Stable scatterer point identification method based on kolmogorov-arnold network

Abstract

The application discloses a stable scatterer point automatic identification method based on a Kolmogorov-Arnold network, relates to the technical field of radar remote sensing InSAR time series processing and geological disaster landslide monitoring, and comprises the following steps: generating a landslide body boundary, acquiring radar time series observation, determining a landslide body monitoring pixel point, and extracting multi-dimensional interference phase features; pairing is carried out according to a combination rule irrelevant to sequence, Kolmogorov network calculation is carried out, and a same-type scattering correlation graph is generated; a space pixel point is screened in a squeezed scatterer point selection framework, a same-type pixel group is obtained when a same-type scattering score of a pixel meets a first threshold parameter and a space connectivity constraint, a consistency index in the group is calculated, effective same-type pixel groups and radar time series observation phases are converged, a distributed scatterer monitoring point is determined according to a representative value of a phase in the group, and a stable scatterer point position generates a point position coordinate and a point position type identifier. The method can realize automatic acquisition of a landslide monitoring point position and improve the effectiveness of the point position.

Description

Technical Field

[0001] This invention relates to the field of radar remote sensing InSAR time series processing and geological disaster landslide monitoring technology, specifically, to a method for automatic identification of stable scatterer locations based on the Kolmogorov-Arnold network. Background Technology

[0002] Landslides are a typical type of geological hazard, influenced by factors such as rainfall, reservoir water levels, and engineering disturbances. They often manifest as slow deformation but can suddenly become unstable. Radar interferometric remote sensing (InSAR) can acquire surface deformation information over a wide area under all-weather conditions, and temporal InSAR reconstructs deformation sequences through multi-temporal observations. Such methods typically rely on monitoring points with relatively stable scattering characteristics at the pixel scale to ensure the sustainable use of interferometric phases. However, within vegetated landslides, the scattering mechanism fluctuates with vegetation growth and water content changes, resulting in scarce and unstable available monitoring points, which affects the automatic acquisition and continuous tracking of monitoring points.

[0003] Existing temporal InSAR monitoring point extraction schemes mainly include permanent scatterers and small baseline methods. Permanent scatterer methods often screen point target scatterers based on indicators such as amplitude dispersion and coherence coefficient. Small baseline methods invert scatterers by constructing a small temporal / small vertical baseline interferometric network and determine usable pixels using criteria such as coherence. For non-point scattering, distributed scatterer processing typically uses statistical tests, coherence criteria, or homogeneous pixel selection strategies within a local window to determine a set of homogeneous pixels. Then, the phases of these homogeneous pixels are filtered or weighted to improve the usable observation density. Related homogeneous pixels / compression frames often combine spatial neighborhood search and connectivity constraints to form pixel groups or representative points for deformation monitoring.

[0004] In recent years, machine learning models have also been used for feature discrimination and classification regression of remote sensing data. Among them, the Kolmogorov-Arnold Network (KAN) is a type of neural network structure that uses one-dimensional learnable functions as basic units. Originating from the Kolmogorov-Arnold representation idea, it learns one-dimensional functions on the connections and sums and combines them to fit nonlinear relationships. It has certain characteristics in tabular data modeling and interpretable mapping. When applying such networks to specific remote sensing discrimination tasks, they are mostly used for single-sample to label mapping, and rarely directly address the chain process of pixel pair relationship discrimination and group to phase convergence in InSAR temporal scattering consistency. At the same time, directly using general models to output classification results usually makes it difficult to naturally express the symmetrical similarity relationship between pixels, spatial connectivity constraints, and the need to handle missing phase samples.

