Adaptive variational fusion method for multi-source lunar DEM based on curvature regularization

Abstract

The present invention relates to a multi-source lunar DEM adaptive variational fusion method based on curvature regularization. The method comprises the following steps: 1) proposing a weighted data fidelity model for slope anomaly removal. By calculating the relative residual between the input DEM and the iterative result, the weight of each input data is dynamically adjusted to improve fusion accuracy; 2) adopting a curvature-constrained total variation regularization fusion model. By introducing a curvature smoothing constraint during the fusion process, the method effectively reduces noise and artifacts while preserving terrain details, thereby generating seamless DEM data with higher spatial consistency. Compared with traditional DEM fusion methods, the method of the present invention effectively addresses issues such as scale differences, noise, data holes, and artifacts, significantly improving the accuracy and detail of the fused DEM data, and can provide high-quality terrain data support for lunar exploration missions.

Description

Technical Field

[0001] The present 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 improves the quality of existing datasets by integrating complementary information from different data sources to generate more accurate, comprehensive, and reliable DEMs. Lunar DEMs not only provide critical foundational data for topographic, morphological, and geological studies, but also play a vital 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, and statistical inference, face challenges with scale discrepancies, noise, data voids, and artifacts when processing multi-source data. This makes it difficult to fully improve the overall quality of the DEM and meet high-precision and high-quality requirements.

[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 provide a multi-source lunar DEM adaptive variational fusion method based on curvature regularization to solve or partially solve the problems of step effect, 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] Build a regularized variational fusion framework;

[0011] Detect outliers in the DEM by calculating slope anomalies in the sliding window and calculate the data fidelity term that represents the model error in the observation model;

[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, 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 follows:

[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 using 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 an optimal technical solution, the regularized variational fusion framework that incorporates the data fidelity term is:

[0024]

[0025]

[0026] in, Represents the fused DEM data, y k Indicates 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 Indicates 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 iteratively 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] 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.

[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: This paper 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, thereby improving the overall accuracy of the fusion result. In response to 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 an optimization algorithm to achieve the generation of high-precision DEM data, ensuring the high quality and high reliability of the fusion results under multi-source and multi-scale conditions. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0044] Figure 2 This is a flowchart 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 the variational fusion results before and after adding adaptive weighting and curvature regularization in the embodiment;

[0047] Figure 5 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 clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0050] Example 1

[0051] In response to the problems existing in the aforementioned existing technologies, 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 curvature-constrained total variation regularized fusion model. It fuses multi-source DEM data under an integrated framework, effectively solving problems such as scale differences, noise, data holes and artifacts, thereby achieving the generation of high-precision DEM.

[0052] To overcome the accuracy discrepancies between multi-scale DEM data, this method designs a weighted data fidelity model that incorporates slope anomaly rejection. By calculating the relative residual between each input DEM and the previous iteration, the weight of each input DEM is dynamically adjusted, thereby improving the overall accuracy of the fusion result. To address the requirements for continuity and smoothness in terrain data, curvature regularization is introduced to effectively reduce noise and data holes while maintaining the integrity of terrain details. Ultimately, an optimization algorithm is used to solve the objective function, achieving the generation of high-precision DEM data and ensuring the high quality and reliability of the fusion results across multiple sources and scales.

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

[0054] Step S1: Regularized variational fusion framework construction.

[0055] In order to build a DEM regularized variational fusion framework, we first establish a degradation model between the multi-scale input DEM data and the target DEM to be fused. Assuming that the input DEM data is obtained from a high-resolution, high-precision result DEM through a series of degradation processes, considering 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] Where x represents the fused DEM, i.e., high-resolution and high-precision DEM, and y k M represents the k-th input DEM data, that is, the degraded DEM, which is projected in the same coordinate system as x. k It is a translation matrix that represents the sub-pixel offset between the degraded DEM and the reference grid where the high-resolution and high-precision DEM is located. 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 gross error elimination matrix 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 a 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 regularization methods. Corresponding to the above observation model, the general form of the energy functional is expressed as:

[0059]

[0060] Where, l p Norm (‖·‖ p ) is used to constrain the residual term between the reconstructed data and the observed data, ensuring high fidelity with the actual data. R(·) is the regularization term, which is used to constrain the ill-posed problem and thus 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, resulting in 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 ​​represented by 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 removal is used to detect and remove 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 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 an outlier and needs to be removed, such as Figure 2 shown.

