Asteroid global terrain three-dimensional reconstruction method for illumination change

Abstract

The present application relates to a kind of asteroid global terrain three-dimensional reconstruction method for illumination change, comprising the following steps: input asteroid optical image, estimate camera pose and generate sparse point cloud, initialize Gaussian radiation field;Using image segmentation large model outputs the segmentation mask of asteroid optical image, prunes Gaussian radiation field;In combination with the mixed mask output by Gaussian radiation field, identify the shadow area of asteroid surface;The camera position, spherical harmonic coefficient and hash coding are combined into incident light angle, input into neural network, and the color value of Gaussian cell of illumination and shadow area is regressed;Add depth normal consistency loss and rotation variance and scale constraint loss, combine photometric loss to jointly supervise the optimization of Gaussian radiation field, calculate Gaussian opacity field, extract the three-dimensional model of asteroid global terrain.The present application can identify the shadow area on asteroid, improve the three-dimensional reconstruction precision of asteroid with surface illumination change.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of deep space exploration, and in particular to a small asteroid global terrain three-dimensional reconstruction method for illumination changes. BACKGROUND

[0002] Three-dimensional reconstruction using optical images is a computer vision technology that aims to recover the three-dimensional information of the original model from the input multi-view images. Small asteroid global terrain three-dimensional reconstruction technology is crucial in scientific research, which helps to study the formation and evolution of the solar system, and provides key support for planetary defense of the Earth. Traditional visual-based small asteroid three-dimensional reconstruction methods, such as SPG and SPC, have problems such as large data demand, high artificial involvement, and long reconstruction period. With the rapid development of small asteroid deep space exploration technology, there is an increasing demand for faster and more intelligent small asteroid three-dimensional reconstruction.

[0003] Due to the wide application of deep learning technology, neural implicit three-dimensional reconstruction methods are used for small asteroid global terrain three-dimensional reconstruction, but such methods have problems such as long training time and large computational overhead. In recent years, 3D Gaussian radiation field (3DGS) has shown excellent reconstruction speed and quality in three-dimensional modeling tasks. This method uses a series of Gaussian primitives to efficiently express the geometric structure and color information of the scene, and combines rasterization technology to greatly speed up the training process.

[0004] However, existing 3DGS methods are mainly designed for regular ground scenes, and have not been optimized for the characteristics of remote sensing images in deep space exploration tasks. Small asteroids in deep space environments are only illuminated by parallel sunlight, which is different from the case of multiple light sources in ground environments, resulting in more complex and variable distribution of reflected light intensity on the surface of small asteroids. In addition, the irregular shape of small asteroids causes occlusion, and the parallel incident sunlight casts shadows on their surfaces. With the rotation of small asteroids, the illumination intensity of the shadow area changes periodically, which causes errors in surface reconstruction. Therefore, the reconstruction technology based on Gaussian radiation field has great development potential in the study of small asteroid global terrain three-dimensional reconstruction in deep space environments.

[0005] For small asteroid global terrain three-dimensional reconstruction methods, the deficiencies of existing technologies mainly manifest in the following aspects: (1) large data demand, high dependence on manual intervention, low automation level, and long reconstruction period; (2) long training time, high memory occupation, and large computational overhead; (3) difficulty in modeling complex illumination changes on the surface of small asteroids, and large reconstruction errors for shadow areas with insufficient illumination. SUMMARY

[0006] The technical problem solved by the present application is to overcome the shortcomings of the prior art and provide a small asteroid global terrain three-dimensional reconstruction method facing illumination changes, which improves the intelligent degree and reconstruction speed of the model based on the existing method, solves the problem of large reconstruction error caused by illumination changes, and realizes high-precision three-dimensional reconstruction using small asteroid optical images taken by a detector.

