Precision-controllable vector data geometric precision reduction method

Abstract

The invention discloses a precision-controllable method for reducing geometric precision of vector data. The method comprises the following steps: firstly, taking the spatial distribution density of vector geographic data into consideration, and selecting corresponding control points through a diaphragm method; secondly, based on a Hermite polynomial, an offset model of space coordinates is established; then, the selected control points are input into an offset model, and optimal offset model parameters are trained through iteration; and finally, increasing disturbance according to the spatial distribution condition of the coordinates, and enhancing the anti-attack capability of the model. The method provided by the invention is suitable for all types of vector data, can meet the regulation that the precision of a public map is not superior to 10 meters, and can realize the controllability of precision reduction. And before and after the precision is reduced, the topological relation retention degree, the graphic form similarity and the spatial direction consistency degree of the data are good, and a new solution is provided for safe application and sharing of the vector data.

Description

Technical Field

[0001] The invention belongs to the technical field of geographic information security, and relates to a method for reducing geometric precision of vector data with controllable precision. Background Art

[0002] Vector data is one of the important geographic data resources. It can be used as a carrier of various spatiotemporal information and plays an important role in national defense construction, economic construction, and social development. Vector data has the characteristics of high precision, contains sensitive information, and is easy to copy and distribute. With the rapid development of computer technology, illegal copying and leakage of vector data are frequent, which not only affects the healthy development of the surveying and mapping geographic information industry, but also threatens national defense security. Ensuring the compliance and safe use of vector data, fully releasing the value of data, and promoting the safe sharing and application of data are key issues that need to be solved in the process of realizing the assetization, factorization, and cross-domain circulation of vector data.

[0003] Geometric precision reduction technology refers to reducing the spatial precision of coordinates or resolution through mathematical transformation and other methods, and processing data into publicly available data. This technology can fundamentally balance the contradiction between vector data security and shared applications. At present, there are two main types of geometric precision reduction models: linear transformation and nonlinear transformation. Nie Shigui et al. used the spatial transformation tool in ArcMap to process vector data and proposed that the projective transformation has the highest degree of precision reduction. The mean error of the transformed data can meet the national requirements for public version map data. However, the data processed by linear transformation is easy to be corrected and restored, the security is not high, and the target precision reduction cannot be achieved accurately. Wang Minxuan et al. took into account the spatial distribution characteristics of vector data, used quadtree to grid the data, and designed a precision reduction model based on regularized thin plate spline function. However, this method has weak topological relationship preservation ability, poor usability and controllability. Existing vector data geometric precision methods are difficult to take into account issues such as usability and controllability. Summary of the invention

[0004] The purpose of the present invention is to provide a method for reducing the geometric accuracy of vector data with controllable accuracy, so as to ensure that the geometric accuracy of vector data can be controlled while maintaining the topological relationship, graphic morphology similarity and spatial direction consistency.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for reducing geometric precision of vector data, comprising:

[0007] Considering the distribution density of vector data, the light barrier method is used to compress the data and select control points;

[0008] Set different apertures of the light barrier, select an appropriate number of control points, and ensure that the control points correspond to the spatial distribution density of the vector data;

[0009] The Hermite polynomial is recursively deduced to obtain the first six polynomials, as shown in the following formula, where x is the parameter of the polynomial, which is also the coordinate value input when the coordinate offset model is established later;

[0010] Using the first 6 terms of the two-dimensional Hermite polynomial, a coordinate offset model is constructed for the x-coordinate and the y-coordinate. The offset model is shown in the following formula: A x , A y is the coefficient matrix of the two-dimensional Hermite polynomial, H i (x), H i (y) are the i-th and j-th order Hermite polynomials with x-coordinate and y-coordinate as independent variables, respectively. p and q are the cutoff orders, and Δx and Δy are the offsets.

[0011] A random number sequence is generated by Logistic chaotic system as the offset of the control point, and the offset is set as close to the target accuracy as possible to reduce the number of iterations. According to the known n (n ≥ p × q) coordinates of the control points before and after the transformation, the coefficient matrix of the two-dimensional Hermite polynomial is solved by the least squares principle [(A x ) pq ], taking the x coordinate as an example, the coordinate offset model can be expanded into the following formula by combining the coefficient matrix: is the offset of different coordinates;

[0012] Taking the x coordinate as an example, the coefficient matrix [(A x ) pq ], substituting into the offset model, it is simplified to the following formula, where Δx c is the offset matrix of the control points, H is the Hermite polynomial matrix, A x As the coefficient matrix, the initial offset model of the x-coordinate can be obtained. The construction process of the initial offset model of the y-coordinate is the same as that of the x-coordinate;

