A relief area high-resolution sar image orthorectification method and system

Abstract

The application discloses a relief area high-resolution SAR image orthorectification method and system, comprising: collecting observation parameters of high-resolution DEM; generating simulated SAR images by using the observation parameters, matching the simulated SAR images with real SAR images, correcting initial positioning deviation, extracting control points of the relief area by twice matching the corrected real SAR images; using a multi-modal matching method based on geometric distortion perception to obtain high-density control points of flat areas in optical reference images and the initial corrected real SAR images; performing statistical analysis based on the control points of the flat areas and the control points of the relief area, constructing a geometric fine correction model, correcting the positioning errors of the corrected SAR images in the azimuth direction and the range direction, and realizing high-precision orthorectification.

Description

Technical Field

[0001] This invention relates to the field of image geometry processing technology, specifically to a method and system for orthorectifying high-resolution SAR images in undulating regions. Background Technology

[0002] SAR imagery, due to its advantages of being available 24 / 7, weather-dependent, and having strong penetration, is widely used in fields such as Earth observation, environmental monitoring, military reconnaissance, agricultural yield estimation, and disaster early warning. SAR imagery achieves imaging by transmitting microwave signals and receiving the echoes reflected from ground objects. It records the slant range information of ground objects along the radar line of sight, resulting in a significant difference between the image and the actual ground surface. To obtain the true spatial distribution of ground objects in a geographic coordinate system, SAR imagery needs to undergo orthorectification to eliminate geometric distortions caused by sensor attitude, terrain undulations, and differences in electromagnetic wave propagation paths.

[0003] Existing SAR image orthorectification typically relies on a high-precision digital elevation model (DEM) and ground control points (GCPs) working together to correct positioning errors through geometric reconstruction or simulation modeling. However, publicly available DEM data (such as SRTM and Copernicus) are insufficient in terms of spatial resolution and terrain detail representation, making it difficult to meet the correction requirements of sub-meter resolution SAR images. This results in inaccurate reflection of terrain features in undulating areas. Furthermore, due to the side-view imaging characteristics of SAR images, shadows, overlays, and perspective compression are prone to occur in mountainous and hilly terrains, causing significant displacement of ground features in the image and affecting geometric positioning accuracy.

[0004] Meanwhile, SAR imagery differs significantly from optical imagery in its imaging mechanism: traditional registration algorithms based on grayscale, gradient, or similarity measures struggle to achieve high-precision matching under multimodal conditions—especially in areas with dramatic terrain undulations, where feature points are prone to mismatches or sparse distribution, leading to insufficient control point extraction and severely impacting the accuracy of subsequent geometric refinement and orthorectification results. Therefore, current technologies need to achieve high-precision geometric positioning and orthorectification of high-resolution SAR imagery in complex terrain areas without ground control points. Summary of the Invention

[0005] Therefore, the technical problem solved by this invention is that existing high-resolution SAR images in areas with complex undulations suffer from large geometric positioning errors and sparse control points due to insufficient resolution of the digital elevation model (DEM), severe geometric distortion, and unstable multimodal matching, making it impossible to achieve high-precision orthorectification of SAR images.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for orthorectification of high-resolution SAR images in undulating regions, which includes acquiring observation parameters of a high-resolution DEM. The observation parameters are used to generate a simulated SAR image, which is then matched with the real SAR image to correct the initial positioning deviation. The control points of the undulating area are extracted by performing a second matching on the corrected real SAR image. Using a geometric distortion-aware multimodal matching method, high-density control points in flat areas are obtained from publicly available high-resolution optical reference images and pre-calibrated real SAR images. Statistical analysis is performed on the control points in the flat area and the control points in the undulating area to construct a geometric calibration model. This model corrects the positioning errors in the azimuth and range directions of the calibrated SAR image, achieving high-precision orthorectification.

[0007] As a preferred embodiment of the orthorectification method for high-resolution SAR images in undulating regions described in this invention, the observation parameters are necessary imaging parameters for projecting elevation data into the SAR imaging geometry, including the incident angle, viewing angle direction, elevation and descent paths, and coordinates of the four corner points.

[0008] As a preferred embodiment of the high-resolution SAR image orthorectification method for undulating regions described in this invention, the extraction of control points for undulating regions includes: calculating the initial offset between the simulated SAR image and the real SAR image using a phase correlation algorithm; and correcting the image range with undulations in the simulated SAR image and the real SAR image as a local region.

