A reversible watermarking algorithm for vector geographic datasets

Abstract

The invention belongs to the field of geographic information security technology, and discloses a reversible watermark algorithm suitable for vector geographic data sets, including: step one, watermark information generation; step two, watermark information embedding: curve filling is performed on point elements, converted into line elements, and then characteristic points are extracted, a polar coordinate system is constructed according to the minimum circumscribed circle generated by the characteristic points, and the generated watermark information is embedded into the polar angle using a prediction error expansion technology to obtain a vector geographic data set after the watermark is embedded; step three, watermark information detection; step four, testing and analysis: anti-modification attack is performed on the vector geographic data set containing the watermark, so as to experimentally verify whether the watermark information is effective, thereby judging the anti-modification attack capability of the watermark; the method converts the type of data, extracts characteristic points using a compression algorithm to embed in a watermark, and combines with the prediction error expansion technology, so that the method can realize watermark embedding and detection as well as lossless recovery.

Description

Technical Field

[0001] The invention belongs to the technical field of geographic information security, and in particular relates to a reversible watermark algorithm suitable for vector geographic data sets. Background Art

[0002] Geographic information data has a wide range of applications in urban planning, natural resource management, environmental monitoring, military and other fields. These data are usually stored in the form of vector data sets, including points, lines, and surfaces. However, with the development of network technology, vector geographic data sets inevitably encounter information security issues such as data infringement during transmission and sharing. Therefore, achieving copyright protection for vector geographic data sets has become a key issue that needs to be urgently addressed in the current field of geographic information security.

[0003] As a cutting-edge technology in the field of information security, digital watermarking technology has been widely used in vector geographic data information security. It achieves copyright protection by directly or indirectly embedding watermark information with copyright information into the coordinates of vector geographic data. As a type of digital watermark, reversible watermarking can restore data to its original state in a reversible way after watermarking is embedded, taking into account both losslessness and robustness.

[0004] Shao Chengyong et al. (Shao Chengyong, Wang Xiaotong, Xu Xiaogang et al. Research on lossless data hiding algorithm for vector maps [J]. Journal of Image and Graphics, 2007(02):206-211.) Based on the idea of ​​difference expansion, the watermark information is embedded by modifying the difference between the coordinates of adjacent vertices in the vector map, thus realizing a lossless data hiding algorithm for vector maps. Cao Liujuan et al. (Cao Liujuan, Men Chaoguang, Sun Jianguo. Principle of reversible watermarking algorithm for two-dimensional vector maps based on spatial features [J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(04):422-427+434.) Based on the condition of maintaining the relative position of the feature points of the vector map, the positions of the feature points are nonlinearly scrambled according to the key, and then the watermark information is embedded in the scrambled feature points. Qiu Yinguo et al. (Qiu Yinguo, Sun Jiuyun, Lu Lijiang. Reversible watermarking algorithm for vector maps based on error correction coding [J]. Computer Application Research, 2018, 35(09): 2762-2765.) applied error correction coding to reversible watermarking, combined the error correction codes generated by binary arrays and their combinations into watermark data, and finally embedded the watermark data into vertex polar coordinates to enhance the algorithm's ability to resist geometric transformation. Xi Xu et al. (Xi Xu, Zhang Xinchang. Reversible watermarking algorithm for vector maps based on interval mapping and maximum disturbance area [J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(11): 2379-2389.) embedded watermark information by modulating the interval state value of the coordinate point using the watermark information bit, and achieved reversible extraction and blind detection of watermark information through one-to-one mapping between interval bits and watermark information bits.

