Polar coordinate visual hidden-key coupled digital elevation model decryption method and device

Abstract

The application discloses a polar coordinate visual hidden and explicit key coupling digital elevation model de-encryption method and device. The method acquires a to-be-de-encrypted DEM and effective elevation points, determines a de-encryption grid, a disturbance amplitude, a chaotic sequence parameter and an interpolation parameter according to an explicit key; generates an elevation disturbance, an attitude parameter and a quadrant parameter based on a Logistic chaotic mapping; forms three-dimensional coordinate seeds by combining grid point plane coordinates and elevation seeds, obtains a polar radius angle and a polar angle through Polar Vision implicit transformation, and generates de-encryption control points by disturbing grid point plane coordinates with normalized angles; and then performs spatial interpolation with the de-encryption control points as controls, obtains the elevation disturbance of each effective elevation point and superimposes the elevation disturbance to original elevations to output the de-encrypted DEM. An authorized party can deduct the disturbance to recover the DEM with the same key and transformation rule. The application can improve the availability of DEM shared data, the authorized reversibility and the anti-control point attack capability under the condition that the elevation de-encryption precision is controllable.

Description

Technical Field

[0001] This invention belongs to the field of surveying and mapping geographic information security processing technology, and in particular relates to a method and device for decrypting digital elevation models with polar coordinate visual hidden and revealed key coupling. Background Technology

[0002] Digital Elevation Models (DEMs) are essential geographic information products for representing the undulations of the Earth's surface. They reflect information such as topographic relief, visibility, hydrological runoff, engineering construction conditions, and spatial analysis conditions, and are widely used in fields such as topographic analysis, hydrological simulation, engineering planning, disaster assessment, 3D geographic modeling, and spatial security analysis. For DEM data that needs to be publicly shared but also involves spatial security protection requirements, the elevation information typically needs to be declassified while maintaining data availability.

[0003] Existing methods for de-classifying or camouflaging DEMs mainly include coordinate transformation, map sheet perturbation, random error superposition, nonlinear transformation, and local perturbation based on control points. These methods have the following shortcomings in practical applications: First, it is difficult to accurately balance the intensity of disturbance with the availability of terrain. If the disturbance amplitude is small, the security of declassification is insufficient; if the disturbance amplitude is too large, it may destroy the topographic relief and local geomorphological relationships, reducing the analytical value of the shared DEM.

[0004] Secondly, while some irreversible decryption methods offer high security, they are not convenient for data recovery, updating, and reuse in authorized scenarios.

[0005] Third, some reversible decryption methods rely heavily on explicit keys or fixed control points. Once the key parameters, control point locations, or perturbation rules are leaked, the decryption results may be recovered by attackers using a small number of corresponding points before and after decryption and spatial interpolation methods.

[0006] Fourth, existing dedensing quality assessments focus primarily on elevation errors, while failing to adequately evaluate the degree to which the topographic relief and local vertical relationships are preserved before and after dedensing, making it difficult to fully reflect the usability of the dedensed DEM.

[0007] Therefore, it is necessary to provide a DEM elevation decryption scheme that combines explicit keys with implicit spatial transformation rules, so that the decryption product can maintain controllable elevation decryption accuracy, reversible authorization recovery, and still retain terrain analysis value when shared, while improving its resistance to control point attacks and interpolation recovery attacks. Summary of the Invention

[0008] To address the problems of existing methods, this invention provides a polar coordinate visual implicit key coupling digital elevation model decryption method and apparatus, which solves the problem that existing DEM elevation decryption methods cannot simultaneously achieve controllability of elevation disturbance, reversibility of authorization, sharing availability, and resistance to control point attacks.

[0009] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A method for decrypting digital elevation models with polar coordinate visual implicit / explicit key coupling includes the following steps: Obtain the digital elevation model to be declassified, read the spatial reference, affine transformation parameters, grid size and elevation value of the digital elevation model to be declassified, and determine the effective elevation point sequence and the plane coordinate range of the digital elevation model to be declassified; The spatial range, number of rows and columns, perturbation amplitude range, chaotic sequence control parameters, initial values, number of pre-iterations, sequence length, and spatial interpolation parameters of the decryption grid are determined based on the explicit key. Initial grid points are generated based on the spatial range and number of rows and columns of the de-dense grid; elevation perturbation parameters, roll attitude parameters, pitch attitude parameters, yaw attitude parameters, and quadrant parameters corresponding to each initial grid point are generated based on the Logistic chaotic mapping; The planar coordinates of each grid point are combined with the preset seed elevation to form a three-dimensional seed coordinate system. The polar radius is calculated based on the roll attitude parameters and pitch attitude parameters, and the polar angle is calculated based on the yaw attitude parameters and quadrant parameters. The polar radius angle and the polar angle are normalized respectively, and the planar coordinates of the grid points are nonlinearly perturbed according to the normalization results to obtain the de-density control points; Using the declassification control points and their elevation disturbance parameters as control, the elevation disturbance of each effective elevation point is calculated using a spatial interpolation method. The elevation disturbance is then superimposed onto the original elevation to output a declassified digital elevation model.

[0010] Furthermore, the explicit key includes a grid key, a chaotic sequence key, a perturbation amplitude key, and an interpolation parameter key; wherein, the grid key is used to determine the spatial range and number of rows and columns of the decrypted grid, the chaotic sequence key is used to determine the control parameters, initial values, pre-iteration number, and sequence length of the Logistic chaotic mapping, the perturbation amplitude key is used to determine the value range of the elevation perturbation parameter and attitude parameter, and the interpolation parameter key is used to determine the spatial interpolation method and its parameters.

