Satellite image neural radiance field surface reconstruction method and device considering geometric prior

Abstract

This invention discloses a method and apparatus for surface reconstruction of satellite imagery neural radiation fields that takes geometric priors into account. The method first reconstructs the initial geometry and renders the initial normal vector based on the neural radiation field of SDF (Surface-Oriented Data). Then, it uses a geometric prior network to predict the prior normal vector. The Poisson equation is used to fuse prior smoothness with initial accuracy, correcting systematic biases. Furthermore, a multi-view photometric consistency adaptive verification is proposed, introducing smoothness constraints in flat areas and preserving geometric features in detailed areas. This invention, through a two-layer mechanism of Poisson correction and adaptive verification, effectively overcomes the generalization error of ground-trained prior networks under satellite views, significantly improving the reconstruction smoothness of weakly textured areas such as roads and water surfaces, while maintaining details such as building edges. It is suitable for large-scale 3D reconstruction of satellite imagery.

Description

Technical Field

[0001] This invention relates to the field of remote sensing image processing technology, specifically a method and apparatus for reconstructing the surface of the neural radiation field of satellite images that takes into account geometric priors. Background Technology

[0002] Satellite imagery, characterized by its wide global coverage, long observation periods, and large imaging range, is a crucial technological means for acquiring information about the Earth's surface. By constructing multi-view observation conditions using multi-temporal satellite imagery data, comprehensive reconstruction of the Earth's surface three-dimensional information can be achieved, providing technical support for large-scale real-scene 3D modeling and possessing significant application value in fields such as digital twins, smart cities, and disaster monitoring.

[0003] Traditional multi-view geometry-based reconstruction methods rely on feature matching and dense reconstruction processes, which are prone to instability and accuracy degradation in weakly textured or complex scenes, and the processing flow is relatively complex. In recent years, neural radiation field methods have simplified the modeling process and improved the expressive power for complex scenes by learning implicit continuous representations of the scene and combining them with volume rendering mechanisms to achieve mapping from 3D space to 2D imagery. Furthermore, neural radiation field methods based on the signed distance function (SDF) introduce the signed distance function to constrain the geometry, which can improve the quality of 3D surface reconstruction. However, in satellite imagery scenes, due to factors such as large scale, significant viewpoint differences, and inconsistencies in radiation, existing methods still have shortcomings in terms of the smoothness and accuracy of reconstructed geometric surfaces, requiring further improvement.

[0004] SDF-based neural radiation field surface reconstruction methods rely on Eikonal regularization to constrain the smoothness of the SDF field, suppressing noise solely through neighborhood information. However, in multi-temporal satellite data, inconsistencies in radiation information, seasonal variations, and dynamic changes can lead to uncertainties in pixel color information, resulting in noise fluctuations on the reconstructed surface that do not match reality. While Eikonal regularization can constrain the first derivative of the SDF, it struggles to distinguish between true surface features and erroneous fluctuations caused by data noise, lacking effective means to guide the smoothing of the reconstructed surface. On a larger scale (such as roads, ground, water surfaces, and building facades), surface smoothness and evenness are difficult to guarantee, exhibiting unevenness and non-smoothness, thus limiting the model's fidelity.

[0005] With the development of deep learning technology, significant progress has been made in geometric information learning methods based on deep convolutional neural networks and Transformers models. The Omnidata method, using a large training dataset, has achieved substantial advancements in normal vector prediction quality and generalization ability to novel scenes, demonstrating high smoothness in planar regions even on satellite imagery. Introducing normal vectors predicted by deep learning methods as prior information into the neural radiation field can provide additional geometric references for scene reconstruction. Existing methods that utilize normal vector priors to enhance neural implicit surface reconstruction include MonoSDF, NeuRIS, and DebSDF. The MonoSDF method constrains volume rendering prediction by combining monocular depth and normal vector information, but it does not consider generalization errors in prior geometry. The NeuRIS method utilizes multi-view... Figure 1 While these methods can validate normal vectors for consistency, their effectiveness depends on a small generalization error. The DebSDF method introduces uncertainty modeling to reduce normal vector estimation errors. However, all these methods assume that outliers in the prior normal vectors are finite and do not correct for prior geometry. They are only applicable to indoor scenes with small generalization errors and are difficult to apply to satellite data with large generalization errors.

[0006] In summary, existing methods for reconstructing neural radiation fields based on geometric priors have significant limitations: (1) When the normal vector prediction model trained on ground data is directly applied to satellite imagery, systematic biases are easily generated due to differences in imaging conditions, observation scale, and perspective, making it difficult to serve as a reliable constraint; (2) The normal vector prior tends to be overly smoothed, which may lead to the loss of geometric features in detailed structures or complex regions; (3) Existing methods focus more on outlier removal and lack the ability to explicitly correct prior normal vectors. When errors dominate, their constraint effect is significantly limited. Summary of the Invention

[0007] This invention aims to address the following technical problems of existing neural radiation field surface reconstruction methods based on symbolic distance functions on multi-temporal satellite data: the problem of uneven surface reconstruction and lack of overall smoothness in large flat areas (such as roads, roofs, and water surfaces); the problem that when directly applying a prior network of normal vectors trained on ground data, systematic biases occur due to generalization errors from the satellite perspective, making it unreliable as a geometric constraint; and existing geometric prior methods lack explicit correction mechanisms for prior normal vectors, which can easily lead to over-smoothing in detailed areas.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for reconstructing the surface of a neural radiation field from satellite imagery, taking into account geometric priors, includes the following steps:

[0010] Step S1: Acquire multi-temporal satellite images and preprocess them to generate a geometrically aligned and tone-consistent satellite image set. Optimize the RPC model parameters based on bundle adjustment to generate a sparse 3D point cloud of the scene and the 3D scene spatial extent.

[0011] Step S2: Based on the satellite image set processed in Step S1, an initial 3D implicit surface reconstruction is performed using the neural radiation field method based on the signed distance function (SDF) to obtain the initial SDF network, and the initial normal vector map corresponding to each image pixel is rendered using a volume rendering method. ;

[0012] Step S3: Use a pre-trained geometric prior network to predict the pixel-by-pixel normal vector of each satellite image processed in Step S1, and obtain the prior normal vector map. ;

[0013] Step S4: Using the initial normal vector map obtained in step S2 and the prior normal vector graph obtained in step S3 As input, by constructing and solving the energy function based on the Poisson equation, the smoothing properties of the prior normal vector are incorporated into the initial normal vector, and the corrected normal vector map is output. ;

[0014] Step S5: Starting with the initial SDF network weights obtained in step S2, use the corrected normal vector diagram output in step S4. Constructing Normal Vector Consistency Loss The SDF network is iteratively optimized by adding it to the total loss function. By minimizing the difference between the volume rendering normal vector and the correction normal vector, the SDF field is guided to become flatter in flat regions.

