Vector map watermarking method based on virtual vertex and DWT frequency coefficient ratio

Abstract

The invention discloses a vector map watermark embedding and extracting method based on a virtual vertex and a DWT frequency coefficient ratio, which is characterized in that a vector map is converted from a space domain to a frequency domain on the basis of a DWT algorithm, and the method is designed on the basis to improve the robustness of a DWT-based watermark under vertex attack and geometric transformation. Specifically, in order to enhance robustness of vertex deletion attacks, virtual vertexes are calculated from adjacent real vertexes of a vector map, the ratio of a DWT high-frequency coefficient obtained through calculation from x coordinates of the virtual vertexes to a coefficient obtained through calculation from y coordinates is selected as an embedded domain, and a watermark correction method is designed, so that a watermark is corrected. According to the method, the consistency between the virtual vertex of the watermark and the VVs newly calculated from the vector map added with the watermark is ensured, and finally, quantitative index modulation is adopted as a watermark embedding strategy, so that the watermark can be blind extracted. The watermark technical scheme provided by the invention shows excellent robustness in coping with attacks such as vertex deletion, vertex addition, map cutting and the like.

Description

Technical Field

[0001] The invention relates to the technical field of vector map watermarking, and in particular to a vector map watermarking method based on virtual vertices and DWT frequency coefficient ratios. Background Art

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

[0003] As an effective means of copyright protection, digital watermarking technology can achieve copyright authentication and authenticity identification by embedding hidden watermark information in vector maps without significantly affecting the visual effect of vector maps. Traditional digital watermarking methods for vector maps are mainly divided into two categories: spatial domain and frequency domain. Spatial domain watermarking technology embeds watermarks by directly modifying the coordinate values ​​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 maps to the frequency domain. For example, algorithms based on discrete wavelet transform (DWT) can effectively resist geometric attacks such as rotation and scaling, but when the number of vertices changes, the robustness of the watermark is relatively weak, and the robustness of the watermark is often unable to be guaranteed, resulting in the loss or erroneous extraction of copyright information. This is because frequency domain watermarks usually rely on the global characteristics of vector maps. 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 watermarks, some studies have proposed methods to introduce virtual vertices. However, the introduction of virtual vertices may cause consistency problems in the watermark embedding and extraction process, that is, when extracting the watermark, the calculation of the virtual vertices may be inconsistent with that when embedding, resulting in a decrease in the accuracy of watermark extraction.

[0004] In the watermarking scheme in the literature [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 relationship between polygons by slightly adjusting the measurement scale of the spatial topological relationship. These schemes use the geometric invariance of the vector map structure to resist geometric attacks and often maintain high fidelity. However, the robustness of the watermark is affected by the topological relationship, which makes them still vulnerable to malicious attacks. In the literature [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 DWT is performed on the distance sequence between feature points and reference lines, and then watermarks are embedded by modulating these distances. However, these hidden watermarks are vulnerable to attacks involving map cropping, vertex deletion, and scaling. In the literature [3] C.Qu, X.Xi, J.Du, and T.Wu, “Robust watermarking scheme for vector geographic databased 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 processed by DWT, and then the transform coefficients are decomposed by 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, references [1]-[3] have been well applied in the copyright protection of vector maps. However, after experimental verification, they still have obvious defects. The first is the vulnerability to vertex attacks: References [1] and [2] show weak robustness when facing attacks such as vertex addition or map clipping. These attacks will change the vertex sequence of the vector map, thereby destroying the robustness and extractability of the watermark. The second is the limitation of the frequency domain method: although reference [3] has a certain resistance to geometric attacks, its performance will be significantly reduced under the influence of changes in the number of vertices and scaling attacks. 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 coefficient. In addition, the current vector map digital watermark protection scheme lacks an effective watermark correction mechanism: in the case of vertex inconsistency, the existing technology often lacks an effective watermark correction method, resulting in reduced accuracy and reliability of watermark extraction. There is also the problem of balancing the invisibility and robustness of the watermark: in order to improve the concealment of the watermark, the existing algorithm may sacrifice its robustness, and vice versa. In practical applications, it is difficult to find the best balance between the two. Finally, the watermark algorithm is not resistant enough to specific types of attacks: specific attacks, such as vertex noise attacks and object deletion attacks, pose challenges to existing watermark algorithms. These attacks can significantly change the characteristics of vector maps, making it difficult to accurately extract the embedded watermark information. Summary of the invention

[0006] The technical problem to be solved by the present invention 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 the DWT frequency coefficient ratio to construct a geometric feature invariant as a stable watermark embedding domain, and through a newly designed watermark correction method, effectively solve the inconsistency problem introduced by virtual vertices, thereby further improving the overall performance of the watermarking scheme.