[0007] The technical solution of the present application is a small asteroid global terrain three-dimensional reconstruction method facing illumination changes, comprising the following steps:

[0008] Step 1, input the small asteroid optical image, estimate the camera pose using the SFM method and generate a sparse point cloud, initialize the Gaussian radiation field using the sparse point cloud, and generate an initial set of Gaussian primitives;

[0009] Step 2, for the initial Gaussian primitive set generated in step 1, use the SAM method to output a segmentation mask of the small asteroid optical image, and use the segmentation mask to prune the Gaussian radiation field;

[0010] Step 3, for the pruned Gaussian radiation field in step 2, output a mixed mask of the small asteroid optical image, and identify the shadow area on the surface of the small asteroid by combining the segmentation mask output by the SAM in step 2;

[0011] Step 4, use position coding to process the coordinates of the camera center, use spherical harmonic coefficients to represent the initial color of the Gaussian primitive, use hash grid to encode the coordinates of the Gaussian primitive, and combine the angle of the incident light to input the four into two neural networks to regress the color value of the Gaussian primitive in the illumination and shadow area respectively;

[0012] Step 5, add depth normal consistency loss, rotation variance and scale constraint loss in the loss function, and combine the photometric loss to jointly supervise the optimization of the Gaussian radiation field;

[0013] Step 6, for the final optimization result of the Gaussian radiation field in step 5, calculate the Gaussian opacity field, and use an improved marching tetrahedron algorithm to generate a three-dimensional model of the global terrain of the small asteroid.

[0014] The advantages of the present application compared with the prior art are:

[0015] (1) The present application adopts an adaptive Gaussian radiation field pruning method, and improves the densification result of the Gaussian primitive by statistical filtering, effectively eliminating the interference of noise in the deep space environment. Depth normal consistency loss, rotation variance and scale constraint loss of Gaussian primitive are also adopted, which improves the accuracy of small asteroid global terrain three-dimensional reconstruction.

[0016] (2) The present application combines the segmentation mask of SAM and the The hybrid mask predicts the shadow area of the asteroid surface, fuses the illumination information into the neural network to regress the color value of the Gaussian cell, extracts the surface model by calculating the Gaussian opacity field and the improved marching tetrahedron algorithm, and improves the accuracy of the three-dimensional reconstruction of the asteroid surface with illumination changes.

[0017] In summary, the method adopted by the application has simple principles, and can achieve the purpose of three-dimensional reconstruction of the global terrain of an asteroid using optical images taken by a detector. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 A flowchart of a method for three-dimensional reconstruction of global terrain of an asteroid with illumination changes. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the application clearer, the application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the application and do not limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other. In order to achieve the above purpose, the application adopts the following technical solutions.

[0020] As shown in Figure 1 A method for three-dimensional reconstruction of global terrain of an asteroid with illumination changes, the specific implementation steps are as follows:

[0021] Step 1, input the optical image of the asteroid, estimate the camera pose and generate the sparse point cloud using the SFM method, initialize the Gaussian radiation field using the sparse point cloud, and generate the initial set of Gaussian cells;

[0022] Step 2, for the initial Gaussian cell set generated in step 1, use the SAM method to output the segmentation mask of the optical image of the asteroid, and use the segmentation mask to prune the Gaussian radiation field;

[0023] Step 3, for the pruned Gaussian radiation field in step 2, output the hybrid mask of the optical image of the asteroid, and combine the segmentation mask output by the SAM in step 2 to identify the shadow area of the asteroid surface;

[0024] Step 4, use position coding to process the coordinates of the camera center, use spherical harmonic coefficients to represent the initial color of the Gaussian cell, use hash grid to encode the coordinates of the Gaussian cell, and combine the angle of the incident light to input the four into two neural networks to regress the color value of the Gaussian cell of the illumination and the shadow area, respectively;

[0025] ​Step 5: Add depth normal consistency loss, rotation variance and scale constraint loss to the loss function, and combine them with photometric loss to jointly supervise the optimization of the Gaussian radiation field;

[0026] Step 6: Based on the final optimization result of the Gaussian radiation field in Step 5, calculate the Gaussian opacity field and use the improved traveling tetrahedron algorithm to generate a three-dimensional model of the asteroid's global terrain.

[0027] In step 1, firstly, dozens of optical images of the asteroid taken by the probe are input, and the pose of the moving camera is estimated from the multi-view optical images using the structure of motion (SFM) method to generate a sparse point cloud of the asteroid model. The Gaussian radiation field is then initialized using this sparse point cloud.

