Image Geometric Location Method and System Based on Adaptive Balanced L1-L2 Norm Regularization

Abstract

The present invention discloses an image geometric positioning method and system based on adaptive balanced L1-L2 norm regularization, which relates to the technical field of spatial data processing, and includes the following steps: obtaining remote sensing satellite image data, performing radiation and geometric correction on the remote sensing satellite image data, and using the SIFT and RANSAC methods for image matching to obtain the processed remote sensing satellite image data; correcting the processed remote sensing satellite image data based on the adaptive balanced L1-L2 norm regularization method, thereby calculating key positioning parameters and improving the reprojection accuracy and geometric positioning accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of spatial data processing, and specifically to an image geometric positioning method and system based on adaptive balanced L1-L2 norm regularization. Background Art

[0002] In the geometric positioning method of bundle adjustment of remote sensing images, ill-posed problems are often encountered. Ill-posed problems are sensitive to observation noise, that is, the observation noise and the ill-posedness of the inversion model system are the reasons for the drastic fluctuations in parameter estimation, which have a negative impact on the subsequent observation and in-depth analysis of spatial data. The parameter solution of an ill-posed problem violates the stability condition of a well-posed solution, that is, the solution of an ill-posed problem exists, is unique but unstable. Parameter estimation of ill-posed problems is a common problem in the fields of geodesy, photogrammetry, and remote sensing, especially for the geometric positioning of remote sensing images. Facing ill-posed problems, regularization methods are often used to solve this problem. The essence of the commonly used Tikhonov regularization is to select reasonable regularization parameters, reduce the influence of small singular values in the coefficient matrix, thereby reducing the condition number and obtaining a more stable solution. However, when the solution of the unknown parameter is sparse, the result of Tikhonov regularization will be over-smoothed, resulting in the loss of sparse high-frequency information. For example, Patent No. 201610134383.0 realizes a high-precision geometric correction method for satellite remote sensing images by slightly correcting RPC parameters. Summary of the Invention

[0003] To solve the deficiencies mentioned in the above background art, the purpose of the present invention is to provide an image geometric positioning method and system based on adaptive balanced L1-L2 norm regularization.

[0004] In a first aspect, the purpose of the present invention can be achieved through the following technical solutions: An image geometric positioning method based on adaptive balanced L1-L2 norm regularization, the method comprising the following steps:

[0005] Obtain remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use the SIFT and RANSAC methods for image matching to obtain processed remote sensing satellite image data;

[0006] Based on the adaptive balanced L1-L2 norm regularization method, perform correction processing on the processed remote sensing satellite image data, thereby calculating key positioning parameters and improving the reprojection accuracy and geometric positioning accuracy.

[0007] In combination with the first aspect, in some implementation manners of the first aspect, the method further comprises: The regularization method of the adaptive balanced L1-L2 norm comprises the following steps:

[0008] The observation vector y is jointly composed of the coefficient matrix A constructed by the rational function model and affine transformation, the ground control points, and the tie points. Appropriate regularization matrix D and threshold ∈ are constructed according to the prior information to initialize the following parameters, including the outer loop index iter, the regularization parameter λ, and the balance parameter θ; initialize the regular solution of the positioning parameters

[0009] Initialize the inner loop index k, and determine whether the number of iterations is less than the maximum number of iterations; if the condition is satisfied, proceed to the next step, update the outer loop index iter and continue the iteration, otherwise output the adaptive regular solution

[0010] Determine whether the penalty parameter p is less than p max , if the condition is satisfied, proceed to the next step; otherwise output the adaptive regular solution

[0011] Calculate the mixing parameter δ using the penalty parameter and the regularization parameter;

[0012] Update the auxiliary variable; update the adaptive regular solution Variance of unit weight Determine the set The bias correction elements in, calculate the bias correction solution

[0013] Update the auxiliary variable Update the balance parameter σ k+1 ; Based on the minimum mean square error criterion, update the regularization parameter λ using the bisection method;