[0015] Step S6: During the iterative optimization process in step S5, the corrected normal vector map is adjusted based on the multi-view texture photometric consistency. Perform pixel-by-pixel confidence evaluation and generate a decision function. This is used to adaptively control whether the normal vector consistency loss participates in the constraints of the current iteration;

[0016] Step S7: Use the SDF network after iterative optimization in step S5 to predict the SDF value of the sampling points in the three-dimensional scene space, and extract the isosurface with an SDF value of zero using the Marching Cubes algorithm to generate a three-dimensional mesh model.

[0017] Furthermore, step S4 specifically includes:

[0018] Step S4.1: Construct the energy function of the Poisson equation ;

[0019] Among them, smoothing term The gradient field used to constrain the correction normal vector is consistent with the gradient field of the prior normal vector. ,in Describing the L2 norm, It is the normal vector. To correct the image's normal vector, For the prior normal vector, and This represents taking the second derivative with respect to the x and y directions of the normal vector graph;

[0020] Authenticity Used to constrain the correction normal vector value and the initial normal vector near;

[0021] Since drastic gradient changes in the prior normal vector are unreliable, the total energy function is rewritten as:

[0022] ;

[0023] ;

[0024] in The weights represent the smoothing term, used to suppress the influence of regions with drastic gradient changes in the prior normal vector;

[0025] Step S4.2: Transform the energy function into a sparse linear system of equations, solve it using the sparse linear least squares method, and output the corrected normal vector diagram. .

[0026] Furthermore, step S6 specifically includes:

[0027] Step S6.1: For the same surface point, render the normal vector using the current SDF network. and correction normal vector For the micro-surface orientation, corresponding texture blocks are constructed under multiple viewpoints, and the multi-view texture consistency index is calculated. and ;

[0028] Step S6.2: Generate a decision function using the threshold decision function. :

[0029] ;

[0030] when When =1, the correction normal vector corresponding to the current pixel is allowed to participate in the normal vector consistency loss calculation; when When =0, it is not included in the calculation.

[0031] Furthermore, the normal vector consistency loss constructed in step S5 Specifically:

[0032] ;

[0033] in, It is the number of light samples in each iteration. and These represent the first and second normal vectors in the rendering and correction normal vector diagrams, respectively. The normal vector corresponding to each pixel. It is a decision function. It is an L1 norm;

[0034] The total loss function is updated as follows:

[0035] ;

[0036] in For color loss, α is the Eikonal regularization loss, and γ are the weights of the normal vector consistency loss.

[0037] Furthermore, step S2 specifically includes:

[0038] Step S2.1: Construct an SDF neural radiation field network, which includes an SDF prediction module and a color prediction module. The SDF prediction module uses the position coordinates of three-dimensional points. As input, after positional encoding, a 256-dimensional feature vector is output through 8 hidden layers. and 1D SDF value The color prediction module uses the direction of the gaze. Location coordinates and eigenvectors As input, 3D color values ​​are output through 4 hidden layers. ;

[0039] Step S2.2: Construct a training sample set. In each iteration, randomly select a satellite image, randomly sample m pixels from the satellite image, and emit ray vectors from the center of the satellite sensor to each pixel. The nearest intersection point is taken with the scene space range calculated in step S1. and Between two points, according to the distance constant Uniformly sample n three-dimensional points:

[0040] ;

[0041] Record the location of each sampling point Direction of sight The image and its corresponding pixel color value constitute the training sample set for the current iteration;

[0042] Step S2.3: Input the 3D point positions sampled in Step S2.2 into the SDF prediction module constructed in Step S2.1 to obtain the SDF value and feature vector of each point; then input the viewing direction, point position, and feature vector into the color prediction module to obtain the predicted color of each point, and use the S-density function to convert the SDF value into opacity. :

[0043] ;

[0044] ;

[0045] in Sampling points SDF value predicted by the network, Here, s is the sigmoid function, and s is a learnable parameter.

[0046] Further calculation of cumulative opacity and predict color :

[0047] ;

[0048] ;

[0049] Step S2.4: Based on the predicted color obtained in step S2.3 and the pixel color recorded in step S2.2, calculate the loss function. And iteratively optimize, loss function For color loss The sum of the regularization loss and the Eikonal loss:

[0050] ;

[0051] ;

[0052] ;

[0053] These are the color values ​​of the image pixels. Take 0.1, The SDF gradient norm is constrained to approach 1 to regularize the SDF, ensuring that it remains uniformly distributed in space.

[0054] Step S2.5: After training is complete, render each image pixel using volume rendering method. Corresponding initial normal vector Normal vector at sampling point Normalized gradient of SDF:

[0055] ;

[0056] Pixel normal vector Accumulated through volume rendering:

[0057] ;

[0058] Based on the initial SDF network training results, the normal vector of each pixel in the satellite image is calculated, and an initial normal vector map is constructed. .

[0059] A satellite imagery neural radiation field surface reconstruction device that takes into account geometric priors includes:

[0060] The image preprocessing module is used to acquire and preprocess multi-temporal satellite images, generate a geometrically aligned and color-consistent satellite image set, and optimize the RPC model parameters based on bundle adjustment to generate a sparse 3D point cloud of the scene and the 3D scene spatial range.

[0061] The initial implicit surface reconstruction module is used to perform initial 3D implicit surface reconstruction based on the satellite image set processed by the image preprocessing module. It employs a neural radiation field method based on the signed distance function (SDF) to obtain the initial SDF network and renders the initial normal vector map corresponding to each image pixel using a volume rendering method. ;

[0062] The prior normal vector prediction module is used to perform pixel-by-pixel normal vector prediction on each satellite image processed in step S1 using a pre-trained geometric prior network, and to obtain a prior normal vector map. ;

[0063] Poisson correction module, used to initialize the normal vector map and prior normal vector graph As input, by constructing and solving the energy function based on the Poisson equation, the smoothing properties of the prior normal vector are incorporated into the initial normal vector, and the corrected normal vector map is output. ;

[0064] The iterative optimization module is used to optimize the network using the initial SDF network weights and the corrected normal vector graph. Constructing Normal Vector Consistency Loss The SDF network is iteratively optimized by adding it to the total loss function. By minimizing the difference between the volume rendering normal vector and the correction normal vector, the SDF field is guided to become flatter in flat regions.

