A non-analytical model-based remote sensing image three-dimensional coordinate solving method

Abstract

The application discloses a kind of methods simple and effective, can reach higher rendezvous precision and faster speed of solution non-analytical model-based remote sensing image three-dimensional coordinate solution method.This application includes the following steps: step 1: the object space positioning model of left and right image is given, and the elevation value and threshold parameter are initialized;Step 2: calculate the object space coordinates under the current elevation value, evaluate the Euclidean distance of the left and right image both solution coordinates as error index, approximate calculation gradient using central difference method, analyze the trend of error with elevation;Step 3: based on gradient information along the error reduction direction adjustment elevation, gradually reduce error index, and combine with the backtracking line search strategy with Armijo condition dynamic adjustment learning rate, using dynamic optimal solution recorder maintains global optimal solution;Step 4: when meeting the preset convergence condition or learning rate is exhausted, stop iteration, output optimal elevation and latitude and longitude coordinate value.The application is applied to the technical field of photogrammetry.

Description

Technical Field

[0001] This invention applies to the technical field of photogrammetry, and particularly relates to a method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model. Background Technology

[0002] Geometric positioning models for remote sensing images achieve spatial information calculation by establishing a mapping relationship between the image-side coordinate system and the object-side spatial coordinate system. Existing methods utilize neural networks to fit geometric positioning models. Deep neural networks construct a high-dimensional feature space through a multi-layered nonlinear mapping structure, exhibiting strong data fitting capabilities and enabling coordinate calculation of remote sensing images. This can provide geometric positioning accuracy comparable to rational function models. This particular method employs an end-to-end learning strategy, establishing a nonlinear mapping relationship between image-side and object-side coordinates through implicit representation, effectively preserving satellite sensor information.

[0003] In satellite remote sensing imagery, rational function models are commonly used for spatial positioning calculations. These models, derived analytically, construct and normalize the corresponding error equations to solve for ground point coordinates. However, neural network positioning models typically struggle to construct a rigorous system of error equations like rational function models, hindering the subsequent determination of the 3D coordinates of ground points. Neural network positioning models primarily focus on coordinate positioning from a single image; they cannot construct an effective joint solution mathematical model for situations requiring the joint determination of target 3D spatial coordinates from two images. Using regression training on the object's 3D coordinates not only increases system complexity but also further complicates the application of neural network positioning models.

[0004] Therefore, it is necessary to propose a three-dimensional coordinate calculation method that can overcome the limitations of its mathematical expression and joint solution while retaining the advantages of neural networks, and realize the accurate calculation of the three-dimensional coordinates of the target point based on the neural network localization model. Summary of the Invention

[0005] This invention addresses the problem that existing neural network localization models cannot create mathematical models for joint solution of two images and lack the ability to accurately calculate the three-dimensional spatial coordinates of the target. It provides a method for calculating the three-dimensional coordinates of remote sensing images based on a non-analytical model.

[0006] The technical solution adopted in this invention is as follows: This invention includes the following steps:

[0007] Step 1: Given the object space localization model of the left and right images, i.e. the corresponding neural network localization model, and initialize the elevation values ​​and related threshold parameters, construct a dynamic optimal solution recorder to record the optimal solution in the optimization process;

[0008] Step 2: Calculate the object space coordinates under the current elevation value. The Euclidean distance between the calculated coordinates of the left and right images is used as an error index. The gradient is approximated by the central difference method. The trend of error variation with elevation is analyzed.

[0009] Step 3: Based on gradient information, adjust the elevation value along the direction of error reduction to gradually reduce the error index. Combine the backtracking search strategy with Armijo conditions to dynamically adjust the learning rate and optimize the adjustment process. Update and maintain the global optimal solution through the dynamic optimal solution recorder.

[0010] Step 4: Stop iterating when the preset convergence condition is met or the learning rate is exhausted, and output the optimal elevation and latitude / longitude coordinates as the three-dimensional spatial coordinates of the target point.