[0011] Furthermore, the Logistic chaotic mapping is:

[0012]

[0013] in, , This represents the sequence of elevation disturbance parameters. This represents the roll attitude parameter sequence. Represents the pitch attitude parameter sequence. This represents the sequence of yaw attitude parameters. Represents the quadrant parameter sequence; For the first Control parameters of a group of chaotic sequences For the first Group of chaotic sequences in The initial state value at that time, The first one determined by the chaotic sequence key Initial values ​​of a group of chaotic sequences This indicates that the initial value is used as the initial state of the Logistic chaotic mapping. For the first Group of chaotic sequences The state value after the next iteration The iteration number is used; after pre-iteration, the corresponding chaotic sequence values ​​are mapped to elevation disturbance parameters, roll attitude parameters, pitch attitude parameters, yaw attitude parameters, and quadrant parameters according to the preset value range.

[0014] Furthermore, the three-dimensional seed coordinates are:

[0015] in, For the first The three-dimensional seed coordinates corresponding to each initial grid point and The first The planar coordinates of the initial grid points To preset the seed elevation, This is a transpose.

[0016] Furthermore, the polar radius angle and polar angle are obtained as follows: Using roll-pitch rotation matrix Applying the three-dimensional seed coordinates, we obtain the rotated three-dimensional coordinates: ; Calculate the polar radius angle based on the elevation and planar components of the rotated three-dimensional coordinates:

[0017] Using yaw rotation matrix Applying the planar components to the rotated three-dimensional coordinates yields the rotated planar coordinates:

[0018] according to For the two planar coordinate components, first calculate the reference angle in the first quadrant, and then combine it with the quadrant parameters. By applying quadrant constraints to the reference angle, the polar angle is obtained:

[0019] in, , The initial total number of grid points, index All represent the corresponding number The parameters, coordinates, or angles of an initial grid point; , They represent the first The roll attitude parameters and pitch attitude parameters corresponding to each initial grid point. Indicates the first The yaw attitude parameters corresponding to each initial grid point For the first The 3D seed coordinates of the initial grid points are rotated by roll-pitch and then become the 3D coordinates of the seed coordinates of the grid points. For the first The polar radius angle corresponding to each initial grid point; and For the first The planar components of the 3D coordinates of the initial grid points after rotation of the 3D seed coordinates. For the first The elevation components of the three-dimensional coordinates after rotating the three-dimensional seed coordinates of each initial grid point; For the first The 3D seed coordinates of each initial grid point are then rotated by yaw to obtain the planar coordinates. and The first The coordinate components of the planar coordinates in two directions after the 3D seed coordinates corresponding to the initial grid points are rotated by yaw; For the first The polar angle corresponding to each initial grid point For the first The first quadrant reference angle corresponding to each initial grid point Indicates polar angle The quadrant in which it is located.

[0020] Furthermore, the planar coordinates of the grid points are subjected to nonlinear perturbation to satisfy:

[0021]

[0022] Declassification control points for:

[0023] in, This is the perturbation scale factor. and These are the perturbed planar coordinates. and They are respectively direction and Grid scale in the direction, and These are the normalized polar radius and polar angle, respectively.

[0024] Furthermore, it also includes an authorized recovery step: using the same explicit key and PolarVision implicit transformation rules as the decryption process, the decryption control points and elevation disturbances are regenerated, and the corresponding elevation disturbances are subtracted from the elevation values ​​of the decrypted digital elevation model to obtain the recovered digital elevation model.

[0025] Furthermore, it also includes a declassification quality evaluation step: calculating the graphic complexity based on the length and angle coefficients of the multi-line segments in the digital elevation model, and calculating the similarity of terrain undulation morphology based on the graphic complexity before and after declassification; constructing an eight-dimensional vertical direction descriptor based on the elevation magnitude relationship of the eight neighboring regions of each effective elevation point, and calculating the consistency of the vertical direction relationship based on the consistency ratio of the eight-dimensional vertical direction descriptors before and after declassification.

[0026] Furthermore, it also includes a control point attack evaluation step: selecting a preset number of corresponding points before and after declassification, estimating the reverse elevation disturbance surface based on the corresponding points, performing attack recovery on the declassified digital elevation model, and evaluating the anti-control point attack capability by the elevation error, terrain undulation similarity, vertical relationship consistency, or graphic complexity of the attack-recovered digital elevation model relative to the original digital elevation model.

[0027] On the other hand, the present invention also provides a digital elevation model decryption device with polar coordinate visual implicit / explicit key coupling, comprising: The DEM reading module is used to acquire the digital elevation model to be declassified, read the spatial reference, affine transformation parameters, raster size and elevation value of the digital elevation model to be declassified, and determine the effective elevation point sequence and the plane coordinate range of the digital elevation model to be declassified. An explicit key configuration module is used to determine the spatial range of the decryption grid, the number of grid rows and columns, the range of perturbation amplitude, the chaotic sequence control parameters, the initial value, the number of pre-iterations, the sequence length, and the spatial interpolation parameters based on the explicit key. The chaotic sequence generation module is used to generate initial grid points based on the spatial range and number of rows and columns of the de-dense grid; and to generate elevation perturbation parameters, roll attitude parameters, pitch attitude parameters, yaw attitude parameters, and quadrant parameters corresponding to each initial grid point based on the Logistic chaotic mapping. The Polar Vision implicit perturbation module is used to form a three-dimensional seed coordinate system by combining the planar coordinates of each grid point with the preset seed elevation, calculate the polar radius angle based on the roll attitude parameters and pitch attitude parameters, calculate the polar angle based on the yaw attitude parameters and quadrant parameters, normalize the polar radius angle and the polar angle respectively, and perform nonlinear perturbation on the planar coordinates of the grid points according to the normalization results to obtain the de-density control points. An elevation disturbance interpolation module is used to calculate the elevation disturbance of each effective elevation point using spatial interpolation methods, with the de-confined control points and their elevation disturbance parameters as control. The declassified DEM output module is used to superimpose the elevation disturbance onto the original elevation and output a declassified digital elevation model. The authorized recovery module is used to regenerate the declassified control points and elevation disturbances using the same explicit key and Polar Vision implicit transformation rules as the declassification process, and to subtract the corresponding elevation disturbances from the elevation values ​​of the declassified digital elevation model to obtain the recovered digital elevation model. The declassification quality evaluation module is used to calculate the graphic complexity based on the length and angle coefficients of the multi-line segments in the digital elevation model, and to calculate the similarity of terrain undulation morphology based on the graphic complexity before and after declassification; it constructs an eight-dimensional vertical direction descriptor based on the elevation size relationship of the eight neighboring areas of each effective elevation point, and calculates the consistency of the vertical direction relationship based on the consistency ratio of the eight-dimensional vertical direction descriptors before and after declassification. The anti-control point attack evaluation module is used to select a preset number of corresponding points before and after decryption, estimate the reverse elevation disturbance surface based on the corresponding points, perform attack recovery on the decrypted digital elevation model, and evaluate the anti-control point attack capability by the elevation error, terrain undulation similarity, vertical relationship consistency or graphic complexity of the attack-recovered digital elevation model relative to the original digital elevation model.

