Moon permanent shadow area high-resolution terrain reconstruction method based on secondary scattering light shadow method
By positioning and clustering the scattering source in the shadowed area of the moon based on the secondary scattering light and shadow method, the corresponding photometric equations and objective functions are constructed, which solves the problem that the existing technology is difficult to achieve high-resolution terrain reconstruction in the permanent shadowed area of the moon, and achieves high-precision and high-resolution terrain reconstruction.
Patent Information
- Application Number
- CN202510040526.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-10
- Publication Date
- 2025-05-16
AI Technical Summary
Existing lunar three-dimensional terrain reconstruction technology is difficult to achieve high-resolution terrain reconstruction in permanent shadow areas of the moon, especially when dealing with the problem of multi-scattering sources.
The method based on the secondary scattering light and shadow method is adopted to locate the scattering source in the shadowed area through the direct sunlight irradiance map and contour information, perform clustering processing and update the field of view table, build the quadratic irradiance model and multi-scattering source luminance equation, combine the regularization terms of smoothing and initial DEM constraints, and establish and optimize the SS-SFS objective function.
High-resolution terrain reconstruction in the permanent shadow area of the moon is realized, which can effectively deal with the problem of multiple scattering sources and improve the accuracy and resolution of terrain reconstruction.
Smart Images
Figure CN120014189A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of three-dimensional terrain reconstruction of lunar surface, and in particular to a high-resolution terrain reconstruction method of a permanent shadow area of the moon based on a secondary scattering light and shadow method. Background Art
[0002] The lunar surface is an unstructured environment with uneven surfaces and irregularly distributed obstacles. The lunar surface environment has a lack of texture and complex landforms. In lunar exploration research, high-resolution topography of the lunar permanently shadowed regions (PSRs) is crucial for polar exploration missions, and can provide spatial data support for landing site selection, rover path planning, and water ice resource exploration.
[0003] At present, the main methods for reconstructing the three-dimensional terrain of the lunar surface include photogrammetry, light and shadow method, and laser altimeter measurement. However, photogrammetry is constrained by the coverage area of stereo imaging and radiation differences, making it difficult to carry out fine mapping of large areas, and the maximum resolution of terrain products reconstructed by laser altimetry data is 5m, which is difficult to meet the terrain requirements in fine-grained detection. Low-light cameras use secondary illumination to perform high-resolution indirect imaging of PSRs, providing image data for light and shadow technology, making high-resolution terrain reconstruction possible. Traditional light and shadow methods are only applicable to high-resolution images of single-light source imaging and cannot handle the problem of multiple scattering sources. 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 high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method, which can effectively process the high-resolution images of indirect imaging of the shadow area of the moon and realize the fine reconstruction of the three-dimensional terrain of the lunar surface.
[0005] The purpose of the present invention can be achieved by the following technical solution: A method for high-resolution terrain reconstruction of the permanent shadow area of the moon based on the secondary scattering light shadow method, comprising the following steps:
[0006] S1. Based on the solar direct irradiance map and contour information, locate the scattering source in the shadow area and obtain all the scattering sources in the shadow area;
[0007] S2, clustering processing is performed on multiple scattering sources, and the view table of the shadow surface element is updated;
[0008] S3. Construct the secondary irradiance model of the shadow area and the multi-scattering source photometric equation, combine the regularization term of the smoothness constraint and the initial DEM (Digital Elevation Model) constraint, establish the SS-SFS (Secondary Scattering Shape from Shading) objective function, and obtain the high-resolution terrain reconstruction result through optimization solution.
[0009] Furthermore, the step S1 includes the following steps:
[0010] S11. Based on the solar direct irradiance map and contour information, extracting the effective solar direct area that can reflect light to the shadow area from the direct area;
[0011] S12. Based on the extracted effective direct illumination area, construct the view table of each shadow surface element of PSRs and locate all scattering sources.
[0012] Furthermore, the specific process of step S11 is as follows:
[0013] Define a map area with PSRs as the center and surrounding reflective terrain with a side length of 8 kilometers. Use a high-precision illumination modeling method based on a variable-resolution horizon to generate a direct solar illumination map of the area at the time of image capture, and remove all facets in shadow.