[0011] Furthermore, the relevant threshold parameters in step 1 include the error threshold, gradient convergence threshold, number of iterations, and learning rate, which are used to control the convergence and stability of the optimization process; the dynamic optimal solution recorder is constructed to record the minimum error value and the corresponding elevation and latitude / longitude coordinates during the iteration process, ensuring that the record is updated if the current error is less than the recorded value during each iteration.

[0012] Furthermore, the method for obtaining the initial elevation value in step 1 is as follows:

[0013] If there is rough DEM data in the experimental area, the elevation values ​​of the pixels are extracted from the DEM data as the initial values ​​using the method based on digital elevation model data.

[0014] If DEM data is unavailable, the method based on image elevation offset is used, by calculating the elevation offset value HEIGHT_OFF of the left image. L Elevation offset value HEIGHT_OFF of the right image R The average value is used as the initial elevation. The formula for this calculation is:

[0015] elevation (0) =(HEIGHT_OFF) L +HEIGHT_OFF R ) / 2.

[0016] Furthermore, the calculation of the object space coordinates under the current elevation value in step 2 includes: inputting the pixel coordinates of corresponding image points and the current elevation value for the left and right images respectively; calculating the corresponding object space latitude and longitude coordinates through the object space positioning model; calculating the two-dimensional Euclidean distance between the latitude and longitude coordinates obtained from the left and right images as an error index for subsequent optimization; if the error index is less than a preset threshold and less than the previously recorded minimum value, then updating the dynamic best solution recorder to store the current elevation value and corresponding coordinates.

[0017] Furthermore, the gradient calculation in step 2 employs the central difference method with a configurable step size, and the calculation formula is as follows:

[0018]

[0019] in, e is the gradient value; (k) This is the current elevation value; and Δ is the Euclidean distance error; Δ is the difference step size; the gradient is used to represent the trend of error change with elevation; the elevation adjustment direction is determined by the gradient to ensure that subsequent adjustments are made in the direction of error reduction; the gradient value is recorded for convergence judgment in subsequent iterative optimization processes.

[0020] Furthermore, the elevation adjustment in step 3 is performed iteratively using the gradient descent method, as follows: Calculate the current elevation e. (k) gradient value Use a learning rate α (k) Control the adjustment range; utilize the learning rate α (k) The elevation is updated to ensure that the error decreases monotonically with each iteration. The calculation formula is as follows:

[0021]

[0022] Furthermore, the backtracking search with Armijo conditions in step 3, which dynamically adjusts the learning rate, is an optimization strategy that combines gradient descent and adaptive step size control. Gradient descent provides a local convergence direction, and the learning rate is gradually reduced to ensure that the error function value is strictly reduced after each iteration. If the updated error does not meet the Armijo conditions, the learning rate is reduced by a certain proportion and recalculated until the error meets the reduction requirements.

[0023] Furthermore, the dynamic optimal solution recorder in step 3 evaluates whether the current error meets the threshold condition at each iteration, and updates the stored data only when the new error value is less than the recorded optimal value. The stored data includes the elevation value, the error value and the corresponding latitude and longitude coordinates. When the optimization terminates, it outputs the set of all optimal solutions that meet the threshold condition.

[0024] Furthermore, the preset convergence condition and learning rate exhaustion in step 4 are used to determine whether to terminate the calculation after each iteration. For the gradient, its absolute value is calculated and compared with a preset gradient convergence threshold. If the absolute value of the gradient is less than the gradient convergence threshold, it is considered that the optimization process has approached the extreme point, and the iteration stops. For the learning rate, if the learning rate continuously decreases during the adjustment process and eventually falls below the preset learning rate, the iteration stops. The rationality of terminating the optimization process is ensured through these dual conditions.