[0005] Although the above algorithms can achieve watermark information embedding and reversible recovery well, they are less robust to point data and cannot be applied to vector data sets composed of points, lines, and surfaces. At present, there is no reversible watermark algorithm that is applicable to vector geographic data sets and has high robustness to common attacks. The present invention can fill this gap. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a reversible watermark algorithm applicable to vector geographic data sets to solve the problems in the prior art. The technical solution adopted by the present invention is:

[0007] A reversible watermarking algorithm for vector geographic datasets, including:

[0008] Step 1, watermark information generation: select an image with copyright information, encrypt the image using Arnold transformation, and convert the encrypted image from two-dimensional to one-dimensional binary sequence;

[0009] Step 2: Watermark information embedding: Fill the point features with curves, convert them into line features, extract feature points, build a polar coordinate system based on the minimum circumscribed circle generated by the feature points, embed the generated watermark information into the polar angle using the prediction error expansion technology, and obtain the vector geographic data set after embedding the watermark;

[0010] Step 3: Watermark information detection: Fill the point features with curves, convert them into line features, extract the feature points, construct a polar coordinate system based on the minimum circumscribed circle generated by the feature points, extract the embedded watermark bits from the polar angles, and perform lossless recovery of the vector geographic data set after the watermark is embedded;

[0011] Step 4: Testing and analysis: Conduct anti-modification attacks on the vector geographic data set containing the watermark to experimentally verify whether the watermark information is valid, thereby determining the watermark's ability to resist modification attacks.

[0012] The present invention has the following beneficial effects: the method converts the type of data, extracts feature points using a compression algorithm to embed watermarks, and combines the method with a prediction error expansion technique, so that the method can embed and detect watermarks as well as achieve lossless recovery; in addition, because the method embeds watermark information into geometric features, the method can resist almost all common types of attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flow chart of watermark generation and embedding of the method of the present invention;

[0014] Figure 2 is a flow chart of watermark detection of the method of the present invention;

[0015] Figure 3is the experimental data of the method of the present invention;

[0016] Figure 4 The data is watermarked using the method of the present invention;

[0017] Figure 5 The data and detection results after the watermarked data is attacked: (a) is an overall translation attack, (b) is an overall rotation attack, (c) is a data compression attack, (d) is a data addition attack, and (e) is a data deletion attack;

[0018] Figure 6 This is a schematic diagram of the predicted value calculation. DETAILED DESCRIPTION

[0019] The following will be combined with the embodiments of the present invention Figure 1-Figure 6 , the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0020] In the vector geographic data set, in order to improve the robustness of the algorithm to point data, it is first converted into line features for processing, and then a polar coordinate system is constructed through the extracted feature points to achieve resistance to geometric attacks. Then, the data is sorted based on the normalized polar angle and polar diameter, and the prediction error expansion technology is further used to embed the watermark information into the polar angle of the point, thereby achieving watermark embedding and lossless recovery. Figure 3 , gives an example of the experimental data (vector geographic data set) of the present invention, after the method of the present invention, the watermark is embedded to form Figure 4 .

[0021] The basic idea of ​​the method of the present invention is: first, the point elements are converted into line elements using the space curve filling algorithm, and then the feature points are extracted from the line elements and the surface elements using the perpendicular distance method to maintain their robustness against addition, deletion and cropping attacks. Further, the polar coordinate system is constructed through the minimum circumscribed circle, and then the watermark information is embedded into the polar angles of other points except the minimum circumscribed circle using the prediction error expansion technology. The process of watermark detection is consistent with the embedding of watermark information, and the embedded watermark data can be restored losslessly through the prediction error expansion technology.

[0022] The present invention proposes a reversible watermark algorithm suitable for vector geographic data sets, comprising the following steps:

[0023] Step 1: Generate watermark information: Select an image with copyright information, encrypt the image using Arnold transformation, and convert the encrypted image from two-dimensional to one-dimensional binary sequence. Figure 1 , the specific process is:

[0024] Step 1.1: Select an image of size n×n with copyright information;

[0025] Step 1.2: Use Arnold variation to encrypt the copyright image and generate an encrypted image I. Specifically, Arnold variation is used to scramble the image, thereby encrypting the watermark information, which can be expressed as:

[0026] Among them, (x, y) is the coordinate of the pixel in the original image, (x′, y′) is the coordinate of the pixel in the new image after transformation, and N is the size of the image.