[0028] Compared with the prior art, the present invention has the following beneficial effects: First, the elevation disturbance amplitude, decryption grid scale, and spatial interpolation parameters can be controlled by an explicit key, allowing for different decryption intensities to be set according to the needs of shared applications, thereby achieving controllable elevation decryption accuracy.

[0029] Second, the authorizing party can use the same explicit key and Polar Vision implicit transformation rules to regenerate the declassified control points and elevation disturbances, and deduct the corresponding elevation disturbances from the declassified DEM, thereby achieving authorized reversible recovery of the DEM.

[0030] Third, the planar position of the declassification control points is not determined solely by the regular grid or explicit coordinate parameters, but is jointly determined by the three-dimensional seed coordinates, attitude parameters, quadrant parameters, and Polar Vision implicit transformation rules, which increases the difficulty for attackers to estimate the true elevation disturbance surface based on only a small number of corresponding points before and after declassification.

[0031] Fourth, the evaluation of terrain undulation and local vertical relationship before and after de-densification is carried out by using graphical complexity and eight-neighbor vertical direction descriptors, which improves the completeness of the de-densification DEM usability evaluation.

[0032] Fifth, by setting up control point attack tests based on a small number of corresponding points, the anti-control point attack capability of the decryption results can be evaluated from aspects such as the error in the recovery elevation, the similarity of terrain undulation, the consistency of vertical relationship, and the complexity of the graphics. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0034] Figure 1 This is a flowchart illustrating the decryption process of the PV-Encry device of the present invention. Figure 2 This is a 3D rendering of the DEM before declassification in this invention; Figure 3 This is a 3D rendering of the DEM after being decrypted using the PV-Encry device according to the present invention. Figure 4 This is a conceptual diagram of the Polar Vision theory of this invention; Figure 5 This is a flowchart illustrating the evaluation of the "availability, reversibility, and safety" indicators of the PV-Encry device decryption product according to the present invention. Figure 6 This is a schematic diagram of the DEM multi-segment division from left to right and from top to bottom according to the present invention; Figure 7 This is a schematic diagram of the vertical direction relationship consistency evaluation method based on eight-dimensional descriptors according to the present invention; Figure 8This is an elevation disturbance surface diagram generated by the PV-Encry device of the present invention; Figure 9 This is the reverse elevation perturbation surface plot generated during the attack test of the PV-Encry decryption product according to the present invention; Figure 10 This is a 3D rendering of the DEM restored after attack testing of the PV-Encry decryption product according to the present invention. Figure 11 This is a block diagram of the module structure of the DEM elevation descaling device of the present invention. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0036] This invention provides a technical solution for DEM elevation declassification, authorized recovery, and declassification quality evaluation. It can generate repeatable elevation perturbation surfaces under the condition of setting perturbation amplitude and grid scale, and realize recovery through authorized keys.

[0037] The technical effects of the present invention will be described in detail below with reference to the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other. In this document, DEM stands for Digital Elevation Model, a common abbreviation in the art; Logistic chaotic mapping is a commonly used name for chaotic mapping in the art; Polar Vision is the name of the implicit polar coordinate visual transformation rule used in this invention, and the implicit Polar Vision transformation in this document has the same meaning as the implicit polar coordinate visual transformation; roll, pitch, and yaw represent roll, pitch, and yaw attitude parameters, respectively; PV-Encry is the name of a software device or program used in one embodiment of the present invention to implement the DEM declassification, authorization recovery, and evaluation process, and is only used to illustrate the specific software implementation in the embodiment, and does not constitute a limitation on the scope of protection of the present invention; an effective elevation point refers to a grid point in the DEM with an effective elevation value; a declassification control point refers to a point obtained by Polar... The Vision implicit transformation perturbation ...

[0038] Example 1: DEM Elevation Decompression Method The DEM to be de-densified is a raster elevation data containing continuous topographic relief information, and its elevation values ​​can reflect the landform of the region. Figure 1 The overall flow of the DEM elevation decryption method of the present invention is shown. The flow includes DEM reading, explicit key configuration, chaotic sequence generation, Polar Vision implicit perturbation, spatial interpolation, elevation perturbation superposition, and decrypted DEM output steps, specifically including: Step 1: Obtain the digital elevation model to be declassified, read the spatial reference, affine transformation parameters, grid size and elevation value of the digital elevation model to be declassified, and determine the effective elevation point sequence and the plane coordinate range of the digital elevation model to be declassified; Step 2: Determine the spatial range of the decryption grid, the number of grid rows and columns, the range of perturbation amplitude, the chaotic sequence control parameters, the initial value, the number of pre-iterations, the sequence length, and the spatial interpolation parameters based on the explicit key; Step 3: Generate initial grid points based on the spatial range and number of rows and columns of the de-dense grid; generate elevation perturbation parameters, roll attitude parameters, pitch attitude parameters, yaw attitude parameters, and quadrant parameters corresponding to each initial grid point based on the Logistic chaotic mapping; Step 4: Combine the planar coordinates of each grid point with the preset seed elevation to form a three-dimensional seed coordinate system. Calculate the polar radius angle based on the roll attitude parameters and pitch attitude parameters, and calculate the polar angle based on the yaw attitude parameters and quadrant parameters. Step 5: Normalize the polar radius angle and the polar angle respectively, and perform nonlinear perturbation on the planar coordinates of the grid points according to the normalization results to obtain the de-density control points; Step 6: Using the declassification control points and their elevation disturbance parameters as control, calculate the elevation disturbance of each effective elevation point using spatial interpolation method, superimpose the elevation disturbance onto the original elevation, and output the declassified digital elevation model.

