposed scheme is lower than the comparison schemes. From Tables 2 and 3, it can be concluded that the proposed scheme exhibits a high level of imperceptibility.

[0148] Table 2: Comparison of maximum error for different schemes:

[0149]

[0150] Table 3: Comparison of average error for different schemes:

[0151]

[0152] The effect of the watermark correction on the robustness of the proposed scheme was also tested. The experimental design involved evaluating the robustness of the proposed scheme under different attacks listed in Table 4, covering four different configurations: no watermark correction, one watermark correction, three watermark corrections and five watermark corrections.

[0153] Table 4: Types of attacks used to evaluate the effect of watermark correction:

[0154]

[0155] The comparison results are recorded in Figure 4BER values represent the average of the extracted watermark when tested using six hosts. Figure 5 The degree of optimization achieved after watermark correction is shown, showing that the maximum improvement in BER after applying three and five corrections is 35.26% and 37.26%, respectively. Figure 4 and Figure 5 The results show that the incorporation of watermark correction into the proposed scheme has a positive impact on improving robustness.

[0156] In subsequent experiments, five watermark corrections were performed to enhance robustness performance, and the robustness experiment attack methods are shown in Table 5.

[0157] Table 5 is the attack method of the robustness experiment:

[0158]

[0159] The bit error rate (BER) is used as a performance indicator for evaluating robustness, and the calculation expression of BER is:

[0160]

[0161] where ⊙ represents the XOR operation, and W(i) and W'(i) represent the i-th bit of the original and extracted watermark image, respectively.

[0162] The experimental results of the present application show that the proposed vector map watermarking scheme based on virtual vertex and DWT frequency coefficient ratio algorithm has better robustness than the algorithms in documents [3-7] when facing vertex deletion, vertex addition, map clipping and other attacks, and can maintain a low bit error rate even when the number of vertices is greatly reduced. In addition, the present application further improves the accuracy of watermark extraction through the designed watermark correction method, ensuring the reliability of the watermark information; in terms of invisibility, the influence of watermark embedding on the visual quality of the vector map is verified to be minimal through the quantitative index, meeting the requirement of concealment; in the composite attack test, the present scheme can still effectively extract the watermark information, proving its stability in complex attack environment, which is also superior to the comparative algorithms. Compared with the prior art, the present application exhibits better results in multiple performance tests, including lower BER and higher invisibility index, thereby verifying its effectiveness and innovation in vector map copyright protection.

[0163] The above-described embodiments are only preferred embodiments of the present application, and the protection scope of the present application is not limited thereto. Any equivalent substitution or transformation made by those skilled in the art based on the present application is within the protection scope of the present application.

Claims

1. A vector map watermark embedding method based on virtual vertex and DWT frequency coefficient ratio, characterized in that, The method comprises the following steps: Step 1, adding virtual vertices VVs to the original vector map G ; adding virtual vertices VVs to the original vector map ; Step 2: For the X coordinate set and Y coordinate set Perform Discrete Wavelet Transform (DWT) to obtain the high-frequency coefficients. and ; Step 3, Obtain the initial ratio sequence by constructing the formula of the ratio-invariant field and calculating ; Step 4, first scale up the initial ratio sequence , then embed the watermark information of the encrypted watermark image , and then scale down to obtain the watermarked ratio sequence ; Step 5, calculating the watermarking ratio sequence and high frequency coefficients obtaining watermark high frequency coefficients ; Step 6, high frequency coefficients of watermark Applying inverse discrete wavelet transform IDWT, obtaining uncorrected X coordinate set containing watermark virtual vertex WVVs ; Step 7, obtaining the corrected watermark high frequency coefficient according to the coordinate set carrying out watermark correction and obtaining the corrected watermark high frequency coefficient , calculating the corrected watermark high frequency coefficient and the ratio of the high frequency coefficient , obtaining the correction ratio according to the ratio ;​​ Step 8, calculating the corrected ratio and the high frequency coefficient obtaining the set of watermarked X coordinates ; Step 10, replace with to generate a vector map containing watermarked virtual vertices WVVs ; finally, remove the WVVs to obtain the final watermarked vector map ; In step 1, the original vector map G Inherent real vertices RVs in a pair of real vertices, the addition of virtual vertices VVs, the addition of virtual vertices VVs is as follows: ; After adding the virtual vertices VVs, the sequence of X coordinates is obtained XV and the sequence of Y coordinates is obtained YV i.e. the set of X coordinates is obtained and the set of Y coordinates is obtained .

2. The vector map watermark embedding method based on the ratio of virtual vertex and DWT frequency coefficient of claim 1, wherein, In step 4, the encrypted watermark image is embedded using a quantization index modulation, QIM .

3. The vector map watermark embedding method based on the ratio of virtual vertex and DWT frequency coefficient of claim 2, wherein, The embedding process is shown in the following equation: ； ； wherein, represents an amplification factor, is a step size of QIM, represents a sequence of ratios after watermarking, represents a pixel count of the watermark.

4. The vector map watermark embedding method based on the ratio of virtual vertex and DWT frequency coefficient of claim 1, wherein, The encrypted watermark image in step 4 Using the original watermark image Obtained by scrambling through Arnold transformation; The calculation of the Arnold transformation is as follows: ； wherein, and respectively represent and pixel positions, denotes the pixel count of the watermark; the parameters and are denoted as a secret key.

5. The vector map watermark embedding method based on the ratio of virtual vertex and DWT frequency coefficient of claim 1, wherein, In step 7, the coordinate set is obtained by deleting the watermark virtual vertexes WVVs in the coordinate set , and then the virtual vertexes VVs are added to the coordinate set to obtain the coordinate set , and then the discrete wavelet transform DWT is performed on the coordinate set to obtain the high frequency coefficients ; Corrected ratio Obtained from the equation: where is the step size of the QIM.

6. A vector map watermark extraction method based on virtual vertex and DWT frequency coefficient ratio, characterized in that, The method comprises the following steps: Step 1, watermarking the vector map adding virtual vertices VVs to obtain a vector map comprising virtual vertices VVs ; Step 2, Discrete Wavelet Transform (DWT) is performed on the set of X coordinates in the vector map and the set of Y coordinates in the vector map to obtain high frequency coefficients and low frequency coefficients, respectively. ;​​​ Step 3, Obtain the initial ratio sequence by constructing the formula of the ratio-invariant field and calculating ; Step 4: The amplification is obtained by multiplying the sequence by a factor of Step 5: According to the amplification sequence Calculate watermark index ; Step 6: Calculate and record the watermark bit and update the index set; Step 7: Determine the final watermark bit according to the recorded watermark bit and the index set, get the un-decrypted watermark image ; Step 8: Decrypting the watermarked image using inverse Arnold transformation to obtain the final watermarked image ; In step 1, the adding process of the virtual vertex VVs is as follows: 。 7. The vector map watermark extraction method based on the ratio of virtual vertex and DWT frequency coefficient of claim 6, wherein, Computing watermark index The formula is as follows: 。 8. The vector map watermark extraction method based on the ratio of virtual vertex and DWT frequency coefficient of claim 6, wherein, The formula for calculating the watermark bit and the index set is as follows: , representing watermark bits, representing index sets, all original element values are 0, used to record watermark bits and indexes.

9. The vector map watermark extraction method based on the ratio of virtual vertex and DWT frequency coefficient of claim 8, wherein, The final watermark bit is determined by the following formula: ， watermark bit representing an un-decrypted watermark, the index value is .

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