[0013] According to the light barrier method, sample points (x s ,y s ), input the initial coordinate offset model, and obtain the sample point after coordinate offset (x rs ,y rs );

[0014] Calculate the root mean square error between the original sample point and the sample point after the precision is reduced, compare the root mean square error with the target precision a, and determine whether the absolute value of the difference between the two meets the set threshold. If it meets the threshold, the initial coordinate offset model is output. If not, the control point offset is iteratively adjusted according to the following formula: Δx c ′ and Δy c ′ is the offset of the control point;

[0015] Repeat the above steps according to the adjusted control point offset until the processed accuracy is within the target allowable error range, then stop the iteration, obtain the optimal model parameters, and output the complete coordinate offset model;

[0016] In order to improve the safety of the model, disturbances are added to the x-coordinate and y-coordinate. First, the center point O(x cen ,y cen ), using this point as the reference point, the data is divided into four parts. The upper right corner is the first part, and the second, third, and fourth parts are obtained in a counterclockwise direction, which are recorded as Part 1-Part 4 respectively;

[0017] Taking the x coordinate as an example, add perturbation according to the following formula. If a point is located in the first part, the perturbation term is In the second part, the disturbance term is equal to The third and fourth parts are and Where Δrx i is the final offset of the x coordinate, μ1, μ2, ω1, ω2 are weight coefficients;

[0018] The y coordinate is subjected to the same perturbation addition process as the x coordinate, and the coordinate x of the original vector data is given by the following formula i and i Add the final offset to get the coordinate x with reduced precision ri and ri , completing the geometric precision reduction of vector data. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the implementation examples of the present invention or the technical solutions in the prior art, the drawings required for use in the implementation examples or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only schematic diagrams of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0020] Figure 1 A flowchart of a method for reducing geometric precision of vector data with controllable precision provided as an implementation example of the present invention;

[0021] Figure 2 Vector data provided for the implementation example of the present invention;

[0022] Figure 3 The comparison result between the vector data with reduced geometric accuracy and the original data provided in the implementation example of the present invention. DETAILED DESCRIPTION

[0023] The following will be combined with the drawings in the implementation examples of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described implementation examples are only part of the implementation examples of the present invention, not all of the implementation examples. Based on the implementation examples in the present invention, all other implementation examples obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0024] In the following, a method for reducing geometric precision of vector data with controllable precision of the present invention is described in detail with reference to the accompanying drawings and implementation examples;

[0025] Examples of reduced geometric precision:

[0026] Considering the distribution density of vector data, the light barrier method is used to compress the data and select control points;

[0027] Set different apertures of the light barrier, select an appropriate number of control points, and ensure that the control points correspond to the spatial distribution density of the vector data;

[0028] The Hermite polynomial is recursively deduced to obtain the first six polynomials, as shown in formula (1), where x is the parameter of the polynomial, which is also the coordinate value input when establishing the coordinate offset model later;

[0029] Using the two-dimensional Hermite polynomial, a coordinate migration model is constructed for the x-coordinate and the y-coordinate. The migration model is shown in formula (2): x , A y is the coefficient matrix of the two-dimensional Hermite polynomial, H i (x), H i (y) are the i-th and j-th order Hermite polynomials with x-coordinate and y-coordinate as independent variables, respectively. p and q are the cutoff orders, and Δx and Δy are the offsets.

[0030] A random number sequence is generated by Logistic chaotic system as the offset of the control point, and the offset is set as close to the target accuracy as possible to reduce the number of iterations. According to the known n (n ≥ p × q) coordinates of the control points before and after the transformation, the coefficient matrix of the two-dimensional Hermite polynomial is solved by the least squares principle [(A x ) pq ], taking the x coordinate as an example, formula (2) can be expanded into formula (3) by combining the coefficient matrix;

[0031] The coefficient matrix [(A x ) pq ], substituting into the migration model, it is simplified to formula (4), where Δx c is the offset matrix of the control points, H is the Hermite polynomial matrix, A x As the coefficient matrix, the initial offset model of the x-coordinate can be obtained. The construction process of the initial offset model of the y-coordinate is the same as that of the x-coordinate;

[0032] According to the light barrier method, sample points (x s ,y s ), input the initial coordinate offset model, and obtain the sample point after coordinate offset (x rs ,y rs );

