Multi-source lunar DEM adaptive variation fusion method based on curvature regularization

Abstract

The invention relates to a multi-source lunar DEM adaptive variation fusion method based on curvature regularization, and the method comprises the following steps: 1), proposing a weighted data fidelity model for slope anomaly elimination, and dynamically adjusting the weight of each input data through calculating the relative residual error of an input DEM and an iteration result, so as to improve the fusion precision; and 2) a curvature-constrained total variation regularization fusion model is adopted, and curvature smooth constraint is introduced in the fusion process, so that noise and artifacts are effectively reduced, and meanwhile, terrain details are reserved, and therefore, seamless DEM data with higher spatial consistency are generated. Compared with a traditional DEM fusion method, the method has the advantages that the problems of scale difference, noise, data voids, artifacts and the like are effectively solved, the precision and detail representation of fused DEM data are remarkably improved, and high-quality topographic data support can be provided for lunar exploration tasks.

Description

Technical Field

[0001] The invention relates to the technical field of remote sensing image processing, and in particular to a multi-source lunar DEM adaptive variational fusion method based on curvature regularization. Background Art

[0002] Multi-source digital elevation model (DEM) fusion can generate more accurate, comprehensive and reliable DEM by integrating complementary information from different data sources, thereby improving the quality of existing data sets. Lunar DEM not only provides key basic data for topographic, morphological and geological research, but also plays an important role in exploration missions such as landing site assessment, safe landing and lunar rover navigation. Traditional DEM fusion methods, such as weighted averaging, filtering and transformation, statistical inference, etc., face problems such as scale differences, noise, data holes and artifacts when processing multi-source data, making it difficult to comprehensively improve the overall quality of DEM and meet the requirements of high precision and high quality.

[0003] In summary, there is currently a lack of a multi-source digital elevation model fusion method to solve or partially solve the above problems. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a multi-source lunar DEM adaptive variational fusion method based on curvature regularization, so as to solve or partially solve the problems of step effect, unsatisfactory overall accuracy and computational efficiency in the DEM fusion process.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] The present invention provides a multi-source lunar DEM adaptive variational fusion method based on curvature regularization, comprising the following steps:

[0007] Construct a total variation regularization fusion model for slope anomaly elimination under curvature constraints;

[0008] The DEM data to be fused is obtained, and the fused DEM data is calculated using the total variation regularization fusion model.

[0009] As a preferred technical solution, the process of constructing a total variation regularization fusion model for eliminating slope anomalies under curvature constraints includes:

[0010] Construct a regularized variational fusion framework;

[0011] The outliers in the DEM are detected by calculating the slope anomaly in the sliding window, and the data fidelity term representing the model error in the observation model is calculated;

[0012] Calculate the curvature regularization term to eliminate the staircase effect;

[0013] Based on the regularized variational fusion framework, the data fidelity term and the regularization term, a total variational regularized fusion model for eliminating slope anomalies under curvature constraints is constructed.

[0014] As a preferred technical solution, the process of constructing a regularized variational fusion framework includes:

[0015] Establish a degradation model between multi-scale input DEM data and the target DEM to be fused;

[0016] Based on the degradation model, the multi-scale DEM fusion is modeled as a functional extreme value optimization problem, and a regularized variational fusion framework is constructed.

[0017] As a preferred technical solution, the regularized variational fusion framework is modeled as:

[0018]

[0019] in, Represents the fused DEM data, y k represents the kth input DEM data, that is, the degraded DEM data, M k is the translation matrix, S k is the resampling matrix, E k is the matrix for eliminating gross errors, x represents the DEM data before degradation, ‖·‖ p Yes p norm, R(·) is the regularization term, λ is the regularization parameter, and K is the total number of input DEM data.

[0020] As a preferred technical solution, the abnormal points in the DEM are judged by the following formula:

[0021] |G-μ G |>T×σ G

[0022] Among them, G is the gradient value of the center pixel of the window, μ G is the average value of the gradient in the local window, σ G is the standard deviation of the gradient in the local window, T is an adjustable threshold, and if the above conditions are met, it is judged as an abnormal point in the DEM.

[0023] As a preferred technical solution, the regularized variational fusion framework with the data fidelity term is:

[0024]

[0025]

[0026] in, Represents the fused DEM data, y k represents the kth input DEM data, that is, the degraded DEM data, M k is the translation matrix, S k is the resampling matrix, E k is the gross error elimination matrix, x represents the DEM data before degradation, ‖·‖2 is the l2 norm, R(·) is the regularization term, λ is the regularization parameter, K is the total number of input DEM data, and r is the number of iterations.