[0014] Determine Whether it holds. If the inequality does not hold, increment the number of iterations by 1 and continue the inner loop until the inequality holds; otherwise, update the outer loop index iter and update the penalty parameter p, and return to initialize the inner loop index and continue the iteration;

[0015] When the outer loop index iter satisfies the maximum number matiter, calculate and output the bias correction solution of the final result

[0016] Combined with the first aspect, in some implementation manners of the first aspect, the method further includes: The process of calculating the mixing parameter δ using the penalty parameter and the regularization parameter is as follows:

[0017] The expression for adaptively balancing the L1-L2 norm is constructed in the following form:

[0018]

[0019] Among them, x represents the parameter to be estimated, θ is the balance parameter, and D is a regularization matrix with symmetric and positive semi - definite characteristics;

[0020] The objective function is constructed in the following form:

[0021]

[0022] Among them, y represents the observation vector; A represents the coefficient matrix; λ is the regularization parameter;

[0023] The alternating direction multiplier method is used for parameter solution, and an intermediate variable z := Dx is introduced to obtain the following expression:

[0024]

[0025] Among them, L(x, z, w) represents the constructed objective function with respect to variables x, z, w; arg min represents finding the parameter value of a function to minimize the result of the objective function L(x, z, w); p is the penalty parameter, w is the augmented Lagrangian vector, and the superscript T represents the matrix transpose;

[0026] The expression for defining the mixed parameter δ is:

[0027] δ = p + λ(1 - σ k ) (4)

[0028] Among them, p and λ are the penalty parameter and the regularization parameter respectively, and σ k is the balance parameter.

[0029] Combined with the first aspect, in some implementation manners of the first aspect, the method further includes: the calculation formula for updating the auxiliary variable:

[0030] The update formula for the auxiliary parameter z is:

[0031]

[0032] Among them, S represents the soft - threshold function, is for updating the auxiliary variable;

[0033] Updating the adaptive regular solution Unit weight variance The calculation formula:

[0034] Parameter The update method is:

[0035]

[0036] Among them, N = A T PA, and the superscript - 1 represents the inverse operation of the matrix;

[0037] Unit weight variance The calculation formula is as follows:

[0038]

[0039] where m and n are the lengths of the observation vector y and the estimated parameter respectively.

[0040] Combined with the first aspect, in some implementations of the first aspect, the method further includes: the determination set The process of calculating the deviation correction solution for the deviation correction element in is as follows:

[0041] The determination set that meets the deviation correction is expressed as follows:

[0042]

[0043] where γ i represents the i-th eigenvalue of the matrix (D T D) -1 N, and g i represents the eigenvector corresponding to the eigenvalue γ i ; represents the i-th eigenvalue of the matrix D T D, and u i represents the eigenvector corresponding to the eigenvalue . As i increases, the eigenvalue γ i will decrease, and the value on the left side of Equation (6) will increase, so the variance of the selected part of the deviation that meets the correction will decrease;

[0044] Based on this condition, the method of removing part of the deviation from the regularization estimation formula (6) to correct the solution deviation is as follows:

[0045]

[0046] where represents the regularized solution after deviation correction.

[0047] Combined with the first aspect, in some implementations of the first aspect, the method further includes: the process of updating the auxiliary variable and updating the balance parameter σ k+1 is as follows:

[0048] Estimate the parameters according to the calculation principle of the alternating direction multiplier method, where the update method of the auxiliary variable is as follows:

[0049]

[0050] The update method for the balance parameter θ is as follows:

[0051]

[0052] Among them, H f (x) = (x - x min ) / (x - x max ) represents the normalization function, and x min and x max represent the minimum and maximum values in the vector x respectively.