[0067] In addition, consider the choice of constraint function. 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). This is because the convex optimization property of the l2 norm is taken into account, 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 k It is used to balance the influence 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 preserve edge texture details while suppressing noise and model errors. This type of model is called an edge-preserving prior model, the most representative of which is the total variation (TV) model, which is specifically defined as:

[0073]

[0074] Where, 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 it is derived. The discrete expression of the TV model is Can be seen as The l1-norm constraint is used to constrain the edge information. Since the l1-norm can effectively prevent edge jumps, it can better preserve edge information. However, in the case of strong noise, the l1-norm constraint may produce a staircase effect in the smooth area.

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

[0076]

[0077] Where, 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 target 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 sake of convenience, 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 curvature constrained total variation regularization fusion model.

[0090] The Alternating Direction Method of Multipliers (ADMM) is used to iteratively 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 were conducted:

[0092] (1) Experimental data.

[0093] To validate 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 was the South Pole LOLA DEM Mosaic, generated by the Lunar Orbiter Laser Altimeter (LOLA) on NASA's Lunar Reconnaissance Orbiter. This experiment was conducted over an area located approximately 89°10' at the lunar south pole. The DEM had a horizontal resolution of 5 meters, and the experimental area was 1000 × 1000 pixels, encompassing an elevation range of -1050.58 meters to -761.14 meters. The data simulation not only accounted for the scale differences between the input DEMs but also considered the effects of noise, data holes, and outliers.

[0094] To generate the simulated dataset, the reference DEM was downsampled to 10-meter resolution, generating a low-resolution DEM of 500 × 500 pixels. Gaussian noise with a mean of 0 and a standard deviation of 1 was added to simulate random noise in the DEM data, resulting in the input low-resolution DEM (y1). Furthermore, to simulate data holes, a randomly generated mask was added to the reference DEM. Artifacts that may be generated by LOLA laser point data during DEM generation were simulated by outliers appearing on a randomly generated line, resulting in the input high-resolution DEM (y2). This high-resolution DEM has the same resolution as the reference data, 5 meters, and an area size of 1000 × 1000 pixels. To more intuitively display the three-dimensional morphology and details of the terrain, a hillshade rendering was generated by simulating the effects of light illumination. 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 a regularized variational method, ultimately generating a high-quality DEM with a 5-meter resolution. The primary goal of multiscale fusion is to improve the spatial resolution of the input DEMs, generating a high-resolution DEM with no data holes or artifacts and high accuracy. To validate 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 patchwork and weighted averaging.

[0097] The elevation accuracy of the results generated by each method was evaluated by calculating two quantitative metrics: mean absolute error (MAE) and root mean square error (RMSE). The results demonstrate that the curvature-constrained adaptive regularized variational fusion method can fully utilize the complementary information of multi-scale lunar DEM data, simultaneously processing data of varying resolutions and accuracy levels, ultimately producing high-quality DEM data. Furthermore, even in the presence of data holes, the variational fusion method can reconstruct seamless DEM data with good spatial consistency. Table 1 shows the accuracy evaluation of the results obtained by 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 weighting method improves the overall accuracy and effectively reduces 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 (a) shows no improvement, (b) adds adaptive weights, (c) adds curvature regularization, and (d) shows both improvements. See Table 2 for an 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 true 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 problems such as scale differences, noise and data holes in an integrated framework, and makes full use of the information of multi-source data. Therefore, 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 magnified image of the rectangular area.