[0065] An adaptive verification module is used to verify the corrected normal vector map based on the photometric consistency of multi-view textures during iterative optimization. Perform pixel-by-pixel confidence evaluation and generate a decision function. This is used to adaptively control whether the normal vector consistency loss participates in the constraints of the current iteration;

[0066] The mesh extraction module is used to predict the SDF values ​​of sampling points in the 3D scene space using the SDF network after iterative optimization, and extract the isosurfaces with SDF values ​​of zero using the Marching Cubes algorithm to generate a 3D mesh model.

[0067] Furthermore, the Poisson correction module includes:

[0068] Energy function building blocks, used to construct the energy function of the Poisson equation. ;

[0069] Among them, smoothing term The gradient field used to constrain the correction normal vector is consistent with the gradient field of the prior normal vector. ,in Describing the L2 norm, It is the normal vector. To correct the image's normal vector, For the prior normal vector, and This represents taking the second derivative with respect to the x and y directions of the normal vector graph;

[0070] Authenticity Used to constrain the correction normal vector value and the initial normal vector near;

[0071] Since drastic gradient changes in the prior normal vector are unreliable, the total energy function is rewritten as:

[0072] ;

[0073] ;

[0074] in The weights represent the smoothing term, used to suppress the influence of regions with drastic gradient changes in the prior normal vector;

[0075] The solution unit is used to transform the energy function into a sparse linear system of equations, solve it using the sparse linear least squares method, and output the corrected normal vector map. .

[0076] Furthermore, the adaptive verification module includes:

[0077] Texture consistency calculation unit, used to calculate the texture consistency of the same surface point using the current SDF network rendering normal vector. and correction normal vector For the micro-surface orientation, corresponding texture blocks are constructed under multiple viewpoints, and the multi-view texture consistency index is calculated. and ;

[0078] Threshold determination unit, used to generate determination function through threshold determination function. :

[0079] ;

[0080] when When =1, the correction normal vector corresponding to the current pixel is allowed to participate in the normal vector consistency loss calculation; when When =0, it is not included in the calculation.

[0081] Furthermore, the normal vector consistency loss constructed in the iterative optimization module Specifically: ;

[0082] in, It is the number of light samples in each iteration. and These represent the first and second normal vectors in the rendering and correction normal vector diagrams, respectively. The normal vector corresponding to each pixel. It is a decision function. It is an L1 norm;

[0083] The total loss function is updated as follows:

[0084] ;

[0085] in For color loss, α is the Eikonal regularization loss, and γ are the weights of the normal vector consistency loss.

[0086] Furthermore, the initial implicit surface reconstruction module includes an SDF prediction submodule and a color prediction submodule, which take the 3D point position and viewing direction as input and output SDF values ​​and color values; the initial normal vector map The prior normal vector is obtained by volume rendering of the normalized gradient of the SDF; the prior normal vector prediction module uses the Omnidata network to generate a full-resolution prior normal vector map for high-resolution satellite imagery using a block prediction and local alignment strategy. .

[0087] The present invention has the following beneficial effects:

[0088] (1) This invention proposes a normal vector correction method based on the Poisson equation, which integrates the local smoothness of the prior normal vector with the geometric accuracy of the initial scene normal vector, overcoming the problem of large generalization error of ground-trained geometric prior network under satellite view, so that geometric prior can be reliably applied to satellite image three-dimensional reconstruction scene.

[0089] (2) The present invention proposes a texture photometric consistency criterion to distinguish between flat regions and detailed regions: a normal vector smoothing constraint is introduced in the flat region, and the constraint is disabled in the detailed region to preserve the fine structure, thus overcoming the problem of excessive surface smoothing after the introduction of prior knowledge.

[0090] (3) The Poisson equation correction (eliminating systematic bias) and multi-view adaptive verification (eliminating residual gross errors after correction) constitute a two-layer screening system. Compared with the existing single uncertainty module scheme, it is more robust in satellite scenarios with large generalization errors and the risk of introducing incorrect constraints is significantly reduced.

[0091] (4) The present invention fully considers the radiometric inconsistency of multi-temporal satellite data. After introducing the normal vector prior, the reconstruction quality on weak textured surfaces (such as pure white building facades) is significantly improved. The universality and effectiveness of the scheme are verified on the DFC2019 international open benchmark dataset. Attached Figure Description

[0092] Figure 1 This is a schematic flowchart of the satellite image neural radiation field surface reconstruction method that takes geometric priors into account in an embodiment of the present invention.

[0093] Figure 2 This is a schematic diagram of the overall framework of an embodiment of the present invention.

[0094] Figure 3 This is a schematic diagram of satellite imagery and normal vector priors in an embodiment of the present invention.

[0095] Figure 4 This is a schematic diagram of the normal vector correction result based on the Poisson equation in an embodiment of the present invention.

[0096] Figure 5 This is a schematic diagram of multi-view texture consistency verification according to an embodiment of the present invention.

[0097] Figure 6 This is a comparison chart of the reconstruction results of the DFC2019 dataset in an embodiment of the present invention.

[0098] Figure 7 This is an error distribution diagram of the DFC2019 dataset in an embodiment of the present invention.

[0099] Figure 8 This is a diagram showing the ablation experiment results of an embodiment of the present invention. Detailed Implementation

[0100] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0101] Please see Figure 1 and Figure 2 This invention provides a satellite image neural radiation field surface reconstruction method that considers geometric priors. First, an SDF-based neural radiation field method is used to perform initial 3D implicit surface reconstruction on multi-temporal satellite images to obtain initial normal vectors. Then, a geometric prior network is used to predict the prior normal vectors of the satellite images. A Poisson equation-based correction method is used to integrate the smoothing characteristics of the prior normal vectors into the initial normal vectors, eliminating systematic biases in the priors and outputting accurate and smooth corrected normal vectors. Finally, a multi-view adaptive normal vector verification method is proposed. The credibility of the corrected normal vectors is evaluated based on texture photometric consistency, allowing only verified normal vectors to participate in constraints. This introduces smoothing constraints in flat areas while preserving the geometric features of detailed areas. Specifically, the method includes the following steps:

[0102] Step S1: Image Acquisition and Preprocessing

[0103] A multi-temporal satellite image dataset (including panchromatic and multispectral image sets) covering the region of interest was collected. The images were cropped, grayscale mapped, and panchromatic and multispectral images were fused. The RPC model parameters were then optimized using bundle adjustment to generate a sparse 3D point cloud. The preprocessing aimed to eliminate radiometric differences and geometric positioning biases in the satellite images, providing high-quality input data with geometric alignment and tonal consistency for subsequent neural radiation field reconstruction. The RPC model optimization was achieved through multi-view feature matching and bundle adjustment. While correcting sensor positioning biases, it generated a sparse point cloud with initial scene structure information, providing spatial extent information for subsequent ray sampling.

