Lightweight remote sensing image geometric positioning method, system and equipment

Abstract

The invention discloses a lightweight remote sensing image geometric positioning method, system and device. The method comprises the following steps: S1, obtaining a remote sensing image and creating a coordinate data set; s2, initializing parameters of the remote sensing image geometric positioning model, and generating an input weight matrix by using orthogonal random projection; s3, training a remote sensing image geometric positioning model according to the coordinate data set, generating hidden layer output through nonlinear feature mapping, and constructing an output weight matrix according to a regularized least square method in combination with a multistage solving strategy; s4, evaluating the performance of the model according to cross validation division, optimizing regularization parameters and then retraining the model; and S5, based on the trained model parameters, inputting test data into the trained remote sensing image geometric positioning model to execute regression calculation, comparing calculated coordinate data with coordinates calculated by the satellite sensor model, recording operation time, and verifying efficiency and accuracy of the model. The method is applied to the technical field of photogrammetry.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of photogrammetry, and particularly relates to a lightweight remote sensing image geometric positioning method, system and device. BACKGROUND

[0002] The geometric positioning model of satellite images is a key link in remote sensing data processing, and its precision and efficiency directly affect the subsequent analysis and application effect. The commonly used geometric positioning model, such as the rational function model, performs reverse projection calculation through iterative solving to achieve positioning coordinate calculation, which leads to an increase in calculation time when a large number of coordinates are calculated. In the scene of a resource-limited embedded platform or a high real-time requirement, the demand for real-time response may not meet the expected time efficiency.

[0003] In recent years, deep learning models (such as multilayer perceptron, convolutional neural network and Transformer) have been widely applied in the field of remote sensing. Some researches try to use deep learning models to fit satellite sensor models to improve the performance of the models. Although deep learning performs well in specific tasks, it usually relies on deep network structure and large-scale parameters, and the training and inference process consumes a large amount of computing resources. The redundant network layer design and parameter size increase the inference delay, making it difficult to meet the real-time requirement, and the strong dependence on hardware accelerators limits its applicability in edge computing environment. In addition, the satellite image geometric positioning task is to accurately correspond and map the satellite image to the three-dimensional geographic coordinate system of the earth's surface, and the mapping relationship between the input and output has clear mathematical constraints, and the task complexity is relatively limited. If a complex network structure is used, not only will the training and inference time be greatly increased due to parameter redundancy, but also it will be difficult to achieve efficient operation in scenes with high real-time requirements or limited resources, so it is not the optimal solution. In addition, an excessively simplified model may lead to insufficient positioning accuracy and cannot meet the application requirements. Therefore, it is necessary to balance the model complexity, computing efficiency and accuracy to achieve efficient remote sensing image geometric positioning. SUMMARY

[0004] To solve the above problems, the application provides a lightweight remote sensing image geometric positioning method, system and device. The method discards the traditional iterative optimization and complex network structure, and initializes and regularizes the analytical solution through orthogonal projection on the basis of extreme learning machine, significantly reduces the training and inference time on the premise of ensuring the positioning accuracy. Compared with the iterative problem of reverse projection calculation of the rational function model, its non-iterative characteristic avoids the convergence delay problem, and compared with the commonly used deep learning method, its parameter size and computing complexity are greatly reduced, avoiding the problem of rapid increase in computing complexity caused by multilayer stacking, and being more suitable for low-power hardware environment.

[0005] The technical scheme adopted by the present application is: the present application comprises a lightweight remote sensing image geometric positioning method, system and device, the method comprising the following steps:

[0006] Step 1: Obtain remote sensing images and create a coordinate data set;

[0007] Step 2: Initialize the parameters of the remote sensing image geometric positioning model, generate an input weight matrix using orthogonal random projection, generate a random bias vector, and adaptively determine the hidden layer dimension according to the statistical characteristics of the input feature data;

[0008] Step 3: Train the remote sensing image geometric positioning model according to the coordinate data set, generate hidden layer output through nonlinear feature mapping, and construct the output weight matrix according to the regularized least squares method combined with a multi-level solving strategy;

[0009] Step 4: Evaluate the model performance according to cross-validation division, retrain the model after optimizing the regularization parameter, and save all key parameters of the final model as a unified standardized file format;

[0010] Step 5: Based on the trained model parameters, input the test data into the trained remote sensing image geometric positioning model to perform regression calculation, the model outputs the predicted coordinate data, which is compared with the coordinate calculated by the satellite sensor model, and the running time of the lightweight remote sensing image geometric positioning model and the satellite sensor model on the test data is recorded to verify the efficiency and accuracy of the model.