[0014] The solar illumination map is then used to calculate the irradiance map. The relative irradiance value of each direct surface element l is defined as
[0015]
[0016] Among them, θ l is the incident angle of surface element l;
[0017] By analyzing the contour information generated by DEM, the effective direct illumination area that can reflect sunlight to the PSR area is screened out. That is, with the assistance of contour lines, the area that may produce effective secondary illumination is extracted.
[0018] Furthermore, the specific process of step S12 is as follows:
[0019] Based on the filtered effective direct illumination area, a view table of each shadow surface element is constructed to encode the visibility relationship between the shadow surface element and these direct illumination surfaces. The view table is used to determine whether the shadow surface element i can see the direct illumination surface element j, which is expressed as:
[0020]
[0021] Through the viewshed construction, the visible incident surface element of each shadow surface element, that is, the coordinates of the corresponding scattering source and its irradiance value are accurately calculated, so as to reconstruct the secondary illumination process of the shadow area and provide the secondary illumination irradiance calculation input value for the SS-SFS photometric equation.
[0022] Furthermore, the step S2 comprises the following steps:
[0023] S21, obtaining the coordinates and gradient features of each scattering source, and clustering the scattering sources using a K-means algorithm to divide the multiple scattering sources into k clusters;
[0024] S22: Update the view table of shadow surface element i.
[0025] Furthermore, the specific process of step S21 is as follows:
[0026] Assume that shadow surface i corresponds to n scattering sources {Sun1,Sun2,...,Sun n}, and k preset cluster centers {C1,C2,...,C k}, each scattering source will be associated with a cluster center, and the goal of the K-means clustering algorithm is to minimize the distance between each scattering source and its nearest cluster center. The formula is as follows:
[0027]
[0028] Among them, δ(S i ,C j ) represents the scattering source S i With cluster center C j The association value is 1 when S i Belongs to C j , otherwise 0; ||S i -C j || represents the scattering source S i With cluster center C j The Euclidean distance between
[0029] After clustering is completed, according to each scattering source S i With its cluster center C j The minimum Euclidean distance is used to divide the n scattering sources into k clusters. The coordinates of the scattering source closest to each cluster center are selected as the coordinates of the cluster center, and the irradiance value of each cluster is the sum of the irradiance values of all scattering sources in the category:
[0030]
[0031] in, is the cluster center C j The irradiance value, S is the scattering source i irradiance value.
[0032] Furthermore, step S3 includes the following steps:
[0033] S31. In the secondary scattering scene, for the incident irradiance of the shadow surface element, the contribution of all direct sunlight surfaces in the field of view is considered, and the secondary scattering light and shadow method brightness equation considering multiple incidents is established;
[0034] S32, combining brightness constraint, smoothness constraint and initial terrain elevation constraint, establishing the objective function of the secondary scattering light and shadow method;
[0035] S33. The Levenberg-Marquardt algorithm is used to minimize the objective function and obtain the high-resolution terrain reconstruction result.
[0036] Furthermore, the brightness equation of the secondary scattered light and shadow method in step S31 is specifically:
[0037]
[0038] Where I represents the image intensity, A represents the terrain-related albedo, and R(Z sfs ) represents the surface reflectivity, T represents the image exposure time, is the secondary illumination irradiance from incident surface element j to shadow surface element i, I j is the irradiance value of incident surface element j;
[0039] is the energy exchange ratio from facet j to facet i, that is, the view factor between incident facet j and shadow facet i in the field of view of shadow facet i;
[0040] A j is the area of incident surface element j, d is the line of sight distance connecting the two surface elements, θ1 is the emission angle of the outgoing scattered light at the incident surface element j, and θ2 is the incident angle of the incident scattered light at the shadow surface element i.
[0041] Furthermore, the objective function of the secondary scattered light and shadow method in step S32 is specifically:
[0042] E t =E Multi_I ++γ1E abs +γ2E smooth
[0043] Among them, E Multi_I is the brightness constraint, E abs is the initial terrain elevation constraint, E sMooth is a smoothness constraint, and γ1 and γ2 are regularization parameters.
[0044] Furthermore, the brightness constraint is specifically:
[0045]
[0046] The initial terrain elevation constraint is specifically:
[0047]
[0048] Among them, Z represents the prior elevation, Z sfs Indicates the optimized elevation;
[0049] The smoothness constraint is specifically:
[0050]
[0051] in, Represents the first partial derivative of the optimized terrain elevation.