[0027] Step 1.3: Convert the image I from two dimensions to a one-dimensional binary sequence, denoted as:

[0028] W r ={w r [i],0≤i≤j},w r [i]∈[0,1]

[0029] Where j = n*n is the robust watermark length, w r [i] represents the i-th value in the binary sequence.

[0030] Step 2: Embed watermark information: Fill the point features with curves, convert them into line features, extract feature points, construct a polar coordinate system based on the minimum circumscribed circle generated by the feature points, embed the generated watermark information into the polar angle using the prediction error expansion technology, and obtain the vector geographic data set after embedding the watermark. Figure 1 , the specific process is:

[0031] Step 2.1: For point features in the vector geographic dataset, use the Hilbert space filling curve to fill them into line features; specifically, the Hilbert space filling curve is used to fill point features into line features, and the specific steps are as follows: first select the order of the Hilbert curve, then generate the Hilbert curve, for each point feature, map its multi-dimensional coordinates to one-dimensional space through the coordinate transformation of the Hilbert curve, sort the transformed one-dimensional coordinates, and connect the sorted points.

[0032] Step 2.2: Use the vertical distance method to compress and simplify the features in the vector geographic dataset, and record the compressed points as feature points P f Specifically, for the perpendicular distance method, three points on the curve are taken in sequence, and the perpendicular distance d between the middle point and the line connecting the other two points is calculated, and compared with the threshold D. If d < D, the middle point is removed; if d ≥ D, the middle point is retained. Then the next three points are taken in sequence and the processing continues until the line ends.

[0033] Step 2.3: Calculate P f The minimum circumscribed circle of o ,y o ), with a radius of r, the center of the circle is the pole, and the ray starting from the pole and passing through the point farthest from the center of the circle and not on the circle is the polar axis to construct a polar coordinate system;

[0034] Step 2.4: Calculate the polar angle θ of each point based on the constructed polar coordinate system i and polar diameter d i Then the polar angle and polar diameter of the feature point are normalized, and the normalized polar angle and polar diameter are used as the coordinates of the point (x nθ ,y nr );

[0035] Step 2.5: Each feature point d i The first α bits of are used as the parameters of the hash function to generate the watermark index of each point, that is, the location where the watermark is embedded;

[0036] Step 2.6: Get the embedded watermark bit according to the watermark index, and based on the order of the normalized feature points, get the original polar angles of the three feature points in the lower right corner adjacent to the point to be embedded in the order from top to bottom and from left to right (such as Figure 6 As shown), and the predicted value of its polar angle is calculated according to formula (1)

[0037]

[0038] Among them, a, b, c, and d are polar angles;

[0039] Step 2.7: Calculate the difference θ between the polar angle of the feature point to be embedded and the predicted value e , and embed the watermark bit into the difference θ e The new difference θ is obtained e ′;

[0040]

[0041] In the formula, bit is the watermark bit to be embedded, and -ε,ε) is the threshold interval for embedding watermark.

[0042] Step 2.8: Change the polar angle of the point to be embedded to θ i ′, so that the difference between it and the predicted value is θ e ′;

[0043]

[0044] Step 2.9: Recalculate the coordinates of the point in the plane rectangular coordinate system according to the embedded polar angle and polar diameter;

[0045] Step 2.10: Repeat steps 2.4 to 2.9, and process the other feature points except those on the minimum circumscribed circle one by one.