[0104] Step S1 specifically includes:

[0105] Step S1.1: Determine the UTM coordinate range of the AOI and convert it to WGS-84 geographic coordinates. Using the RPC parameters of the satellite imagery, project the AOI onto the panchromatic and multispectral imagery, and crop it according to the minimum bounding rectangle. After cropping, update the row and column offsets of the RPC parameters, i.e., subtract the starting row / column number of the target area in the image from the original offset, to ensure that the cropped image still has accurate geographic location under the new RPC model.

[0106] Step S1.2: Perform tone mapping processing on the cropped multispectral and panchromatic images respectively, using a gamma-corrected tone mapping technique to convert the 16-bit data into 8-bit data:

[0107]

[0108] in, It is the grayscale value (0~65535) of the input image. It is the grayscale value (0~255) of the output image. This is the gamma parameter, set to 1 / 2.2.

[0109] Step S1.3: Extract the blue, green and red bands from the multispectral image, and use the Brovey panchromatic sharpening algorithm to fuse the high spatial resolution of the panchromatic image with the color information of the multispectral image to generate a high-resolution color image.

[0110] Step S1.4: Using feature extraction, feature matching, and bundle adjustment methods in COLMAP software, an optimization objective function is constructed based on the feature points extracted from multi-view satellite imagery and their matching relationships. This minimizes reprojection errors, corrects RPC translation errors, and simultaneously generates a 3D sparse point cloud with an initial scene structure. Based on this, a minimum circumscribed sphere is constructed using this sparse point cloud as input. The resulting sphere's center coordinates and radius parameters represent the spatial extent of the 3D scene to be reconstructed.

[0111] The preprocessing step provides RGB satellite imagery and orientation information for subsequent 3D implicit surface reconstruction of the scene (step S2).

[0112] Step S2: Initial 3D Implicit Surface Reconstruction

[0113] like Figure 2 As shown, an SDF-based neural radiation field method is used to perform initial 3D implicit surface reconstruction on the satellite imagery preprocessed in step S1. Based on the satellite imagery output from step S1, the SDF-based neural radiation field method is used for initial 3D implicit surface reconstruction. This method uses the signed distance from any point in 3D space to the nearest scene surface as the implicit geometric representation of the scene. A multilayer perceptron (MLP) is used to predict the SDF and color values ​​of spatial points. Combined with an SDF-based volume rendering formula, the 3D scene is projected onto the 2D image space. Scene geometry is learned by minimizing the difference between the rendered color and the real image color. The SDF network weights obtained from the initial reconstruction encode the 3D geometric information of the scene. Based on this network, the initial normal vector map corresponding to each image pixel can be rendered using a volume rendering method. The initial normal vector has geometric accuracy locally, but due to the inherent radiometric inconsistencies in multi-temporal satellite data, it lacks overall smoothness in large flat areas (such as roads, roofs, and water surfaces), resulting in an uneven and noisy surface.

[0114] Step S2 specifically includes:

[0115] Step S2.1: Construct the SDF neural radiation field network. The network consists of two parts: an SDF prediction module and a color prediction module. The SDF prediction module uses the position coordinates of three-dimensional points. As input, after positional encoding, it passes through 8 hidden layers (each 256-dimensional, using the Softplus activation function) to output a 256-dimensional feature vector. and 1D SDF value The color prediction module uses the direction of the gaze. Location coordinates and eigenvectors As input, 3D color values ​​are output through 4 hidden layers. .

[0116] Step S2.2: Construct the training sample set. In each iteration, randomly select a satellite image, randomly sample m pixels (m = 512) from the image, and emit ray vectors from the center of the satellite sensor to each pixel. The nearest intersection point is taken with the scene space range calculated in step S1. and Between two points, according to the distance constant Uniformly sample n three-dimensional points (n is 64):

[0117]

[0118] Record the location of each sampling point Direction of sight The image and its corresponding pixel color value constitute the training sample set for the current iteration.

[0119] Step S2.3: Calculate pixel predicted color based on SDF-based volume rendering. Specifically, the 3D point positions sampled in step S2.2 are input into the SDF prediction module constructed in step S2.1 to obtain the SDF value and feature vector of each point; then, the viewing direction, point position, and feature vector are input into the color prediction module to obtain the predicted color of each point, and the S-density function is used to convert the SDF value into opacity. :

[0120]

[0121]

[0122] in Sampling points SDF value predicted by the network, Here, s is the sigmoid function, and s is a learnable parameter.

[0123] Cumulative Opacity and predict color Further calculations can be performed:

[0124]

[0125]

[0126] Step S2.4: Based on the predicted color obtained in step S2.3 and the pixel color recorded in step S2.2, calculate the loss function. And iteratively optimize. Loss function For color loss The sum of the regularization loss and the Eikonal loss:

[0127]

[0128]

[0129]

[0130] These are the color values ​​of the image pixels. Take 0.1, The SDF gradient norm is constrained to approach 1 to regularize the SDF, ensuring its uniform distribution in space. The initial SDF network weights are obtained through 300,000 iterations of training based on the loss function.

[0131] Step S2.5: After training is complete, render each image pixel using volume rendering method. Corresponding initial normal vector Normal vector at sampling point Normalized gradient of SDF:

[0132]

[0133]

[0134] Based on the initial SDF network training results, the normal vector of each pixel in the satellite image is calculated, and an initial normal vector map is constructed. The initial 3D implicit surface reconstruction is estimated by multi-temporal satellite imagery. Its predicted initial normal vector map has local geometric accuracy, but lacks smoothness in large flat areas.