[0028] The standard Gaussian radiation field method represents a 3D scene using a set of 3D Gaussian primitives, which are semi-transparent and anisotropic. Each 3D Gaussian primitive... Using 3D covariance matrix and mean Explicit parameterization:

[0029] ,

[0030] in, Defined as Specifically, the 3D covariance matrix is ​​decomposed into a scaling matrix. and a rotation matrix This is to facilitate optimization. Mean It can be regarded as the center of the 3D Gaussian unit. It is a 3D point near that location.

[0031] In addition, each 3D Gaussian element also has color. and opacity These two properties are used for differentiable point-based functions. Hybridization. Therefore, the k-th 3D Gaussian element in the scene contains the following five properties:

[0032] ,

[0033] in, It is a rotation matrix Quaternions, It is a scaling matrix A three-dimensional vector, It is the center of the 3D Gaussian primitive. The center of the 3D Gaussian primitive is initialized using the position and color information of the sparse point cloud. and color The distance from each point in the sparse point cloud to its nearest neighbor is calculated to initialize the 3D vector. , in addition, quaternions and opacity are initialized to zero.

[0034] The standard Gaussian radiance field locally approximates the perspective camera projection by an affine transformation to enable efficient rasterization rendering. Specifically, first, each 3D Gaussian cell is transformed to the camera coordinate system by the world-to-camera transformation matrix and then projected to the image plane by a local affine transformation :

[0035] ,

[0036] where the change matrix is derived from the camera pose estimated by the SFM method, the affine transformation is computed by the camera intrinsic parameters, is the covariance matrix in the camera coordinate system, and then the 2D Gaussian covariance matrix is obtained by skipping the last row and column. The matrix is used to compute the on the image plane and will be used in the subsequent point-based blending.

[0037] The standard Gaussian radiance field method sorts the 2D Gaussian projected to the image plane by depth, from front to back. Then, it adopts a differentiable point-based blending to integrate the weighted color into the rendered image:

[0038] ,

[0039] where is the final rendered pixel color, denotes the set of Gaussian cells aggregated by the rasterizer according to the color , is the index of the sorted Gaussian cell, is defined as , which serves as the blending weight of the point-based rendering.

[0040] In step 2, a visual segmentation large model (SAM) is used to generate the segmentation mask of the foreground in the asteroid image:

[0041] ,

[0042] where is the l-th input RGB image, is the estimator of the SAM, is the output segmentation mask from the 1th viewpoint. Pixels inside the foreground are set to 1, and pixels in the background are set to 0. Next, the center of the 3D Gaussian primitive is projected from the three-dimensional world space to the two-dimensional image plane, which is given by:

[0043] ,

[0044] where, is the center of the kth 3D Gaussian primitive in the scene, is the corresponding projected coordinate on the image. If is located inside the foreground of the segmentation mask , the primitive is kept; otherwise, it is discarded. During the optimization process, it is ensured that each 3D Gaussian primitive appears in the foreground of all segmentation masks, thus eliminating all background noise:

[0045] ,

[0046] where L is the summation of all viewpoints, denotes the remaining 3D Gaussian primitives. Directly pruning using the segmentation masks output by SAM can cause valid 3D Gaussian primitives to be removed incorrectly. To preserve valid 3D Gaussian primitives, a morphological dilation method is employed to obtain segmentation masks with larger foregrounds, which is given by:

[0047] ,

[0048] where, is the structuring element, is the pixel coordinate on the image, denotes the dilation operation, denotes the translation of the structuring element to the coordinate , is the dilated mask, which generates a binary image.

[0049] Next, a statistical filtering method is applied to adaptively prune 3D Gaussian primitives that are either too small or too scattered. Assuming there are K 3D Gaussian primitives in the Gaussian radiation field, the mean and variance of their scales are calculated. The scale is defined as the average size of each 3D Gaussian primitive in the x, y, and z axes:

[0050] ,

[0051] ,

[0052] where, and are the sample mean and variance of the 3D Gaussian primitive scales, is the kth primitive in The size on the axis. For each 3D Gaussian cell, when it is reserved, otherwise discarded. The threshold and are calculated as follows:

[0053] ,

[0054] where, is an adjustable coefficient of the scale variance, and can be regarded as the upper and lower limits of the scale.