[0011] Further, the step 1 of obtaining remote sensing images and creating a coordinate data set is to calculate the spatial three-dimensional coordinates of virtual grid points using a satellite sensor model, create a data set containing image pixel coordinates and object space coordinates, and normalize the remote sensing image coordinate data.

[0012] Further, the specific steps of generating an input weight matrix using orthogonal random projection and generating a random bias vector in step 2 are as follows:

[0013] Step 201: Generate a random matrix, randomly generate a temporary matrix R for a given coordinate data set temp ∈R l ×d , where R represents the set of real numbers, l is the dimension of the hidden layer, d is the dimension of the coordinate, and the elements are independently sampled from the standard normal distribution ;

[0014] Step 202: Generate an orthogonal input weight matrix W in by performing QR matrix decomposition on R temp , obtaining:

[0015] Rtemp = Q orth R tri

[0016] where Q orth ∈R l×d is an orthogonal matrix, the column vectors q1, q2,..., q orth of Q d satisfy R tri ∈R l×d is an upper triangular matrix, the elements r tri of R i，j are r i is the i-th column of R temp ; take the transpose matrix orth of the orthogonal matrix Q ：，i to construct an input weight matrix with dimension d x l:

[0017]

[0018] Step 203: generate a random bias vector, the elements are sampled from the standard normal distribution .

[0019] Further, the specific steps of step 2 of adaptively determining the hidden layer dimension are:

[0020] Step 204: according to the standardized coordinate matrix X, calculate the complexity of the input coordinate data, and the variance of each coordinate dimension is:

[0021]

[0022] In the above formula, Var(X ：，i ) represents the variance of the i-th coordinate; X j，i represents the element in the j-th row and the i-th column of the matrix X; u i is the mean of the i-th coordinate;

[0023] Step 205: use the total variance to represent the complexity of the feature space, and the expression of the total variance is:

[0024]

[0025] Step 206: calculate the hidden layer dimension L dyn according to the input feature variance:

[0026]

[0027] In the above formula, C is a constant term; λ is a variance scaling factor; l max and l minwhere clip(x, a, b) = max(a, min(x, b)) is a clipping function.

[0028] Further, the specific steps of generating the hidden layer output of step 3 are:

[0029] Step 301: Network architecture design, the model structure is divided into input layer, hidden layer and output layer three main parts; the input layer is set to a dimension of 3, used to receive the normalized coordinate data, the hidden layer output is nonlinearly transformed by the activation function to generate high-dimensional feature representation; the output layer is set to a dimension of 2, directly outputting the calculated coordinate value;

[0030] Step 302: Calculate the linear relationship between the hidden layer output matrix H and the target value matrix y, and construct the output weight matrix W out The solution form is:

[0031]

[0032] Where, a is the regularization parameter; argmin() is the optimization operator; ||·||F represents the Frobenius norm; F

[0033] The analytical solution of the regularized least squares is:

[0034] W out = (H T H+ aI) -1 H T y

[0035] Where, W out is the output weight matrix; H is the hidden layer output matrix; H T is the transpose matrix of H; a is the regularization parameter; I is the identity matrix; (·) -1 is the matrix inverse operator; y is the target value matrix.

[0036] Step 303: Calculate H T H and H T y in batches, divide the data set into several batches, calculate and for each batch, and accumulate the results of all batches N is the total number of batches.

[0037] Step 304: Calculate the hidden layer output covariance matrix and add the regularization term A = H T ​H+αI, when the matrix is positive definite, use linear equation solving based on Cholesky decomposition; when the matrix is non-positive definite but is a square matrix, use linear equation solving based on LU decomposition; when the matrix is ill-conditioned, use SVD pseudo-inverse as a degenerate strategy:

[0038] W out = V∑ -1 U T H T y

[0039] where V is a right singular vector matrix, satisfying V T V = I;∑ -1 is a diagonal matrix, whose diagonal elements are: σ i is a singular value, ∈ is a set threshold value, used to filter small singular values; U is a left singular vector matrix, satisfying U T U = I;