[0046] Step 3: Watermark information detection: Fill the point features with curves, convert them into line features, extract the feature points, construct a polar coordinate system based on the minimum circumscribed circle generated by the feature points, extract the embedded watermark bits from the polar angles, and use the prediction error expansion technology in step 3.5 to losslessly restore the vector geographic dataset after the watermark is embedded. Figure 2 , the specific process is:

[0047] Step 3.1: For the point features in the vector geographic dataset, fill them into line features using the Hilbert space filling curve;

[0048] Step 3.2: Use the vertical distance method to compress and simplify the features in the vector geographic dataset, and record the compressed points as feature points P f ′;

[0049] Step 3.3: Calculate P f ′, and the center of the smallest circumscribed circle is O′(x o ′,y o ′), with a radius of r′, and a polar coordinate system is constructed with the center of the circle as the pole and the ray starting from the pole and passing through the point farthest from the center of the circle and not on the circle as the polar axis;

[0050] Step 3.4: Calculate the polar angle θ of each feature point based on the constructed polar coordinate system i ' and polar diameter d i ′, and then normalize the polar angle and polar diameter of the feature point, and use the normalized polar angle and polar diameter as the coordinates of the point (x nθ ′,y nr ′);

[0051] Step 3.5: Based on the order of the normalized feature points, obtain the original polar angles of the three feature points in the lower right corner adjacent to the feature point to be embedded in the order from top to bottom and from left to right, and calculate the predicted value of its polar angle according to formula (1):

[0052] Step 3.6: For each feature point d i The first α bits of ′ are used as the parameters of the hash function to generate the watermark index of each point, and then the embedded watermark bits are extracted through the predicted value according to formula (4);

[0053]

[0054] Step 3.7: Generate the final extracted watermark information using majority voting method based on the extracted watermark index and watermark bit; specifically, for the majority voting method, when multiple watermark bits are detected for the same index, count the number of watermark bits 0 and 1 corresponding to the index, and take the watermark bit with the larger number as the watermark bit finally mapped to the watermark index.

[0055] Step 3.8: Restore the embedded polar angle according to formula (5), and then calculate the original coordinates of the feature point in the plane rectangular coordinate system according to the restored polar angle;

[0056]

[0057] Step 4: Watermark information detection:

[0058] like Figure 3 , Figure 4 , the copyright information (watermark) to be embedded is "WaterMark", and watermark detection is performed on the vector geographic dataset after the watermark is embedded. The experimental results show that this method can accurately detect the watermark information in the data.

[0059] like Figure 5 ,The modification attack of vector geographic dataset refers to its intentional or unintentional modification, including overall translation, overall rotation, data compression, data addition, data deletion, etc. ,The experimental results show that this method can correctly detect the correct watermark information for watermarked vector geographic datasets that have been attacked by different types, and effectively protect the copyright information of the data.