[0027] As a preferred technical solution, the process of calculating the curvature regularization term for eliminating the step effect includes:

[0028] A total variation model is constructed, and based on the total variation model, a curvature regularization term for eliminating the step effect is calculated.

[0029] As a preferred technical solution, the total variation regularization fusion model for eliminating slope anomalies under curvature constraints is modeled as follows:

[0030]

[0031]

[0032] φ(κ)=a+b|κ| 2

[0033]

[0034] in, Represents the fused DEM data, y k represents the kth input DEM data, that is, the degraded DEM data, M k is the translation matrix, S k is the resampling matrix, E k is the gross error elimination matrix, x represents the DEM data before degradation, ‖·‖2 is the l2 norm, R(·) is the regularization term, λ is the regularization parameter, K is the total number of input DEM data, r is the number of iterations, is the total variation, k is the curvature, and a and b are two positive constants.

[0035] As a preferred technical solution, the process of calculating the fused DEM data using the total variation regularization fusion model includes:

[0036] Based on the total variation regularized fusion model, the corresponding augmented Lagrangian functional is obtained, and the alternating direction multiplier method is used to iterate and alternately solve the sub-minimization problem to obtain the fused DEM data.

[0037] As a preferred technical solution, the augmented Lagrangian functional is:

[0038]

[0039] Where K is the total number of input DEM data, ω k is the weight, A k is the degradation matrix, y k represents the kth input DEM data, that is, the degraded DEM data, x represents the DEM data before degradation, λ is the regularization parameter, φ(κ) is a function of the curvature κ, Λ is the Lagrange multiplier, and μ is a positive parameter.

[0040] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0041] (1) Realizing the fusion of high-precision DEM: The present invention fuses multi-source DEM data by constructing a total variation regularized fusion model for eliminating slope anomalies under curvature constraints, effectively solving problems such as scale differences, noise, data holes and artifacts, thereby achieving the generation of high-precision DEM.

[0042] (2) Overcoming the accuracy differences of multi-scale DEM data: The present invention introduces a weighted data fidelity model for slope anomaly elimination. By calculating the relative residual between each input DEM and the result of the previous iteration, the weight of each input DEM is dynamically adjusted to improve the overall accuracy of the fusion result. In view of the continuity and smoothness requirements of terrain data, curvature regularization is introduced to effectively reduce noise and data holes while maintaining the integrity of terrain details. Finally, the objective function is solved by the optimization algorithm to achieve the generation of high-precision DEM data, ensuring the high quality and reliability of the fusion results under multi-source and multi-scale conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a schematic diagram of the process of adaptive variational fusion of multi-source lunar DEM based on curvature regularization in the embodiment;

[0044] Figure 2 This is a flow chart of removing outliers in a sliding window in an embodiment;

[0045] Figure 3 Input DEM and hillshade map in the embodiment;

[0046] Figure 4 This is a comparison chart of variational fusion results before and after adding adaptive weighting and curvature regularization in the embodiment;

[0047] Figure 5 The result diagrams of different methods in the embodiments;

[0048] Figure 6 Schematic diagram of an electronic device in an embodiment. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0050] Example 1

[0051] In view of the problems existing in the aforementioned prior art, this embodiment provides a curvature constrained adaptive regularized variational fusion method for multi-source lunar DEM, which mainly includes a weighted data fidelity model for slope anomaly removal and a total variation regularized fusion model for curvature constraints. It fuses multi-source DEM data under an integrated framework to effectively solve problems such as scale differences, noise, data holes and artifacts, thereby achieving the generation of high-precision DEM.

[0052] In order to overcome the problem of accuracy differences between multi-scale DEM data, this method designs a weighted data fidelity model that introduces slope anomaly elimination. By calculating the relative residual between each input DEM and the previous iteration result, the weight of each input DEM is dynamically adjusted to improve the overall accuracy of the fusion result. In view of the continuity and smoothness requirements of terrain data, curvature regularization is introduced to effectively reduce noise and data holes while maintaining the integrity of terrain details. Finally, the objective function is solved by the optimization algorithm to achieve the generation of high-precision DEM data, ensuring the high quality and reliability of the fusion results under multi-source and multi-scale conditions.