[0040] Step 305: Construct the output of the remote sensing image geometric positioning model, use the model to predict the data:

[0041]

[0042] where, is the m-dimensional prediction output value of the i-th sample; i is the sample index; m is the output data dimension; j is the hidden layer index; l is the hidden layer dimension; is the hidden layer neuron accumulation; is the activation function; k is the input data dimension index; d is the coordinate dimension; X i,k is the k-dimensional coordinate value of the i-th sample; W in,k,j is the weight of the k-dimensional input coordinate and the j-th neuron; b hid,j is the bias vector of the j-th hidden layer neuron; W out,j,m is the weight of the j-th hidden layer neuron and the m-dimensional output.

[0043] Step 306: Evaluate the indicators, calculate the root mean square error RMSE, the mean absolute error MAE and the determination coefficient R 2 to quantify the accuracy and reliability of the model output, the formula is:

[0044]

[0045] Further, the specific steps of step 4 are:

[0046] Step 401: Data division, use KFold method to randomly divide the data into K subsets;

[0047] Step 402: Model retraining, select one of the subsets as the validation set each time, the rest as the training set, repeat the model training process, and record the evaluation index each time;

[0048] Step 403: Index statistics, statistics of each fold RMSE, MAE, R 2 , training time and condition number, the mean and standard deviation, evaluate the model stability;

[0049] Step 404: Optimal regularization parameter search, search for the optimal α in the logarithmic space, execute cross-validation for each α value by traversing the preset α range, minimize the prediction error of the model on the validation set, the formula is:

[0050]

[0051] Step 405: After determining the optimal hyperparameter α through the foregoing optimization process, retrain the model, save the key model parameters after training, including hidden layer dimension, regularization parameter, input weight, bias and output weight; These parameters are combined with other related model configurations to save as a unified model file, which is convenient for subsequent loading and application.

[0052] Further, the lightweight remote sensing image geometric positioning system comprises:

[0053] A data acquisition module is configured to acquire remote sensing image data and corresponding coordinate information.

[0054] A data preprocessing module is configured to perform preliminary processing on the collected remote sensing image data and standardize the remote sensing image data.

[0055] A data training module is configured to perform a model training process, calculate the hidden layer output according to the preprocessed data set, and optimize the weight output layer.

[0056] An inference module is configured to use pre-trained model weights to realize fast coordinate prediction for new input data.

[0057] A result processing and output module is configured to perform inverse standardization and format conversion on the inference results, and output them in a suitable format for user or other system calls.

[0058] Further, the lightweight remote sensing image geometric positioning device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to realize the lightweight remote sensing image geometric positioning method.

[0059] The present application has the beneficial effects that: the present application discloses a lightweight remote sensing image geometric positioning method, system and device, mainly solves the problems of calculation complexity and precision in remote sensing image positioning; the present application obtains remote sensing images and creates a coordinate data set, generates an input weight matrix and a random bias vector by using orthogonal random projection, adaptively determines the dimension of the hidden layer, generates the hidden layer output, and optimizes the output weight by using the regularization least square method; the present application also introduces a cross-validation mechanism to optimize the regularization parameter and improve the generalization ability of the model; by this method, the present application improves the training speed and inference efficiency of remote sensing image coordinate prediction, can effectively process large-scale data, and is suitable for real-time and resource-limited remote sensing scenes. At the same time, the present application maintains good prediction accuracy and stability on the basis of efficient operation, adapts to various complex data distributions, realizes accurate and reliable coordinate calculation, and has good practical application value. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 It is a lightweight remote sensing image geometric positioning method overall step flow chart;

[0061] Figure 2 It is a network basic structure schematic diagram;

[0062] Figure 3 It is a lightweight remote sensing image geometric positioning system schematic diagram;

[0063] Figure 4 It is a lightweight remote sensing image geometric positioning device schematic diagram. DETAILED DESCRIPTION

[0064] In the present embodiment, the present application includes a lightweight remote sensing image geometric positioning method, system and device.