[0053] Combined with the first aspect, in some implementation manners of the first aspect, the method further includes: The mean square error matrix MSE of obtaining the adaptive regular solution can be expressed in the following form:

[0054]

[0055] In the formula C() represents the variance matrix of represents the true value of the unknown parameter, represents the bias term of the parameter , and I represents the identity matrix;

[0056] The regularization parameter δ is determined by minimization, and the optimal δ is obtained by minimizing the trace of, and the expression is:

[0057]

[0058] where trace() represents the trace of the square matrix;

[0059] By taking the first-order derivative of Equation (13), the root where the first-order derivative is zero is obtained, which is the result of the regularization parameter. The expression of the first-order derivative is as follows:

[0060]

[0061] The bisection method is used to approximate the root δ of Equation (14). Among them the true value of is not known a priori, and the estimate of the unknown parameter is used for initialization.

[0062] Combined with the first aspect, in some implementation manners of the first aspect, the method further includes: The calculation process of updating the penalty parameter p:

[0063] Judge If it does not hold, then update k = k + 1 and continue the inner loop; otherwise, update the outer loop index iter = iter + 1 and update the solution of p:

[0064] p = scale s × p(15)

[0065] Continue to repeat the initialization of the inner loop index. Otherwise, finally output the adaptive regularized solution with deviation correction according to Equation (9).

[0066] In a second aspect, to achieve the above object, the present invention discloses an image geometric positioning system based on adaptive balanced L1-L2 norm regularization, including:

[0067] A data processing module, configured to obtain remote sensing satellite image data, perform radiometric and geometric correction on the remote sensing satellite image data, and perform image matching using the SIFT and RANSAC methods to obtain the processed remote sensing satellite image data;

[0068] A geometric positioning module, configured to perform correction processing on the processed remote sensing satellite image data based on the adaptive balanced L1-L2 norm regularization method, so as to calculate key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy.

[0069] In another aspect of the present invention, to achieve the above object, a terminal device is disclosed, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The computer program stored in the memory can run on the processor. When the processor loads and executes the computer program, the above-mentioned image geometric positioning method based on adaptive balanced L1-L2 norm regularization is adopted.

[0070] Advantages of the present invention:

[0071] Due to the existence of the L1 norm in the present invention, additional penalty parameters will be introduced. They increase the difficulty of selecting regularization parameters. The present invention focuses on the generalization of regularization parameter selection and reduces the interference of these penalty parameters. The estimation of unknown model parameters seriously hinders the deviation calculation based on the L1-L2 norm regularization method, which can usually be calculated iteratively. It can be inferred from this that it is difficult to obtain a reliable initial value of the parameter and the effect is difficult to define. The present invention analyzes the effect based on the approximation theory, thereby overcoming this problem. The present invention combines the smoothness of the L2 norm and the sparsity advantage of the L1 norm, overcomes the ill-conditioned problem in the geometric positioning process, can calculate key positioning parameters, and while improving the reprojection accuracy and geometric positioning accuracy, also makes the geometric positioning process based on regularization more stable and robust. Description of the Drawings

[0072] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings;

[0073] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0074] Figure 2 It is a schematic diagram of the work flow of the present invention;

[0075] Figure 3 It is a schematic diagram of the system structure of the present invention;

[0076] Figure 4 It is a scene diagram of experimental data in a certain area in this embodiment;

[0077] Figure 5 An enlarged view of the reprojection error distribution calculated by eight different regularization methods for 42 connection points;

[0078] Figure 6 It is an analysis diagram of the error distribution of 42 connection points before and after bundle adjustment in this embodiment. Specific embodiments

[0079] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0080] Embodiment 1:

[0081] As Figure 1 shown, an image geometric positioning method based on adaptive balanced L1-L2 norm regularization, the method includes the following steps:

[0082] S101: Obtain remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and perform image matching using the scale-invariant feature transform algorithm SIFT and the random sample consensus algorithm RANSAC method to obtain the processed remote sensing satellite image data;

[0083] S102: Based on the adaptive balanced L1-L2 norm regularization method, perform correction processing on the processed remote sensing satellite image data, thereby solving the key positioning parameters and improving the reprojection accuracy and geometric positioning accuracy.