[0025] The beneficial effects of this invention are as follows: 1. This invention targets the spatial positioning model of left and right image objects. By using a dynamic optimal solution recorder combined with gradient descent and backtracking search dynamic learning rate adjustment mechanisms, and iteratively optimizing elevation values, it achieves the 3D intersection coordinate solution of the neural network positioning model in spatial positioning. The method is simple and effective, achieving high intersection accuracy and fast solution speed; 2. The 3D coordinate solution method proposed in this invention has strong versatility. It can not only be applied to the 3D coordinate solution of conventional rational function models, but also extended to the intersection coordinate solution problem of other models that cannot be explicitly expressed analytically. It is also suitable for complex terrain areas lacking accurate terrain data, providing reliable technical support for remote sensing image processing and geographic information system applications. Attached Figure Description

[0026] Figure 1 This is a flowchart of the present invention;

[0027] Figure 2 This is a flowchart of a specific embodiment of the present invention. Detailed Implementation

[0028] like Figure 1 As shown, in this embodiment, the present invention includes the following steps:

[0029] Step 1: Given the object space localization model of the left and right images, i.e. the corresponding neural network localization model, and initialize the elevation values ​​and related threshold parameters, construct a dynamic optimal solution recorder to record the optimal solution in the optimization process;

[0030] Step 2: Calculate the object space coordinates under the current elevation value. The Euclidean distance between the calculated coordinates of the left and right images is used as an error index. The gradient is approximated by the central difference method. The trend of error variation with elevation is analyzed.

[0031] Step 3: Based on gradient information, adjust the elevation value along the direction of error reduction to gradually reduce the error index. Combine the backtracking search strategy with Armijo conditions to dynamically adjust the learning rate and optimize the adjustment process. Update and maintain the global optimal solution through the dynamic optimal solution recorder.

[0032] Step 4: Stop iterating when the preset convergence condition is met or the learning rate is exhausted, and output the optimal elevation and latitude / longitude coordinates as the three-dimensional spatial coordinates of the target point.

[0033] In this embodiment, the following is in conjunction with the appendix Figure 2 To further describe, the specific implementation steps of the present invention are as follows:

[0034] S1. Initialization Phase: Given the object space localization model for the left and right images, i.e., the corresponding neural network model, the parameters that need to be set include: initial elevation value, error threshold τ, gradient convergence threshold, number of iterations k, and learning rate α. (0) Construct a dynamic optimal solution recorder in e represents the minimum error value during the iteration process. fin x represents the corresponding elevation value. fin For the corresponding latitude and longitude coordinates, in each iteration, if the current error meets the threshold and is smaller, then the record is updated.

[0035] S2. Determination of initial elevation value: There are two ways to obtain the initial elevation value.

[0036] 1) Based on digital elevation model data. If coarse DEM data exists for the experimental area, the elevation values ​​corresponding to the pixels are extracted from the DEM as initial values.

[0037] 2) Based on image elevation offset. If DEM data is unavailable, the elevation offset value HEIGHT_OFF from the left image is used. L Elevation offset value HEIGHT_OFF of the right image R The average value is used as the initial elevation. The formula for this calculation is:

[0038] elevation (0) =(HEIGHT_OFF) L +HEIGHT_OFF R ) / 2

[0039] After initialization is complete, the iterative optimization phase begins.

[0040] S3. Error Calculation: First, calculate the object space coordinates corresponding to the current elevation value, using the neural network localization model NN based on the left and right images. L and NN R Perform spatial coordinate calculation, inputting the pixel coordinates of corresponding image points (l) L s L ) and (l R s R ), and combined with the current elevation parameter e (k) The object space positioning model outputs the corresponding object space latitude and longitude coordinates x and y respectively. L and x R ,Right now

[0041] NN L (l L s L e (k) )→(x L ), NNR (l R s R e (k) )→(x R )

[0042] The two-dimensional Euclidean spatial distance between the latitude and longitude coordinates of the left and right images is calculated as the intersection error index, also known as the error measure.

[0043] S4. If the error at the current elevation during iteration is less than the set threshold. And less than the previously recorded minimum value Then update the best decoder. Save the current elevation as e fin The current error is saved as The latitude and longitude coordinates of the calculated model at the current elevation are then averaged to obtain the intersection latitude and longitude coordinate value x. fin .