[0135] Step S3: Predicting the prior normal vector

[0136] A pre-trained geometric prior network is used to predict the pixel-by-pixel normal vectors of the satellite imagery output in step S1, thereby obtaining the prior normal vector map. The prior network, trained on a large-scale multi-task learning framework, possesses cross-scene generalization capabilities, and its predictions exhibit high smoothness in local neighborhoods. However, since the training data for the prior network primarily originates from terrestrial scenes, which differ significantly from satellite imagery in viewpoint, scale, and imaging conditions, the absolute values ​​of the predicted normal vectors exhibit systematic biases and cannot be directly used to constrain scene reconstruction. Therefore, while the prior normal vectors possess smoothness characteristics, they must be corrected before constraining the learning of scene geometry.

[0137] This embodiment uses the Omnidata normal vector prediction network to predict the normal vectors of each satellite image after preprocessing in step S1. The Omnidata method is based on a multi-task learning framework and uses visual and geometric cues such as color, normal vectors, depth, and feature points to train the network, exhibiting strong generalization ability. The normal vector prediction results are shown below. Figure 3 .

[0138] Since the Omnidata network only supports 512×512 resolution input, a block prediction strategy is adopted for high-resolution satellite imagery: the image is divided into 512×512 overlapping sub-blocks, and the normal vector is predicted for each sub-block separately; for overlapping regions, a linear transformation is estimated using the difference in normal vectors between adjacent sub-blocks, and this transformation is applied to one of the sub-blocks to achieve local alignment of the normal vector directions. Finally, the normal vectors are stitched together to obtain a prior normal vector map with full resolution. The prior normal vector maintains smoothness in the local neighborhood, but its absolute value exhibits systematic bias.

[0139] Step S4: Normal vector correction based on the Poisson equation

[0140] The prior normal vector obtained in step S3 and the initial normal vector obtained in step S2 As input, the complementary properties of the two normal vectors are fused using the Poisson equation. The core principle is that the gradient field of the prior normal vector (i.e., the second derivative of the normal vector) carries information about surface smoothness, while the value of the initial normal vector carries information about geometric accuracy. This step constructs an energy function constrained by smoothing and fidelity terms: the smoothing term constrains the gradient field of the corrected normal vector to be consistent with the gradient field of the prior normal vector, thus inheriting the smoothness characteristic of the prior; the fidelity term constrains the value of the corrected normal vector to be close to the initial normal vector, thus maintaining the initial geometric accuracy. Simultaneously, adaptive weight coefficients are introduced to suppress the influence of regions with drastic gradient changes in the prior normal vector (i.e., unreliable prior regions) on the correction result. Finally, the energy function is solved using the sparse linear least squares method, outputting the corrected normal vector map. The corrected normal vector possesses both the geometric accuracy of the initial normal vector and the local smoothness of the prior normal vector.

[0141] Step S4 specifically includes:

[0142] Step S4.1: Construct the energy function of the Poisson equation Normal vector correction can be viewed as an optimization problem that simultaneously satisfies two conditions: the gradient field of the corrected normal vector should be consistent with the gradient field of the prior normal vector (smoothing term), and the value of the corrected normal vector should be close to that of the initial normal vector (fidelity term). The energy function is defined as:

[0143]

[0144] The second-order gradient field of the smoothing term constrains the correction normal vector to be consistent with the second-order gradient field of the prior normal vector, so as to inherit the smoothing properties of the prior:

[0145]

[0146]

[0147] in Describing the L2 norm, It is the normal vector. To correct the normal vectors at pixel positions in the normal vector map, Let be the normal vector of the pixel position in the prior normal vector map. and This represents taking the second derivative with respect to the x and y directions of the normal vector graph.

[0148] To ensure the accuracy of the corrected normal vector, the corrected normal vector should be consistent with the initial normal vector:

[0149]

[0150] in Let represent the initial normal vector. Furthermore, since drastic gradient changes in the prior normal vector are unreliable, the total energy function is rewritten as:

[0151]

[0152]

[0153] in This represents the weight of the smoothing term, used to mitigate the effects of large gradient errors in the prior normal vector.

[0154] Step S4.2: Solve for the energy function. The energy function can be transformed into a large sparse linear system of equations, which is solved using the sparse linear least squares method, and the corrected normal vector diagram is output. .like Figure 4 As shown, the corrected normal vector possesses both accuracy and smoothness.

[0155] Step S5: Iterative optimization of the SDF network based on the correction normal vector

[0156] Using the correction normal vector output in step S4 A normal vector consistency loss is constructed and added as an additional geometric supervision signal to the total loss function. Iterative training continues starting from the initial SDF network weights obtained in step S2. The principle is that by minimizing the difference between the volume rendering normal vector and the corrected normal vector, the smoothness and accuracy information of the corrected normal vector is passed to the SDF network, guiding the SDF field to tend towards flatness in flat regions while maintaining overall geometric accuracy. Because consistency constraints are applied using volume rendering-based normal vectors (rather than only constraining points on the SDF zero isosurface), the volume rendering process constrains a large number of sampling points in 3D space, which is beneficial for maintaining the global continuity and consistency of the SDF field.

[0157] Step S5 specifically includes:

[0158] Step S5.1: Construct the normal vector consistency loss. Based on volume rendering normal vectors. With the correction normal vector The difference between them constructs the normal vector consistency loss:

[0159]

[0160] It is the normal vector consistency loss, which is divided into absolute value error and angle error. It is the number of light samples in each iteration. and These represent the first and second normal vectors in the rendering and correction normal vector diagrams, respectively. The normal vector corresponding to each pixel. It is a decision function that is adaptively calculated based on multi-view texture information (calculated by step S6). It is an L1 norm

[0161] Step S5.2: Update the total loss function. After adding the normal vector consistency loss, the total loss function is updated as follows:

[0162]

[0163] in, , The definition is consistent with step S2.4. The weight for the consistency loss of the normal vector can be 0.1.

[0164] Step S5.3: Iterative Optimization. Starting with the initial SDF network weights obtained in Step S2, continue training for approximately 300,000 iterations based on the updated total loss function. In each iteration, randomly sample pixel rays, calculate the rendering color and rendering normal vector, and based on... The parameters of the SDF network and the color network are updated through backpropagation. Guided by the normal vector consistency loss, the SDF field gradually flattens in flat regions while maintaining overall geometric accuracy.