[0065] As shown in Figure 1 , the specific process of the lightweight remote sensing image geometric positioning method of the present embodiment is as follows:

[0066] S1. Obtain remote sensing images and create a coordinate data set;

[0067] S2. Initialize the parameters of the remote sensing image geometric positioning model, generate the input weight matrix by using orthogonal random projection, generate the random bias vector, and adaptively determine the dimension of the hidden layer according to the statistical characteristics of the input feature data;

[0068] S3. Train the remote sensing image geometric positioning model according to the coordinate data set, generate the hidden layer output by nonlinear feature mapping, and construct the output weight matrix according to the regularization least square method combined with the multi-level solving strategy;

[0069] S4. Evaluate the model performance according to the cross-validation division, retrain the model after optimizing the regularization parameter, and save all key parameters of the final model as a unified standardized file format;

[0070] S5. Based on the trained model parameters, input the test data into the trained remote sensing image geometric positioning model to perform regression calculation, the model outputs the predicted coordinate data, which is compared with the coordinate calculated by the satellite sensor model, and the running time of the lightweight remote sensing image geometric positioning model and the satellite sensor model on the test data is recorded to verify the efficiency and accuracy of the model.

[0071] The more specific process of the embodiment is:

[0072] S1. Obtain remote sensing images and create coordinate data sets, which are calculated by satellite sensor models to calculate virtual grid point space three-dimensional coordinates, create data sets containing image pixel coordinates and object space coordinates, and normalize the remote sensing image coordinate data; the specific steps are:

[0073] S101. Determine the width and height values of the image, uniformly divide the grid points at certain intervals to form a two-dimensional plane grid;

[0074] S102. Set several discrete height layers in the height direction according to the height range;

[0075] S103. Use the satellite sensor model to project the two-dimensional plane coordinates of the grid points to the ground space to obtain the corresponding relationship between the geographic coordinates and image coordinates of each grid point, and obtain the coordinate data set;

[0076] S104. Normalize the coordinate data, the formula is:

[0077]

[0078] Where X is the normalized coordinate value; data is the coordinate data; data0 is the translation parameter; n is the number of coordinate points; data s is the scale parameter; data max is the maximum value of the coordinate data; data min is the minimum value of the coordinate data;

[0079] S105. Generate a standardized coordinate matrix X∈R n×d , where n is the number of coordinate points, d is the dimension of the coordinate, d = 3 represents the dimension containing longitude, latitude and height, and the training and test data sets are constructed;

[0080] S2. Initialize the parameters of the geometric positioning model of remote sensing image, generate input weight matrix by orthogonal random projection, generate random bias vector, and adaptively determine the dimension of hidden layer according to the statistical characteristics of input feature data.

[0081] The specific steps of initializing input weight and bias are as follows:

[0082] S201. Generate a random matrix. Randomly generate a temporary matrix R for a given coordinate data set temp ∈R l×d , where R represents the set of real numbers, l is the dimension of the hidden layer, d is the dimension of the coordinates, and the elements are independently sampled from the standard normal distribution .

[0083] S202. Generate an orthogonal input weight matrix W in by QR decomposition method. Perform QR matrix decomposition on R temp to obtain:

[0084] R temp = Q orth R tri

[0085] where Q orth ∈R l×d is an orthogonal matrix, and the column vectors q1, q2,..., q orth of Q d satisfy R tri ∈R l×d is an upper triangular matrix, and the elements r tri of R i，j are r i is the i-th column of R temp .

[0086] Take the transpose matrix orth of the orthogonal matrix Q to construct an input weight matrix with dimension d x l:

[0087]

[0088] S203. Bias initialization. Generate a random bias vector, and the elements are sampled from the standard normal distribution N(0, 1).

[0089] The specific steps of adaptively determining the dimension of the hidden layer are as follows:

[0090] S204. According to the standardized coordinate matrix X, calculate the complexity of the input coordinate data. The variance of each coordinate dimension is:

[0091]

[0092] In the above formula, Var(X ：，i ) represents the variance of the i-th coordinate; X j，i represents the element in the j-th row and i-th column of matrix X; u i is the mean of the i-th coordinate;

[0093] S205. The total variance is used to represent the complexity of the feature space, and the expression of the total variance is:

[0094]

[0095] S206. The hidden layer dimension L dyn is calculated according to the input feature variance:

[0096]

[0097] In the above formula, C is a constant term; λ is a variance scaling factor; l max and l min are the upper and lower limits of the number of neurons; clip(x, a, b) = max(a, min(x, b)) is a clipping function.