[0053] See also Figure 1 , the method comprises the following steps:

[0054] Step S1, regularized variational fusion framework construction.

[0055] In order to construct the DEM regularized variational fusion framework, the degradation model between the multi-scale input DEM data and the target DEM to be fused is first established. Assuming that the input DEM data is obtained by a series of degradation processes of high-resolution and high-precision result DEM, considering the degradation factors such as scale change, spatial coverage change, noise level and data holes, the multi-scale DEM data observation model is constructed as follows:

[0056] y k =E k S k M k x+n k 1)

[0057] In the formula, x represents the fused DEM, i.e., high-resolution and high-precision DEM, and y k M represents the kth input DEM data, that is, the degraded DEM, which is projected in the same coordinate system as x. k It is a translation matrix, which represents the sub-pixel offset between the degraded DEM and the reference grid of the high-resolution and high-precision DEM. k is a resampling matrix used to resample the size of the resulting DEM to the same size as the kth input DEM. k It is a matrix for eliminating gross errors, which is used to eliminate gross errors, including points that cannot be observed in the input DEM for the result DEM, data holes, and abnormal points. k It is considered to be the random error after eliminating gross errors.

[0058] By establishing a degradation model, multi-scale DEM fusion can be expressed as an inverse problem, which can be transformed into a functional extreme value optimization problem using the regularization method. Corresponding to the above observation model, the general form of the energy functional is expressed as:

[0059]

[0060] In the formula, l p Norm (‖·‖ p ) is used to constrain the residual term between the reconstructed data and the observed data to ensure high fidelity with the actual data. R(·) is a regularization term, which is used to constrain the ill-posed problem to obtain a stable approximate solution. By adjusting the regularization parameter λ, a balance can be achieved between the data fidelity term and the regularization term to obtain an ideal processing result.

[0061] In order to obtain the reconstructed DEM after fusion, it is necessary to minimize the above functional value, that is, to solve the minimum value of the following formula. Therefore, the regularized variational fusion framework can be expressed as:

[0062]

[0063] Step S2: weighted data fidelity model for slope anomaly elimination.

[0064] First, determine the degradation matrix of the observation model in the data fidelity term. The degradation matrix is ​​composed of M k , S k 、E k Matrix composition, where the translation matrix M k It is obtained by calculating the vertex coordinate offset of the result DEM and the input DEM in the same coordinate system. k It is obtained from the scale relationship between the two DEM data, and E kThe slope anomaly elimination is used to detect and eliminate the data holes and elevation anomalies that appear when the high-resolution and high-precision DEM is degraded to the k-th input DEM. This method detects the anomalies in the DEM by calculating the slope anomaly in the sliding window, as shown in the following formula:

[0065] |G-μ F |>T×σ G 4)

[0066] Where G is the gradient value of the center pixel of the window, μ G is the average value of the gradient in the local window, σ G is the standard deviation of the gradient in the local window, and T is an adjustable threshold to control the degree of outlier removal. The gradient of each pixel is calculated by the Sobel operator. Therefore, the local mean and standard deviation of the gradient are calculated in the sliding window. If the gradient value of a pixel deviates from the average gradient in its neighborhood by more than the threshold, the pixel is considered to be an outlier and needs to be removed. Figure 2 shown.

[0067] In addition, consider the choice of constraint functions. The fidelity term corresponds to the model error in the observation model, which mainly includes noise and errors generated in the parameter estimation process. This method uses the l2 norm to constrain the fidelity term (i.e., p = 2), which takes into account the convex optimization property of the l2 norm, making the solution process more efficient. In addition, the l2 norm performs well in processing random noise, can smooth terrain data, and avoid excessive punishment of small errors. For lunar DEM data, the use of the l2 norm can better balance noise suppression and terrain detail retention, thereby improving the overall accuracy and computational efficiency of the model. Therefore, a data fidelity term model based on the adaptive weighted l2 norm is constructed, and the formula is as follows:

[0068]

[0069] The weight ω of the above model is k It is used to balance the impact of different input DEMs on the fusion result DEM. The weight is calculated by the relative residual between each input DEM and the reconstruction result generated by the previous iteration, and is continuously updated during the iteration, so that the contribution of each input DEM can be dynamically adjusted, as shown in the following formula:

[0070]

[0071] Step S3, curvature constrained total variation regularization fusion model.