[0055] Similarly, statistical filtering is used for the position of the 3D Gaussian cell. First, define a neighborhood for each cell and assign the nearest H cells to it. Then, calculate the average distance of this cell to all other cells in the neighborhood as follows:

[0056] ,

[0057] where, is the distance of the kth 3D Gaussian cell to the hth cell in its neighborhood, is the new distance attribute of the kth cell. Next, calculate the mean and variance of the distance of the K 3D Gaussian cells in the radiation field, and the threshold and :

[0058] ,

[0059] ,

[0060] where, and are the sample mean and variance of the distance, is an adjustable coefficient of the distance variance, and can be regarded as the adaptive threshold of the Gaussian radiation field. For each 3D Gaussian cell, when its distance attribute satisfies it is reserved; otherwise, it is pruned to get the pruned Gaussian radiation field. This helps to prune 3D Gaussian cells with excessively dispersed positions.

[0061] In step 3, for the pruned Gaussian radiation field, input the asteroid image from the training perspective, and the SAM can output the pixel-level segmentation mask. Input the corresponding perspective of the asteroid image, and the preliminarily trained Gaussian radiation field can output a mixed mask as follows:

[0062] ,

[0063] ,

[0064] where, is the blending weight defined in step 1 rendering process. The Gaussian radiance field has learned the approximate shape of the asteroid after preliminary training, so The blending mask can be regarded as an instance-level mask. By performing bitwise operations on the segmentation mask and the blending mask , the shadow region mask can be identified:

[0065] ,

[0066] where, is the index of the viewpoint, is the complement of . Mark the 3D Gaussian primitives projected to the shadow region, and use a separate MLP to regress their color values in the subsequent step. For the sake of distinction, the MLP for the shadow region is called shadow-MLP, while the MLP for the normal illumination is called illumination-MLP, and the architecture of the two is the same.

[0067] In step 4, although the reflectivity of the surface of different types of asteroids (C-type, S-type, M-type) is different, their surface illumination reflection model can be uniformly simplified to the Lambertian reflection model, the formula is as follows:

[0068] ,

[0069] where, is the reflected light intensity, is the incident light intensity, is the diffuse reflection coefficient of the surface material, is the direction of the incident light source, is the direction of the surface normal. The incident light intensity and the surface diffuse reflection coefficient are considered as fixed values for a given asteroid. However, the reflected light intensity will change due to the angle between the surface normal and the incident light direction, which varies with the shape of the asteroid. Calculate the angle between the incident light and each 3D Gaussian primitive and use it as one of the inputs to the MLP to regress the color:

[0070] ,

[0071] ,

[0072] where, is the center of the kth 3D Gaussian primitive, is the center of the Gaussian radiance field, is the position of the sun calculated according to the orbit, is the angle between the k-th 3D Gaussian cell and the incident light.

[0073] The camera extrinsics are estimated using SFM, and the camera center position is used as another input to the MLP to regress the color of the 3D Gaussian cell. Position encoding (PE) is applied to the camera center:

[0074] ,

[0075] where, is the scalar component of the camera center position coordinates. This procedure means mapping a low-dimensional space to a high-dimensional space .

[0076] In addition, the multi-resolution voxel grid is hashed (HE) to represent the Gaussian radiance field. The voxels surrounding the 3D Gaussian cell are identified, and a tri-linear interpolation is performed on each cell using the hash feature vectors of its corners. Then, the hash encodings at different resolutions are concatenated to obtain the hash feature:

[0077] ,

[0078] where R denotes the multi-resolution level. At the same time, the initial color of the 3D Gaussian cell is represented using 16-dimensional spherical harmonic coefficients, which are kept and optimized during the training process along with the hash feature for each 3D Gaussian cell. The angle between the incident light and the 3D Gaussian cell, the position encoding of the camera center, the spherical harmonic coefficients, and the hash feature are input into two shallow neural networks with the same structure, respectively, to regress the color values of the Gaussian cell in well-lit and shadowed areas.