[0039] First, input the digital elevation model (DEM) to be declassified, such as... Figure 2 As shown, its spatial reference, affine transformation parameters, raster size, and elevation value are read. For raster points with elevation values ​​greater than a preset effective threshold, a sequence of effective elevation points is formed according to the row and column scanning order. :

[0040] in, and For the first The plane coordinates of the effective elevation points This represents the original elevation value of that point. Simultaneously, the DEM's planar coordinate range is determined based on the DEM's affine transformation parameters and raster extent.

[0041] in, DEM plane coordinates x Minimum and maximum values ​​in direction DEM plane coordinates y Minimum and maximum values ​​in direction.

[0042] Secondly, the spatial extent, number of rows and columns, perturbation amplitude range, chaotic sequence control parameters, initial values, pre-iteration count, sequence length, and spatial interpolation parameters of the decryption grid are determined based on the explicit key. The spatial extent of the decryption grid can be consistent with the DEM plane coordinate range, or it can be determined within the DEM plane coordinate range or an appropriately extended range according to shared security requirements.

[0043] Let the number of rows and columns of the de-dense grid be... and Initial regular grid points are generated based on the spatial extent and number of rows and columns of the de-dense grid:

[0044] in, For the first An initial rule grid point, For grid point numbers, and The first The initial regular grid points are in direction and Planar coordinates in the direction. The grid scale can be represented as:

[0045]

[0046] in, and They are respectively direction and Grid scale in the direction. and The de-dense mesh is in Minimum and maximum coordinates in the direction, and The de-dense mesh is in Minimum and maximum coordinates in the direction, and The de-dense mesh is in direction and The number of grid divisions in each direction.

[0047] Furthermore, elevation perturbation parameters corresponding to each grid point are generated based on the Logistic chaotic mapping. Roll attitude parameters pitch posture parameters yaw attitude parameters and quadrant parameters Let the total number of de-dense grid points be... For any parameter sequence The initial conditions for the Logistic chaotic mapping are:

[0048] The iterative relationship of the Logistic chaotic mapping is as follows:

[0049] in, , This represents the sequence of elevation disturbance parameters. This represents the roll attitude parameter sequence. Represents the pitch attitude parameter sequence. This represents the sequence of yaw attitude parameters. Represents the quadrant parameter sequence; For the first Control parameters of a group of chaotic sequences For the first Group of chaotic sequences in The initial state value at that time, The first one determined by the chaotic sequence key Initial values ​​of a group of chaotic sequences This indicates that the initial value is used as the initial state of the Logistic chaotic mapping. For the first Group of chaotic sequences The state value after the next iteration The iteration number; determined by the number of pre-iterations. Eliminate the After the initial transient effects on the chaotic sequence, continue iterating. This yields the chaotic sequence values ​​corresponding to each grid point:

[0050] in, For the first The number of pre-iterations for a group of chaotic sequences. This represents the total number of de-dense grid points. , For the first The group of chaotic sequences corresponds to the first The chaos value of the initial grid point.

[0051] Elevation disturbance parameters Obtained by mapping from the elevation disturbance parameter sequence:

[0052] When the elevation disturbance value range is set to When the above formula is used, it can be written as:

[0053] Among them, is the first The elevation disturbance parameters corresponding to each initial grid point and These represent the lower and upper limits of the elevation disturbance parameter, respectively. For the elevation disturbance parameter sequence corresponding to the first The chaos value of the initial grid point; when the elevation disturbance value range is set to hour, , ,in This represents the maximum elevation disturbance amplitude.

[0054] Roll attitude parameters pitch posture parameters and yaw attitude parameters They are obtained respectively by mapping the corresponding chaotic sequences:

[0055]

[0056]

[0057] Quadrant parameters The quadrant parameter sequence is discretized to obtain:

[0058] in, This is used to constrain the quadrant in which the polar angle lies. Therefore, the first... Each initial grid point corresponds to a set of parameters: .

[0059] in, Used to control the elevation disturbance of this grid point; For the first The roll attitude parameters corresponding to each initial grid point and These are the lower and upper limits of the roll attitude parameters, respectively. For the roll attitude parameter sequence corresponding to the first Chaos values ​​of the initial grid points; For the first The pitch attitude parameters corresponding to each initial grid point and These are the lower and upper limits of the pitch attitude parameter, respectively. For the pitch attitude parameter sequence corresponding to the first Chaos values ​​of the initial grid points; For the first The yaw attitude parameters corresponding to each initial grid point and These are the lower and upper limits of the yaw attitude parameters, respectively. The yaw attitude parameter sequence corresponds to the first Chaos values ​​of the initial grid points; For the first Quadrant parameters corresponding to each initial grid point The quadrant parameter sequence corresponds to the first The chaos value of the initial grid point.

[0060] Then, for each initial regular grid point Combine its planar coordinates with the preset seed elevation to form a three-dimensional seed coordinate system:

[0061] in, For the first The three-dimensional seed coordinates corresponding to the initial regular grid points and These are the planar coordinates of the grid point. To preset the seed elevation, you can use the DEM spatial range function value, DEM elevation statistical value, or a preset constant value. By expanding the coordinates of the two-dimensional grid points into three-dimensional seed coordinates, subsequent Polar Vision implicit transformations can introduce attitude angle perturbation relationships in three-dimensional space.