[0084] Specifically, remote sensing satellite images and RPC parameter files are obtained through the CCD camera carried by Ziyuan-3 remote sensing satellite. After the obtained images are radiometrically and geometrically corrected, the SIFT and RANSAC methods are used for image matching. In order to obtain high-precision reprojection accuracy and spatial geometric positioning results, bundle adjustment is carried out by combining image homologous point pairs and their ground control point data. In order to overcome the problem of ill-conditioning of the coefficient matrix in the process of bundle adjustment, the regularization method based on adaptive balanced L1-L2 norm proposed in this invention is adopted to realize the stable and efficient solution of the key positioning parameters, namely the connection point position correction parameters and the affine transformation parameters, so as to improve the reprojection accuracy and geometric positioning accuracy.

[0085] As Figure 2 shown, wherein, the regularization method of the adaptive balanced L1-L2 norm includes the following steps:

[0086] Initialize the following parameters by inputting the coefficient matrix A constructed by the rational function model and affine transformation, the observation vector y jointly composed of ground control points and connection points, constructing a suitable regularization matrix D and threshold ∈ according to prior information, including the outer loop index iter, the regularization parameter λ and the balance parameter θ; initialize the regularized solution of the positioning parameters

[0087] Initialize the inner loop index k, and judge whether the number of iterations is less than the maximum number of iterations; if the condition is satisfied, proceed to the next step to update the outer loop index iter, otherwise output the adaptive regularized solution

[0088] Judge whether the penalty parameter p is less than p max , if the condition is satisfied, proceed to the next step; otherwise output the adaptive regularized solution

[0089] Calculate the mixed parameter δ using the penalty parameter and the regularization parameter;

[0090] Update the auxiliary variable; update the adaptive regularized solution Variance of unit weight Judge the set The deviation correction elements in, calculate the deviation correction solution

[0091] Update the auxiliary variable Update the balance parameter σ k+1 ; Based on the minimum mean square error criterion, update the regularization parameter λ using the dichotomy method;

[0092] Judge Whether it holds. If the inequality does not hold, the iteration count is incremented by 1, and the inner loop continues until the inequality holds; otherwise, the outer loop index iter and the penalty parameter p are updated, and the iteration resumes from the initialization of the inner loop index.

[0093] When the outer loop index iter meets the maximum number of times matiter, calculate and output the bias-corrected solution of the final result.

[0094] Among them, the process of calculating the mixed parameter δ using the penalty parameter and the regularization parameter is as follows:

[0095] The expression for the adaptive balanced L1-L2 norm is constructed in the following form:

[0096]

[0097] Among them, x represents the parameter to be estimated, θ is the balance parameter between 0 and 1, and D is a regularization matrix with symmetric and positive semi-definite characteristics.

[0098] The objective function φ(x) is constructed in the following form:

[0099]

[0100] Among them, y represents the observation vector; A represents the coefficient matrix, and λ is the regularization parameter.

[0101] The alternating direction multiplier method is used for parameter solution, and an intermediate variable z := Dx is introduced to obtain the following expression:

[0102]

[0103] Among them, L(x,z,w) represents the constructed objective function with respect to variables x, z, w; arg min represents finding the parameter value of a function to minimize the result of the objective function L(x,z,w); p is the penalty parameter, w is the augmented Lagrangian vector, and the superscript T represents the matrix transpose.

[0104] The expression for defining the mixed parameter is:

[0105] δ = p + λ(1 - σ k ) (4)

[0106] Among them, p and λ are the penalty parameter and the regularization parameter respectively, and σ k is the balance parameter.

[0107] Among them, the calculation formula for updating the auxiliary variable:

[0108] The update formula for the auxiliary parameter z is:

[0109]

[0110] Among them, S represents the soft threshold function, To update the auxiliary variable

[0111] Update the adaptive regular solution Unit weight variance The calculation formula of:

[0112] Parameter The update method of is:

[0113]

[0114] Among them, N = A T PA, the superscript -1 represents the inverse operation of the matrix;

[0115] Unit weight variance The calculation formula is:

[0116]

[0117] Among them, m and n are the lengths of the observation vector y and the estimated parameter Length.