[0009] The corrected local regions are then subjected to secondary matching using normalized cross-correlation coefficients. The results are then subjected to consistency screening to extract control points for the fluctuation areas with high confidence.

[0010] As a preferred embodiment of the high-resolution SAR image orthorectification method for undulating regions described in this invention, the phase correlation algorithm includes: performing Fourier transform on the simulated SAR image and the real SAR image respectively, extracting the normalized cross power spectrum, obtaining the phase difference between the simulated SAR image and the real SAR image, obtaining the correlation plane through inverse Fourier transform, and locating the correlation peak to obtain the initial offset. The phase correlation algorithm is expressed as follows: in, Fourier transform yields the frequency domain signal of the analog image; Represents simulated SAR imagery; Complex conjugate in the frequency domain of a real image; Represents actual SAR imagery; The translational offset between the two images; Inverse Fourier Transform; C Complex coherence coefficient.

[0011] As a preferred embodiment of the high-resolution SAR image orthorectification method for undulating regions described in this invention, the multimodal matching method for geometric distortion sensing includes generating a geometric distortion mask from the simulated SAR imaging results, identifying invisible areas, and shielding shadow areas and overlapping areas.

[0012] For stable region image blocks after geometric mask screening, an anisotropic Gaussian derivative filter is used for filtering. Descriptor vectors are constructed based on the amplitude information of the filtering response in different directions and normalized. Local correlation is calculated by normalized cross-correlation to determine the best matching pair. The matching results are obtained and consistency screening is performed. Point pairs that are mistakenly identified as matching are removed from the matching results, and the correctly matched point pairs after screening are retained to generate a control point set for the flat region.

[0013] The normalized cross-correlation is expressed as: in, This represents the normalized cross-correlation matching value; Ω represents the normalized cross-correlation function; Ω represents the adaptive search domain.

[0014] As a preferred embodiment of the high-resolution SAR image orthorectification method for undulating regions described in this invention, the descriptor vector includes: filtering the input image using an anisotropic Gaussian derivative filter rotated in K directions to obtain local structural responses at different directions and scales; and constructing a descriptor vector based on the amplitude information of the filtering responses in each direction to characterize local structural features.

[0015] The descriptor vector is represented as follows: in, Direction angle; The intensity of the filter response in the K direction.

[0016] As a preferred embodiment of the orthorectification method for high-resolution SAR images in undulating regions described in this invention, the statistical analysis includes: calculating the systematic offsets in the azimuth and range directions based on the control points in the undulating and flat regions, used to quantify the positioning error of the SAR image to be corrected; and solving for the key parameters of the geometric refinement model by fitting the systematic offsets and the local nonlinear errors caused by the terrain. Input the pixel coordinates of the SAR image to be corrected into the geometric calibration model, and use the parameters... Calculate the correction amount and perform positioning error correction in the azimuth and range directions to achieve high-precision orthophoto correction.

[0017] The geometric calibration model is a mathematical model that optimizes the geometric accuracy of images by establishing a mapping relationship between image pixel coordinates and standard coordinates.

[0018] The geometric errors of the azimuth and range offsets are expressed as follows: in, Represents a geometrically refined model; These represent the key parameters of the geometrically refined model.

[0019] The parameters The optimization can be expressed using the least squares method as follows: in, This represents the x-coordinate of the i-th sampling point; This represents the ordinate of the i-th sampling point; Basis function matrix; Control point set; Indicates the range error; Azimuth error.

[0020] In this embodiment, the geometric calibration model is used to reconstruct the mapping relationship between SAR pixel coordinates and standard geographic coordinates based on the azimuth and range residuals of the control points, so as to achieve joint compensation for overall systematic offset and local nonlinear errors caused by terrain. The geometric calibration model can also adopt different function structures to adapt to different terrain conditions, different control point densities, or different error distribution characteristics, for example: The model can take the form of a pure polynomial, such as a second- or third-order two-dimensional polynomial, for scenarios with gentle terrain changes and where systematic errors dominate, such as plains and urban built-up areas. In this model, β represents the coefficients of each polynomial term, used to describe the overall offset trend of pixel coordinates in the azimuth and distance directions.