[0062] like Figure 4 As shown, the Polar Vision implicit transformation is used to map the attitude parameters generated by the explicit key to angle parameters. Specifically, it utilizes the roll-pitch rotation matrix. Acting on 3D seed coordinates Obtain the rotated three-dimensional coordinates The relationship is as follows: ,therefore:

[0063] in, For the first The 3D coordinates obtained by rotating the 3D seed coordinates using roll-pitch. and These are the planar components of the rotated 3D coordinates. These are the elevation components of the rotated three-dimensional coordinates.

[0064] Calculate the polar radius angle based on the elevation and planar components of the rotated three-dimensional coordinates:

[0065] in, For the first The polar radius angle corresponding to each grid point This represents the planar distance component of the rotated 3D coordinates.

[0066] Then use the yaw rotation matrix Acting on The planar components are used to obtain the rotated planar coordinates. :

[0067] in, For the first The planar coordinates of each grid point after yaw rotation and These are the coordinate components of the plane coordinates in two directions.

[0068] according to First, calculate the reference angle in the first quadrant, considering the two planar coordinate components:

[0069] in, It is a reference angle in the first quadrant and satisfies Combined with quadrant parameters By applying quadrant constraints to the reference angle, the polar angle is obtained:

[0070] in, Used to determine polar angle The quadrant in which it is located. Therefore, the polar angle... It is determined by the yaw rotation result and the quadrant parameters.

[0071] Then and Normalized to The normalized polar radius angle is obtained. and normalized polar angle The normalization formula is:

[0072]

[0073] in, and These are the minimum and maximum polar radius angles of all grid points, respectively. and These are the minimum and maximum polar angles for all grid points, respectively. If... Then let ;like Then let .

[0074] The planar coordinates of the grid points are then subjected to nonlinear perturbation based on the normalized results.

[0075]

[0076] in, This is the perturbation scale factor. and These are the perturbed planar coordinates. From this, the declassification control points are obtained:

[0077] Through the above process, the planar position of the decryption control point is no longer a regular grid point, but a nonlinear perturbation result jointly controlled by the explicit key and the implicit transformation rules of Polar Vision.

[0078] Finally, using declassification control points and its corresponding elevation disturbance parameters To control the elevation, spatial interpolation is used to calculate the effective elevation point. elevation disturbance Spatial interpolation methods can be selected according to actual needs, such as inverse distance weighted interpolation, thin plate spline interpolation, radial basis function interpolation, or Kriging interpolation.

[0079] When using inverse distance weighted interpolation, effective elevation points The weight at a point can be expressed as:

[0080] in, Effective elevation points To the One declassification control point Planar distance, The distance decay exponent, This represents the number of declassification control points. Then, the effective elevation points... The elevation disturbance is:

[0081] like Figure 8 As shown, the elevation disturbance surface can be obtained by interpolating the declassification control points and their elevation disturbance parameters. The elevation disturbance values ​​of each effective elevation point are then superimposed onto the original elevation to obtain the declassified elevation values.

[0082] in, For the decrypted DEM, the first The elevation values ​​of each valid elevation point. After processing all valid elevation points, the following can be obtained: Figure 3 The dedensed DEM shown here, while maintaining the overall topographic relief characteristics, has undergone controlled dedensing of elevation values.

[0083] Example 2: Authorization Recovery Method like Figure 5As shown, the present invention also provides an authorization recovery process. During authorization recovery, the decrypted DEM and an explicit key consistent with the decryption process are input, and the same chaotic sequence, attitude parameters, quadrant parameters, decryption control points, and elevation disturbance surface are regenerated according to the steps in Embodiment 1.

[0084] For each valid elevation point in the de-densified DEM Recalculate the elevation disturbance at the same location. And deduct the elevation disturbance from the declassified elevation value:

[0085] in, The restored elevation value. The elevation values ​​are those in the decrypted DEM. Since the authorizing party possesses the same explicit key and Polar Vision implicit transformation rules, it can regenerate elevation perturbations consistent with the decryption process, thereby achieving reversible recovery of the authorized DEM.

[0086] The results of authorized restoration can be evaluated by assessing the elevation error, similarity of terrain undulations, and consistency of vertical relationships between the restored DEM and the original DEM. A smaller restoration error indicates better reversibility of the authorized restoration.

[0087] Example 3: Declassification Quality Evaluation Method like Figure 5 As shown, the present invention can also evaluate the quality of de-densified DEMs, including elevation accuracy control, similarity of terrain undulations, and consistency of vertical relationships.

[0088] In terms of elevation accuracy control, the elevation error can be calculated by the elevation difference between the effective elevation points before and after de-classification. Let the number of effective elevation points be... Before and after declassification The elevations of the three valid elevation points are as follows: and Then the elevation error can be expressed as:

[0089] By adjusting the perturbation amplitude range, grid scale, and spatial interpolation parameters in the explicit key, the elevation error of the decrypted DEM can be controlled, thereby meeting the decryption accuracy requirements under different sharing scenarios.

[0090] In terms of similarity in terrain undulations, such as Figure 6 As shown, a DEM can be converted into a multi-segment structure by scanning along the rows. For each multi-segment, the length factor is calculated. and angle coefficient The sum of the two is used as the graph complexity:

[0091] The graphic complexity of the DEM before and after de-densification is calculated separately, and the consistency of the topographic relief morphology before and after de-densification is evaluated based on the degree of similarity between the two. The closer the graphic complexity, the higher the degree to which the de-densified DEM retains the topographic relief morphology of the original DEM.

[0092] Regarding consistency in vertical relationships, such as Figure 7 As shown, an eight-neighbor vertical direction descriptor is constructed for each valid elevation point. The eight directions include top left, top, top right, left, right, bottom left, bottom, and bottom right. If the elevation of a neighboring point is greater than the elevation of the current point, the corresponding direction is denoted as... Otherwise, record as Therefore, each valid elevation point can be represented by an eight-dimensional vertical direction descriptor:

[0093] in, , .