[0044] S5. Perform gradient calculation: The gradient represents the trend of error change along the elevation direction to adjust the elevation value. The central difference method is used to calculate the error gradient, by adding a difference step size Δ before and after the elevation value to calculate the numerical derivative of the error. The truncation error of the central difference method is O(Δ). 2 This can reduce the impact of numerical differentiation error on the optimization process. The calculation formula is:

[0045]

[0046] S6. Gradient Descent: After obtaining the gradient information, the elevation value is iteratively adjusted using the gradient descent method to gradually reduce the error. The specific steps are as follows:

[0047] S61. Calculate the current elevation e (k) gradient value

[0048] S62. Use a learning rate α (k) Control the adjustment range;

[0049] S63. Using the learning rate α (k) The elevation is updated to ensure that the error decreases monotonically with each iteration. The iterative calculation formula is as follows:

[0050] S7. Dynamic Adjustment of Learning Rate: The choice of learning rate affects the optimization effect. An excessively large learning rate may cause the optimal point to be skipped, while an excessively small learning rate will affect the adjustment speed. This invention uses a backtracking search mechanism to dynamically adjust the learning rate, ensuring that the error is strictly reduced after each elevation update, and accelerating the convergence speed when conditions permit. The specific steps are as follows:

[0051] S71. Start with a large learning rate, calculate the new elevation and assess the error;

[0052] S72. If the new error is smaller than the current error, accept this elevation update and slightly increase the learning rate to accelerate subsequent convergence;

[0053] S73. If the new error does not decrease, reduce the learning rate, recalculate the new elevation value and check until a learning rate that reduces the error is found, or the learning rate is reduced to a minimum.

[0054] S8. The iterative process incorporates optimization strategies, including gradient descent direction, Armijo conditions, and convergence guarantees.

[0055] S81. Gradient descent direction. During optimization, the elevation follows the negative gradient direction. Update the parameters to ensure that the objective function gradually decreases in the local range.

[0056] S82. Armijo Condition. To ensure a strict reduction in error after each update, the Armijo condition is introduced in the backtracking search as a criterion for accepting the new elevation. The Armijo condition requires that the error at the new elevation is not only less than the current error, but also meets a certain reduction threshold. The formula is:

[0057]

[0058] Where c∈(0,1) is the relaxation coefficient, which controls the magnitude of the descent.

[0059] S83. Convergence Guarantee. When the error function satisfies certain conditions within its defined range, the algorithm guarantees that the generated error sequence is monotonically decreasing and tends to stabilize. Gradient of the error function. If an algorithm is convergent within its domain and satisfies Lipschitz continuity and has a lower bound, then the algorithm is convergent.

[0060] 1) Monotonic convergence. Guaranteed by the Armijo condition of backtracking search, the iterative sequence... Monotonic and non-increasing.

[0061] 2) Global convergence. When When Lipschitz continuity is satisfied (constant L), meaning the gradient change is not too drastic, the sequence {e} generated by the algorithm... (k)}satisfy:

[0062]

[0063] That is, it will converge to a steady point. These conditions ensure that the error will not decrease indefinitely, but will tend to a steady point.

[0064] S9. Iteration Termination Determination: Use dual termination conditions, including gradient convergence and learning rate exhaustion, to determine whether to stop iteration using two different criteria.

[0065] 1) Gradient convergence determination. After each iteration, it is determined whether the convergence condition is met. If the absolute value of the gradient is less than the gradient convergence threshold, it indicates that the trend of error change with elevation has become relatively flat. Further adjustment of elevation has very limited effect on improving the error. It is considered that the optimization process has approached the extreme point, and the iteration is stopped.

[0066] 2) Learning rate exhaustion determination. If the learning rate continuously decreases during the adjustment process and eventually falls below the preset learning rate, i.e., α... (k) <α (0) If the iteration stops, then stop.

[0067] S10. Optimal solution output: If the minimum error is less than the threshold Output optimal elevation e fin The intersection of latitude and longitude coordinates x fin .