[0098] S207. Determine whether the hidden layer dimension is specified. If the hidden layer dimension is not specified (i.e., the specified value is empty), use the dimension l dyn calculated according to the input data features; if the preset dimension value is provided, directly use the specified value as the hidden layer dimension. In a resource-limited environment, a lightweight model that adapts to the current hardware conditions can be quickly generated.

[0099] In the initialization stage, the pre-compiled Numba function is also used to accelerate inference. In the model initialization stage, the core calculation steps are pre-compiled, and the hidden layer output and prediction results can be quickly generated in the prediction process.

[0100] S3. Train the remote sensing image geometric positioning model according to the coordinate data set, generate the hidden layer output through nonlinear feature mapping, and construct the output weight matrix according to the regularized least squares method combined with a multi-level solving strategy.

[0101] The specific steps are as follows:

[0102] S301. Network architecture design. As shown in Figure 2 , a single hidden layer feedforward neural network architecture is used, and the model structure is divided into three main parts: input layer, hidden layer and output layer. The input layer is set to a dimension of 3 to receive normalized coordinate data, the hidden layer output is nonlinearly transformed by an activation function to generate a high-dimensional feature representation. The output layer is set to a dimension of 2 to directly output the calculated coordinate values.

[0103] S302. Calculate the linear relationship between the hidden layer output matrix H and the target value matrix y, and construct the output weight matrix W. out The solution form is as follows:

[0104]

[0105] Where α is the regularization parameter; arg min() is the optimization operator; ||·|| F This represents the Frobenius norm.

[0106] The analytical solution for regularized least squares is:

[0107] W out =(H T H+αI) -1 H T y

[0108] Among them, W out H is the output weight matrix; H is the hidden layer output matrix; H T Let H be the transpose of H; α be the regularization parameter; I be the identity matrix; (·) -1 The operator for finding the inverse of a matrix is ​​given; y is the target matrix.

[0109] S303. Calculate H in batches. T H and H T y divides the dataset into several batches, and calculates for each batch. and Sum the results of all batches N represents the total number of batches.

[0110] S304. Calculate the hidden layer output covariance matrix after adding a regularization term: A = H T For H+αI, when the matrix is ​​positive definite, a linear equation based on Cholesky decomposition is used to solve it; when the matrix is ​​non-positive definite but an symmetrical matrix, a linear equation based on LU decomposition is used to solve it; when the matrix is ​​ill-conditioned, the SVD pseudo-inverse is used as a degenerate strategy.

[0111] W out =V∑ -1 U T H T y

[0112] Where V is a right singular vector matrix, satisfying V T V = I; ∑ -1 It is a diagonal matrix, and its diagonal elements are: σ i Here, ∈ represents the singular values, and ∈ is a set threshold used to filter out excessively small singular values; U is the left singular vector matrix, satisfying U T U = I.

[0113] S305. The output of the remote sensing image geometric positioning model is constructed, and the model is used to predict data:

[0114]

[0115] wherein, is the mthdimensional prediction output value of the ithsample; i is the sample index; m is the output data dimension; j is the hidden layer index; and l is the hidden layer dimension; is the hidden layer neuron accumulation; is the activation function; k is the input data dimension index; d is the coordinate dimension; X i,k is the kthdimensional coordinate value of the ithsample; W in,k,j is the weight of the kthinput coordinate and the jthneuron; b hid,j is the bias vector of the jthhidden layer neuron; W out,j,m is the weight of the jthhidden layer neuron and the mthoutput.

[0116] S306. Evaluation index. The root mean square error RMSE, the mean absolute error MAE and the determination coefficient R 2 are calculated to quantify the accuracy and reliability of the model output, and the formula is:

[0117]

[0118] S4. The model performance is evaluated according to cross-validation, the model is retrained after optimization of the regularization parameter, and all key parameters of the final model are saved as a unified standardized file format. The cross-validation and model optimization use K-fold cross-validation to improve the generalization ability of the model and determine the optimal regularization parameter a.

[0119] The specific steps are:

[0120] S401. Data division. The data is randomly divided into K subsets using the KFold method, wherein the KFold method is a cross-validation (Cross-Validation) technique commonly used in machine learning and model evaluation, which is used to divide the data set into K mutually exclusive subsets (called “folds”, Fold), and through multiple rounds of training and validation, the model performance is more stably evaluated;

[0121] S402. Model retraining. Each time one of the subsets is selected as the validation set, the rest is used as the training set, the model training process is repeated, and the evaluation index of each time is recorded.