[0094] Eight-dimensional vertical descriptors are constructed for the DEM before and after de-densification, and the eight-dimensional descriptors of corresponding elevation points are compared to see if they are completely consistent. If they are consistent, they are denoted as:

[0095] Otherwise, record as:

[0096] The consistency of vertical relationships can be expressed as:

[0097] in, This represents the number of valid elevation points. The higher the value, the better the local vertical relationship between the de-densified DEM and the original DEM is preserved.

[0098] Example 4: Evaluation Method for Resistance to Control Point Attacks like Figure 5 As shown, the present invention can also evaluate the security of the declassified DEM through control point attack testing. The basic idea of ​​control point attack testing is as follows: assuming that the attacker knows a preset number of corresponding points before and after declassification, and uses these corresponding points to estimate the reverse elevation disturbance surface, and then performs an attack to recover the declassified DEM.

[0099] like Figure 8As shown, the elevation disturbance surface generated during the declassification process is obtained by spatial interpolation of the declassification control points and their elevation disturbance parameters. Since the planar positions of the declassification control points are subjected to nonlinear disturbances by the Polar Vision implicit transformation rule, the true elevation disturbance surface has an implicit control structure.

[0100] like Figure 9 As shown, the attacker estimates the reverse elevation perturbation surface based only on a preset number of corresponding points before and after decryption. Since the attacker cannot accurately know the complete explicit key, the construction method of the three-dimensional seed coordinates, the attitude angle rotation relationship, the quadrant constraints, and the normalization perturbation method, the estimated reverse elevation perturbation surface differs from the true elevation perturbation surface.

[0101] During attack recovery, the estimated reverse elevation perturbation surface is applied to the de-dense DEM, resulting in the following: Figure 10 The attack recovery DEM is shown. Then, the attack recovery DEM is compared with... Figure 1 The original DEM is compared to the DEM shown, and the attack recovery elevation mean square error, terrain undulation similarity, vertical relationship consistency and graphic complexity are calculated.

[0102] If the attacked and recovered DEM still has a large elevation error relative to the original DEM, or if its terrain undulation similarity and vertical direction relationship consistency are not restored to the authorized recovery level, it indicates that the present invention has the ability to resist attacks on control points based on a preset number of corresponding points and interpolation recovery.

[0103] Example 5: Device Structure like Figure 11 As shown, the present invention also provides a decryption device for a digital elevation model coupled with a polar coordinate vision implicit and explicit key. The device includes a DEM reading module, an explicit key configuration module, a chaotic sequence generation module, a Polar Vision implicit perturbation module, an elevation perturbation interpolation module, a decrypted DEM output module, an authorization recovery module, a decryption quality evaluation module, and an anti-control point attack evaluation module.

[0104] The DEM reading module is used to acquire the digital elevation model to be declassified, read the spatial reference, affine transformation parameters, raster size and elevation value of the digital elevation model to be declassified, and determine the effective elevation point sequence and the plane coordinate range of the digital elevation model to be declassified. An explicit key configuration module is used to determine the spatial range of the decryption grid, the number of grid rows and columns, the range of perturbation amplitude, the chaotic sequence control parameters, the initial value, the number of pre-iterations, the sequence length, and the spatial interpolation parameters based on the explicit key. The chaotic sequence generation module is used to generate initial grid points based on the spatial range and number of rows and columns of the de-dense grid; and to generate elevation perturbation parameters, roll attitude parameters, pitch attitude parameters, yaw attitude parameters, and quadrant parameters corresponding to each initial grid point based on the Logistic chaotic mapping. The Polar Vision implicit perturbation module is used to form a three-dimensional seed coordinate system by combining the planar coordinates of each grid point with the preset seed elevation, calculate the polar radius angle based on the roll attitude parameters and pitch attitude parameters, calculate the polar angle based on the yaw attitude parameters and quadrant parameters, normalize the polar radius angle and the polar angle respectively, and perform nonlinear perturbation on the planar coordinates of the grid points according to the normalization results to obtain the de-density control points. An elevation disturbance interpolation module is used to calculate the elevation disturbance of each effective elevation point using spatial interpolation methods, with the de-confined control points and their elevation disturbance parameters as control. The declassified DEM output module is used to superimpose the elevation disturbance onto the original elevation and output a declassified digital elevation model. The authorized recovery module is used to regenerate the declassified control points and elevation disturbances using the same explicit key and Polar Vision implicit transformation rules as the declassification process, and to subtract the corresponding elevation disturbances from the elevation values ​​of the declassified digital elevation model to obtain the recovered digital elevation model. The declassification quality evaluation module is used to calculate the graphic complexity based on the length and angle coefficients of the multi-line segments in the digital elevation model, and to calculate the similarity of terrain undulation morphology based on the graphic complexity before and after declassification; it constructs an eight-dimensional vertical direction descriptor based on the elevation size relationship of the eight neighboring areas of each effective elevation point, and calculates the consistency of the vertical direction relationship based on the consistency ratio of the eight-dimensional vertical direction descriptors before and after declassification. The anti-control point attack evaluation module is used to select a preset number of corresponding points before and after decryption, estimate the reverse elevation disturbance surface based on the corresponding points, perform attack recovery on the decrypted digital elevation model, and evaluate the anti-control point attack capability by the elevation error, terrain undulation similarity, vertical relationship consistency or graphic complexity of the attack-recovered digital elevation model relative to the original digital elevation model.

[0105] The above modules can be implemented using software, hardware, or a combination of both. When implemented using software, the corresponding program can be stored in a computer-readable storage medium and executed by a processor to implement the steps described in this invention.

[0106] Example 6: Experimental Results In a set of 10-meter resolution DEM experiments, the following settings were made: De-dense grid, elevation disturbance range is: .