[0079] In step 5, the photometric loss is used to supervise the training of the Gaussian radiance field:

[0080] ,

[0081] where, is the L1 loss between the real image and the rendered image, is the structural similarity index (SSIM) loss, is an adjustable coefficient for balancing the two losses. However, in the surface reconstruction task, the photometric loss alone lacks the necessary geometric constraints. Therefore, a depth-normal consistency loss is introduced to align the 3D Gaussian cells with the surface of the asteroid:

[0082] ,

[0083] where, is the index of the voxel intersected by the ray, is the mixing weight of the 3D Gaussian voxel, is the normal of the ith voxel, is the surface normal direction obtained by applying finite difference method on the depth map.

[0084] Since the surface of asteroid is usually covered by a weathered layer composed of broken rocks and dust, the surface texture is weak and the details are small. Therefore, it is necessary to limit the size of 3D Gaussian voxel and punish those with excessive scale to avoid producing too smooth local area, the scale constraint loss is represented as:

[0085] ,

[0086] where, i.e. limiting the scale of 3D Gaussian voxel by the maximum size on x, y, z axis.

[0087] For the direction loss of Gaussian voxel, the rotation quaternion of 3D Gaussian voxel is counted, and their variance is maximized, the rotation variance loss is represented as:

[0088] ,

[0089] where, represents the kth component of the quaternion of the kth Gaussian voxel, is the sample variance calculation, the sample variance is calculated for all Gaussian voxel quaternion components of the same dimension.

[0090] Finally, the total loss function includes four parts:

[0091] ,

[0092] where, represents the photometric loss, represents the depth-normal consistency loss, represents the scale constraint loss, represents the rotation variance loss, , , , is the weight of the corresponding loss function.

[0093] Step 6, calculate the Gaussian opacity field based on the final optimization result of Gaussian radiance field, and use the improved marching tetrahedron algorithm to generate the three-dimensional model of the global terrain of asteroid. Use the rendering method of sampling along the ray to construct a continuous Gaussian opacity field from the discrete 3D Gaussian voxel. The specific process is as follows:

[0094] ​First, the world coordinate system is converted to the local coordinate system of each primitive, and the scale is normalized:

[0095] ,

[0096] where (G) is the attribute of 3D Gaussian primitive, is the camera center, is the ray direction. Any point along the ray can be represented as where is the depth of the ray. After coordinate transformation, (G) is the attribute in the corresponding Gaussian coordinate system. In this local coordinate system, the Gaussian value of any point along the ray becomes one-dimensional Gaussian, which can be represented as:

[0097]

[0098] ,

[0099] For this one-dimensional Gaussian, the solution of the maximum value has a closed expression, and the calculation formula is as follows:

[0100] ,

[0101] For a single Gaussian primitive, the opacity of any point along the ray in space can be represented as:

[0102] ,

[0103] This means that the opacity along the ray monotonically increases and remains constant after reaching the maximum value. Therefore, given a set of 3D Gaussian primitives, the opacity of any point along the ray can be represented as:

[0104] ,

[0105] where is the blending weight defined in step 1 rendering process. Since any point in space can be seen by any training view, the opacity of any point in space can be defined by the minimum opacity value of all training views and observation directions:

[0106] ,

[0107] After constructing the Gaussian opacity field, a 3D bounding box can be generated for the position of each 3D Gaussian primitive. Then, the opacity at the center of each primitive and its bounding box vertices is calculated, and the opacity value minus 0.5 is taken as the signed distance function (SDF) value:​​

[0108] ,

[0109] Using the maximum dimension of each base element As the center of the base element and the dimension of its bounding box vertex, combined with the SDF value, the marching tetrahedron algorithm is used to extract the grid. Finally, the bisection method is used to determine the zero level set, and the global terrain three-dimensional model of the asteroid is extracted.