[0021] Secondly, the present invention provides a high-resolution SAR image orthorectification system for undulating regions, comprising an acquisition unit for acquiring observation parameters of a high-resolution DEM. The matching unit generates a simulated SAR image using the observation parameters, matches it with the real SAR image and corrects the initial positioning deviation, and extracts control points in the undulating area by performing a second matching on the corrected real SAR image. The screening unit generates a simulated SAR image using the observation parameters, matches it with the real SAR image and corrects the initial positioning deviation, and extracts control points in the undulating area by performing a second matching on the corrected real SAR image. The correction unit performs statistical analysis based on the control points in the flat area and the control points in the undulating area to construct a geometric calibration model, corrects the azimuth and range positioning errors of the calibrated SAR image, and achieves high-precision orthorectification.

[0022] Thirdly, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program is executed by the processor, it implements any step of the orthorectification method for high-resolution SAR images in undulating regions as described in the first aspect of the present invention.

[0023] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the orthorectification method for high-resolution SAR images in undulating regions as described in the first aspect of the present invention.

[0024] The beneficial effects of this invention are as follows: The high-resolution SAR image orthorectification method for undulating areas provided by this invention achieves high-precision geometric positioning and orthorectification of SAR images under complex terrain. The use of a two-step checking mechanism significantly improves the reliability of matching simulated and real images, enabling rapid and accurate extraction of control points. Furthermore, the introduction of a geometric distortion-aware multimodal matching algorithm effectively eliminates interference from distortion areas such as shadows and overlays, making it applicable even in complex undulating terrain. This invention achieves precise geometric correction without the need for ground control points, reducing labor costs and reliance on fieldwork. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart of a method for orthorectifying high-resolution SAR images in undulating regions. Detailed Implementation

[0027] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0028] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0029] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0030] Reference Figure 1 As an embodiment of the present invention, a method for orthorectifying high-resolution SAR images in undulating regions is provided, comprising the following steps: S1: Acquire observation parameters of high-resolution DEM.

[0031] Furthermore, the observation parameters are the necessary imaging parameters used to project elevation data into the SAR imaging geometry, including the incident angle, viewing direction, ascent and descent trajectories, and coordinates of the four corner points.

[0032] It should be noted that a high-resolution DEM is a digital model that is obtained through high-precision surveying and mapping technology and can accurately represent the topographic relief of the land surface. Publicly available medium-to-high-resolution DEM data can be selected, and coordinate unification, hole filling and abnormal elevation correction processing should be completed before input to ensure that it is on the same geographic coordinate reference as the SAR image. The two together constitute the input dataset for subsequent geometric simulation and correction.

[0033] To achieve spatial scale matching with SAR imagery, the resolution of the DEM can be enhanced using a terrain feature-aware super-resolution model (TfaSR). This model employs a network structure that combines depth residuals and deformable convolutions, effectively extracting multi-scale terrain features from the DEM. It is trained and optimized using joint constraints of global elevation consistency loss and local structure preservation loss, enhancing local undulation details while preserving the overall terrain trend. The DEM reconstructed by super-resolution will provide more refined terrain input for subsequent SAR geometric simulations.

[0034] The method of using a terrain feature-aware super-resolution model (TfaSR) to enhance the resolution of a Digital Elevation Model (DEM) requires first acquiring the original DEM and its multi-scale terrain-derived features. This involves analyzing the original DEM raster within the input region Ω. The slope, curvature, and topographic relief are calculated to fully characterize the topographic changes at different scales.

[0035] The feature can be obtained through the following formula: in, slope, curvature, undulation, This represents the average elevation within the neighborhood.

[0036] By studying different scales Multi-scale feature calculation can simultaneously capture the gentle trend of terrain and local steep changes, and the standardized multi-scale feature set can be used to calculate the topographical features. Together with the original DEM, it serves as input to the TfaSR model. This model, with its core framework of depth residual structure and deformable convolutional modules, aims to simultaneously capture both the global structure and local undulations of the terrain.

[0037] The calculation expression for a single residual module is as follows: in, Non-linear activation functions are typically in the form of ReLU; * indicates a convolution operation; The perturbation parameters at time K; The state value at time K; The constant term at time K.

[0038] To enhance the model's adaptability to complex terrain, the convolution kernel position is adaptively adjusted using a deformable convolution operator, defined as follows: in, R represents the coordinates of the sampling point at the corresponding output position; R represents the convolution sampling domain. This represents the offset, which can be dynamically adjusted to adapt to non-linear undulating terrain such as ridges and valleys.