[0107] Figure 2 This is a 3D rendering of the DEM before declassification. Figure 3 This is a 3D rendering of the DEM after decryption using the method of this invention. (From...) Figure 2 and Figure 3 It can be seen that the local elevation values ​​of the DEM changed after dedensation, but the overall topographic relief pattern still maintained a certain consistency.

[0108] Experimental results show that the mean square error of elevation disturbance after decompression is approximately The similarity of the terrain undulations before and after declassification is approximately The vertical relationship consistency is approximately After authorization is restored, the similarity of terrain undulations is approximately... The vertical relationship consistency is approximately .

[0109] In the control point attack test, a preset number of corresponding points before and after decryption were selected, and inverse distance weighted interpolation was used to generate, as shown below. Figure 9 The reverse elevation disturbance surface is shown. Figure 8 This refers to the elevation disturbance surface actually generated during the declassification process. Figure 9 The reverse elevation perturbation surface is estimated for control point attack tests. There are significant differences between the two. Figure 9 The reverse elevation disturbance surface shown is applied to the decompression DEM to obtain the following results. Figure 10 The attack-recovered DEM is shown. The elevation error of the attack-recovered DEM relative to the original DEM is approximately... The consistency of the vertical relationship after the attack is approximately Unauthorized recovery has not been achieved. The horizontal line indicates that interpolation attacks based on a preset number of corresponding points are unlikely to completely recover the original DEM.

[0110] The above results demonstrate that the present invention can improve the resistance of decrypted DEMs to attacks based on interpolation recovery of a preset number of corresponding points while maintaining the reversibility of authorization.

[0111] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0112] It should be understood that the above description of the preferred embodiments is quite detailed, but this should not be construed as limiting the scope of protection of this invention. It is neither necessary nor possible to exhaustively describe all possible implementations. Those skilled in the art, guided by this invention, can make substitutions or modifications without departing from the scope of the claims, all of which fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for decrypting digital elevation models using polar coordinate visual implicit / explicit key coupling, characterized in that, Includes the following steps: Obtain the digital elevation model to be declassified, read the spatial reference, affine transformation parameters, grid size and elevation value of the digital elevation model to be declassified, and determine the effective elevation point sequence and the plane coordinate range of the digital elevation model to be declassified; The spatial range, number of rows and columns, perturbation amplitude range, chaotic sequence control parameters, initial values, number of pre-iterations, sequence length, and spatial interpolation parameters of the decryption grid are determined based on the explicit key. Initial grid points are generated based on the spatial extent and number of rows and columns of the de-dense grid. Based on the Logistic chaotic mapping, the elevation perturbation parameters, roll attitude parameters, pitch attitude parameters, yaw attitude parameters, and quadrant parameters corresponding to each initial grid point are generated. The planar coordinates of each grid point are combined with the preset seed elevation to form a three-dimensional seed coordinate system. The polar radius is calculated based on the roll attitude parameters and pitch attitude parameters, and the polar angle is calculated based on the yaw attitude parameters and quadrant parameters. The polar radius angle and the polar angle are normalized respectively, and the planar coordinates of the grid points are nonlinearly perturbed according to the normalization results to obtain the de-density control points; Using the declassification control points and their elevation disturbance parameters as control, the elevation disturbance of each effective elevation point is calculated using a spatial interpolation method. The elevation disturbance is then superimposed onto the original elevation to output a declassified digital elevation model.

2. The method for decrypting a digital elevation model using polar coordinate visual implicit / explicit key coupling according to claim 1, characterized in that, The explicit keys include a grid key, a chaotic sequence key, a perturbation amplitude key, and an interpolation parameter key; wherein, the grid key is used to determine the spatial range and number of rows and columns of the decrypted grid, the chaotic sequence key is used to determine the control parameters, initial values, pre-iteration number, and sequence length of the Logistic chaotic mapping, the perturbation amplitude key is used to determine the value range of the elevation perturbation parameters and attitude parameters, and the interpolation parameter key is used to determine the spatial interpolation method and its parameters.

3. The method for decrypting a digital elevation model using polar coordinate visual implicit / explicit key coupling as described in claim 1, characterized in that, The Logistic chaotic mapping is: in, , This represents the sequence of elevation disturbance parameters. This represents the roll attitude parameter sequence. Represents the pitch attitude parameter sequence. This represents the sequence of yaw attitude parameters. Represents the quadrant parameter sequence; For the first Control parameters of a group of chaotic sequences For the first Group of chaotic sequences in The initial state value at that time, The first one determined by the chaotic sequence key Initial values ​​of a group of chaotic sequences This indicates that the initial value is used as the initial state of the Logistic chaotic mapping. For the first Group of chaotic sequences The state value after the next iteration The iteration number is used; after pre-iteration, the corresponding chaotic sequence values ​​are mapped to elevation disturbance parameters, roll attitude parameters, pitch attitude parameters, yaw attitude parameters, and quadrant parameters according to the preset value range.

4. The method for decrypting a digital elevation model using polar coordinate visual implicit / explicit key coupling as described in claim 1, characterized in that, The three-dimensional seed coordinates are: in, For the first The three-dimensional seed coordinates corresponding to each initial grid point and The first The planar coordinates of the initial grid points To preset the seed elevation, This is a transpose.