[0122] S403. Index statistics. The mean and standard deviation of the RMSE, MAE, R 2 , training time and condition number of each fold are calculated to evaluate the stability of the model.

[0123] S404. Optimal regularization parameter search. Search for the optimal a in the logarithmic space by traversing the preset a range, perform cross-validation for each a value, minimize the prediction error of the model on the validation set, formula is:

[0124]

[0125] Select the a that minimizes the RMSE based on the cross-validation result as the hyperparameter of the final model.

[0126] S405. After determining the optimal hyperparameter a through the foregoing optimization process, retrain the model, save the key model parameters after training, including the hidden layer dimension, regularization parameter, input weight, bias and output weight. These parameters are combined with other related model configurations to save as a unified model file, facilitating subsequent loading and application.

[0127] S5. Based on the model parameters after training, input the test data into the trained remote sensing image geometric positioning model to perform regression calculation, the model outputs the predicted coordinate data, which is compared with the coordinate calculated by the satellite sensor model, and the running time of the lightweight remote sensing image geometric positioning model and the satellite sensor model on the test data is recorded, verifying the efficiency and accuracy of the model.

[0128] Experiment 1

[0129] To verify the fitting accuracy of the method proposed in the present application, five remote sensing images from two satellites were selected as test data. By calculating the fitting accuracy of the method in the present application in the X direction, Y direction and in the plane on the test data set, the root mean square error (RMSE) and the maximum error (MAX) were used as evaluation indicators to reflect the positioning accuracy and error distribution characteristics of the present application. The results are shown in Table 1.

[0130] Table 1 Fitting accuracy of the present application (unit: pixel)

[0131]

[0132] From the experimental results, it can be seen that the lightweight remote sensing image geometric positioning method proposed in the present application has high fitting accuracy. In all test images, the RMSE is kept at the 10 -4 level, the MAE is kept at the 10 -3 level, meeting the measurement requirements, verifying the effectiveness of the present application.

[0133] Experiment 2

[0134] To evaluate the advantages of the present application in terms of computational efficiency, a comparison experiment of operation time of the present application method and rational function model in different computing modes is designed. Two scenes of satellite images are selected, and the operation time is tested under the data volume of 100,000, 500,000 and 1,000,000 respectively. The time required for completion is counted by processing each point in the to-be-calculated point in a point-by-point loop. At the same time, the data normalization and reverse normalization process in the present application method are included in the overall time statistics range. The results are shown in Table 2.

[0135] Table 2: Comparison of prediction time (unit: seconds)

[0136]

[0137]

[0138] From the experimental results, it can be seen that the present application method has a faster reasoning speed. The present application shows stable and efficient operation performance in both computing modes, and the time consumption is better than that of the rational function model. In the orthographic projection calculation, the time consumption of the rational function model increases approximately linearly with the increase of data volume, and in the inverse projection calculation, the time consumption increases significantly due to the iterative calculation of the rational function model. The above experimental results reflect the advantages of the present application in operation efficiency.

[0139] In summary, the present application not only maintains the prediction accuracy, but also realizes faster calculation efficiency. The technical feasibility of the present application is verified.

[0140] As shown in Figure 3 , the embodiment further provides a lightweight remote sensing image geometric positioning system, which comprises a data acquisition module, a data preprocessing module, a data training module, an inference module and a result processing and output module, wherein:

[0141] The data acquisition module is used to acquire remote sensing image data and its corresponding coordinate information.

[0142] The data preprocessing module is used to preliminarily process the acquired remote sensing image data, and standardize the remote sensing image data.

[0143] The data training module is used to execute the training process of the model, calculate the hidden layer output according to the preprocessed data set, and optimize the weight output layer.

[0144] The inference module is used to use the pre-trained model weight to realize fast coordinate prediction of new input data.

[0145] The result processing and output module is used to perform reverse standardization and format conversion on the inference result, and output in a suitable format for user or other system calling.

[0146] As shown in Figure 4As shown, this embodiment further provides a lightweight remote sensing image geometric positioning device. The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the lightweight remote sensing image geometric positioning method described above.