[0039] This structure allows the model to maintain terrain continuity at a global scale while capturing subtle morphological changes at a local scale.

[0040] At each feature mapping layer, spatial average pooling is first used to extract channel global descriptors. Then, two fully connected layers and a sigmoid function are used to generate channel weights, thereby achieving adaptive weighting of the salient terrain feature channels. The final expression for feature fusion is: in, Indicates channel weight; This indicates the channel values ​​to be merged.

[0041] The above mechanism enables the TfaSR model to dynamically adjust the importance of terrain features at various scales, ensuring both enhanced response in areas of abrupt slope change and maintaining structural smoothness in gentle areas.

[0042] To balance global consistency and local detail fidelity, the joint optimization loss function can be defined as follows: in, This represents the reconstructed super-resolution DEM; Indicates a reference high-precision DEM; Represents the gradient field of the DEM; Represents the weighting coefficients of the global loss term; This represents the weighting coefficient of the local loss term.

[0043] The first term in the formula ensures that the overall terrain trend is consistent with the original DEM, while the second term ensures that the details of the edge and slope structure are preserved.

[0044] Finally, the model is trained and used for inference. A training sample set containing various terrain types (such as mountains, hills, plains, and valleys) is used, and the model parameters are trained end-to-end using the Adam optimizer. in, The set of parameters representing the terrain feature perception super-resolution model; This represents the optimal model parameters obtained by minimizing the loss function; Represented by the parametric model The generated super-resolution DEM; This represents the reference high-resolution DEM used for supervised training.

[0045] After training convergence, the model is applied to the DEM data of the target area to obtain a high-resolution DEM with a magnification of r=4, i.e., increasing from 30m to 7.5m. This magnification achieves a good balance between accuracy improvement and computational efficiency. The obtained high-resolution DEM is then quality-assessed, and the output results maintain spatial resolution consistent with SAR imagery. Its generation process can be represented as follows: in, Indicates magnification factor; This represents the super-resolution DEM reconstructed using a terrain feature-sensing super-resolution model. This indicates the output high-resolution DEM, whose spatial resolution is consistent with that of the SAR image. This represents the upsampling operator.

[0046] Comparative experiments conducted in a typical mountainous test area have verified that the super-resolution DEM generated in this embodiment has a reduced elevation mean square error (RMSE) of approximately 35% and a peak signal-to-noise ratio (PSNR) increase of approximately 2.8 dB compared to the original DEM. This indicates that the method can effectively improve the ability to restore terrain details and fully meet the requirements of high-resolution SAR geometric correction for terrain accuracy.

[0047] The TfaSR model was used to realize DEM super-resolution reconstruction based on multi-scale terrain features, which effectively improved the spatial continuity and structural fidelity of terrain representation, and provided a high-precision terrain foundation for subsequent SAR geometric simulation and orthorectification.

[0048] S2: Use the observation parameters to generate a simulated SAR image, match it with the real SAR image and correct the initial positioning deviation, and extract the control points of the undulating area by performing a second matching on the corrected simulated SAR image.

[0049] Furthermore, the observation parameters used to generate simulated SAR images include reading the incident angle from SAR image metadata. Viewing direction, azimuth The lifting rail markings and the coordinate imaging parameters of the four corner points.

[0050] The azimuth angle can be represented by the coordinates of the four corner points of the SAR image as follows: in, This indicates the coordinates of the last row boundary point of the SAR image.

[0051] The above geometric parameters can be used to determine the radar wave incident direction and line-of-sight projection relationship of the SAR sensor, providing a basis for subsequent geometric modeling.

[0052] Based on the geometric principles of SAR imaging, using the elevation data of high-resolution DEMs Line-of-sight projection is calculated along the radar incident direction to determine whether each terrain point is occluded. For each pixel, the determination condition can be expressed as: in, This indicates that the pixel is visible. It indicates that something is obscured.

[0053] If a sudden change in elevation on the incident path interrupts the line of sight, that point is identified as a "shadow area"; if there is overlap between adjacent points, it can be classified as an "overlapping area".

[0054] Based on the projection determination results, all pixels are classified according to their visibility status, and mask images of visible areas, shadow areas, and overlapping areas are generated. This mask image is used to represent the visible range from a SAR geometric perspective, and is specifically defined as follows: in, This represents the gray-scale accumulation coefficient defined within the overlapping area, indicating the number of times the area is illuminated by radar waves.