[0052] Compared with the prior art, the present invention has the following advantages:
[0053] The present invention realizes the efficient positioning of the scattering sources corresponding to the face elements in the shadow area by using contour lines and illumination models to assist in visual analysis. Then, the extracted multiple scattering sources are clustered based on gradient and elevation features, successfully simplifying the number of multiple scattering sources. Subsequently, a photometric equation considering the secondary irradiance in the shadow area is constructed, and the optimization objective function of the secondary scattering light and shadow method is established by combining the smoothing and initial DEM constraint regularization terms, thereby realizing the generation of a high-resolution terrain model of the lunar PSRs, which can effectively process high-resolution images of indirect imaging of the lunar shadow area and realize the fine reconstruction of the three-dimensional terrain of the lunar surface.
[0054] In order to solve the problem of high computational complexity in the process of locating scattering sources in shadow areas, the present invention proposes an auxiliary processing framework based on contour lines and illumination models, including the generation of irradiance maps of direct sunlight areas and contour-assisted scattering source positioning in shadow areas. Through the direct sunlight irradiance map and contour line information, the effective direct sunlight areas that can reflect light to the shadow areas are extracted from the direct sunlight areas, and then the view table of the PSRs face element is constructed based on this, which can improve the efficiency of constructing the view table and thus efficiently locate all scattering sources.
[0055] The present invention proposes a clustering simplification method which takes into account the geometric characteristics of scattering sources. By effectively clustering multiple scattering sources, the number of considered scattering sources is minimized, thereby simplifying the calculation complexity of the subsequent loss function, which is beneficial to solving the problem of complex objective function construction and optimization of the light and shadow method caused by multiple scattering sources.
[0056] The present invention completes the construction and optimization of the SS-SFS objective function by constructing a secondary irradiance model for the shadow area and a multi-scattering source photometric equation, and combining the regularization terms of the smoothness constraint and the initial DEM constraint, thereby solving the problem that the traditional light and shadow method cannot process multi-light source indirect imaging images, and can realize the generation of high-resolution terrain models of the lunar PSRs, which is well suitable for processing indirect imaging images for fine reconstruction of the three-dimensional terrain in the shadow area of the moon. BRIEF DESCRIPTION OF THE DRAWINGS
[0057] Figure 1 It is a schematic diagram of the method flow of the present invention;
[0058] Figure 2 It is a schematic diagram of the application process of the embodiment;
[0059] Figure 3 This is a schematic diagram of the process of locating the surface element scattering source and constructing the viewshed in the shadow area;
[0060] Figure 4 Schematic diagram of the simplified process of clustering multiple scattering sources;
[0061] Figure 5 This is a schematic diagram of the experimental area data set in the embodiment;
[0062] Figure 6a~6e The LOLADEM and reconstructed SS-SFSDEM in the examples, as well as the renderings of each DEM;
[0063] Figure 7 It is the absolute difference map of pixel-by-pixel elevation between SS-SFSDEM and LOLADEM in the embodiment;
[0064] Figure 8 It is a comparison diagram of SS-SFSDEM and LOLADEM elevation profiles of detailed terrain in the embodiment;
[0065] Figure 9a-9b Schematic diagram of the elevation difference between LOLADEM, SS-SFSDEM and LOLA laser points in the embodiment. DETAILED DESCRIPTION
[0066] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.
[0067] Example
[0068] like Figure 1 As shown, a high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light shadow method includes the following steps:
[0069] S1. Based on the solar direct irradiance map and contour information, locate the scattering source in the shadow area and obtain all the scattering sources in the shadow area;
[0070] S2, clustering processing is performed on multiple scattering sources, and the view table of the shadow surface element is updated;
[0071] S3. Construct the secondary irradiance model of the shadow area and the photometric equation of multiple scattering sources, combine the regularization term of the smoothness constraint and the initial DEM constraint, establish the objective function of the SS-SFS secondary scattering light and shadow method, and obtain the high-resolution terrain reconstruction result through optimization solution.
[0072] This embodiment applies the above solution, such as Figure 2 As shown in the figure, it mainly includes three parts: (1) positioning of multiple scattering sources that illuminate shadow planes; (2) simplification of multiple scattering sources; and (3) construction and optimization of the objective function of the multi-scattering source light and shadow method optimization. In view of the high computational complexity of the shadow area scattering source positioning process, a set of contour line and illumination model auxiliary processing frameworks are proposed, including the generation of irradiance maps in direct sunlight areas and contour line-assisted shadow area scattering source positioning.