[0147] In summary, this invention successfully solves the following two problems:

[0148] (1) Back projection calculation of rational function models requires iterative solution and has a convergence delay. However, the method of this invention shows stable and efficient computational performance in both forward and back projection calculation modes.

[0149] (2) Existing neural network models are typically complex in structure and have redundant parameters, resulting in low training and inference efficiency, making them unsuitable for real-time geometric localization calculations. An effective balance needs to be achieved between model complexity, computational efficiency, and accuracy. The method of this invention achieves relatively fast computational efficiency while maintaining prediction accuracy.

[0150] Although the embodiments of the present invention are described with reference to actual solutions, they do not constitute a limitation on the meaning of the present invention. Modifications to the embodiments and combinations with other solutions based on this specification will be obvious to those skilled in the art.

Claims

1. A lightweight remote sensing image geometric positioning method, characterized in that, It includes the following steps: Step 1: Acquire remote sensing imagery and create a coordinate dataset; Step 2: Initialize the parameters of the remote sensing image geometric positioning model, generate the input weight matrix using orthogonal random projection, generate a random bias vector, and adaptively determine the hidden layer dimension based on the statistical characteristics of the input feature data; Step 3: Train a geometric localization model for remote sensing images based on the coordinate dataset, generate hidden layer output through nonlinear feature mapping, and construct the output weight matrix based on regularized least squares method combined with multi-level solution strategy; Step 4: Evaluate model performance based on cross-validation, optimize regularization parameters, retrain the model, and save all key parameters of the final model in a unified standardized file format. Step 5: Based on the trained model parameters, input the test data into the trained remote sensing image geometric positioning model to perform regression calculation. The model outputs the predicted coordinate data, which is compared with the coordinates calculated by the satellite sensor model. The running time of the lightweight remote sensing image geometric positioning model and the satellite sensor model on the test data is recorded to verify the efficiency and accuracy of the model.

2. The lightweight remote sensing image geometric positioning method according to claim 1, characterized in that: The step 1 of acquiring remote sensing images and creating a coordinate dataset involves using a satellite sensor model to calculate the three-dimensional coordinates of virtual grid points, creating a dataset containing image pixel coordinates and object space coordinates, and then normalizing the remote sensing image coordinate data.

3. The lightweight remote sensing image geometric positioning method according to claim 1, characterized in that: The specific steps for generating the input weight matrix and the random bias vector using orthogonal random projection in step 2 are as follows: Step 201: Generate a random matrix. For the given coordinate dataset, randomly generate a temporary matrix R. temp ∈R l×d Where R represents the set of real numbers, l is the dimension of the hidden layer, and d is the dimension of the coordinates, whose elements follow a standard normal distribution. Independent sampling in the middle; Step 202: Generate the orthogonalized input weight matrix W using the QR decomposition method. in , for R temp Performing QR matrix decomposition yields: R temp =Q orth R tri Q orth ∈R l×d Q is an orthogonal matrix. orth The column vectors q1, q2, ..., q d satisfy R tri ∈R l×d It is an upper triangular matrix. xtri element r i，j for r i It is R temp The i-th column; take the orthogonal matrix Q orth transpose matrix Construct an input weight matrix of dimension d×l: Step 203: Generate a random bias vector, with elements following a standard normal distribution. Sampling.

4. The lightweight remote sensing image geometric positioning method according to claim 1, characterized in that: The specific steps for adaptively determining the hidden layer dimension in step 2 are as follows: Step 204: Based on the standardized coordinate matrix X, calculate the complexity of the input coordinate data. The variance of each coordinate dimension is: In the above formula, Var(X) :,i ) represents the variance of the i-th dimension coordinate; X j，i This represents the element in the j-th row and i-th column of matrix X; u i Let be the mean of the i-th dimension coordinates; Step 205: Use the total variance to characterize the feature space complexity. The expression for the total variance is: Step 206: Calculate the hidden layer dimension L based on the input feature variance. dyn : In the above formula, C is a constant term; λ is the variance scaling factor; l max and l min The upper and lower limits are the number of neurons; clip(x,a,b)=max(a,min(x,b)) is the cutoff function.