[0060] The embodiments described above are only descriptions of the preferred modes of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations, modifications, and substitutions made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A reversible watermarking algorithm suitable for vector geographic data sets, characterized in that: include: Step 1, watermark information generation: select an image with copyright information, encrypt the image using Arnold transformation, and convert the encrypted image from two-dimensional to one-dimensional binary sequence; Step 2: Embedding watermark information: Fill the point features with curves, convert them into line features, extract feature points, build a polar coordinate system based on the minimum circumscribed circle generated by the feature points, embed the generated watermark information into the polar angle using the prediction error expansion technology, and obtain the vector geographic data set after embedding the watermark; The step one comprises: Step 1.1: Select an image of size n×n with copyright information; Step 1.2: Encrypt the copyright image using Arnold transformation to generate an encrypted image I; Step 1.3: Convert the image I from two dimensions to a one-dimensional binary sequence, denoted as: IN r ={in r [i], 0≤i≤j},w r [i]∈[0,1] Where j = n*n is the robust watermark length, w r [i] represents the value of the i-th in the binary sequence; The second step comprises: Step 2.1: For point features in the vector geographic dataset, use the Hilbert space filling curve to fill them into line features; Step 2.2: Use the vertical distance method to compress and simplify the features in the vector geographic dataset, and record the compressed points as feature points P f ; Step 2.3: Calculate P f The minimum circumscribed circle of o ,y o ), with a radius of r, the center of the circle is the pole, and the ray starting from the pole and passing through the point farthest from the center of the circle and not on the circle is the polar axis to construct a polar coordinate system; Step 2.4: Calculate the polar angle θ of each feature point based on the constructed polar coordinate system i and polar diameter d i Then the polar angle and polar diameter of the feature point are normalized, and the normalized polar angle and polar diameter are used as the coordinates of the point (x nθ ,y nr ); Step 2.5: Each feature point d i The first α bits of are used as the parameters of the hash function to generate the watermark index of each point as the location where the watermark is embedded; Step 2.6: Get the embedded watermark bit according to the watermark index, and based on the order of the normalized feature points, get the original polar angles of the three feature points adjacent to the point to be embedded in order, and calculate the predicted value of its polar angle according to the following formula: Among them, a, b, c, and d are polar angles; Step 2.7: Calculate the difference θ between the polar angle of the feature point to be embedded and the predicted value e , and embed the watermark bit into the difference θ e The new difference θ is obtained e '; In the formula, bit is the watermark bit to be embedded, (-ε, ε) is the threshold interval for embedding watermark; Step 2.8: Change the polar angle of the point to be embedded to θ i ', so that the difference between it and the predicted value is θ e '; Step 2.9: Recalculate the coordinates of the point in the plane rectangular coordinate system according to the embedded polar angle and polar diameter; Step 2.10: Repeat steps 2.4 to 2.9, process the other feature points except those on the minimum circumscribed circle in turn, and complete the watermark information embedding, so as to embed the watermark information into the polar angles of other points except those on the minimum circumscribed circle through the prediction error expansion technology.

2. A reversible watermarking algorithm suitable for vector geographic data sets according to claim 1, characterized in that: The method also includes step three, watermark information detection: filling the point features with curves, converting them into line features, extracting feature points, constructing a polar coordinate system based on the minimum circumscribed circle generated by the feature points, extracting the embedded watermark bits from the polar angles, and losslessly restoring the vector geographic data set after the watermark is embedded.

3. A reversible watermarking algorithm suitable for vector geographic data sets according to claim 2, characterized in that: The step three comprises: Step 3.1: For the point features in the vector geographic dataset, fill them into line features using the Hilbert space filling curve; Step 3.2: Use the vertical distance method to compress and simplify the features in the vector geographic dataset, and record the compressed points as feature points P f '; Step 3.3: Calculate P f ', record the center of the smallest circumscribed circle O'(x o ',y o '), with a radius of r', the center of the circle is the pole, and the ray starting from the pole and passing through the point farthest from the center of the circle and not on the circle is the polar axis to construct a polar coordinate system; Step 3.4: Calculate the polar angle θ of each feature point based on the constructed polar coordinate system i ' and polar diameter d i ', then normalize the polar angle and polar diameter of the feature point, and use the normalized polar angle and polar diameter as the coordinates of the point (x nθ ',y nr '); Step 3.5: Based on the order of the normalized feature points, obtain the original polar angles of the three feature points adjacent to the point to be embedded in order, and calculate the predicted value of their polar angles according to formula (1): Step 3.6: For each feature point d i The first α bits of ' are used as the parameters of the hash function to generate the watermark index of each point, and the embedded watermark bit bit is extracted by the predicted value according to the following formula e ; Step 3.7: Generate the final extracted watermark information using majority voting method according to the extracted watermark index and watermark bit; Step 3.8: Restore the embedded polar angle according to the following formula, and then calculate the original coordinate θ of the feature point in the plane rectangular coordinate system based on the restored polar angle: d ; 4. A reversible watermarking algorithm suitable for vector geographic data sets according to any one of claims 1 to 3, characterized in that: It also includes step 4, testing and analysis: conducting anti-modification attacks on the vector geographic data set containing the watermark to experimentally verify whether the watermark information is valid, thereby determining the watermark's ability to resist modification attacks; Among them, anti-modification attacks include overall translation, overall rotation, data compression, data addition, and data deletion.

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