[0165] Step S6: Adaptive Normal Vector Verification Based on Multi-View Photometric Consistency

[0166] Because the correction normal vector obtained in step S4 The solution is based on the residual minimization criterion. In areas with sharp geometric features (such as tree outlines and building edges) where the gradients of the prior and initial normal vectors differ significantly, the correction result may be overly smoothed, resulting in the loss of detail. In this step, during the iterative optimization process of step S5, the reliability of the corrected normal vector is evaluated pixel-by-pixel through multi-view texture photometric consistency: for the same surface point, using both the scene rendering normal vector and the corrected normal vector as the micro-surface orientation, corresponding texture blocks are constructed from multiple viewpoints, and photometric consistency indices are calculated. If the consistency guided by the corrected normal vector is better than that of the rendering normal vector, the corrected normal vector is considered reliable and allowed to participate in constraints; otherwise, it is discarded. This mechanism distinguishes different types of regions: in flat regions with sparse textures, the corrected normal vector usually improves consistency, normal vector constraints are preserved, and smoothness is introduced; in detailed regions with rich textures, the corrected normal vector may cause a decrease in consistency due to over-smoothing, constraints are discarded, thus preserving geometric details.

[0167] like Figure 5 As shown, during the iterative optimization process in step S5, the correction normal vector is... Perform pixel-by-pixel confidence assessment.

[0168] Step S6 specifically includes:

[0169] Step S6.1: Calculate the multi-view texture photometric consistency index. Establish the relationship between micro-surface orientation and multi-view texture similarity at each scene point: for a spatial point on the surface, given the SDF value and normal vector of that point, the corresponding pixel position can be located and texture blocks extracted on images from various viewpoints. The rendering normal vectors of the current SDF network are then used... and correction normal vector For micro-surface orientation, corresponding texture blocks are constructed for the same surface point under multiple viewpoints, and the multi-view texture consistency index (NCC) is calculated, denoted as follows: and .

[0170] Step S6.2: Adaptive Decision. The threshold decision function determines whether the correction normal vector participates in the constraints of the current iteration.

[0171]

[0172] For a decision function, if and only if and When the normal vector constraint is considered reliable, this process filters out the inaccurate parts of the correction normal vector, improving the robustness of the method. At the same time, in areas with rich visual features, the method tends not to use constraint information with strong smoothness, thus preserving surface details.

[0173] Step S7: Extraction of 3D Mesh Model

[0174] After step S5 iteration, 128×128×128 spatial points are uniformly sampled within the 3D scene space calculated in S1. The trained SDF network is used to predict the SDF values ​​of the uniformly distributed sampling points in 3D space. The MarchingCubes algorithm is used to extract isosurfaces with zero SDF values, which are then transformed into a continuous and smooth 3D mesh model, deriving the final 3D surface reconstruction result. Because the SDF network is geometrically guided by the correction normal vector in step S5, the extracted mesh model has a smooth surface in flat areas and retains features in detailed areas. The overall reconstruction accuracy and smoothness are superior to the basic method without normal vector constraints.

[0175] Example:

[0176] This invention uses the DFC2019 dataset to evaluate the performance of the method. The DFC2019 dataset includes four scenes: JAX_004, JAX_068, JAX_214, and JAX_260. DFC2019 is a publicly available benchmark dataset for 3D reconstruction of multi-temporal high-resolution satellite imagery, which includes the corresponding ground truth values ​​from airborne lidar.

[0177] Figure 6 The reconstruction results of the proposed method on the DFC2019 dataset are presented. Compared with the basic method without normal vector constraints, the proposed method exhibits more regular and smoother results. For the JAX_004 scene, the road surface reconstructed by the basic method lacking global constraints shows unevenness, while the proposed method shows a smoother road surface reconstruction result, similar to the airborne radar result. In the JAX_260 scene, the house surface reconstructed by the basic method showed erroneous bulges, which were eliminated after introducing normal vector priors. Figure 7The error distribution diagram of the method of the present invention is shown. The lower the value, the smaller the error. The method of the present invention has a lighter color in the planar part. The method of the present invention also shows a smoother error change and less noise in the planar part, indicating that the method of the present invention has higher surface reconstruction accuracy.

[0178] Figure 8 The results of the ablation experiments are presented, comparing three configurations and different error values ​​(mean absolute error (MAE), median absolute error (MED), and percentage of errors less than 1 meter (Perc-1m)): Figure 8 In (a), the normal vector of the network output is directly used to constrain the neural implicit surface learning, which leads to geometric errors such as boundary depressions and protrusions in the reconstructed surface; Figure 8 (b) The normal vector constraint corrected by the Poisson equation has no obvious geometric errors on the surface but is too smooth; Figure 8 In section (c), the use of corrected normal vectors and normal vector constraints after multi-view adaptive verification ensures that geometric details, such as vegetation and building edges, are well preserved while maintaining a flat plane, demonstrating the effectiveness of the method of the present invention.

[0179] This invention also provides a satellite image neural radiation field surface reconstruction device that takes geometric priors into account, corresponding to the above method, comprising:

[0180] The image preprocessing module is used to acquire and preprocess multi-temporal satellite images, generate a geometrically aligned and color-consistent satellite image set, and optimize the RPC model parameters based on bundle adjustment to generate a sparse 3D point cloud of the scene and the 3D scene spatial range.

[0181] The initial implicit surface reconstruction module is used to perform initial 3D implicit surface reconstruction based on the satellite image set processed by the image preprocessing module. It employs a neural radiation field method based on the signed distance function (SDF) to obtain the initial SDF network and renders the initial normal vector map corresponding to each image pixel using a volume rendering method. ;

[0182] The prior normal vector prediction module is used to perform pixel-by-pixel normal vector prediction on each satellite image processed in step S1 using a pre-trained geometric prior network, and to obtain a prior normal vector map. ;

[0183] Poisson correction module, used to initialize the normal vector map and prior normal vector graph As input, by constructing and solving the energy function based on the Poisson equation, the smoothing properties of the prior normal vector are incorporated into the initial normal vector, and the corrected normal vector map is output. ;

[0184] The iterative optimization module is used to optimize the network using the initial SDF network weights and the corrected normal vector graph. Constructing Normal Vector Consistency Loss The SDF network is iteratively optimized by adding it to the total loss function. By minimizing the difference between the volume rendering normal vector and the correction normal vector, the SDF field is guided to become flatter in flat regions.

[0185] An adaptive verification module is used to verify the corrected normal vector map based on the photometric consistency of multi-view textures during iterative optimization. Perform pixel-by-pixel confidence evaluation and generate a decision function. This is used to adaptively control whether the normal vector consistency loss participates in the constraints of the current iteration;

[0186] The mesh extraction module is used to predict the SDF values ​​of sampling points in the 3D scene space using the SDF network after iterative optimization, and extract the isosurfaces with SDF values ​​of zero using the Marching Cubes algorithm to generate a 3D mesh model.