[0072] The focus of prior model research is to enhance the ability to retain data edge texture details while suppressing noise and model errors. This type of model is called edge-preserving prior model, the most representative of which is the total variation (TV) model, which is specifically defined as:

[0073]

[0074] In the formula, and Represents the first-order gradient of x in the horizontal and vertical directions respectively, and β is a very small positive constant used to ensure that the denominator of the prior term is not 0 when the derivative is taken. The discrete expression of the TV model is Can be seen as The l1-norm constraint of . Since the l1-norm can effectively maintain edge jumps, it can better preserve edge information. However, in the case of strong noise, the l1-norm constraint may produce a step effect in the smooth area.

[0075] The curvature regularization term can rely on strong prior information, emphasize the continuity of the data, and ensure a smooth surface. By reducing the drastic changes in pixel values, the missing information is naturally filled, making the restored image more coherent and realistic. Curvature regularization can effectively eliminate the staircase effect while maintaining the edge of the image. Therefore, a prior model based on curvature regularization is adopted:

[0076]

[0077] In the formula, This is the total variation mentioned above, and κ is the curvature. The curvature calculation formula is as follows:

[0078]

[0079] φ(κ) is a function of curvature as follows:

[0080] φ(κ)=a+b|κ| 2 10)(

[0081] Where a and b are two positive constants. When b is 0, it is the classic total variation regularization.

[0082] Combined with the determined data fidelity term and regularization term, the energy function of the objective is finally expressed as:

[0083]

[0084] After constructing the above regularized expression, the objective function is optimized and solved using the optimization algorithm to obtain the reconstructed fusion result. For the convenience of expression, the degradation matrix is ​​simply expressed as A k =E k S k M k , thus obtaining the following minimization problem:

[0085]

[0086] The corresponding augmented Lagrangian functional can be defined as:

[0087]

[0088] Where Λ is the Lagrange multiplier and μ is a positive parameter.

[0089] Step S4, solving the constructed total variation regularization fusion model of curvature constraints.

[0090] The alternating direction method of multipliers (ADMM) is used to iterate and alternately solve the sub-minimization problem. ADMM is a commonly used optimization algorithm that optimizes the objective function by alternately solving the sub-minimization problem. This method has good convergence and computational efficiency when dealing with large-scale problems.

[0091] To illustrate the effectiveness of this method, the following experiments are conducted:

[0092] (1) Experimental data.

[0093] In order to verify the effectiveness and advantages of the curvature-constrained adaptive regularized variational fusion method, experiments were conducted using a simulated dataset of the lunar South Pole DEM. The reference data used in the experiment is the South Pole LOLA DEM Mosaic, which is generated by the Lunar Orbiter Laser Altimeter (LOLA) on NASA's Lunar Reconnaissance Orbiter. This experiment selected an area located at about 89°10' at the lunar South Pole for the experiment. The horizontal resolution of the DEM is 5 meters, the experimental area size is 1000×1000 pixels, and the elevation range is -1050.58 meters to -761.14 meters. The data simulation not only focuses on the scale differences between the input DEMs, but also considers the effects of noise, data holes, and outliers.

[0094] In order to generate the simulated data set, the reference DEM was downsampled to a resolution of 10 meters to generate a low-resolution DEM of 500×500 pixels, and Gaussian noise with a mean of 0 and a standard deviation of 1 was added to it to simulate the random noise in the DEM data, thereby obtaining the input low-resolution DEM (y1). At the same time, in order to simulate the data hole phenomenon, a randomly generated mask was added to the reference DEM, and the abnormal points appearing on a randomly generated straight line were used to simulate the artifacts that may be generated by the LOLA laser point data when generating the DEM, and the input high-resolution DEM (y2) was obtained. The resolution of this high-resolution DEM is consistent with the reference data, which is 5 meters, and the area size is 1000×1000 pixels. In order to more intuitively display the three-dimensional morphology and details of the terrain, a mountain shadow rendering was generated by simulating the illumination effect of the light source. Figure 3 The two input DEMs and their corresponding hillshade maps are shown, and the locations of the simulated artifacts are marked. Figure 3In the figure, (a) is the input low-resolution DEM y1, (b) is the input high-resolution DEM y2, (c) is the input low-resolution DEM y1 hillshade map, and (d) is the input high-resolution DEM y2 hillshade map.