[0118] Among them, the judgment set The deviation correction element in, calculate the deviation correction solution The process is as follows:

[0119] Judge the set that meets the deviation correction The expression of is as follows:

[0120]

[0121] Among them, γ i Represents the i-th eigenvalue of the matrix (D T D) -1 N, g i Represents the eigenvector corresponding to the eigenvalue γ i ; Represents the i-th eigenvalue of the matrix D T D, u i Represents the eigenvector corresponding to the eigenvalue As i increases, the eigenvalue γ i Will decrease, the value on the left side of formula (6) will increase, and the variance of the selected part of the deviation that meets the correction will decrease; on this basis, part of the deviation is removed from the regularization estimation formula (6) to correct the solution deviation The method is:

[0122]

[0123] Among them, represents the regularized solution after deviation correction.

[0124] Among them, the updated auxiliary variable updates the balance parameter σ k+1 process:

[0125] Estimate the parameters according to the calculation principle of the alternating direction multiplier method, where the auxiliary variable update method is:

[0126]

[0127] The update method of the balance parameter θ is:

[0128]

[0129] Among them, H f (x) = (x - x min ) / (x - x max ) represents the normalization function, x min and x max represent the minimum and maximum values in the vector x respectively.

[0130] Combined with the first aspect, in some implementation manners of the first aspect, the method further includes: the obtained adaptive regular solution The mean square error matrix MSE can be expressed in the following form:

[0131]

[0132] In the formula C() represents variance matrix of, represents the true value of the unknown parameter, represents the parameter bias term of, I represents the identity matrix;

[0133] The regularization parameter δ is determined by minimization, then the optimal δ is obtained by minimizing trace of, and the expression is:

[0134]

[0135] where trace() represents the trace of the square matrix;

[0136] By taking the first-order derivative of equation (13) to obtain the root where the first-order derivative is zero, which is the result of the regularization parameter, and the expression of the first-order derivative is as follows:

[0137]

[0138] The root δ of formula (14) is approximated using the bisection method, where the true value of x is not known a priori, and the estimation of unknown parameters is used for initialization

[0139] Combined with the first aspect, in some implementations of the first aspect, the method further includes: the calculation process of updating the penalty parameter p

[0140] Judge If not, update k = k + 1 and continue the inner loop; otherwise, update the outer loop index iter = iter + 1 and update the solution for p

[0141] p = scale s × p (15)

[0142] Continue to repeat the initialization of the inner loop index. Otherwise, finally output the bias-corrected adaptive regularized solution according to formula (9)

[0143] Specifically, the solution of the present invention is further elaborated below through embodiments

[0144] In this experiment, the left image is used as the reference image. Therefore, the reprojection error of the right image is used to evaluate the relative accuracy of the bundle adjustment solution, and its distribution in the u and v directions is as Figure 5 shown. Compared with other similar algorithms, the proposed BL1L2N algorithm of the present invention has the shortest arrow length, which means that the reprojection error of the proposed BL1L2N is the smallest, that is, it has the highest relative positioning accuracy. Specifically, the reprojection error of the LS solution is biased towards the u - direction, while the offset in the v - direction is very small. In contrast, the arrows of ElasticNet are tilted towards both the v - direction and the u - direction. The above results are consistent with the results in Table 2. As shown in Table 2, the relative accuracy is qualitatively evaluated. In terms of this relative positioning accuracy, the improvement rates of the results of different regularization methods relative to the relative positioning accuracy of LS are 94.827%, 94.445%, 98.287%, 94.837%, 94.827%, 98.193%, 99.428% and 99.428% respectively. It can be seen that the regularization method is an effective method to improve the relative accuracy of satellite image geometric positioning. In addition, the improvement rates of the relative positioning accuracy of the proposed BL1L2N of the present invention relative to other regularization methods except LS are 4.601%, 4.983%, 1.142%, 4.591%, 4.601%, 1.235% and 0.0006% respectively, which strongly proves the superiority of the proposed BL1L2N in the reprojection accuracy of remote sensing images