[0068] S11. Termination Settings: Local extreme points are determined by the gradient magnitude threshold, limiting the maximum number of iterations and the minimum learning rate to prevent infinite iteration.

[0069] To further verify and illustrate the effectiveness of the non-analytical model-based three-dimensional coordinate calculation method for remote sensing images described in this invention, the performance of this invention is evaluated through experimental tests on multiple sets of satellite remote sensing image stereo pairs, in conjunction with specific embodiments. This study designed and conducted two experiments. The first experiment verified the accuracy of the stereo positioning three-dimensional coordinate calculation of this invention, and the second experiment compared the computational speed to verify the advantages of this invention in computational efficiency. The design and results of each experiment are described below.

[0070] Experiment 1

[0071] In this experiment, four pairs of satellite image stereo pairs were selected as test data, and corresponding points in the images were extracted for 3D stereo intersection coordinate calculation. The experiment utilized a neural network positioning model combined with the method proposed in this invention to calculate the 3D coordinates of the corresponding points. The neural network positioning model is a fit to the satellite sensor model, and the calculated 3D coordinates are compared and analyzed with those calculated by the satellite sensor model. The root mean square error (RMSE) in the x, y, and z directions of the check point is calculated to quantify the positioning accuracy of this invention. The results are shown in Table 1.

[0072] Table 1. Stereo intersection accuracy based on the non-analytical model of this invention (unit: meters)

[0073]

[0074] The experimental results show that the proposed 3D coordinate calculation method based on a non-analytical model can accurately obtain 3D coordinates in different stereo image pairs. Errors in the x, y, and z directions are all controlled within a low range, especially the RMSE error in the z direction, which can reach the millimeter level, demonstrating high calculation accuracy. These results prove that the present invention can be effectively applied to non-analytical models such as neural networks for 3D coordinate calculation, meeting the practical needs of 3D positioning of remote sensing images.

[0075] Experiment 2

[0076] To further verify the computational efficiency advantages of this invention, a comparative experiment on the time performance of different computational models was designed. The experiment recorded the time required for stereo intersection using the rational function model, the time required for calculating 3D coordinates using the present invention combined with the rational function model, and the time required for calculating 3D coordinates using the present invention combined with the neural network model. The results are shown in Table 2.

[0077] In this example, the error equation for stereo localization using a rational function model can be expressed as:

[0078]

[0079] Among them, (l l s l ), (l r s r (x, y, z) represents the coordinates of the corresponding image point, and (X, Y, Z) represents the object coordinates to be solved.

[0080] make

[0081] V = AΔ - B

[0082] Calculate coordinate corrections

[0083] Δ=[ΔZ ΔY ΔX] T =(A T A) -1 A T B

[0084] The solution is obtained through iterative solving until the correction value reaches the preset convergence condition, and finally the corresponding three-dimensional coordinates of the ground point are output.

[0085] Table 2 Comparison of 3D coordinate solution time (unit: seconds)

[0086]

[0087] The experimental results show that the computational method of this invention, combined with a neural network model, can achieve rapid calculation of three-dimensional coordinates, with the computation time for all four sets of experiments being within 0.3 seconds. Furthermore, even when using a rational function model, the computation speed can be improved by incorporating this invention. Compared to the stereo intersection method using a rational function model, the computation time is significantly reduced, demonstrating the computational efficiency advantage of this invention.

[0088] Based on the experimental results regarding the accuracy and computation time of stereo intersection, this invention not only achieves high-precision three-dimensional coordinate calculation, ensuring that errors in all directions are controlled within a reasonable range, but also demonstrates a significant advantage in computational efficiency. This verifies the technical feasibility of the invention.