[0005] The existing solutions mentioned above have several drawbacks in vegetation cover landslide monitoring scenarios: First, point selection based on amplitude dispersion or coherence thresholds is sensitive to time-varying vegetation conditions, making it difficult to consistently obtain a sufficient number of usable monitoring pixels. Second, the determination of homogeneous pixel sets relies heavily on local window statistics and empirical parameters, making it difficult to characterize the nonlinear relationships of similar scattering behaviors among pixels, easily leading to uneven pixel group quality and spatial fragmentation. Third, even with the introduction of a general learning model, without explicitly constructing a graph of inter-pixel relationships and combining spatial adjacency and connectivity constraints, it is difficult to directly apply the degree of similarity to intra-group phase weighted convergence, thus affecting the formation of the representative phase of the distributed scatterer and the effectiveness of the points.

[0006] No effective solutions have yet been proposed to address the problems in the relevant technologies. Summary of the Invention

[0007] To address the problems in related technologies, this invention proposes an automatic identification method for stable scatterer locations based on the Kolmogorov-Arnold network, thereby overcoming the aforementioned technical problems in existing related technologies.

[0008] Therefore, the specific technical solution adopted by the present invention is as follows:

[0009] In a first aspect, the present invention proposes an automatic identification method for stable scatterer locations based on the Kolmogorov-Arnold network, comprising:

[0010] Acquire boundary data of the monitoring area of ​​vegetation-covered landslides and generate landslide boundaries; acquire time-series observations of multi-temporal geometry interferometric synthetic aperture radar;

[0011] Based on landslide boundary and radar time-series observations, the monitoring pixel points of the landslide body are determined, and multidimensional interferometric phase features are extracted from the monitoring pixel points of the landslide body to obtain the monitoring pixel feature vector;

[0012] The monitoring pixel feature vectors are paired in multiple dimensions using order-independent combination rules to generate multi-dimensional pixel pairing features. These features are then input into a pre-configured Kolmogorov network for calculation and analysis to obtain pixel-like scattering scores. Based on these scores, a similar scattering correlation map is generated.

[0013] Based on the similar scattering correlation map and the squeeze scattering body point selection framework, spatially adjacent pixels are screened for each landslide monitoring pixel point. If the similar scattering score of a pixel satisfies the first threshold parameter and the spatial connectivity constraint, a similar pixel group is obtained. The intra-group consistency index is calculated for the similar pixel group. If the intra-group consistency index satisfies the second threshold parameter, a valid similar pixel group is determined. If the intra-group consistency index does not satisfy the second threshold parameter, an invalid label is generated.

[0014] Phase convergence is performed on effective similar pixel groups and radar time-series observations. Based on the phase convergence results and the similar scattering scores of pixels, the phase representative value within the group is determined, and the distributed scatterer monitoring point is determined according to the phase representative value within the group.

[0015] Spatial inclusion determination is performed on the monitoring points of distributed scatterers and the boundaries of landslide bodies to obtain stable scatterer locations. Based on the stable scatterer locations, point coordinates and point type identifiers are generated to achieve the stability of automatic identification of scatterer locations.

[0016] Further, the boundary data of the vegetation-covered landslide monitoring area is acquired and the landslide boundary is generated. The acquisition of multi-temporal geometric interferometric synthetic aperture radar (IPAR) time-series observations includes: acquiring boundary data of the vegetation-covered landslide monitoring area and performing boundary closure checks on the boundary data to obtain the landslide boundary; acquiring multi-temporal IAR single-view complex images based on the same satellite platform, orbital direction, imaging mode, and polarization conditions, and selecting one temporal phase as the master image to define the same observation geometry; registering the remaining temporal IAR single-view complex images to the pixel grid of the master image to generate the correspondence between the pixel grid and geographic coordinates; generating the first interferometric phase sequence based on preset time baseline thresholds and vertical baseline thresholds and incorporating them into the interferometric pair set, and calculating the multi-temporal amplitude sequence for each pixel of each temporal image; and generating radar time-series observations based on the first interferometric phase sequence and the multi-temporal amplitude sequence.