[0055] At the geometric level only (without involving electromagnetic scattering modeling), grayscale values ​​are defined as the cumulative number of scattering events covered by radar waves along the slant range, establishing a geometric grayscale field. For each pixel... Its grayscale can be defined by the following formula: in, This indicates the number of scattering events of that pixel along the radar incident direction. This represents the weight of the k-th scattering.

[0056] Therefore, the gray level of the shadow area is 0, the gray level of the visible area is 1, and the gray level of the overlay area increases with the number of overlays. Through this gray level definition, a brightness level distribution corresponding to the real SAR image can be formed geometrically.

[0057] grayscale Projecting the image onto the SAR slant range coordinate system achieves a transformation from the geographic coordinate system to the SAR slant range-azimuth coordinate system, ensuring that the generated simulated SAR image is geometrically consistent with the real SAR image. Comparing the two allows for visual verification of their geometric consistency. The simulation results can intuitively reflect the spatial distribution of shadows, overlays, and line-of-sight occlusion, providing a high-confidence geometric prior for subsequent two-step matching and geometric refinement.

[0058] Furthermore, the extraction of control points for undulating regions includes calculating the initial offset between the simulated SAR image and the real SAR image using a phase correlation algorithm.

[0059] Furthermore, the phase correlation algorithm includes obtaining the overall translation amount based on simulated SAR imagery and real SAR imagery data, and then participating in subsequent matching after geometric alignment.

[0060] The phase correlation algorithm is expressed as follows: in, Fourier transform yields the frequency domain signal of the analog image; Represents simulated SAR imagery; Complex conjugate in the frequency domain of a real image; Represents actual SAR imagery; The translational offset between the two images; Inverse Fourier Transform; C Complex coherence coefficient.

[0061] The corrected local regions are then subjected to secondary matching using normalized cross-correlation coefficients. The results are then subjected to consistency screening to extract control points for the fluctuation areas with high confidence.

[0062] It should be noted that the secondary matching is performed within a local window, centered on the offset result of the first matching, and the matching results are filtered based on the relevant peak signal-to-noise ratio threshold. This step uses the normalized cross-correlation (NCC) method for local similarity measurement. If the secondary offset satisfies: in, If a pixel-level threshold is used, the match is considered reliable; otherwise, abnormal matches are discarded.

[0063] Based on the image coordinates and imaging geometric parameters of the matched point pairs verified through two-step detection, the control point positions in the geographic coordinate system are calculated. These control points are typically located in areas with stable terrain undulations and can serve as initial constraints for subsequent multimodal matching and geometric refinement. Furthermore, according to different scenario requirements, the control point set can be subjected to confidence filtering and spatial weighted interpolation to reduce false matching interference and improve the spatial uniformity of control points.

[0064] S3: Using a multimodal matching method based on geometric distortion sensing, high-density control points in flat areas are obtained in the corrected simulated SAR image.

[0065] Furthermore, the geometric distortion-aware multimodal matching method includes generating a geometric distortion mask from the simulated SAR imaging results, identifying invisible areas, and masking shadow areas and overlapping areas.

[0066] It should be noted that the geometric distortion mask is used to identify invisible areas to shield against interference from shadow and overlapping areas, and to perform matching within the visible stable area to reduce the risk of mismatches and ensure the accuracy of the effective area and the reliability of the results.

[0067] For stable region image blocks after geometric mask screening, an anisotropic Gaussian derivative filter is used for filtering. Descriptor vectors are constructed based on the amplitude information of the filtering response in different directions, and the local correlation is calculated after normalization to obtain the matching results.

[0068] It should be noted that for stable region image blocks after geometric masking, an anisotropic Gaussian derivative filter with multi-directional rotation is used for convolution to extract local structural responses. The anisotropic Gaussian kernel is defined as follows: in, Represents the anisotropy coefficient. This represents the anisotropy factor, used to adjust the directional stretch ratio; Indicates the direction angle; This represents the ruler parameter.