5. The lightweight remote sensing image geometric positioning method according to claim 1, characterized in that: The specific steps for generating the hidden layer output in step 3 are as follows: Step 301: Network architecture design. The model structure is divided into three main parts: input layer, hidden layer, and output layer. The input layer is set to have a dimension of 3 to receive the normalized coordinate data. The output of the hidden layer performs a non-linear transformation on the input data through an activation function to generate a high-dimensional feature representation. The output layer is set to have a dimension of 2 and directly outputs the calculated coordinate values. Step 302: Calculate the linear relationship between the hidden layer output matrix H and the target value matrix y, and construct the output weight matrix W. out The solution form is as follows: Where α is the regularization parameter; arg min() is the optimization operator; ||·|| F Denotes the Frobenius norm; The analytical solution for regularized least squares is: W out =(H T H+αI) -1 H T y Among them, W out H is the output weight matrix; H is the hidden layer output matrix; H T Let H be the transpose of H; α be the regularization parameter; I be the identity matrix; (·) -1 The operator for finding the inverse of a matrix is ​​given; y is the target matrix. Step 303: Calculate H in batches T H and H T y divides the dataset into several batches, and calculates for each batch. and Sum the results of all batches N is the total number of batches; Step 304: Calculate the hidden layer output covariance matrix with the regularization term added, resulting in A = H. T For H+αI, when the matrix is ​​positive definite, a linear equation based on Cholesky decomposition is used to solve it; when the matrix is ​​non-positive definite but an symmetrical matrix, a linear equation based on LU decomposition is used to solve it; when the matrix is ​​ill-conditioned, the SVD pseudo-inverse is used as a degenerate strategy. W out =V∑ -1 U T H T y Where V is a right singular vector matrix, satisfying V T V = I; ∑ -1 It is a diagonal matrix, and its diagonal elements are: σ i Here, ∈ represents the singular values, and ∈ is a set threshold used to filter out excessively small singular values; U is the left singular vector matrix, satisfying U T U = I; Step 305: Construct the output of the geometric positioning model of the remote sensing image, and use the model to make predictions on the data: in, Let be the predicted output value of the m-th dimension of the i-th sample; i is the sample index; m is the output data dimension; j is the hidden layer index; l is the hidden layer dimension; This is for accumulating neurons in the hidden layer; is the activation function; k is the input data dimension index; d is the coordinate dimension; X i，k W represents the k-th dimension coordinate value of the i-th sample; in，k，j b represents the weights of the k-th dimension input coordinates and the j-th neuron. hid,j W is the bias vector of the j-th hidden layer neuron; out，j，m Let be the output weights of the j-th hidden layer neuron and the m-th dimension. Step 306: Evaluation metrics, calculate root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 The formula used to quantify the accuracy and reliability of the model output is:

6. The lightweight remote sensing image geometric positioning method according to claim 1, characterized in that: The specific steps of step 4 are as follows: Step 401: Data partitioning. Use the KFold method to randomly divide the data into K subsets; Step 402: Model retraining. Each time, select one subset as the validation set and the rest as the training set. Repeat the model training process and record the evaluation metrics each time. Step 403: Indicator statistics, calculate RMSE, MAE, and R for each discount. 2 The mean and standard deviation of training time and condition number are used to evaluate model stability. Step 404: Optimal Regularization Parameter Search. Search for the optimal α in the logarithmic space. By traversing a preset range of α, perform cross-validation for each α value to minimize the model's prediction error on the validation set. The formula is: Step 405: After determining the optimal hyperparameter α through the aforementioned optimization process, retrain the model. After training is completed, save the key model parameters, including hidden layer dimension, regularization parameter, input weight, bias and output weight. These parameters, along with other relevant model configurations, are combined and saved into a single model file for easy loading and application later.

7. A lightweight remote sensing image geometric positioning system, characterized in that, The system includes: The data acquisition module is used to acquire remote sensing image data and its corresponding coordinate information; The data preprocessing module is used to perform preliminary processing on the acquired remote sensing image data and standardize the remote sensing image data; The data training module is used to execute the model training process, calculate the hidden layer output based on the preprocessed dataset, and optimize the weight output layer. The inference module is used to quickly predict the coordinates of new input data using pre-trained model weights. The results processing and output module is used to de-standardize and convert the inference results, and output them in a suitable format for use by users or other systems.

8. A lightweight remote sensing image geometric positioning device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a lightweight remote sensing image geometric positioning method according to any one of claims 1 to 6.

Images