[0104] In summary, this method constrains the fusion results by introducing a curvature-constrained total variation regularization fusion model. This method can maintain terrain edge details while eliminating the stair-step effect, thereby improving the overall accuracy and detail of the DEM. Furthermore, a weighted data fidelity model based on slope anomaly removal is developed. The model dynamically adjusts weights based on the quality of the input DEM, thereby achieving more accurate multi-source data fusion. This method can achieve high-precision fusion of multi-source, multi-scale lunar DEM data within an integrated variational optimization framework, successfully addressing issues 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 is described. Of course, in addition to software implementation, the present invention does not exclude other implementation methods, such as logic devices or a combination of software and hardware. In other words, the execution body of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0108] 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. Memory is an example of a computer-readable medium.

[0109] Computer-readable media includes permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. The 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 disc read-only memory (CD-ROM), digital versatile disc (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 transitory media such as modulated data signals and carrier waves.

[0110] This paper addresses the high-precision requirements of multi-source lunar DEM data fusion by providing a curvature-constrained adaptive variational fusion scheme. By dynamically adjusting weights and introducing curvature regularization, high-precision fusion of multi-source, multi-scale DEM data is achieved. Experimental results demonstrate that this method excels in noise suppression, data hole filling, artifact removal, and detail preservation, significantly improving the overall quality of the fusion results. This paper can provide reliable, high-quality DEM data support for exploration missions such as landing site assessment, safe landing, and lunar rover navigation.

[0111] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A multi-source lunar DEM adaptive variational fusion method based on curvature regularization, characterized by: The steps include: Construct a total variation regularization fusion model for slope anomaly elimination under curvature constraints; Obtain the DEM data to be fused, and use the total variation regularization fusion model to calculate the fused DEM data. The process of constructing a total variation regularization fusion model for eliminating slope anomalies under curvature constraints includes: Build a regularized variational fusion framework; Detect outliers in the DEM by calculating slope anomalies in the sliding window and calculate the data fidelity term that represents the model error in the observation model; Calculate the curvature regularization term to eliminate the staircase effect; Based on the regularized variational fusion framework, the data fidelity term and the regularization term, a total variational regularized fusion model for slope anomaly elimination under curvature constraints is constructed. 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. The regularized variational fusion framework is modeled as: in, Represents the fused DEM data, Indicates the The input DEM data, that is, the degraded DEM data, is the translation matrix, is the resampling matrix, is the gross error elimination matrix, Indicates the DEM data before degradation, yes norm, is the regularization term, is the regularization parameter, is the total number of input DEM data, The abnormal points in the DEM are judged by the following formula: in, is the gradient value of the center pixel of the window, is the average value of the gradient in the local window, is the standard deviation of the gradient within the local window, is an adjustable threshold. If the above conditions are met, it is judged as an abnormal point in DEM. The regularized variational fusion framework with the data fidelity term is: in, Represents the fused DEM data, Indicates the The input DEM data, that is, the degraded DEM data, is the translation matrix, is the resampling matrix, is the gross error elimination matrix, Indicates the DEM data before degradation, yes norm, is the regularization term, is the regularization parameter, is the total number of input DEM data, is the number of iterations, The process of calculating the curvature regularization term for eliminating the staircase effect includes: Construct a total variation model, and based on the total variation model, calculate the curvature regularization term that eliminates the step effect, The total variation regularization fusion model for slope anomaly elimination under curvature constraint is modeled as: in, Represents the fused DEM data, Indicates the The input DEM data, that is, the degraded DEM data, is the translation matrix, is the resampling matrix, is the gross error elimination matrix, Indicates the DEM data before degradation, yes norm, is the regularization term, is the regularization parameter, is the total number of input DEM data, is the number of iterations, is the total variation, is the curvature, and are two positive constants.

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 calculating the fused DEM data using the total variation regularization 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 iteratively and alternately solve the sub-minimization problem to obtain the fused DEM data.

3. The multi-source lunar DEM adaptive variational fusion method based on curvature regularization according to claim 2 is characterized in that: The augmented Lagrangian functional is: in, is the total number of input DEM data, is the weight, is the degradation matrix, Indicates the The input DEM data, that is, the degraded DEM data, Indicates the DEM data before degradation, is the regularization parameter, It's about curvature function, is the Lagrange multiplier, is a positive parameter.

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