[0069] Set direction angle set And calculate the filtering results in each direction. A descriptor vector is constructed based on the amplitude information of the directional filter responses to represent local structural features. The direction with the largest amplitude among all directional filter responses is determined as the main direction of the current pixel, represented as: in, This indicates the direction with the largest magnitude among all directional responses, and represents the main direction of the current pixel. Indicates the direction angle Lower filter response amplitude; This indicates the position where the function is maximized.

[0070] Furthermore, based on the principal direction and the response amplitudes in each direction, a multi-dimensional descriptor vector is constructed, represented as: in, Indicates the direction angle; This represents the intensity map of the filtered response in each direction.

[0071] To generate multi-directional anisotropic Gaussian features for multimodal matching, the descriptor is normalized, which can be represented as: in, This represents the normalized directional eigenvector. express The Euclidean norm is used for amplitude normalization.

[0072] It should be noted that by using geometrically distorted normalized cross-correlation (GNCC) to calculate local correlation and determine the best matching pair, this method can maintain matching stability in the presence of local geometric distortion.

[0073] The normalized cross-correlation is expressed as: in, This represents the normalized cross-correlation matching value; Ω represents the normalized cross-correlation function; Ω represents the adaptive search domain.

[0074] in, Indicates the sampling interval. It is determined by the difference in residuals between the two inspections.

[0075] The matching results are subjected to consistency screening to remove mismatched points and generate a set of control points for flat areas.

[0076] It should be noted that consistency screening is used to estimate the matching points using a model, and affine or thin-plate spline models are used to eliminate outliers, thus retaining high-confidence matching points that satisfy spatial consistency, which significantly improves the robustness of the geometric refinement stage. The generated high-density control point set provides a high-quality geographical constraint basis for subsequent geometric refinement and orthorectification of SAR images.

[0077] S4: Based on the control points in the flat area and the control points in the undulating area, perform statistical analysis to construct a geometric calibration model, correct the positioning errors in the azimuth and range directions of the calibrated SAR image, and achieve high-precision orthorectification.

[0078] It should be noted that the control points in the flat areas and the control points in the undulating areas provide a precise correspondence from the image coordinate system to the geographic coordinate system. By calculating the systematic offsets in the azimuth and range directions, the overall positioning error of the image to be corrected can be quantified.

[0079] The offset can be expressed as: in, Indicates the range error; Azimuth error; This represents the r-direction component of SAR data; This represents the a-direction component of SAR data; This represents the reference value in the r direction; this represents the reference value in the a direction.

[0080] Based on this, a geometrically refined model is constructed to fit the system offset and local nonlinear errors. This model can simultaneously compensate for linear drift and local deformation caused by terrain. It can be implemented using polynomial or thin-plate spline basis functions, and the parameters are solved by least-squares optimization. It describes the geometric transformation relationship from SAR pixel coordinates to geographic coordinates, and can be applied to any pixel. The correction amounts in the azimuth and range directions are calculated to compensate for the overall and local geometric errors of the SAR image, thereby obtaining the finely calibrated positioning results.

[0081] The geometric calibration model is a mathematical model that optimizes the geometric accuracy of images by establishing a mapping relationship between image pixel coordinates and standard coordinates.

[0082] The geometric errors of the azimuth and range offsets are expressed as follows: in, Represents a geometrically refined model; These represent the key parameters of the geometrically refined model.

[0083] In this embodiment, the geometric calibration model employs a mapping fitting algorithm based on a combination of thin-plate splines and polynomials. This algorithm constructs a basis function matrix in the pixel coordinate space, composed of radial basis functions and low-order polynomials, enabling the model to simultaneously describe both the overall system offset and the local nonlinear distortions caused by terrain undulations. Specifically, the radial basis functions of the thin-plate splines can flexibly fit errors caused by local bending, compression, or stretching due to mountainous terrain, while the low-order polynomial terms describe the overall distortion at the sensor scale, ensuring numerical stability of the model even in high-resolution, highly undulating regions. By inputting the control point coordinates into the model, a basis function matrix consisting of B(x,y) can be obtained, serving as the function space basis for fitting the errors.

[0084] In the algorithm described above, β is the hyperparameter vector in the geometric calibration model, essentially a set of weight coefficients for all basis functions (including polynomial and radial basis functions). β determines the contribution of different types of errors to the mapping relationship: for example, β in the polynomial part corresponds to the magnitude of the overall deformation, while β in the radial basis part determines the strength and distribution of local corrections. As a hyperparameter, β needs to be solved through least-squares optimization to minimize the squared residual between the model-predicted positioning error and the actual control point error. Therefore, β not only reflects the fitting result but also embodies the sensitivity and expressive power of the calibration model to different error sources.