[0145] Table 1: RMSE of reprojection error of the right image of 42 tie points

[0146]

[0147] Table 2: Geometric positioning accuracy residuals of 42 connection points after adjustment

[0148]

[0149] To further evaluate the geometric positioning accuracy of BL1L2N, the absolute geometric positioning accuracies of different regularization methods (as the RMSE of the residuals of 42 connection points) are listed in Table 2. It can be seen from Table 2 that L1 and ElasticNet cannot obtain reasonable geometric positioning accuracy and are consistent with the geometric positioning accuracy of direct resection without adjustment. The absolute geometric positioning accuracy of the LS method reaches a planar accuracy of 10.754 m in the XY direction and an elevation accuracy of 13.471 m in the Z direction, far exceeding other regularization methods. The root mean square errors of the planar accuracy and elevation accuracy of the BL1L2N method proposed in the present invention are almost equal, approximately 5.3 m and 5.8 m respectively, but this represents a substantial improvement compared to the spatial positioning methods of L1 and ElasticNet of the same type. Although the level of geometric positioning accuracy is jointly determined by the accuracy of camera calibration parameters, the accuracy of control points, and the accuracy of spatial data processing algorithms; but by comparing the absolute positioning accuracy of LS (as shown in Figure 6 ) it can be seen that the regularization method improves the relative accuracy of reprojection and can potentially improve the absolute geometric positioning accuracy.

[0150] Example:

[0151] The purpose of the present invention is to explore the generalization of the selection of regularization parameters to reduce the penalty parameter interference caused by the alternating direction multiplier method. Based on the deviation analysis during the solution process of the bundle adjustment model, a judgment condition for determining the deviation removal range is derived to ensure its rationality. To achieve the above purpose, the present invention discloses an image geometric positioning method based on adaptive balanced L1-L2 norm regularization. Since the normal equation of the bundle adjustment for image geometric positioning is an ill-posed problem, in the absence of ground control points (GCPs), the traditional least squares method cannot obtain a convergent solution. In the case of terrain correlation, rational polynomial coefficient parameters (RPCs) can be estimated by using at least 40 GCPs. And due to a large number of high correlation coefficients, the normal matrix of the rational function model is also ill-posed. The proposed BL1L2N can be used to solve these two problems.

[0152] In this example, as Figure 4As shown, ZY-3 stereo satellite images located in a certain area were selected, with a coverage range of (112.83°E to 113.57°E, 34.33°W to 34.95°W). In order to obtain high-precision spatial geometric positions from high-resolution satellite images, a bundle adjustment model based on the rational function model (RFM) was used, and its basic form can be expressed as:

[0153]

[0154] where (s, l) are the normalized image point coordinates in the u and v directions, and (U, V, W) represent the normalized ground point coordinates. In addition, P i (i = 1, 2, 3, 4) are third-order polynomials, and each polynomial has 20 RPCs. △s and △l are the systematic error correction parameters in the x and y directions respectively, and their expressions are:

[0155]

[0156] where r0, r1, r2, f0, f1, f2 are the compensation parameters for these systematic errors. The error equations can be obtained by using the first-order Taylor linearization equation for series expansion and can be expressed in matrix form:

[0157]

[0158] where v cp and v tp are the residual error vectors of the ground control points and tie points measurements in the u and v directions. A and B are the corresponding coefficient matrices; x is the correction vector of the ground control point coordinates corresponding to the tie points; t is the vector of systematic errors, or the parameters of the affine transformation; l is the constant vector calculated from the initial values; the subscripts cp and tp are the GCP and tie points respectively. Since there are many unknown parameters in the bundle adjustment process, the affine transformation coefficient t is separated from the coordinate correction of the ground point x. After linear transformation, the expression of t can be obtained as follows:

[0159]

[0160] where P is the corresponding weighted matrix. N t is the Schur complement matrix, and the computational complexity can be reduced by reducing the dimension of the normal matrix . However, similar to the normal matrix , N t is still severely ill-conditioned, with a condition number exceeding 3.009×10^13. Therefore, a regularization method should be applied to obtain a stable solution.