[0017] Furthermore, based on landslide boundary and radar time-series observations, landslide monitoring pixel points are determined, and multidimensional interferometric phase features are extracted from these monitoring pixel points to obtain monitoring pixel feature vectors. These vectors include: projecting the landslide boundary onto the pixel grid based on the correspondence between the landslide boundary and pixel grid with geographic coordinates, performing spatial inclusion determination, assigning unique pixel indices to the determined landslide boundary pixels, and obtaining landslide monitoring pixel points; extracting multi-temporal amplitude sequences from the landslide monitoring pixel points using radar time-series observations as input values ​​for amplitude fluctuation features; constructing multidimensional interferometric phase features based on amplitude fluctuation features, interferometric continuity features, and phase jump features; and calculating two components of the amplitude fluctuation features from the multi-temporal amplitude sequences to obtain the mean amplitude of the first component and the amplitude dispersion index of the second component. The second interferometric phase sequence is extracted from each landslide monitoring pixel using radar time-series observations. Based on a preset interferometric threshold parameter, an interferometric marker is generated for each interferometric phase sample. The two components of the interference continuity feature are calculated for the interferometric marker to obtain the number of effective interferometric samples of the first component and the longest continuous effective length of the second component. The phase difference sequence is judged for jumps using a preset phase jump threshold parameter to obtain the interferometric phase samples of adjacent time phases. The two components of the phase jump judgment feature are calculated for the interferometric phase samples of adjacent time phases to obtain the number of jumps of the first component that satisfy the phase jump threshold parameter and the median of the phase difference amplitude of the second component that satisfies the phase jump threshold parameter. The components are then organized according to the amplitude fluctuation feature, interference continuity feature, and phase jump feature to obtain the monitoring pixel feature vector.

[0018] Furthermore, by using a preset phase jump threshold parameter to determine the jump in the phase difference sequence, the interference phase samples of adjacent time phases are obtained as follows: Interference pairs consisting of adjacent acquisition times are selected from the interference pair set to obtain an adjacent interference pair set; adjacent interference phase sequences are obtained based on each landslide monitoring pixel point and the corresponding interference phase samples are read from the adjacent interference pair set; the phase difference of adjacent samples in the adjacent interference phase sequences is calculated sequentially according to the acquisition time order to obtain a phase difference sequence; the phase difference amplitude is calculated for each phase difference sample in the phase difference sequence, and a jump determination is performed on the phase difference amplitude using the preset phase jump threshold parameter. If the phase difference amplitude meets the preset phase jump threshold parameter, a jump is determined; based on the jump determination result, interference phase samples of adjacent time phases of the jump information are obtained.

[0019] Furthermore, multi-dimensional pairing of monitoring pixel feature vectors is performed using order-independent combination rules to generate multi-dimensional pixel pairing features. These features are then input into a pre-configured Kolmogorov network for computation and analysis to obtain pixel-like scattering scores. Based on these scores, a similar scattering correlation map is generated, including: determining a preset search window size parameter for each landslide monitoring pixel in the set, and filtering other landslide monitoring pixel points falling within the preset search window to obtain pixel pairs; reading the monitoring pixel feature vectors for each pixel pair and pairing them to obtain pixel pairing features; calculating the absolute values ​​of the component sums and differences between the six corresponding components using order-independent combination rules to obtain twelve-dimensional pixels; pairing features of the twelve-dimensional pixels using a fixed component order method; and ensuring that the order of inputting the monitoring pixel feature vectors into the twelve-dimensional pixel pairing features remains consistent based on the pairing results. The twelve-dimensional pixel pairing features are input into the input layer of a Kolmogorov network, and the twelve-dimensional pixels are divided into three groups of inputs using feature amplitude fluctuation features, interference continuity features, and phase jump features. These three groups of inputs are then input into three parallel sub-layers of the feature grouping mapping layer. Neurons in the Kolmogorov network connect the three parallel sub-layers and configure one-dimensional learnable functions. The outputs of each one-dimensional learnable function are summed to obtain the outputs of the three parallel sub-layers. The outputs of the three parallel sub-layers are then input into a feature fusion layer, and neurons in the Kolmogorov network fuse and map the outputs to obtain fused features. The fused features are then input into a single output neuron of the output layer to generate pixel-like scattering scores. Based on preset score normalization parameters, the pixel-like scattering scores are limited to a preset range. Landslide monitoring pixels are used as nodes, and pixel-like scattering scores are used as edge weight pairs. Connections are established using these pixel pairs to obtain a similar scattering correlation graph.