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

[0008] Step 1: Add virtual vertices VVs to the original vector map G to obtain a vector map G containing virtual vertices VVs. vv ;

[0009] Step 2: X coordinate set X vv and Y coordinate set Y vv Perform discrete wavelet transform DWT to obtain high-frequency coefficients H xv and H yv ;

[0010] Step 3, constructing a ratio invariant domain formula and calculating to obtain an initial ratio sequence K;

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

[0012] Step 5: According to the watermarked ratio sequence K′ and the high frequency coefficient H yy Calculate the watermark high frequency coefficient H xv′ ;

[0013] Step 6: Watermark high frequency coefficient H xv′ Apply the inverse discrete wavelet transform IDWT to obtain the uncorrected X coordinate set X containing the watermark virtual vertices WVVs vv′ ;

[0014] Step 7: According to the coordinate set X vv′ Perform watermark correction and obtain the corrected watermark high frequency coefficient H xv″ , calculate the corrected watermark high frequency coefficient H xv″ and high frequency coefficient H yv The correction ratio K is calculated based on the ratio K″. c ;

[0015] Step 8: According to the correction ratio K c And the high frequency coefficient H yv Calculate the watermarked X coordinate set X vc ;

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

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

[0018]

[0019] After adding the virtual vertices VVs, we get the X coordinate sequence XV and the Y coordinate sequence YV, that is, we get 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] Furthermore, the embedding process is shown in the following formula:

[0022]

[0023] Where M represents the magnification factor, τ is the step size of QIM, K′ represents the ratio sequence after watermarking, and N W Indicates the pixel count of the watermark.

[0024] Furthermore, the encrypted watermark image W in step 4 e Using the original watermark image W org Obtained by perturbation through Arnold transform;

[0025] The Arnold transform is calculated as follows:

[0026]

[0027] Where (b, d) and (b′, d′) represent W org and W e The pixel position, N w Indicates the pixel count of the watermark; parameters m, n and N W Represented as a secret key.

[0028] Further, in step 7, by vv′ Delete the watermark virtual vertex WVVs from the coordinate set X′, and then add the virtual vertex VVs to the coordinate set X′ to obtain the coordinate set X vv″ , then, for the coordinate set X vv″ Perform discrete wavelet transform DWT to obtain the corrected watermark high frequency coefficient X xv″ ;

[0029] Correction ratio K C Obtained by the following formula: where τ is the step size of QIM.

[0030] A vector map watermark extraction method based on virtual vertices and DWT frequency coefficient ratios comprises the following steps:

[0031] Step 1: Add virtual vertices VVs to the watermarked vector map G′ to obtain a vector map G containing virtual vertices VVs. vv′ ;

[0032] Step 2: Vector map G vv″ The X-coordinate set V″′ in x and Y coordinate set V″′ y Perform discrete wavelet transform DWT to obtain high-frequency coefficients H xv″ and H yv″ ;

[0033] Step 3, constructing a ratio invariant domain formula and calculating to obtain an initial ratio sequence K″′;

[0034] Step 4: Amplify K″′ by M times to obtain the amplified sequence K″′ M ;

[0035] Step 5: According to the amplification sequence K″′ M Calculate the watermark index Idx′;

[0036] Step 6: Calculate and record the watermark position and index set;

[0037] Step 7: Determine the final watermark position based on the recorded watermark position and index set to obtain the undecrypted watermark image W′ e ;

[0038] Step 8: Decrypt the watermark image W′ using the inverse Arnold transform e To obtain the final watermark image W′.