[0085] In other alternative implementations, the geometric calibration model can also be implemented using various alternative algorithms. For example, a piecewise continuous distortion correction surface can be constructed using a bicubic spline interpolation model. By fitting the control point error piecewise on a two-dimensional grid, this is suitable for regions with high control point density and smooth error changes. Alternatively, a Gaussian process regression model can be used, which automatically models the correlation of spatial errors through the covariance function. This can achieve higher fitting accuracy when control points are sparse or errors have a strong spatial correlation structure. In some scenarios where only overall compensation is required, the model can also be simplified to an affine transformation plus a local correction term, achieving fast correction through linear parameters and offsets. Furthermore, on devices with limited computing resources, a piecewise linear correction table method can be used to model the error in local regions as a linear function, thereby significantly improving computational efficiency while maintaining a certain level of accuracy.

[0086] The parameters The optimization can be expressed using the least squares method as follows: in, This represents the x-coordinate of the i-th sampling point; This represents the ordinate of the i-th sampling point; Basis function matrix; Control point set; Indicates the range error; Azimuth error.

[0087] Based on the fitting results, the corrected SAR image is geometrically refined using the parameters. For the coordinates of each pixel in the SAR image The model calculates correction values ​​and adds them to the original pixel coordinates, thus correcting positioning errors in the azimuth and range directions and ensuring that the image is geometrically consistent with the geographic reference coordinate system. By mapping the image coordinates to the geographic coordinate system, the slant range-geographic mapping relationship is accurately reconstructed, generating an orthophoto.

[0088] By outputting high-resolution SAR images that have undergone geometric and orthorectification correction, error distribution maps or accuracy assessment reports are generated to verify the correction effect.

[0089] This invention, under the constraint of high-density control points, performs unified modeling and parameter optimization of system offset and local nonlinear error, and combines high-resolution DEM to achieve accurate projection from slant range coordinates to geographic coordinates, providing a reliable technical foundation for subsequent ground feature extraction, change detection and high-precision mapping applications.

[0090] This embodiment also provides a high-resolution SAR image orthorectification system for undulating regions, including: The acquisition unit acquires observation parameters of the high-resolution DEM.

[0091] The matching unit generates a simulated SAR image using the observation parameters, matches it with the real SAR image and corrects the initial positioning deviation, and extracts control points in the undulating area by performing a secondary matching on the corrected real SAR image.

[0092] The screening unit generates a simulated SAR image using the observation parameters, matches it with the real SAR image and corrects the initial positioning deviation, and extracts control points in the undulating area by performing a secondary match on the corrected real SAR image.

[0093] The correction unit performs statistical analysis based on the control points in the flat area and the control points in the undulating area to construct a geometric calibration model, corrects the azimuth and range positioning errors of the calibrated SAR image, and achieves high-precision orthorectification.

[0094] This embodiment also provides a computer device applicable to the orthorectification method of high-resolution SAR images in undulating areas, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the orthorectification method of high-resolution SAR images in undulating areas as proposed in the above embodiment.