[0161] Second aspect, as Figure 3As shown below, to achieve the above object, the present invention discloses an image geometric positioning system based on adaptive balanced L1-L2 norm regularization, including:

[0162] A data processing module 11, configured to obtain remote sensing satellite image data, perform radiometric and geometric corrections on the remote sensing satellite image data, and perform image matching using the SIFT and RANSAC methods to obtain processed remote sensing satellite image data;

[0163] A geometric positioning module 12, configured to perform correction processing on the processed remote sensing satellite image data based on the adaptive balanced L1-L2 norm regularization method, thereby calculating key positioning parameters and improving the reprojection accuracy and geometric positioning accuracy.

[0164] Based on the same inventive concept, the present invention also provides a computer device, which includes: one or more processors, and a memory for storing one or more computer programs; the program includes program instructions, and the processor is configured to execute the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is used to implement one or more instructions, specifically for loading and executing one or more instructions in the computer storage medium to implement the above method.

[0165] It should be further noted that, based on the same inventive concept, the present invention also provides a computer storage medium, on which a computer program is stored. When the computer program is run by a processor, the above method is executed. The storage medium may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electro-magnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the computer-readable storage medium include: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, the computer-readable storage medium may be any tangible medium that contains or stores a program, and the program may be used by or in combination with an instruction execution system, apparatus, or device.

[0166] In the description of this specification, the descriptions referring to the terms "one embodiment", "example", "specific example", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present disclosure. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0167] The above shows and describes the basic principles, main features, and advantages of the present disclosure. Those skilled in the art should understand that the present disclosure is not limited by the above embodiments. The above embodiments and the descriptions in the specification only illustrate the principles of the present disclosure. Without departing from the spirit and scope of the present disclosure, the present disclosure will have various changes and improvements, and these changes and improvements all fall within the scope of the present disclosure claimed.

Claims

1. An image geometric positioning method based on adaptive balanced L1-L2 norm regularization, characterized in that: The method comprises the following steps: Acquire remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use SIFT and RANSAC methods for image matching to obtain processed remote sensing satellite image data; Based on the adaptive balanced L1-L2 norm regularization method, the processed remote sensing satellite image data is corrected to solve the key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy; The regularization method of the adaptive balanced L1-L2 norm comprises the following steps: The coefficient matrix A constructed by the rational function model and affine transformation, the ground control points and the connection points together form the observation vector y, and the regularization matrix D and the threshold ∈ are constructed according to the prior information to initialize the following parameters, including the outer loop index iter, the regularization parameter λ and the balance parameter θ; the regularization solution of the initialization positioning parameters Initialize the inner loop index k and determine whether the number of iterations is less than the maximum number of iterations; if the condition is met, proceed to the next step and update the outer loop index iter to continue iterating, otherwise output the adaptive regularization solution Determine whether the penalty parameter p is less than p max ; If the condition is met: p<p max , then proceed to the next step; otherwise, output the adaptive regularization solution Calculate the mixing parameter δ using the penalty parameter and the regularization parameter; The process of calculating the mixing parameter δ using the penalty parameter and the regularization parameter is as follows: The expression of the adaptive balanced L1-L2 norm is constructed as follows: Where x represents the parameter to be estimated, θ is the equilibrium parameter, and D is a regularization matrix with symmetric and positive and semi-positive definite characteristics; The objective function is constructed as follows: Where y represents the observation vector; A represents the coefficient matrix; λ is the regularization parameter; The alternating direction multiplier method is used to solve the parameters, and the intermediate variable z:=Dx is introduced to obtain the following expression: Where L(x,z,w) represents the objective function constructed about variables x,z,w; arg min represents finding a function parameter value that minimizes the result of the objective function L(x,z,w); p is the penalty parameter, w is the augmented Lagrangian vector, and the superscript T represents the matrix transpose; The expression for defining the mixing parameter δ is: δ=p+λ(1-θ) (4) Where p and λ are the penalty parameter and regularization parameter respectively, and θ is the balance parameter Update auxiliary variables; Update adaptive regularized solution Unit weight variance Judgment Set The bias correction elements in the calculation of the bias correction solution Update auxiliary variables Update the equilibrium parameter σ k+1 ; Based on the minimum mean square error criterion, the regularization parameter λ is updated using the bisection method; judge If the inequality does not hold, the number of iterations is increased by 1, and the inner loop continues until the inequality holds; otherwise, the outer loop index iter and penalty parameter p are updated, and the inner loop index is returned to the initialization to continue the iteration; When the outer loop index iter meets the maximum number of times matiter, calculate and output the deviation correction solution of the final result 2. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 1, characterized in that: The calculation formula for updating the auxiliary variable is: The auxiliary parameter z update formula is: Where S represents the soft threshold function, To update auxiliary variables; Update the adaptive regularization solution Unit weight variance The calculation formula is: parameter The update method is: Where N = A T PA, the superscript -1 indicates the inverse operation of the matrix; Unit weight variance The calculation formula is: Where m and n are the length of the observation vector y and the estimated parameter Length.

3. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 2, characterized in that: The judgment set The deviation correction elements in the calculation of the deviation correction solution The process is as follows: Determine the set that meets the deviation correction The expression is as follows: Among them, γ i Represents the matrix (D T D) -1 The i-th eigenvalue of N, g i Denotes the corresponding eigenvalue γ i The eigenvector of Denotes the matrix D T The i-th eigenvalue of D, u i Indicates the corresponding eigenvalue The eigenvector of , as i increases, the eigenvalue γ i will decrease, and the value on the left side of formula (6) will increase, then the variance of the selected part of the deviation that satisfies the correction will decrease; Based on this condition, some deviations are removed from the regularized estimation formula (6) to correct the solution deviation The method is: in, represents the bias-corrected regularization solution.

4. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 3, characterized in that: The updating auxiliary variable Update the equilibrium parameter σ k+1 The process: The parameters are estimated according to the calculation principle of the alternating direction multiplier method, where the auxiliary variables The update method is: The update method of the equilibrium parameter θ is: Among them, H f (x)=(xx min ) / (xx max ) represents the normalization function, x min and x max Represent the minimum and maximum values ​​in vector x respectively.

5. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 4, characterized in that: The adaptive regularization solution The mean square error matrix MSE can be expressed as follows: In the formula C() means The variance matrix of represents the true value of the unknown parameter, Representation parameters The deviation term, I represents the unit matrix; The regularization parameter δ is given by The optimal δ is determined by minimizing The expression is obtained by the trace of: Where trace() represents the trace of the square matrix; By taking the first-order derivative of equation (13), we can obtain the root whose first-order derivative is zero, which is the regularization parameter result. The expression of the first-order derivative is as follows: The bisection method is used to approximate the root δ of equation (14), where The true value of is not known a priori, and the estimated value of the unknown parameter is used Initialize.

6. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 5, characterized in that: The calculation process of updating the penalty parameter p is: judge If not, update k=k+1 and continue the inner loop; otherwise, update the outer loop index iter=iter+1 and update the solution p: p=scale s ×p (15) Continue to repeatedly initialize the inner loop index, otherwise, finally output the adaptive regularization solution of deviation correction according to formula (9) 7. An image geometric positioning system based on adaptive balanced L1-L2 norm regularization, adopting the image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to any one of claims 1 to 6, characterized in that: include: The data processing module is used to obtain remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use SIFT and RANSAC methods to perform image matching to obtain processed remote sensing satellite image data; The geometric positioning module is used to correct the processed remote sensing satellite image data based on the adaptive balanced L1-L2 norm regularization method, so as to solve the key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy.

8. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: The memory stores a computer program that can be run on a processor. When the processor loads and executes the computer program, the image geometry positioning method based on adaptive balanced L1-L2 norm regularization described in any one of claims 1 to 6 is adopted.

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