[0039] Furthermore, the formula for calculating the watermark index Idx′ is as follows:

[0040]

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

[0042] N bt and N id They represent watermark positions and index sets respectively. All original element values ​​are 0 and are used to record watermark positions and indexes.

[0043] Furthermore, the final watermark position is determined by the following formula:

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

[0045] Beneficial effects of the present invention:

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

[0047] (2) By calculating and using the DWT high-frequency coefficient ratio as the watermark embedding domain, the stability and anti-attack capability of the watermarking scheme are improved;

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

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

[0050] (5) The watermarking scheme proposed in the present invention shows excellent robustness in dealing with attacks such as vertex deletion, vertex addition, and map clipping. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a watermark embedding flow chart of the present invention;

[0052] Figure 2 It is a watermark extraction flow chart of the present invention;

[0053] Figure 3 These are the six vector maps used in the verification process of the present invention;

[0054] Figure 4 This is a comparison chart of the results of different watermark correction times of the present invention;

[0055] Figure 5 This is a comparison diagram of optimized images under different watermark correction times of the present invention;

[0056] Figure 6 It is a diagram of the robustness experimental results of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

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

[0059] First, the digital watermarking algorithm proposed in this invention, its basic idea, methodology, watermark embedding and extraction are as follows: The overall scheme of this invention is based on the DWT algorithm, which converts the vector map from the spatial domain to the frequency domain. On this basis, a method is designed to improve the robustness of the DWT-based watermark under vertex attacks and geometric transformations. To address this problem, three strategies are proposed: 1. In order to enhance the robustness against vertex deletion attacks, virtual vertices (VVs) are calculated from the adjacent real vertices (RVs) of the vector map. In order to further resist geometric attacks, the ratio of the DWT high-frequency coefficients calculated from the x-coordinate of the VVs to the coefficients calculated from the y-coordinate is selected as the embedding domain. 2. Quantization index modulation (QIM) is used as a 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 inconsistencies between the WVVs and the newly calculated VVs from the watermarked vector map, which weakens the robustness. In order to solve this inconsistency, a novel watermark correction method is designed.

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

[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-frequency and high-frequency coefficients. Various filters can be used to obtain DWT coefficients, among which the Haar filter is 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. Taking the x coordinate of the vector map as an example, the DWT of the Haar filter is used to process the vector map as follows:

[0062]

[0063] where L and H represent the low-frequency and high-frequency coefficients, respectively. DWT-based watermarks embed watermarks by modifying L or H, so their stability is crucial to the robustness of the watermark. Since vertex deletion does not change the coordinate values ​​of the retained 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, their virtual vertices {(x i ,y i ), (x i+1 ,y i+1 )} is calculated as follows:

[0065]

[0066] The vertex sequence of a vector map with virtual vertices is denoted as V′, where:

[0067]

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

[0069]

[0070] Taking the x coordinate as an example, the x coordinate sequence XV obtained after adding the virtual vertex VVs is expressed as:

[0071]

[0072] Performing one-dimensional discrete wavelet transform (DWT) on XV, we can get the low-frequency coefficient L xv and high frequency coefficient H xv :

[0073]

[0074] Regarding the embedding strategy of Quantization Index Modulation (QIM), 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 using QIM to embed a watermark w into host data h is as follows, where s represents the data to be embedded with the watermark:

[0076]

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

[0078]

[0079] Assume that 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 conditions:

[0080]

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

[0082]

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

[0084]

[0085] There is an inconsistency problem in virtual vertices. The inconsistency of virtual vertices VVs refers to the difference between the watermarked virtual vertices WVVs and the virtual vertices calculated from the watermarked real vertices WRVs.

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

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

[0088] Among them, H′ xv Represents the high-frequency coefficients of the watermark from the Discrete Wavelet Transform (DWT).

[0089] In order to obtain the watermarked x-coordinate sequence XV′, the watermark high-frequency coefficients and the original low-frequency coefficients are subjected to inverse DWT. 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] CVVs are calculated by taking the average between adjacent WRVs as follows:

[0093]

[0094] Among them, Value cvv Represents the coordinate value of a CVVs.