[0033] Calculate the root mean square error between the original sample point and the sample point after the precision is reduced, compare the root mean square error with the target precision a, and judge whether the absolute value of the difference between the two meets the set threshold. If it meets the threshold, output the initial coordinate offset model. If not, iterate and adjust the control point offset according to formula (5), Δx c ′ and Δy c ′ is the offset of the control point;

[0034] Repeat the above steps according to the adjusted control point offset until the processed accuracy is within the target allowable error range, then stop the iteration, obtain the optimal model parameters, and output the complete coordinate offset model;

[0035] In order to improve the safety of the model, disturbances are added to the x-coordinate and y-coordinate. First, the center point O(x cen ,y cen ), using this point as the reference point, the data is divided into four parts. The upper right corner is the first part, and the second, third, and fourth parts are obtained in a counterclockwise direction, which are recorded as Part 1-Part 4 respectively;

[0036] Taking the x coordinate as an example, according to equation (6), if a point is located in the first part, the disturbance term is In the second part, the disturbance term is equal to The third and fourth parts are and Where Δrx i is the final offset of the x coordinate, μ1, μ2, ω1, ω2 are weight coefficients;

[0037] The y coordinate is subjected to the same disturbance adding process as the x coordinate, and the coordinate x of the original vector data is given by equation (7) i and i Add the final offset to get the coordinate x with reduced precision ri and ri , complete the geometric accuracy reduction of vector data, where Δry i is the final offset of the y coordinate;

[0038] The above description of the disclosed examples enables professionals in the field to implement or use the present invention. Various modifications to these embodiments will be apparent to professionals in the field, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will conform to the widest range consistent with the principles and novel features disclosed herein.

Claims

1. A method for reducing geometric precision of vector data with controllable precision, the specific steps are as follows, including: S1: Use the light barrier method to compress the vector data and select control points. Select an appropriate number of control points and ensure that the spatial distribution density of the control points corresponds to that of the vector data. S2: Use the two-dimensional Hermite polynomial to construct a coordinate offset model for the x-coordinate and the y-coordinate. The offset model is shown in the following formula: A x , A y is the coefficient matrix of the two-dimensional Hermite polynomial, H i (x), H i (y) are the i-th and j-th order Hermite polynomials with x-coordinate and y-coordinate as independent variables, respectively. p and q are the cutoff orders, and Δx and Δy are the offsets; S3: Use the Logistic chaotic system to generate a random number sequence as the offset of the control point, and try to set the offset close to the target accuracy to reduce the number of iterations. According to the known n (n ≥ p × q) coordinates of the control points before and after the transformation, the coefficient matrix of the two-dimensional Hermite polynomial is solved by the least squares principle [(A x ) pq ]; S4: Taking the x coordinate as an example, the coefficient matrix [(A x ) pq ], substituted into the offset model, and simplified to the following formula, where Δx c is the offset matrix of the x coordinate of the control point, H is the Hermite polynomial matrix, A x As the coefficient matrix, the initial offset model of the x-coordinate can be obtained. The construction process of the initial offset model of the y-coordinate is the same as that of the x-coordinate; S5: Select sample points (x s ,y s ), input the initial coordinate offset model, and obtain the sample point after coordinate offset (x rs ,y rs ); S6: Calculate the root mean square error (RMSE) between the original sample points and the sample points after the precision is reduced s , compare the root mean square error with the target accuracy a, and determine whether the absolute value of the difference between the two meets the set threshold. If it meets the threshold, the initial coordinate offset model is output. If not, the control point offset is iteratively adjusted according to the following formula, Δx c ′ and Δy c ′ is the offset of the control point, Δy c is the offset matrix of the y coordinate of the control point; S7: Repeat the above steps according to the adjusted control point offset until the processed accuracy is within the target allowable error range, then stop the iteration, obtain the optimal model parameters, and output the complete coordinate offset model; S9: Calculate the center point O(x cen ,y cen ), using this point as the reference point, the data is divided into four parts. The upper right corner is the first part, and the second, third, and fourth parts are obtained in a counterclockwise direction, which are recorded as Part 1-Part 4 respectively; S10: Taking the x coordinate as an example, add disturbance according to the following formula. If a point is located in the first part, the disturbance term is In the second part, the disturbance term is equal to The third and fourth parts are and Where Δrx i is the final offset of the x-coordinate, μ1, μ2, ω1, ω2 are weight coefficients, and the perturbation adding process of the y-coordinate is the same as that of the x-coordinate; S11: The coordinate x of the original vector data is given by the following formula i and i Add the final offset to get the coordinate x with reduced precision ri and ri , completing the geometric precision reduction of vector data.

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