[0187] Compared with the prior art, the present invention has the following features and effects:

[0188] (1) The innovative normal vector correction mechanism effectively overcomes satellite domain generalization error.

[0189] By constructing an energy function based on the Poisson equation, the smoothness of the gradient field of the prior normal vector is integrated with the numerical accuracy of the initial normal vector, and adaptive weights are introduced to suppress the influence of unreliable prior regions. This mechanism directly addresses the problem of large generalization errors of geometric priors from a satellite perspective, which is difficult to handle with existing technologies. It enables ground-trained normal vector prediction networks to be reliably applied to 3D reconstruction of satellite imagery, filling a technological gap in this field.

[0190] (2) Adaptive detail preservation mechanism to avoid over-smoothing

[0191] An adaptive verification based on multi-view texture photometric consistency is introduced, with a pixel-level decision function controlling the effective area of ​​normal vector constraints. This mechanism retains smoothness constraints in flat areas (such as roads and water surfaces) to improve flatness, and automatically deactivates constraints in textured detail areas (such as building edges and tree outlines) to preserve geometric features, overcoming the defect of excessive overall surface smoothing after introducing priors.

[0192] (3) A two-layer robust screening system significantly improves reconstruction stability in complex scenarios.

[0193] The Poisson equation correction (eliminating systematic biases) and multi-view adaptive verification (eliminating residual gross errors after correction) constitute a two-layer screening mechanism. Compared with existing single uncertainty modeling schemes, this invention has stronger robustness on multi-temporal satellite data with large generalization errors and significant radiometric inconsistencies, and the risk of introducing incorrect constraints is greatly reduced.

[0194] (4) Significantly improves the reconstruction quality of weakly textured surfaces

[0195] Experiments on the DFC2019 international open benchmark dataset show that the problems of uneven roads and bulging building surfaces that exist in the basic method without using prior knowledge are effectively suppressed. The mean absolute error and median error of the reconstructed surface are significantly reduced, and the flatness of large areas with weak texture (such as pure white building facades) is close to the true value of airborne lidar, which verifies the universality and effectiveness of the invention.

[0196] 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 variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for surface reconstruction of neural radiance field from satellite images with geometric priors, characterized in that, Includes the following steps: Step S1: Acquire multi-temporal satellite images and preprocess them to generate a geometrically aligned and tone-consistent satellite image set. Optimize the RPC model parameters based on bundle adjustment to generate a sparse 3D point cloud of the scene and the 3D scene spatial extent. Step S2: based on the satellite image set processed in step S1, an initial three-dimensional implicit surface reconstruction is performed using a neural radiance field method based on a signed distance function (SDF), an initial SDF network is obtained, and an initial normal vector map corresponding to each image pixel is rendered by a volume rendering method ; Step S3: using the pre-trained geometric prior network to perform per-pixel normal vector prediction on each satellite image processed in the step S1 to obtain a prior normal vector map ; Step S4: Using the initial normal vector map obtained in step S2 and the prior normal vector graph obtained in step S3 As input, by constructing and solving the energy function based on the Poisson equation, the smoothing properties of the prior normal vector are incorporated into the initial normal vector, and the corrected normal vector map is output. ; Step S5: Starting with the initial SDF network weights obtained in step S2, use the corrected normal vector diagram output in step S4. Constructing Normal Vector Consistency Loss The SDF network is iteratively optimized by adding it to the total loss function. By minimizing the difference between the volume rendering normal vector and the correction normal vector, the SDF field is guided to become flatter in flat regions. Step S6: During the iterative optimization process in step S5, the corrected normal vector map is adjusted based on the multi-view texture photometric consistency. Perform pixel-by-pixel confidence evaluation and generate a decision function. This is used to adaptively control whether the normal vector consistency loss participates in the constraints of the current iteration; Step S7: Use the SDF network after iterative optimization in step S5 to predict the SDF value of the sampling points in the three-dimensional scene space, and extract the isosurface with an SDF value of zero using the Marching Cubes algorithm to generate a three-dimensional mesh model.

2. The satellite image neural radiation field surface reconstruction method considering geometric priors according to claim 1, characterized in that, Step S4 specifically includes: Step S4.1: Construct the energy function of the Poisson equation ; Among them, smoothing term The gradient field used to constrain the correction normal vector is consistent with the gradient field of the prior normal vector. ,in Describing the L2 norm, It is the normal vector. To correct the image's normal vector, For the prior normal vector, and This represents taking the second derivative with respect to the x and y directions of the normal vector graph; Authenticity Used to constrain the correction normal vector value and the initial normal vector near; Since drastic gradient changes in the prior normal vector are unreliable, the total energy function is rewritten as: ； ； in The weights represent the smoothing term, used to suppress the influence of regions with drastic gradient changes in the prior normal vector; Step S4.2: Transform the energy function into a sparse linear system of equations, solve it using the sparse linear least squares method, and output the corrected normal vector diagram. .

3. The satellite image neural radiation field surface reconstruction method considering geometric priors according to claim 1, characterized in that, Step S6 specifically includes: Step S6.1: For the same surface point, render the normal vector using the current SDF network. and correction normal vector For the micro-surface orientation, corresponding texture blocks are constructed under multiple viewpoints, and the multi-view texture consistency index is calculated. and ; Step S6.2: Generate a decision function using the threshold decision function. : ； when When =1, the correction normal vector corresponding to the current pixel is allowed to participate in the normal vector consistency loss calculation; when When =0, it is not included in the calculation.

4. The satellite image neural radiation field surface reconstruction method considering geometric priors according to claim 1, characterized in that, The normal vector consistency loss constructed in step S5 Specifically: ； in, It is the number of light samples in each iteration. and These represent the first and second normal vectors in the rendering and correction normal vector diagrams, respectively. The normal vector corresponding to each pixel. It is a decision function. It is an L1 norm; The total loss function is updated as follows: ； in For color loss, α is the Eikonal regularization loss, and γ are the weights of the normal vector consistency loss.