[0073] Aiming at the problem that multiple scattering sources make the construction and optimization of the objective function of the light and shadow method complicated, a clustering simplification method considering the geometric characteristics of the scattering sources is proposed to minimize the number of scattering sources considered.
[0074] Aiming at the problem that traditional light and shadow methods cannot handle indirect imaging of multiple light sources, a secondary irradiance model of the shadow area and a photometric equation of multiple scattering sources were constructed. The regularization terms of smoothness constraints and initial DEM constraints were combined to complete the construction and optimization of the SS-SFS objective function.
[0075] Specific:
[0076] 1. Location of scattering sources in shadow areas
[0077] Light and shadow reconstruction requires known light source geometry and irradiance information, so the scattering source in the shadow area is located first. For complex secondary scattering scenes, this scheme proposes a shadow area scattering source location method that efficiently restores the PSRs lighting process. Through the direct sunlight irradiance map and contour information, the effective direct sunlight area that can reflect light to the shadow area is extracted from the direct sunlight area. Based on the extracted effective direct sunlight area, the view table of the PSRs face element is constructed to locate all scattering sources. Figure 3 This workflow is demonstrated.
[0078] To ensure accurate restoration of secondary illumination, we first define a map region of surrounding reflective terrain centered on the PSRs with a side length of 8 km. A high-precision illumination modeling method based on a variable-resolution horizon is used to generate a direct solar illumination map of the region at the time of image capture, removing all facets in shadow. Then, the solar illumination map is used to calculate the irradiance map, and the relative irradiance value of each direct facet l is defined as
[0079]
[0080] Among them, θ l represents the incident angle of surface element l.
[0081] Due to terrain shading, not all areas with direct sunlight can reflect light to the shadow area. This solution further screens out effective direct sunlight areas that can reflect sunlight to the PSR area by analyzing the contour information generated by DEM (Digital Elevation Model). Contour lines are curves that represent the height of the terrain. Through them, we can understand the undulations and slope direction of the terrain, and thus determine which areas have the conditions to effectively reflect light to the PSR. This method significantly reduces unnecessary calculations and improves the efficiency of viewshed table construction. Figure 3 As shown in (a), the area in the red box cannot scatter light into the PSRs due to terrain occlusion, while the area in the white box may illuminate part of the PSRs. With the help of contour lines, these areas that may produce effective secondary illumination are accurately extracted.
[0082] Finally, based on the filtered effective direct illumination area, a view table of each shadow surface element is constructed to encode the visibility relationship with these direct illumination surfaces. The view table is used to determine whether the shadow surface element i can see the direct illumination surface element j, which can be expressed as:
[0083]
[0084] Through the viewshed construction, the visible incident surface element of each shadow surface element, that is, the coordinates of the corresponding scattering source and its irradiance value are accurately calculated, so as to reconstruct the secondary illumination process of the shadow area and provide the secondary illumination irradiance calculation input value for the SS-SFS photometric equation.
[0085] 2. Multi-scattering source clustering simplification
[0086] After obtaining all the direct surface elements corresponding to the shadow area, i.e., the scattering sources, in order to reduce the complexity of constructing and optimizing the SS-SFS loss function, this scheme proposes a clustering simplification method that considers the geometric characteristics of the scattering sources. By effectively clustering multiple scattering sources, the number of scattering sources considered is minimized, thereby simplifying the complexity of the loss function calculation. Figure 4 A simplified workflow for clustering of multiple scattering sources is demonstrated.
[0087] In this scheme, the coordinates and gradient features of each scattering source are first obtained, and the K-means algorithm is used to cluster these scattering sources. Assume that the shadow surface element i corresponds to n scattering sources {Sun1, Sun2, ..., Sun n}, and k preset cluster centers {C1,C2,...,C k}, each scatter source will be associated with a cluster center. The goal of the K-means clustering algorithm is to minimize the distance between each scatter source and its nearest cluster center, as follows:
[0088]
[0089] Among them, δ(S i ,C j ) represents the scattering source S i With cluster center C j The association value is 1 when S i Belongs to C j , otherwise 0; ||S i -C j || represents the scattering source S i With cluster center C j The Euclidean distance between .