[0095] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0096] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the orthorectification method for high-resolution SAR images in undulating areas as proposed in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0097] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for orthorectifying high-resolution SAR images in undulating regions, characterized in that, include: Acquire observation parameters of high-resolution DEM; The observation parameters are used to generate a simulated SAR image, which is then matched with the real SAR image to correct the initial positioning deviation. The control points of the undulating area are extracted by performing a second matching on the corrected real SAR image. Using a geometric distortion-aware multimodal matching method, high-density control points in flat areas are obtained from publicly available high-resolution optical reference images and pre-calibrated real SAR images. The geometric distortion sensing multimodal matching method includes generating a geometric distortion mask from the simulated SAR imaging results, identifying invisible areas, and masking shadow areas and overlapping areas; For stable region image blocks after geometric mask screening, an anisotropic Gaussian derivative filter is used for filtering. Descriptor vectors are constructed based on the amplitude information of the filtering response in different directions and normalized. Local correlation is calculated by normalized cross-correlation to determine the best matching pair. The matching results are obtained and consistency screening is performed. Point pairs that are mistakenly identified as matching are removed from the matching results, and the correct matching point pairs after screening are retained to generate a control point set for the flat region. The normalized cross-correlation is expressed as: in, This represents the normalized cross-correlation matching value; Ω represents the normalized cross-correlation function; Ω represents the adaptive search domain. Based on the control points in the flat area and the control points in the undulating area, a geometric calibration model is constructed to correct the positioning errors in the azimuth and range directions of the calibrated SAR image, thereby achieving high-precision orthorectification. The statistical analysis includes calculating the systematic offsets in the azimuth and range directions based on control points in undulating and flat areas, which are used to quantify the positioning error of the SAR image to be corrected; and solving for the key parameters of the geometric calibration model by fitting the systematic offsets and local nonlinear errors caused by terrain. Input the pixel coordinates of the SAR image to be corrected into the geometric calibration model, and use the parameters... Calculate the correction amount, perform positioning error correction in the azimuth and range directions, and achieve high-precision orthogonal correction; The geometric precision correction model is a mathematical model that optimizes the geometric accuracy of an image by establishing a mapping relationship between image pixel coordinates and standard coordinates. The geometric errors of the azimuth and range offsets are expressed as follows: in, Represents a geometrically refined model; Key parameters of the geometrically refined model; The parameters The optimization can be expressed using the least squares method as follows: in, This represents the x-coordinate of the i-th sampling point; This represents the ordinate of the i-th sampling point; Basis function matrix; Control point set; Indicates the range error; Azimuth error.

2. The orthorectification method for high-resolution SAR images in undulating regions as described in claim 1, characterized in that: The observation parameters are the necessary imaging parameters for projecting elevation data into SAR imaging geometry, including incident angle, viewing direction, ascent and descent trajectories, and coordinates of the four corner points.

3. The orthorectification method for high-resolution SAR images in undulating regions as described in claim 2, characterized in that: The control points for extracting undulating regions include calculating the initial offset between the simulated SAR image and the real SAR image using a phase correlation algorithm, and correcting the image range with undulations in the simulated SAR image and the real SAR image as a local region. The corrected local regions are then subjected to secondary matching using normalized cross-correlation coefficients. The results are then subjected to consistency screening to extract control points for the fluctuation areas with high confidence.

4. The orthorectification method for high-resolution SAR images in undulating regions as described in claim 3, characterized in that: The phase correlation algorithm includes performing Fourier transform on the simulated SAR image and the real SAR image respectively, extracting the normalized cross power spectrum, obtaining the phase difference between the simulated SAR image and the real SAR image, obtaining the correlation plane through inverse Fourier transform, and locating the correlation peak to obtain the initial offset. The phase correlation algorithm is expressed as follows: in, Fourier transform yields the frequency domain signal of the analog image; Represents simulated SAR imagery; Complex conjugate in the frequency domain of a real image; Represents actual SAR imagery; The translational offset between the two images; Inverse Fourier Transform; C Complex coherence coefficient.

5. The orthorectification method for high-resolution SAR images in undulating regions as described in claim 4, characterized in that: The descriptor vector includes filtering the input image using an anisotropic Gaussian derivative filter rotated in K directions to obtain local structural responses at different directions and scales. A descriptor vector is constructed based on the amplitude information of the filtered responses in each direction to characterize local structural features. The descriptor vector is represented as follows: in, Direction angle; The intensity of the filter response in the K direction.

6. A high-resolution SAR image orthorectification system for undulating regions, based on the high-resolution SAR image orthorectification method for undulating regions according to any one of claims 1 to 5, characterized in that: Includes an acquisition unit for acquiring observation parameters of a high-resolution DEM; The matching unit generates a simulated SAR image using the observation parameters, matches it with the real SAR image and corrects the initial positioning deviation, and extracts control points in the undulating area by performing a second matching on the corrected real SAR image. The screening unit generates a simulated SAR image using the observation parameters, matches it with the real SAR image and corrects the initial positioning deviation, and extracts control points in the undulating area by performing a second matching on the corrected real SAR image. The correction unit performs statistical analysis based on the control points in the flat area and the control points in the undulating area to construct a geometric calibration model, corrects the azimuth and range positioning errors of the calibrated SAR image, and achieves high-precision orthorectification.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the orthorectification method for high-resolution SAR images in undulating regions as described in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the orthorectification method for high-resolution SAR images in undulating regions as described in any one of claims 1 to 5.

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