5. The method for decrypting a digital elevation model using polar coordinate visual implicit / explicit key coupling according to claim 4, characterized in that, The polar radius angle and polar angle are obtained as follows: Using roll-pitch rotation matrix Applying the three-dimensional seed coordinates, we obtain the rotated three-dimensional coordinates: ; Calculate the polar radius angle based on the elevation and planar components of the rotated three-dimensional coordinates: Using yaw rotation matrix Applying the planar components to the rotated three-dimensional coordinates yields the rotated planar coordinates: according to For the two planar coordinate components, first calculate the reference angle in the first quadrant, and then combine it with the quadrant parameters. By applying quadrant constraints to the reference angle, the polar angle is obtained: in, , The initial total number of grid points, index All represent the corresponding number The parameters, coordinates, or angles of an initial grid point; , They represent the first The roll attitude parameters and pitch attitude parameters corresponding to each initial grid point. Indicates the first The yaw attitude parameters corresponding to each initial grid point For the first The 3D seed coordinates of the initial grid points are rotated by roll-pitch and then become the 3D coordinates of the seed coordinates of the grid points. For the first The polar radius angle corresponding to each initial grid point; and For the first The planar components of the 3D coordinates of the initial grid points after rotation of the 3D seed coordinates. For the first The elevation components of the three-dimensional coordinates after rotating the three-dimensional seed coordinates of each initial grid point; For the first The 3D seed coordinates of each initial grid point are then rotated by yaw to obtain the planar coordinates. and The first The coordinate components of the planar coordinates in two directions after the 3D seed coordinates of the initial grid points are rotated by yaw; For the first The polar angle corresponding to each initial grid point For the first The first quadrant reference angle corresponding to each initial grid point Indicates polar angle The quadrant in which it is located.

6. The method for decrypting a digital elevation model using polar coordinate visual implicit / explicit key coupling according to claim 5, characterized in that, Nonlinear perturbation of the planar coordinates of the grid points satisfies: Declassification control points for: in, This is the perturbation scale factor. and These are the perturbed planar coordinates. and They are respectively direction and Grid scale in the direction, and These are the normalized polar radius and polar angle, respectively.

7. The method for decrypting a digital elevation model using polar coordinate visual implicit / explicit key coupling according to claim 1, characterized in that, It also includes an authorized recovery step: using the same explicit key and Polar Vision implicit transformation rules as the decryption process, the decryption control points and elevation disturbances are regenerated, and the corresponding elevation disturbances are subtracted from the elevation values ​​of the decrypted digital elevation model to obtain the recovered digital elevation model.

8. The method for decrypting a digital elevation model using polar coordinate visual implicit / explicit key coupling according to claim 1, characterized in that, It also includes a declassification quality evaluation step: calculating the graphic complexity based on the length and angle coefficients of the multi-line segments in the digital elevation model, and calculating the similarity of terrain undulation morphology based on the graphic complexity before and after declassification; An eight-dimensional vertical direction descriptor is constructed based on the elevation magnitude relationship of the eight neighboring areas of each effective elevation point, and the consistency of the vertical direction relationship is calculated based on the consistency ratio of the eight-dimensional vertical direction descriptors before and after declassification.

9. The method for decrypting a digital elevation model using polar coordinate visual implicit / explicit key coupling according to claim 1, characterized in that, It also includes a control point attack evaluation step: selecting a preset number of corresponding points before and after decryption, estimating the reverse elevation disturbance surface based on the corresponding points, performing attack recovery on the decrypted digital elevation model, and evaluating the anti-control point attack capability by the elevation error, terrain undulation similarity, vertical relationship consistency or graphic complexity of the attack-recovered digital elevation model relative to the original digital elevation model.

10. A decryption device for a digital elevation model with polar coordinate visual implicit / explicit key coupling, characterized in that, include: The DEM reading module is used to acquire the digital elevation model to be declassified, read the spatial reference, affine transformation parameters, raster size and elevation value of the digital elevation model to be declassified, and determine the effective elevation point sequence and the plane coordinate range of the digital elevation model to be declassified. An explicit key configuration module is used to determine the spatial range of the decryption grid, the number of grid rows and columns, the range of perturbation amplitude, the chaotic sequence control parameters, the initial value, the number of pre-iterations, the sequence length, and the spatial interpolation parameters based on the explicit key. The chaotic sequence generation module is used to generate initial grid points based on the spatial range and number of rows and columns of the de-dense grid; Based on the Logistic chaotic mapping, the elevation perturbation parameters, roll attitude parameters, pitch attitude parameters, yaw attitude parameters, and quadrant parameters corresponding to each initial grid point are generated. The Polar Vision implicit perturbation module is used to form a three-dimensional seed coordinate system by combining the planar coordinates of each grid point with the preset seed elevation, calculate the polar radius angle based on the roll attitude parameters and pitch attitude parameters, calculate the polar angle based on the yaw attitude parameters and quadrant parameters, normalize the polar radius angle and the polar angle respectively, and perform nonlinear perturbation on the planar coordinates of the grid points according to the normalization results to obtain the de-density control points. An elevation disturbance interpolation module is used to calculate the elevation disturbance of each effective elevation point using spatial interpolation methods, with the de-confined control points and their elevation disturbance parameters as control. The declassified DEM output module is used to superimpose the elevation disturbance onto the original elevation and output a declassified digital elevation model. The authorized recovery module is used to regenerate the declassified control points and elevation disturbances using the same explicit key and Polar Vision implicit transformation rules as the declassification process, and to subtract the corresponding elevation disturbances from the elevation values ​​of the declassified digital elevation model to obtain the recovered digital elevation model. The declassification quality evaluation module is used to calculate the graphic complexity based on the length and angle coefficients of the multi-line segments in the digital elevation model, and to calculate the similarity of terrain undulation morphology based on the graphic complexity before and after declassification. An eight-dimensional vertical direction descriptor is constructed based on the elevation magnitude relationship of the eight neighboring regions of each effective elevation point, and the consistency of the vertical direction relationship is calculated based on the consistency ratio of the eight-dimensional vertical direction descriptors before and after declassification. The anti-control point attack evaluation module is used to select a preset number of corresponding points before and after decryption, estimate the reverse elevation disturbance surface based on the corresponding points, perform attack recovery on the decrypted digital elevation model, and evaluate the anti-control point attack capability by the elevation error, terrain undulation similarity, vertical relationship consistency or graphic complexity of the attack-recovered digital elevation model relative to the original digital elevation model. The polar coordinate visual implicit key coupling digital elevation model decryption device is used to perform the steps in the polar coordinate visual implicit key coupling digital elevation model decryption method according to any one of claims 1-9.

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