Claims

1. A method for global three-dimensional terrain reconstruction of asteroids accommodating illumination variations, characterized in that, The specific implementation steps are as follows: Step 1: Input an optical image of the asteroid, use the SFM method to estimate the camera pose and generate a sparse point cloud, use the sparse point cloud to initialize the Gaussian radiation field, and generate an initial set of Gaussian elements. Step 2: For the initial Gaussian element set generated in Step 1, use the SAM method to output the segmentation mask of the asteroid optical image, and use the segmentation mask to prune the Gaussian radiation field. Step 3: Output the asteroid optical image based on the Gaussian radiation field pruned in Step 2. The hybrid mask, combined with the segmentation mask output by SAM in step 2, identifies the shadowed areas on the asteroid's surface; Step 4: Use position encoding to process the coordinates of the camera center, use spherical harmonic coefficients to represent the initial color of the Gaussian elements, use hash grid encoding to encode the coordinates of the Gaussian elements, and combine the angle of the incident light rays to input the four into two neural networks, which are used to regress the color values ​​of the Gaussian elements in the illuminated and shadowed areas, respectively. Step 5: Add depth normal consistency loss, rotation variance and scale constraint loss to the loss function, and combine them with photometric loss to jointly supervise the optimization of the Gaussian radiation field; Step 6: Based on the final optimization result of the Gaussian radiation field in Step 5, calculate the Gaussian opacity field and use the improved traveling tetrahedron algorithm to generate a three-dimensional model of the asteroid's global terrain.

2. The method for three-dimensional reconstruction of global terrain of asteroids oriented towards illumination variations according to claim 1, characterized in that, In step 1, firstly, the optical images of the asteroid captured by the probe are input, and the pose of the moving camera is estimated from the multi-view optical images using the structure of motion recovery (SFM) method to generate a sparse point cloud of the asteroid model. The Gaussian radiation field is then initialized using this sparse point cloud. The standard Gaussian radiation field method represents a 3D scene using a set of 3D Gaussian primitives. These primitives are semi-transparent and anisotropic. Each 3D Gaussian primitive... Using 3D covariance matrix and mean Explicit parameterization: ， in, Defined as The 3D covariance matrix is ​​decomposed into a scaling matrix. and a rotation matrix mean Considered the central location of 3D Gaussian elements, These are 3D points near that location; each 3D Gothic element also has color. and opacity These two properties are used for differentiable point-based functions. In the hybrid scene, the k-th 3D Gaussian element contains the following five properties: ， in, It is a rotation matrix Quaternions, It is a scaling matrix A three-dimensional vector, The center of the 3D Gaussian primitive is initialized using the position and color information of the sparse point cloud. and color The distance from each point in the sparse point cloud to its nearest neighbor is calculated to initialize the 3D vector. In addition, quaternions and opacity Then perform zero initialization; A standard Gaussian radiation field is locally approximated through perspective camera projection via affine transformation to achieve efficient rasterization rendering; this includes, firstly, using a world-to-camera transformation matrix. Each 3D Gaussian primitive is transformed to the camera coordinate system, and then subjected to local affine transformation. Project it onto the image plane: ， Wherein, the transformation matrix Camera pose estimated by the SFM method, affine transformation This is calculated using the camera's internal parameters. This is the covariance matrix in the camera coordinate system. Then, by skipping the last row and the last column, we obtain the 2D Gaussian covariance matrix. ,matrix Used to calculate on the image plane And will be in the subsequent point-based Used in combination; The standard Gaussian radiation field method sorts the 2D Gaussians projected onto the image plane by depth, from front to back, and then employs a differentiable point-based approach. Blending integrates weighted colors into the rendered image: ， in, It is the final rendered pixel color. Indicates based on color Converged by rasterizer A set of Gaussian elements, It is the index of the sorted Gaussian elements. Defined as It serves as a blending weight for point-based rendering.