[0095] (2) Experimental results and accuracy verification.

[0096] Two DEMs of different resolutions and qualities were used as input data and fused using the regularized variational method, ultimately generating a high-quality DEM data with a resolution of 5 meters. The main goal of multi-scale fusion is to improve the spatial resolution of the input DEM and generate a high-resolution DEM with no data holes, no artifacts, and high accuracy. To verify the effectiveness of the fusion method, the fusion results were compared with several commonly used DEM processing methods, including bilinear interpolation, inverse distance weighted interpolation, spline interpolation, Kriging interpolation, as well as splicing and filling and weighted averaging methods.

[0097] The elevation accuracy of the results generated by each method was evaluated by calculating the mean absolute error (MAE) and root mean square error (RMSE), two quantitative indicators. The results show that the curvature-constrained adaptive regularized variational fusion method can make full use of the complementary information of multi-scale lunar DEM data, process data of different resolutions and different accuracy levels at the same time, and finally obtain high-quality DEM data. In addition, in the presence of data holes, the variational fusion method can also reconstruct seamless DEM data with good spatial consistency. See Table 1 for the accuracy evaluation of the results of different methods.

[0098] Table 1 Accuracy evaluation of results of different methods

[0099]

[0100] In addition, ablation experiments were conducted to clarify the specific contributions of each improvement to the overall model and verify the effectiveness of these improvement measures in improving the quality of DEM data. By comparing and analyzing the effects of the unimproved model, adaptive weighting improvement, curvature regularization improvement, and the combination of the two improvements, quantitative evaluation indicators show that the improvements of adaptive weighting and curvature regularization have improved the quality of DEM data to varying degrees. Figure 4 It can be seen that the improved adaptive weighted method improves the overall accuracy and effectively reduces the noise by dynamically adjusting the weights; and the improved curvature regularization method significantly enhances the fidelity and continuity of terrain details by introducing curvature constraints, further verifying the significant advantages of this method in improving the quality of DEM data. Figure 4 In (a), there is no improvement, in (b), adaptive weights are added, in (c), curvature regularization is added, and in (d), both are improved. See Table 2 for the accuracy evaluation of the variational fusion results before and after adding adaptive weights and curvature regularization.

[0101] Table 2 Accuracy evaluation of variational fusion results before and after adding adaptive weights and curvature regularization

[0102]

[0103] Figure 5 The hillshade rendering results of DEM generated by different methods are shown. As can be seen from the figure, the interpolation method only uses limited low-frequency information when restoring the real terrain surface, resulting in blurred terrain details. The splicing filling method uses a low-resolution DEM containing random noise for interpolation filling in the holes, and obvious artifacts appear at the seams of multi-scale data. Although the weighted average method combines the information of low-resolution DEM and high-resolution DEM, it is still affected by the random noise in the low-resolution DEM. In contrast, the variational fusion method effectively solves the problems of scale differences, noise and data holes in an integrated framework, and makes full use of the information of multi-source data, so the generated results are closest to the reference data. Figure 5 In the figure, (a) is the result of different methods, and (b) is a local enlarged view of the rectangular area.

[0104] In summary, this method constrains the fusion results by introducing a total variation regularization fusion model with curvature constraints, which can eliminate the step effect while maintaining the details of the terrain edge, thereby improving the overall accuracy and detail performance of the DEM. In addition, a weighted data fidelity model based on slope anomaly removal is developed. The model can dynamically adjust the weights according to the quality of the input DEM, thereby achieving more accurate multi-source data fusion. This method can achieve high-precision fusion of multi-source and multi-scale lunar DEM data under the framework of integrated variational optimization, successfully solving problems such as scale differences, noise, data holes and artifacts, thereby significantly improving the overall accuracy and quality of the fused terrain data.

[0105] Example 2

[0106] This embodiment provides an electronic device, including: one or more processors and a memory, wherein the memory stores one or more programs, and the one or more programs include instructions for executing the multi-source lunar DEM adaptive variational fusion method based on curvature regularization described in Example 1.