[0095] Next, we study the impact of virtual vertex inconsistency on watermark extraction. Since the virtual vertices used in watermark extraction are CVVs instead of WVVs, the DWT high-frequency coefficients H″ in the watermark extraction stage xv You can use Value cvv Substituting into (2), the calculation is as follows:

[0096]

[0097] According to (16), H″ xv (i) By xv (i)along Unit translation. H″ xv (i) and H′ xv (i) There are only two situations in which the relationship between the quantization index modulation (QIM) intervals is: one is in the same interval, and the other is in adjacent intervals. xv (i) and H′ xv (i) When all virtual vertices are in the same interval, the inconsistency of the virtual vertices is negative, otherwise it is positive.

[0098] Therefore, although there may still be virtual vertex inconsistencies after correction, the increase in the probability of negative inconsistency indicates that watermark correction theoretically enhances the robustness of the watermark algorithm. In order to further improve the robustness of the watermark algorithm, the watermark correction process can be repeated multiple times on the watermarked vector map until the optimal watermark is extracted from the corrected vector map.

[0099] Regarding the watermark correction strategy, the purpose of watermark correction is to reduce the probability of inconsistency of positive virtual vertices. The basic idea is to pre-extract the watermark from the coefficients in the watermarked vector map to obtain the watermark w′. Then w′ is compared with the original watermark w in the watermarking process. If they are inconsistent, a correction method is used to modify the coefficients at the inconsistent points to ensure that the correct watermark information can be extracted.

[0100] Inconsistency between CVVs and WVVs may lead to H″ xv and H′ xv There are differences between them, which leads to potential errors in watermark extraction. xv The watermark information corresponding to the quantization interval is correct watermark information. The most direct watermark correction method is to modify H″ xv value so that it falls within the range of H′ xv In the same quantization interval. The watermark correction model is expressed by the following formula:

[0101]

[0102] Among them, H″ c represents the corrected discrete wavelet transform (DWT) high frequency coefficients, and Represents the floor rounding function. Similar to formula (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 are still inconsistencies in virtual vertices after watermark correction, the increase in the probability of negative inconsistency indicates that watermark correction theoretically enhances the robustness of the watermark algorithm. In order to further improve the robustness of the watermark algorithm, the watermark correction process can be repeated multiple times on the watermarked vector map until the optimal watermark is extracted from the corrected vector map.

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

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

[0107]

[0108] When the vector map is scaled by a factor η (η≠0), the ratio R of the corresponding coefficients η As shown below:

[0109]

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

[0111] Based on the above basic ideas, methodology, the specific steps of watermark embedding and extraction are described in detail as follows:

[0112] Reference Figure 1 As shown in FIG. 1 , it is a flow chart of watermark embedding, and embedding includes the following steps:

[0113] First, add virtual vertices VVs to the original vector map G to obtain a vector map G containing virtual vertices VVs. vv ; The original vector map G has inherent real vertices RVs, and virtual vertices VVs are added to a pair of real vertices. The addition of virtual vertices VVs follows formula (4); After adding virtual vertices VVs, the X coordinate sequence XV and the Y coordinate sequence YV can be obtained, that is, the X coordinate set X is obtained. vv and the Y coordinate set Y vv .

[0114] Then the coordinate set X vv and coordinate set Y vv Perform discrete wavelet transform DWT to obtain high-frequency coefficients H xv and H yv ;

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

[0116] Then get the encrypted watermark image We , encrypted watermark image W e Using the original watermark image W org Obtained by perturbing the Arnold transform; the Arnold transform is calculated as follows:

[0117]

[0118] Where (b, d) and (b′, d′) represent W org and W e The pixel position, N W Indicates the pixel count of the watermark; parameters m, n and N w Represented as a secret key.

[0119] The initial ratio sequence K is then amplified and subsequently embedded into the encrypted watermark image W e The watermark information is then scaled down to obtain the watermarked ratio sequence K′; where quantization index modulation QIM is used to embed the encrypted watermark image W e , the embedding process is shown in the following formula:

[0120]

[0121] Where M represents the magnification factor, τ is the step size of QIM, K′ represents the ratio sequence after watermarking, and N W Indicates the pixel count of the watermark.