5. The satellite image neural radiation field surface reconstruction method considering geometric priors according to claim 1, characterized in that, Step S2 specifically includes: Step S2.1: Construct an SDF neural radiation field network, which includes an SDF prediction module and a color prediction module. The SDF prediction module uses the position coordinates of three-dimensional points. As input, after positional encoding, a 256-dimensional feature vector is output through 8 hidden layers. and 1D SDF value The color prediction module uses the direction of the gaze. Location coordinates and eigenvectors As input, 3D color values ​​are output through 4 hidden layers. ; Step S2.2: Construct a training sample set. In each iteration, randomly select a satellite image, randomly sample m pixels from the satellite image, and emit ray vectors from the center of the satellite sensor to each pixel. The nearest intersection point is taken with the scene space range calculated in step S1. and Between two points, according to the distance constant Uniformly sample n three-dimensional points: ； Record the location of each sampling point Direction of sight The image and its corresponding pixel color value constitute the training sample set for the current iteration; Step S2.3: Input the 3D point positions sampled in Step S2.2 into the SDF prediction module constructed in Step S2.1 to obtain the SDF value and feature vector of each point; then input the viewing direction, point position, and feature vector into the color prediction module to obtain the predicted color of each point, and use the S-density function to convert the SDF value into opacity. : ； ； in Sampling points SDF value predicted by the network, Here, s is the sigmoid function, and s is a learnable parameter. Further calculation of cumulative opacity and predict color : ； ； Step S2.4: Based on the predicted color obtained in step S2.3 and the pixel color recorded in step S2.2, calculate the loss function. And iteratively optimize, loss function For color loss The sum of the regularization loss and the Eikonal loss: ； ； ； These are the color values ​​of the image pixels. Take 0.1, The SDF gradient norm is constrained to approach 1 to regularize the SDF, ensuring that it remains uniformly distributed in space. Step S2.5: After training is complete, render each image pixel using volume rendering method. Corresponding initial normal vector Normal vector at sampling point Normalized gradient of SDF: ； Pixel normal vector Accumulated through volume rendering: ； Based on the initial SDF network training results, the normal vector of each pixel in the satellite image is calculated, and an initial normal vector map is constructed. .

6. A satellite image neural radiation field surface reconstruction device that takes geometric priors into account, characterized in that, include: The image preprocessing module is used to acquire and preprocess multi-temporal satellite images, generate a geometrically aligned and color-consistent satellite image set, and optimize the RPC model parameters based on bundle adjustment to generate a sparse 3D point cloud of the scene and the 3D scene spatial range. The initial implicit surface reconstruction module is used to perform initial 3D implicit surface reconstruction based on the satellite image set processed by the image preprocessing module. It employs a neural radiation field method based on the signed distance function (SDF) to obtain the initial SDF network and renders the initial normal vector map corresponding to each image pixel using a volume rendering method. ; The prior normal vector prediction module is used to predict the pixel-by-pixel normal vector of each satellite image processed in step S1 using a pre-trained geometric prior network, thereby obtaining a prior normal vector map. ; Poisson correction module, used to initialize the normal vector map and prior normal vector graph As input, by constructing and solving the energy function based on the Poisson equation, the smoothing properties of the prior normal vector are incorporated into the initial normal vector, and the corrected normal vector map is output. ; The iterative optimization module is used to optimize the network using the initial SDF network weights and the corrected normal vector graph. Constructing Normal Vector Consistency Loss The SDF network is iteratively optimized by adding it to the total loss function. By minimizing the difference between the volume rendering normal vector and the correction normal vector, the SDF field is guided to become flatter in flat regions. An adaptive verification module is used to verify the corrected normal vector map based on the photometric consistency of multi-view textures during iterative optimization. Perform pixel-by-pixel confidence evaluation and generate a decision function. This is used to adaptively control whether the normal vector consistency loss participates in the constraints of the current iteration; The mesh extraction module is used to predict the SDF values ​​of sampling points in the 3D scene space using the SDF network after iterative optimization, and extract the isosurfaces with SDF values ​​of zero using the Marching Cubes algorithm to generate a 3D mesh model.

7. The satellite image neural radiation field surface reconstruction device considering geometric priors according to claim 6, characterized in that, The Poisson correction module includes: Energy function building blocks, used to construct the energy function of the Poisson equation. ; Among them, smoothing term The gradient field used to constrain the correction normal vector is consistent with the gradient field of the prior normal vector. ,in Describing the L2 norm, It is the normal vector. To correct the image's normal vector, For the prior normal vector, and This represents taking the second derivative with respect to the x and y directions of the normal vector graph; Authenticity Used to constrain the correction normal vector value and the initial normal vector near; Since drastic gradient changes in the prior normal vector are unreliable, the total energy function is rewritten as: ； ； in The weights represent the smoothing term, used to suppress the influence of regions with drastic gradient changes in the prior normal vector; The solution unit is used to transform the energy function into a sparse linear system of equations, solve it using the sparse linear least squares method, and output the corrected normal vector map. .

8. The satellite image neural radiation field surface reconstruction device considering geometric priors according to claim 6, characterized in that, The adaptive verification module includes: Texture consistency calculation unit, used to calculate the texture consistency of the same surface point using the current SDF network rendering normal vector. and correction normal vector For the micro-surface orientation, corresponding texture blocks are constructed under multiple viewpoints, and the multi-view texture consistency index is calculated. and ; Threshold determination unit, used to generate determination function through threshold determination function. : ； when When =1, the correction normal vector corresponding to the current pixel is allowed to participate in the normal vector consistency loss calculation; when When =0, it is not included in the calculation.

9. The satellite image neural radiation field surface reconstruction device considering geometric priors according to claim 6, characterized in that, The normal vector consistency loss constructed in the iterative optimization module Specifically: ； in, It is the number of light samples in each iteration. and These represent the first and second normal vectors in the rendering and correction normal vector diagrams, respectively. The normal vector corresponding to each pixel. It is a decision function. It is an L1 norm; The total loss function is updated as follows: ； in For color loss, α is the Eikonal regularization loss, and γ are the weights of the normal vector consistency loss.

10. The satellite image neural radiation field surface reconstruction device considering geometric priors according to claim 6, characterized in that, The initial implicit surface reconstruction module includes an SDF prediction submodule and a color prediction submodule, which take the 3D point position and viewing direction as input and output SDF values ​​and color values; the initial normal vector map The prior normal vector is obtained by volume rendering of the normalized gradient of the SDF; the prior normal vector prediction module uses the Omnidata network to generate a full-resolution prior normal vector map for high-resolution satellite imagery using a block prediction and local alignment strategy. .

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