[0107] like Figure 6 As mentioned above, at the hardware level, the electronic device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory, and may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to achieve the above Figure 1The multi-source lunar DEM adaptive variational fusion method based on curvature regularization. Of course, in addition to the software implementation, the present invention does not exclude other implementations, such as logic devices or a combination of software and hardware, etc., that is, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0108] The memory may include non-permanent storage in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0109] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0110] Aiming at the high-precision requirements of multi-source lunar DEM data fusion, the present invention provides a curvature-constrained adaptive variational fusion scheme. By dynamically adjusting weights and introducing curvature regularization, high-precision fusion of multi-source and multi-scale DEM data is achieved. Experimental results show that this method performs well in noise suppression, data hole filling, artifact elimination, and detail preservation, and significantly improves the overall quality of the fusion results. The present invention can provide reliable high-quality DEM data support for exploration tasks such as landing site assessment, safe landing, and lunar rover navigation.

[0111] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A multi-source lunar DEM adaptive variational fusion method based on curvature regularization, characterized in that: The steps include: Construct a total variation regularization fusion model for slope anomaly elimination under curvature constraints; The DEM data to be fused is obtained, and the fused DEM data is calculated using the total variation regularization fusion model.

2. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 1 is characterized in that: The process of constructing a total variation regularization fusion model for eliminating slope anomalies under curvature constraints includes: Construct a regularized variational fusion framework; The outliers in the DEM are detected by calculating the slope anomaly in the sliding window, and the data fidelity term representing the model error in the observation model is calculated; Calculate the curvature regularization term to eliminate the step effect; Based on the regularized variational fusion framework, the data fidelity term and the regularization term, a total variational regularized fusion model for eliminating slope anomalies under curvature constraints is constructed.

3. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 2 is characterized in that: The process of constructing the regularized variational fusion framework includes: Establish a degradation model between multi-scale input DEM data and the target DEM to be fused; Based on the degradation model, the multi-scale DEM fusion is modeled as a functional extreme value optimization problem, and a regularized variational fusion framework is constructed.

4. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 2 is characterized in that: The regularized variational fusion framework is modeled as: in, Represents the fused DEM data, y k represents the kth input DEM data, that is, the degraded DEM data, M k is the translation matrix, s k is the resampling matrix, E k is the matrix for eliminating gross errors, x represents the DEM data before degradation, ‖·‖ p Yes p norm, R(·) is the regularization term, λ is the regularization parameter, and K is the total number of input DEM data.

5. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 2 is characterized in that: The abnormal points in the DEM are judged by the following formula: |G-μ G |>T×σ G Among them, G is the gradient value of the center pixel of the window, μ G is the average value of the gradient in the local window, σ G is the standard deviation of the gradient in the local window, T is an adjustable threshold, and if the above conditions are met, it is judged as an abnormal point in the DEM.

6. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 2 is characterized in that: The regularized variational fusion framework with the data fidelity term is: in, Represents the fused DEM data, y k represents the kth input DEM data, that is, the degraded DEM data, M k is the translation matrix, S k is the resampling matrix, E k is the gross error elimination matrix, x represents the DEM data before degradation, ‖·‖2 is the l2 norm, R(·) is the regularization term, λ is the regularization parameter, K is the total number of input DEM data, and r is the number of iterations.

7. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 2 is characterized in that: The process of calculating the curvature regularization term for eliminating the step effect includes: A total variation model is constructed, and based on the total variation model, a curvature regularization term for eliminating the step effect is calculated.

8. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 2 is characterized in that: The total variation regularization fusion model for slope anomaly elimination under curvature constraint is modeled as: in, Represents the fused DEM data, y k represents the kth input DEM data, that is, the degraded DEM data, M k is the translation matrix, S k is the resampling matrix, E k is the gross error elimination matrix, x represents the DEM data before degradation, ‖·‖2 is the l2 norm, R(·) is the regularization term, λ is the regularization parameter, K is the total number of input DEM data, r is the number of iterations, is the total variation, κ is the curvature, a and b are two positive constants.

9. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 1 is characterized in that: The process of calculating the fused DEM data using the total variation regularized fusion model includes: Based on the total variation regularized fusion model, the corresponding augmented Lagrangian functional is obtained, and the alternating direction multiplier method is used to iterate and alternately solve the sub-minimization problem to obtain the fused DEM data.

10. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 9 is characterized in that: The augmented Lagrangian functional is: Among them, K is the total number of input DEM data, ω k is the weight, A k is the degradation matrix, y k represents the kth input DEM data, that is, the degraded DEM data, x represents the DEM data before degradation, λ is the regularization parameter, φ(κ) is a function of the curvature κ, Λ is the Lagrange multiplier, and μ is a positive parameter.

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