[0122] According to the watermarked rate sequence K′ and the high frequency coefficient H yv Calculate the watermark high frequency coefficient H xv ′; the calculation formula is: H xv ′(i)=H yv (i)×K′(i).

[0123] Then the watermark high frequency coefficient H xv ' Apply inverse discrete wavelet transform IDWT to obtain the uncorrected X coordinate set X containing the watermark virtual vertices WVVs vv ′; According to the coordinate set X vv ′ Perform watermark correction and obtain the corrected watermark high frequency coefficient H xv ″, specifically, by vv ', the watermark virtual vertex WVVs is deleted to obtain the coordinate set X', and then the virtual vertex VVs added above is added to the coordinate set X' to obtain the coordinate set X vv ″, then for the coordinate set X vv Perform discrete wavelet transform DWT to obtain the corrected watermark high frequency coefficient H xv Calculate the corrected watermark high frequency coefficient H xv ″ and high frequency coefficient Hyv The correction ratio K is calculated based on the ratio K″. c ;

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

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

[0126] Use the X coordinate set X vc Replace the original vector map G and add the virtual vertex VVs to obtain the X coordinate set X vv To generate a vector map G containing watermark virtual vertices WVVs vv ′; Finally, remove WVVs to obtain the final watermarked vector map G′. Watermark embedding is completed.

[0127] The watermark extraction process also involves adding virtual vertices (VVs) and constructing ratio invariance in the wavelet domain, which is the same as the watermark embedding process. 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 virtual vertices VVs. vv ′; for the vector map G vv The X-coordinate set V″′ in ″ x and Y coordinate set V″′ y Perform discrete wavelet transform DWT to obtain high-frequency coefficients H xv ″ and H yv ″; The initial ratio sequence K″′ is obtained by constructing a formula of the ratio invariant domain and calculating; this process can refer to the corresponding steps during embedding, and the two are consistent and will not be described in detail.

[0129] Then K″′ is amplified 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] Calculate and record the watermark bit and update the index set according to the following formula:

[0133] N bt and N id Represent the watermark position and index set respectively. All original element values ​​are 0, which are used to record the watermark position and index. First, the watermark is embedded repeatedly. For example, the value of the 50th watermark position is 1, which is embedded 20 times in total. In the extraction stage, among these 20 times, only 18 results are 1 and 2 results are 0. At this time, a voting mechanism is used to determine whether the result of the 50th watermark position is 0 or 1. Obviously, 18 times of 1 and 2 times of 0 are extracted, and the result should be 1.

[0134] Determine the final watermark position based on the recorded watermark position and index set, and obtain the undecrypted watermark image W′ e ; The final watermark position is determined by the following formula:

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

[0136] Finally, the inverse Arnold transform is used to decrypt the watermark image W′ e To obtain the final watermark image W′. As shown below:

[0137]

[0138] Where (b, d) and (b′, d′) represent W′ and W′ respectively. e The pixel position of the watermark is extracted.

[0139] The embedding extraction method of this application is experimentally compared with the existing method, as follows:

[0140] The invisibility and robustness of the proposed watermarking scheme are verified in a computer with 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 called coastline map, river map, building map, green space map, road map and waterway map, as shown in Figure 1. Figure 3As shown, (a) is the coastline; (b) is the river; (c) is the building; (d) is the green space; (e) is the road; and (f) is the waterway. The coastline map and river map both use the Chinese Geodetic Coordinate System 2000 (CGCS2000) and can be downloaded from the China Geographic Information Directory Service website (https: / / www.webmap.cn). The building map, green space map, and road map use the local coordinate system and are provided by a Chinese surveying and mapping institute. The waterway map can be obtained from the OpenStreetMap website (http: / / download.geofabrik.de).

[0141] Table 1 provides details of these vector maps:

[0142]

[0143] And select the literature [3] (C.Qu, high-capacityreversibledata hiding method for 2D vector maps based on virtualcoordinates," Computer-Aided Design, vol.47, pp.108-117, 2014.); Reference [5] (Xi Xu, Zhang Xinchang, Bao Jianteng, Zhang Yazhou, "An improved DFT and QR code vector map digital watermarking algorithm," Surveying and Mapping Science, vol.47, no.10, pp.190-197, 2022, doi:10.16251 / j.cnki.1009-2307.2022.10.025.); Reference [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 Reference [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.) for comparison.