[0089] 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 method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model, characterized in that, Includes the following steps: Step 1: Given the neural network localization models for the left and right images, and initialize the elevation values ​​and related threshold parameters, construct a dynamic optimal solution recorder to record the minimum error value and the corresponding elevation and latitude / longitude coordinates during the iteration process, ensuring that the record is updated if the current error is less than the recorded value in each iteration; Step 2: Calculate the object space coordinates under the current elevation value. The Euclidean distance between the calculated coordinates of the left and right images is used as an error index. The gradient is approximated by the central difference method. The trend of error variation with elevation is analyzed. The calculation of the object space coordinates under the current elevation value in step 2 includes: for the left image and the right image, respectively inputting the pixel coordinates of the corresponding image points and the current elevation value; The corresponding object space latitude and longitude coordinates are obtained by solving the neural network positioning model; the two-dimensional Euclidean distance between the latitude and longitude coordinates obtained by solving the left and right images is calculated as an error index for subsequent optimization; if the error index is less than a preset threshold and less than the previously recorded minimum value, the dynamic best solution recorder is updated to store the current elevation value and corresponding coordinates. Step 3: Based on gradient information, adjust the elevation value along the direction of error reduction to gradually reduce the error index. Combine the backtracking search strategy with Armijo conditions to dynamically adjust the learning rate and optimize the adjustment process. Update and maintain the global optimal solution through the dynamic optimal solution recorder. Step 4: Stop iterating when the preset convergence condition is met or the learning rate is exhausted, and output the optimal elevation and latitude / longitude coordinates as the three-dimensional spatial coordinates of the target point.

2. The method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model according to claim 1, characterized in that: The relevant threshold parameters in step 1 include the error threshold, gradient convergence threshold, number of iterations, and learning rate, which are used to control the convergence and stability of the optimization process.

3. The method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model according to claim 1, characterized in that: The method for obtaining the initial elevation value in step 1 is as follows: If there is rough DEM data in the experimental area, the elevation values ​​of the pixels are extracted from the DEM data as the initial values ​​using the method based on digital elevation model data. If DEM data is unavailable, an image-based elevation offset method is used, which calculates the elevation offset of the left image. Elevation offset values ​​of the right image The average value is used as the initial elevation, and the formula is as follows: 。 4. The method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model according to claim 1, characterized in that: The gradient calculation in step 2 uses the central difference method with a configurable step size, and the calculation formula is as follows: ， in, The gradient value; This is the current elevation value; and This represents the Euclidean distance error. This is the differential step size.

5. The method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model according to claim 1, characterized in that: The elevation adjustment in step 3 is performed iteratively using the gradient descent method, as follows: Calculate the current elevation. gradient value Use a learning rate Control the adjustment range; utilize the learning rate The elevation is updated to ensure that the error decreases monotonically with each iteration. The calculation formula is as follows: 。 6. The method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model according to claim 1, characterized in that: The backtracking search with Armijo conditions in step 3 is an optimization strategy that combines gradient descent and adaptive step size control. Gradient descent provides a local convergence direction, and the learning rate is gradually reduced to ensure that the error function value is strictly reduced after each iteration. If the updated error does not meet the Armijo conditions, the learning rate is reduced by a certain proportion and recalculated until the error meets the reduction requirements.

7. The method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model according to claim 1, characterized in that: The dynamic optimal solution recorder in step 3 evaluates whether the current error meets the threshold condition at each iteration. It updates the stored data only when the new error value is less than the recorded optimal value. The stored data includes the elevation value, the error value, and the corresponding latitude and longitude coordinates. When the optimization terminates, it outputs the set of all optimal solutions that meet the threshold condition.

8. The method for solving three-dimensional coordinates of remote sensing images based on a non-analytical model according to claim 1, characterized in that: The preset convergence condition and learning rate exhaustion in step 4 are used to determine whether to terminate the calculation after each iteration. For the gradient, its absolute value is calculated and compared with the preset gradient convergence threshold. If the absolute value of the gradient is less than the gradient convergence threshold, it is considered that the optimization process has approached the extreme point and the iteration stops. For the learning rate, if the learning rate continuously decreases during the adjustment process and eventually falls below the preset learning rate, the iteration stops. The rationality of terminating the optimization process is ensured through these two conditions.

Images