3. The method for three-dimensional reconstruction of global terrain of asteroids oriented towards illumination variations according to claim 2, characterized in that, In step 2, the visual segmentation large model (SAM) is used to generate a segmentation mask for the foreground in the asteroid image: ， in, It is the l-th input RGB image. It is an estimator for SAM. This is the output segmentation mask from the l-th viewpoint, where pixels in the foreground are set to 1 and background pixels are set to 0. Next, the center of the 3D Gaussian primitives is projected from the three-dimensional world space onto the two-dimensional image plane, as shown in the following formula: ， in, It is the center of the k-th 3D Gaussian element in the scene. These are the corresponding projected coordinates on the image, if Located in the segmentation mask If a primitive is found within the foreground, it is retained; otherwise, it is discarded. During optimization, each 3D Gaussian primitive is made to appear in the foreground of all segmentation masks, thereby eliminating all background noise. ， Where L is the sum of all viewpoints, The remaining 3D Gaussian elements are represented; the 3D Gaussian elements are expanded using a morphological dilation method to obtain a segmentation mask with a larger foreground, as shown in the following formula: ， in, It is a structural element. These are pixel coordinates on the image. This indicates an expansion operation. Indicates that the structural element Translate to coordinates , It is an inflated mask that generates a binary image. Next, a statistical filtering method is applied to adaptively remove 3D Gaussian elements with inappropriate scale and excessive dispersion. This includes: assuming there are K 3D Gaussian elements in the Gaussian radiation field, calculating the mean and variance of their scales, where the scale is defined as the average size of each 3D Gaussian element along the x, y, and z axes. ， ， in, and These are the sample mean and variance at the 3D Gaussian scale, respectively. Is the k-th primitive in The dimensions on the axis, for each 3D high-order element, when If it is, it is kept; otherwise, it is discarded. Statistical filtering is applied to the positions of 3D Gaussian primitives. First, a neighborhood is defined for each primitive, and the H nearest primitives are assigned to it. Then, the average distance between that primitive and all other primitives in the neighborhood is calculated, as follows: ， in, It is the distance between the k-th 3D Gaussian primitive and the h-th primitive in its neighborhood. To introduce a new distance attribute for the k-th primitive, we next calculate the mean and variance of the distances of the K 3D Gaussian primitives in the radiation field, as well as the threshold. and For each 3D Gaussian primitive, when its distance property satisfies If it is pruned, it is preserved; otherwise, it is pruned to obtain the pruned Gaussian radiation field.

4. The method for three-dimensional reconstruction of global terrain of asteroids oriented towards illumination variations according to claim 3, characterized in that, In step 3, for the pruned Gaussian radiation field, the asteroid image from the training viewpoint is input, and SAM outputs a pixel-level segmentation mask. The corresponding viewpoint of the asteroid image is input, and the Gaussian radiation field after preliminary training can output... Hybrid Mask As shown below: ， ， in, These are the blending weights defined during the rendering process in step 1. The Gaussian radiation field has already learned the approximate shape of the asteroid after initial training, therefore... The hybrid mask is treated as an instance-level mask, by segmenting the mask. and Hybrid Mask Perform bitwise operations to identify the mask in the shadow area. : , in, It is the viewpoint index. yes The complement of the MLP is used to mark the 3D Gaussian elements projected onto the shadow area, and their color values ​​are subsequently regressed using a separate MLP. For ease of distinction, the MLP for the shadow area is called the shadow-MLP, while the MLP for normal lighting is called the lighting-MLP. The architecture of the two is the same.

5. A method for three-dimensional reconstruction of global terrain of an asteroid oriented to varying illumination, as described in claim 4, is characterized in that... In step 4, the surface illumination reflection model for different types of asteroids is the Lambert reflection model, and the formula is as follows: , in, It is the intensity of reflected light. It is the intensity of the incident light. It is the diffuse reflectance coefficient of the surface material. It is the direction of the incident light source. The direction of the surface normal is used. Treating the incident light intensity and surface diffuse reflection coefficient as fixed values ​​for a given asteroid, the angle between the incident light and each 3D Gaussian unit is calculated and used as one of the inputs to the MLP to regress color. , , in, It is the center of the k-th 3D Gaussian element. It is the center of the Gaussian radiation field. It is the position of the sun calculated based on its orbit. It is the angle between the k-th 3D Gaussian element and the incident light; SFM is used to estimate the camera's extrinsics. The camera's center position is used as another input to the MLP to regress the 3D Gaussian colors. Position encoding PE is applied to the camera center. , in, These are the scalar components of the camera center position coordinates; this process implies transforming the lower-dimensional space... Mapping to higher-dimensional space ; A multi-resolution voxel mesh is hash-encoded HE to represent the Gaussian radiation field. Voxels surrounding 3D Gaussian primitives are identified, and each primitive is trilinearly interpolated using the hash eigenvectors of their corners. Then, hash encoding at different resolutions is performed. When concatenated, the hash characteristics are obtained: , Where R represents the multi-resolution level, the initial color of the 3D Gaussian unit is represented by spherical harmonic coefficients, the spherical harmonic coefficients of each 3D Gaussian unit are preserved and optimized together with the hash features during training, the angle between the incident light and the 3D Gaussian unit, the position encoding of the camera center, the spherical harmonic coefficients and the hash features are input together into two shallow neural networks with the same structure, which are used to regress the color values ​​of the Gaussian units in the lit and shadow areas.