[0020] Furthermore, the outputs of the three parallel sub-layers are input into the feature fusion layer, and the neurons in the Kolmogorov network are used to perform fusion mapping on the outputs of the three parallel sub-layers. The calculation formula for the fused features is as follows:

[0021] ;

[0022] In the formula, Z u,v Represents the fusion feature of pixel pairs; X u,v,j J represents the j-th component value of the 12-dimensional pixel pairing feature; j represents the input component index; J b This represents the set of input component indices corresponding to branch b; b represents the branch identifier. Let q be a one-dimensional learnable function of the Kolmogorov-Arnold neurons of branch b in the feature grouping mapping layer on the input connection j. This indicates the number of Kolmogorov-Arnold neurons in branch b; R represents a one-dimensional learnable function in the feature fusion layer that receives the output of the q-th group mapping of branch b and connects it to the t-th Kolmogorov-Arnold neuron in the feature fusion layer; t represents the neuron index in the feature fusion layer; f This indicates the number of Kolmogorov-Arnold neurons in the feature fusion layer; denoted as a one-dimensional learnable function corresponding to the t-th Kolmogorov-Arnold neuron in the feature fusion layer; amp represents the amplitude fluctuation feature branch; cont represents the interference continuous feature branch; jump represents the phase jump feature branch.

[0023] Furthermore, based on the similar scattering correlation diagram and the squeeze scatterer point selection framework, spatially adjacent pixels are screened for each landslide monitoring pixel. If the similar scattering score of a pixel satisfies the first threshold parameter and the spatial connectivity constraint, a similar pixel group is obtained. The intra-group consistency index is calculated for each similar pixel group. If the intra-group consistency index satisfies the second threshold parameter, a valid similar pixel group is determined; otherwise, an invalid label is generated. This includes: taking each landslide monitoring pixel as the center, determining a set of spatially adjacent pixels in the pixel grid according to a preset adjacency type parameter, where the adjacency type parameter limits the spatial adjacency relationship to four-adjacency or eight-adjacency; reading the corresponding edge weights in the similar scattering correlation diagram for the set of spatially adjacent pixels to obtain the similar scattering score, and excluding spatially adjacent pixels whose similar scattering scores do not meet the first threshold parameter; using the landslide monitoring pixel as a seed node, and selecting the remaining... Spatially adjacent pixels are expanded for search based on pixel grid connectivity. During the expansion search, propagation occurs only along connections where the pixel-like scattering scores satisfy the first threshold parameter. Spatial connectivity constraints are determined based on the expanded search pixel set. Based on these constraints, the pixel set and the seed node are determined to belong to the same connected component in the pixel grid. Based on the pixel set determined by spatial connectivity constraints, similar pixel groups are obtained. Using the similar scattering scores in the similar scattering association graph, all pixel pairs within the similar pixel group are statistically analyzed to obtain the mean score and dispersion within the group. According to a preset consistency mapping parameter, the mean score and dispersion within the group are mapped and calculated to obtain the consistency index within the group. The consistency index within the group is compared with the second threshold parameter. If the consistency index within the group satisfies the second threshold parameter, a valid similar pixel group is determined; otherwise, an invalid marker is generated.