[0090] After clustering is completed, according to each scattering source S i With its cluster center C j The minimum Euclidean distance is used to divide n scattering sources into k clusters. The coordinates of the scattering source closest to each cluster center are selected as the coordinates of the cluster center, and the irradiance value of each cluster is the sum of the irradiance values of all scattering sources in the category. The formula is as follows:
[0091]
[0092] in, is the cluster center C j The irradiance value, S is the scattering source i irradiance value.
[0093] Finally, the view table of shadow surface element i is updated. In this way, the processing of multiple scattering sources is effectively simplified and the computational complexity is reduced.
[0094] 3. Loss Function Construction and Optimization
[0095] The traditional light and shadow method refines the low-resolution DEM by the photometric relationship between image intensity and surface shape when processing images of infinitely far point light source scenes. The above relationship is described by the following brightness equation:
[0096]
[0097] Where I represents the image intensity; A represents the terrain-related albedo; R(Z sfs) represents the surface reflectance, using the Lunar-Lamber model; T represents the image exposure time; Represents the irradiance of the incident surface element. Since the light source is at infinity and the light and shadow method restores the relative elevation, it is usually set to 1.
[0098] In the secondary scattering scenario, the incident irradiance of the shadow plane needs to consider the contribution of all the direct sun planes in its field of view. This solution constructs the secondary scattering multi-light source light and shadow method loss function, which is as follows:
[0099] For each shadow surface i, the view factor between the incident surface j and the shadow surface i in its field of view is The calculation formula is:
[0100]
[0101] in, A represents the energy exchange ratio from panel j to panel i; j is the area of the incident surface element j; d is the line of sight distance connecting the two surface elements; γ1 is the emission angle of the outgoing scattered light at the incident surface element j, and θ2 is the incident angle of the incident scattered light at the shadow surface element i.
[0102] The secondary illumination irradiance from incident surface element j to shadow surface element i is:
[0103]
[0104] Among them, I j is the irradiance value of the incident surface element j. Therefore, the brightness equation of the secondary scattering light and shadow method considering multiple incidents is as follows:
[0105]
[0106] Then, the objective function of the secondary scattering light and shadow method is constructed, including brightness constraints, smoothness constraints, and initial terrain elevation constraints:
[0107] E t =E Multi_I ++γ1E abs +γ2E smooth (9)
[0108] Among them, the first term E Multi_I is the data term, the last two are regularization terms, and γ1 and γ2 are regularization parameters. The first term is mainly the deviation between the estimated surface reflectivity and the acquired image intensity:
[0109]
[0110] The absolute elevation constraint is constructed based on the a priori elevation of the initial low-resolution DEM as follows:
[0111]
[0112] Among them, Z represents the prior elevation, Z sfs Indicates the optimized elevation.
[0113] The smoothness constraint is defined as follows:
[0114]
[0115] in, Represents the first partial derivative of the optimized terrain elevation.
[0116] These partial derivatives and the surface normal are calculated using the central difference method. The initial albedo A(x,y) is set to 1 and its scale is incorporated into the image exposure time T. Then, the image exposure time T(x,y) is derived using the relationship that image intensity equals exposure time multiplied by reflectivity. Finally, the Levenberg-Marquardt algorithm is used to minimize the objective function.
[0117] The effectiveness of this solution has not been verified. This embodiment uses ShadowCam images and LOLA DEM as experimental data. The high sensitivity of the ShadowCam camera can effectively utilize the sunlight reflected from the nearby terrain to the shadow area, and can obtain high-resolution images (about 2 meters) of the shadow area of the moon. The detailed information of the images used is shown in Table 1. The laser altimetry LOLADEM of the corresponding area is selected as the low-resolution DEM that provides elevation constraints, and the projected image is manually aligned to the LOLADEM. Figure 5 The experimental dataset is presented, including the initial DEM and ShadowCam images, where the ShadowCam images and PSR range shp are covered on the 9km×9km LOLA DEM. The area is located between Shackleton Crater and Slater Crater, with complex terrain including craters of various sizes.