6. A method for three-dimensional reconstruction of global terrain of an asteroid oriented to varying illumination, as described in claim 5, is characterized in that... In step 5, photometric loss is used. To supervise the training in the Gaussian radiation field: ， in, It is the L1 loss between the real image and the rendered image. It is the structural similarity index loss. It is an adjustable coefficient used to balance the two types of loss and introduces depth-normal consistency loss. Used to align 3D Gaussian elements with the surface of an asteroid: ， in, This serves as the index for the primitives that intersect along the ray's path. It is a hybrid weight of 3D Gaussian units. It is the normal of the i-th primitive. The surface normal direction is obtained by applying the finite difference method to the depth map; The scale constraint loss is expressed as: ， in, That is, the scale of 3D Gaussian elements is limited by the maximum size on the x, y, and z axes; For the orientation loss of Gaussian elements, we calculate the rotation quaternions of 3D Gaussian elements and maximize their variance. The rotation variance loss is expressed as: ， in, The quaternion representing the k-th Gaussian element. One portion, It is the calculation of sample variance, which is calculated for the quaternion components of the same dimension of all Gaussian elements; Ultimately, the total loss function consists of four parts: ， in, Indicates luminosity loss, This represents the depth-normal consistency loss. Represents the scale constraint loss. Indicates the rotational variance loss. , , , These are the weights of the corresponding loss function.

7. A method for three-dimensional reconstruction of global terrain of an asteroid oriented to varying illumination, as described in claim 6, is characterized in that... In step 6, a continuous Gaussian opacity field is constructed from discrete 3D Gaussian primitives using a ray-sampling rendering method. The specific process is as follows: First, transform the world coordinate system to the local coordinate system of each primitive, and then normalize the scale: ， in,( ) is a property of 3D Gaussian primitives. It is the center of the camera. It refers to the direction of the ray, along any point on the ray. It can be represented as ,in It is the depth of the ray, after coordinate transformation, ( ) represents the attribute in the corresponding Gaussian coordinate system; In this local coordinate system, the Gaussian value at any point along the ray becomes a one-dimensional Gaussian, expressed as: ， For this one-dimensional Gaussian, the solution to its maximum value has a closed-form expression, and the calculation formula is as follows: ， For a single Gaussian element, the opacity at any point along the ray in space is represented as: ， Given a set of 3D Gaussian primitives, the opacity at any point along a ray can be represented as: ， in, The blending weights are defined during the rendering process in step 1, and are used to define any point in space by the minimum opacity value across all training views and viewing directions. Opacity: ， After constructing the Gaussian opacity field, for each 3D Gaussian primitive... The location generates a 3D bounding box. Then, the opacity at the center of each primitive and at its bounding box vertices is calculated, and the opacity value is subtracted by 0.5 to obtain the signed distance function (SDF) value. ， Use the maximum scale of each primitive Using the primitive center and its bounding box vertex scale as the basis, combined with the SDF value, the traveling tetrahedron algorithm is used to extract the mesh; finally, the binary search method is used to determine the zero level set, and the global terrain 3D model of the asteroid is extracted.

8. A method for three-dimensional reconstruction of global terrain of an asteroid oriented to varying illumination, as described in claim 3, is characterized in that... threshold and Calculate as follows: ， in, It is the adjustable coefficient of scale variance. and It can be seen as the upper and lower limits of the scale.

9. A method for three-dimensional reconstruction of global terrain of an asteroid oriented to varying illumination, as described in claim 3, is characterized in that... threshold and The calculation method is as follows: ， ， in, and These are the sample mean and variance of the distance. It is the adjustable coefficient of the distance variance. and It can be viewed as an adaptive threshold for the Gaussian radiation field.

10. A method for three-dimensional reconstruction of global terrain of an asteroid oriented to varying illumination, as described in claim 3, is characterized in that... Different types of asteroids include C-type, S-type, and M-type.

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