[0144] In order to evaluate the invisibility of the proposed scheme, the maximum error (E max ) and the average error (E avg ) as evaluation indicators. These indicators are defined as follows:

[0145]

[0146] Where max(·) represents the function for calculating 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 indices of the proposed schemes in five previous works [3], [4], [5], [6] and [7] are calculated for comparison. The error statistics are recorded in Tables 2 and 3. From these two tables, it is obvious that the E max and E avg are all lower than the map accuracy and close to zero. Comparative solutions [3], [5] and [6] also achieve high invisibility by setting a very small embedding strength, resulting in error statistics close to zero. [4] and [7] control the error by embedding parameters related to map accuracy, so their solutions also achieve good invisibility. In addition, E avg It can be concluded from Tables 2 and 3 that the solution of the present invention exhibits a high level of invisibility.

[0148] Table 2 compares the maximum errors of different schemes:

[0149]

[0150] Table 3 is a comparison of the average errors of different schemes:

[0151]

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

[0153] Table 4 shows the attack types used to evaluate the watermark correction effect:

[0154]

[0155] The comparison results are recorded in Figure 4, where the BER value represents the average value of the watermarks extracted when testing with six hosts. Figure 5 The degree of optimization achieved after applying watermark correction is demonstrated, showing that the maximum BER improvement is 35.26% and 37.26% after applying three and five corrections, respectively. Figure 4 and Figure 5 The results show that incorporating watermark correction into the proposed scheme has a positive impact on improving the robustness.

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

[0157] Table 5 shows the attack methods of the robustness experiment:

[0158]

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

[0160]

[0161] where ⊙ denotes an XOR operation, and W(i) and W′(i) refer to the i-th bit of the original and extracted watermark images, respectively.

[0162] The experimental results of the present invention show that the proposed vector map watermarking scheme based on virtual vertices and DWT frequency coefficient ratios shows excellent robustness compared to the algorithms in the literature [3-7] in the face of attacks such as vertex deletion, vertex addition, and map clipping, and can maintain a low bit error rate even when the number of vertices is greatly reduced. In addition, the present invention further improves the accuracy of watermark extraction through the designed watermark correction method, ensuring the reliability of watermark information; in terms of invisibility, it is verified through quantitative indicators that the impact of watermark embedding on the visual quality of the vector map is extremely small, meeting the requirements of concealment; in the composite attack test, this scheme can still effectively extract the watermark information, proving its stability in complex attack environments, and is also better than the comparison algorithm. Compared with the prior art, the present invention shows better results in multiple performance tests, including lower BER and higher invisibility indicators, thereby verifying its effectiveness and innovation in vector map copyright protection.

[0163] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or change made by a person skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A vector map watermark embedding method based on virtual vertices and DWT frequency coefficient ratios, characterized in that: The following steps are involved: Step 1: Add virtual vertices VVs to the original vector map G to obtain a vector map G containing virtual vertices VVs. vv ; Step 2: X coordinate set X vv and Y coordinate set Y vv Perform discrete wavelet transform DWT to obtain high-frequency coefficients H xv and H yv ; Step 3, constructing a ratio invariant domain formula and calculating to obtain an initial ratio sequence K; Step 4: First amplify the initial ratio sequence K, and then embed the encrypted watermark image W e The watermark information is then scaled down to obtain the watermarked ratio sequence K′; Step 5: According to the watermarked ratio sequence K′ and the high frequency coefficient H yv Calculate the watermark high frequency coefficient H xv′ ; Step 6: Watermark high frequency coefficient H xv′ Apply the inverse discrete wavelet transform IDWT to obtain the uncorrected X coordinate set X containing the watermark virtual vertices WVVs vv′ ; Step 7: According to the coordinate set X vv′ Perform watermark correction and obtain the corrected watermark high frequency coefficient H xv″ , calculate the corrected watermark high frequency coefficient H xv″ and high frequency coefficient H yv The correction ratio K is calculated based on the ratio K″. c ; Step 8: According to the correction ratio K c And the high frequency coefficient H yv Calculate the watermarked X coordinate set X vc ; Step 10: Use X vc Replace X vv To generate a vector map G containing watermark virtual vertices WVVs vv′ ; Finally, remove the WVVs to obtain the final watermarked vector map G′.