[0118] Table 1 Detailed information of images used in the experiment
[0119] Image Name Shooting time Angle of incidence Outgoing Angle Resolution M016603040S 2023-02-13 87.055° 0.023° 1.83m
[0120] The proposed method was used to generate a high-resolution DEM (1.8 m) using ShadowCam images (1.8 m) and LOLA DEM (5 m), and the accuracy of the reconstructed DEM was verified by correlation analysis and comparison with LOLA laser points. Figure 6a~6d The initial LOLA DEM and SS-SFSDEM are shown in Figure 6a and 6b ) as shown. Figure 6c and 6dThe hillshade renderings of LOLA DEM and SS-SFSDEM are shown in Figure 2. Figure 6e Qualitative comparison with the ShadowCam image shown in Figure 2 shows that the SS-SFS DEM effectively preserves almost all the impact craters in the original ShadowCam image, while the LOLA DEM fails to identify some impact craters. In addition, the correlation coefficients between the hillshade renderings of different DEMs and the ShadowCam image are calculated. Compared with the LOLA DEM (0.46), the SS-SFSDEM has a higher correlation value (0.83), indicating that the SS-SFSDEM has more terrain details and its rendering has improved correlation with the image.
[0121] Figure 7 The absolute difference of pixel-by-pixel elevation between SS-SFSDEM and LOLA DEM is shown. Figure 7 It can be seen that the maximum difference between LOLADEM and SS-SFSDEM is 2.25m, and the mean absolute difference (MAD) and standard deviation (Stdv) are 0.144m and 0.138m, respectively. This difference is mainly due to the fact that SS-SFSDEM provides a higher spatial resolution and captures more detailed terrain information than LOLA DEM. The smaller MAD value between LOLA DEM and SS-SFSDEM indicates that the initial elevation constraint provided by LOLA DEM is crucial to ensure the overall accuracy of the proposed SS-SFS method in large-area reconstruction.
[0122] Figure 8 A detailed comparison of the elevation profiles of LOLADEM and SS-SFSDEM is shown. The profile intersects a crater that does not exist in LOLADEM and is partially reconstructed in SS-SFSDEM, showing a distinct concave shape while remaining consistent with LOLADEM in low-frequency areas. The comparison of elevation profiles shows that the SS-SFS method has the advantage of reconstructing the small-scale topography missing in LOLADEM. The recovered details are also the main source of the difference between LOLADEM and SS-SFSDEM.
[0123] In addition, the low-frequency topographic accuracy of SS-SFSDEM was verified by using the adjusted LOLA laser points and filtering out the points with distribution slopes less than 8°. Figure 9a-9b As shown (laser points are superimposed on ShadowCam imagery, and colors indicate the absolute error between the DEM and the adjusted LOLA laser points). Figure 9a and 9bThe differences between the laser points and the LOLA DEM and SS-SFSDEM are shown. The differences between the SS-SFSDEM and the laser points are mostly below 0.5m, and some differences greater than 1 meter are observed in the shadow areas of the image. The Stdv of the LOLA DEM and SS-SFSDEM are 0.099m and 0.133m, and the MAD is 0.105m and 0.157m, respectively. The results show that the low-frequency accuracy of the SS-SFSDEM relative to the reference laser points is comparable to that of the LOLA DEM.
[0124] In summary, this scheme uses indirect imaging images and low-resolution terrain models as input, and finally reconstructs a high-resolution terrain model at the image pixel level through key technologies such as shadow area scattering source positioning, multi-scattering source simplification, and multi-scattering source light and shadow method objective function construction. This scheme can effectively process high-resolution images of indirect imaging in the shadow area of the moon and realize fine reconstruction of the three-dimensional terrain of the lunar surface.
Claims
1. A high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light shadow method, characterized in that: The following steps are involved: S1. Based on the solar direct irradiance map and contour information, locate the scattering source in the shadow area and obtain all the scattering sources in the shadow area; S2, clustering processing is performed on multiple scattering sources, and the view table of the shadow surface element is updated; S3. Construct the secondary irradiance model of the shadow area and the photometric equation of multiple scattering sources, combine the regularization term of the smoothness constraint and the initial DEM constraint, establish the objective function of the SS-SFS secondary scattering light and shadow method, and obtain the high-resolution terrain reconstruction result through optimization solution.
2. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 1 is characterized in that: The step S1 comprises the following steps: S11. Based on the solar direct irradiance map and contour information, extracting the effective solar direct area that can reflect light to the shadow area from the direct area; S12. Based on the extracted effective direct illumination area, construct the view table of each shadow surface element of PSRs and locate all scattering sources.
3. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 2 is characterized in that: The specific process of step S11 is as follows: Define a map area with PSRs as the center and surrounding reflective terrain with a side length of 8 kilometers. Use a high-precision illumination modeling method based on a variable-resolution horizon to generate a direct solar illumination map of the area at the time of image capture, and remove all facets in shadow. The solar illumination map is then used to calculate the irradiance map. The relative irradiance value of each direct surface element l is defined as Among them, θ l is the incident angle of surface element l; By analyzing the contour information generated by DEM, the effective direct illumination area that can reflect sunlight to the PSR area is screened out. That is, with the assistance of contour lines, the area that may produce effective secondary illumination is extracted.
4. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 3 is characterized in that: The specific process of step S12 is as follows: Based on the filtered effective direct illumination area, a view table of each shadow surface element is constructed to encode the visibility relationship with these direct illumination surfaces. The view table is used to determine whether the shadow surface element i can see the direct illumination surface element j, which is expressed as: Through the viewshed construction, the visible incident surface element of each shadow surface element, that is, the coordinates of the corresponding scattering source and its irradiance value are accurately calculated, so as to reconstruct the secondary illumination process of the shadow area and provide the secondary illumination irradiance calculation input value for the SS-SFS photometric equation.
5. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 4 is characterized in that: The step S2 comprises the following steps: S21, obtaining the coordinates and gradient features of each scattering source, and clustering the scattering sources using a K-means algorithm to divide the multiple scattering sources into k clusters; S22: Update the view table of shadow surface element i.
6. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 5 is characterized in that: The specific process of step S21 is as follows: Assume that shadow surface i corresponds to n scattering sources {Sun1,Sun2,...,Sun n }, and k preset cluster centers {C1,C2,...,C k }, each scattering source will be associated with a cluster center, and the goal of the K-means clustering algorithm is to minimize the distance between each scattering source and its nearest cluster center. The formula is as follows: Among them, δ(S i ,C j ) represents the scattering source S i With cluster center C j The association value is 1 when S i Belongs to C j , otherwise 0; ||S i -C j || represents the scattering source S i With cluster center C j The Euclidean distance between After clustering is completed, according to each scattering source S i With its cluster center C j The minimum Euclidean distance is used to divide the n scattering sources into k clusters. The coordinates of the scattering source closest to each cluster center are selected as the coordinates of the cluster center, and the irradiance value of each cluster is the sum of the irradiance values of all scattering sources in the category: in, is the cluster center C j The irradiance value, S is the scattering source i irradiance value.
7. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 6 is characterized in that: The step S3 comprises the following steps: S31. In the secondary scattering scene, for the incident irradiance of the shadow surface element, the contribution of all direct sunlight surfaces in the field of view is considered, and the secondary scattering light and shadow method brightness equation considering multiple incidents is established; S32, combining brightness constraint, smoothness constraint and initial terrain elevation constraint, establishing the objective function of the secondary scattering light and shadow method; S33. The Levenberg-Marquardt algorithm is used to minimize the objective function and obtain the high-resolution terrain reconstruction result.
8. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 7 is characterized in that: The brightness equation of the secondary scattered light and shadow method in step S31 is specifically: Where I represents the image intensity, A represents the terrain-related albedo, and R(Z sfs ) represents the surface reflectivity, T represents the image exposure time, is the secondary illumination irradiance from incident surface element j to shadow surface element i, I j is the irradiance value of incident surface element j; is the energy exchange ratio from facet j to facet i, that is, the view factor between incident facet j and shadow facet i in the field of view of shadow facet i; A j is the area of incident surface element j, d is the line of sight distance connecting the two surface elements, θ1 is the emission angle of the outgoing scattered light at the incident surface element j, and θ2 is the incident angle of the incident scattered light at the shadow surface element i.
9. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 8 is characterized in that: The objective function of the secondary scattering light and shadow method in step S32 is specifically: AND t =And Multi_I ++γ1E abs +γ2E smooth Among them, E Multi_I is the brightness constraint, E abs is the initial terrain elevation constraint, E smooth is a smoothness constraint, and γ1 and γ2 are regularization parameters.
10. The high-resolution terrain reconstruction method for the permanent shadow area of the moon based on the secondary scattering light and shadow method according to claim 9 is characterized in that: The brightness constraint is specifically: The initial terrain elevation constraint is specifically: Among them, Z represents the prior elevation, Z sfs Indicates the optimized elevation; The smoothness constraint is specifically: in, Represents the first partial derivative of the optimized terrain elevation.