2. The vector map watermark embedding method based on virtual vertices and DWT frequency coefficient ratios as claimed in claim 1, characterized in that: In step 1, the original vector map G has inherent real vertices RVs, and virtual vertices VVs are added to a pair of real vertices. The process of adding virtual vertices VVs is as follows: After adding virtual vertices VVs, we get the X coordinate sequence XV and the Y coordinate sequence YV, that is, we get the X coordinate set X vv and the Y coordinate set Y vv .

3. The vector map watermark embedding method based on virtual vertices and DWT frequency coefficient ratios as claimed in claim 1, characterized in that: In step 4, quantization index modulation QIM is used to embed the encrypted watermark image W e .

4. The vector map watermark embedding method based on virtual vertices and DWT frequency coefficient ratios as claimed in claim 3, characterized in that: The embedding process is shown in the following formula: Where M represents the magnification factor, τ is the step size of QIM, K′ represents the ratio sequence after watermarking, and N W Indicates the pixel count of the watermark.

5. The vector map watermark embedding method based on virtual vertices and DWT frequency coefficient ratios as claimed in claim 1, characterized in that: The encrypted watermark image W in step 4 e Using the original watermark image W org Obtained by perturbation through Arnold transform; The Arnold transform is calculated as follows: Where (b, d) and (b′, d′) represent W org and W e The pixel position, N w Indicates the pixel count of the watermark; parameters m, n and N w Represented as a secret key.

6. The vector map watermark embedding method based on virtual vertices and DWT frequency coefficient ratios as claimed in claim 1, characterized in that: In step 7, by vv′ Delete the watermark virtual vertex WVVs from the coordinate set X′, and then add the virtual vertex VVs to the coordinate set X′ to obtain the coordinate set X vv″ , then, for the coordinate set X vv″ Perform discrete wavelet transform DWT to obtain high frequency coefficients H xv″ ; Correction ratio K c Obtained by the following formula: where τ is the step size of QIM.

7. A vector map watermark extraction method based on virtual vertices and DWT frequency coefficient ratios, characterized in that: The following steps are involved: Step 1: Add virtual vertices VVs to the watermarked vector map G′ to obtain a vector map G containing virtual vertices VVs. vv′ ; Step 2: Vector map G vv″ The X-coordinate set V″′ in x and Y coordinate set V″′y to perform discrete wavelet transform DWT, and obtain high-frequency coefficients H xv″ and H yv″ ; Step 3, constructing a ratio invariant domain formula and calculating to obtain an initial ratio sequence K″′; Step 4: Amplify K″′ by M times to obtain the amplified sequence K″′ M ; Step 5: According to the amplification sequence K″′ M Calculate the watermark index Idx′; Step 6: Calculate and record the watermark position and update the index set; Step 7: Determine the final watermark position based on the recorded watermark position and index set to obtain the undecrypted watermark image W′ e ; Step 8: Decrypt the watermark image W′ using the inverse Arnold transform e To obtain the final watermark image W′.

8. The vector map watermark extraction method based on virtual vertices and DWT frequency coefficient ratios as claimed in claim 7, characterized in that: The formula for calculating the watermark index Idx′ is as follows:

9. The vector map watermark extraction method based on virtual vertices and DWT frequency coefficient ratios as claimed in claim 7, characterized in that: The formula for calculating the watermark bit and index set is as follows: N bt Represents the watermark bit, N id Represents an index set, all original element values ​​are 0, used to record watermark positions and indexes.

10. The vector map watermark extraction method based on virtual vertices and DWT frequency coefficient ratios according to claim 7, characterized in that: The final watermark position is determined by the following formula: W′e(i) represents the watermark bit of the undecrypted watermark, with index value i.

Images