[0024] Furthermore, phase convergence is performed on effective similar pixel groups and radar time-series observations. Based on the phase convergence results and pixel similar scattering scores, the phase representative value within the group is determined. The distributed scatterer monitoring points are then determined based on the phase representative values ​​within the group. This process includes: extracting the interferometric phase sequence of each pixel within each effective similar pixel group using radar time-series observations; using the seed node of the effective similar pixel group as the reference pixel and reading the pixel similar scattering score between each pixel in the group and the reference pixel according to the similar scattering correlation map; converting the pixel similar scattering score into non-negative phase convergence weights using preset weight mapping parameters and normalizing the phase convergence weights; converting the interferometric phase samples into unit complex numbers; weighting the phase convergence weights and converting the weighted convergence result into phase values ​​to obtain the phase representative value sequence within the group; associating the phase representative value sequence within the group with the pixel position of the seed node, and determining the distributed scatterer monitoring points based on the association results.

[0025] Further, the interferometric phase samples are converted into unit complex number representations; and the phase convergence weights are weighted and converged, and the weighted convergence result is converted into phase values ​​to obtain the in-group phase representative value sequence, including: performing phase convergence for each interferometric pair index within the effective same pixel group; based on each pixel within the effective same pixel group, reading the interferometric phase sample corresponding to the interferometric pair index in the interferometric phase sample set corresponding to the pixel; converting the read interferometric phase samples into unit complex number representations, and calculating the cosine value of the interferometric phase sample as the real part of the unit complex number, and calculating the sine value of the interferometric phase sample as the imaginary part of the unit complex number to obtain the unit complex number of the interferometric phase sample value; judging the state of the interferable marker and the integrity of the interferometric phase samples; if the interferable marker is invalid or the interferometric phase sample is missing, resetting the phase convergence weight of the corresponding pixel under the interferometric pair index to zero; when the interferable marker is invalid or the interferometric phase sample is missing, the phase convergence weight of the corresponding pixel under the interferometric pair index is reset to zero; when the interferable marker is invalid or the interferometric phase sample is missing, the phase convergence weight of the corresponding pixel under the interferometric pair index is reset to zero; when the interferable marker is invalid or the interferometric phase sample is missing, the phase convergence weight of the corresponding pixel is reset to zero; when the phase convergence weight of the interferometric phase sample is invalid or the interferometric phase sample is missing, the phase convergence weight of the interferometric phase sample ... When the interferometer is marked as valid, the phase convergence weight under the interferometer pair index is assigned the weight of the normalized non-negative phase convergence after conversion by the preset weight mapping parameters; the phase convergence weights under all interferometer pair indices are subjected to secondary normalization, and the sum of the valid phase convergence weights under the same interferometer pair index is the preset value; if the denominator of the secondary normalization is zero, all unit complex numbers corresponding to the reference pixel under the interferometer pair index are weighted and summed to obtain the weighted convergence result; where the weight of each unit complex number is the phase convergence weight under the corresponding interferometer pair index; the weighted convergence result is converted into a phase value, the real and imaginary parts of the weighted convergence result are read, and the phase angle of the weighted convergence result is obtained by using the two-parameter arctangent operation, and the phase angle is recorded as the in-group phase representative value; the in-group phase representative values ​​corresponding to all interferometer pair indices are sorted according to the index order to obtain the in-group phase representative value sequence.

[0026] Furthermore, spatial inclusion determination is performed on the distributed scatterer monitoring points and landslide boundaries to obtain stable scatterer locations. Based on the stable scatterer locations, point coordinates and point type identifiers are generated to achieve the stability of automatic scatterer point identification. This includes: for each distributed scatterer monitoring point, reading the location information of the bound landslide monitoring pixel in the pixel grid, and determining the corresponding geographic coordinates of the distributed scatterer monitoring point based on the mapping relationship between the pixel grid and geographic coordinates; unifying the geographic coordinates of the point and the landslide boundary to the same coordinate reference, and performing spatial inclusion determination; if the geographic coordinates of the point fall within the landslide boundary range, it is determined to be included; if the geographic coordinates of the point do not fall within the landslide boundary range, it is determined not to be included; for the distributed scatterer monitoring points that are spatially included, stable scatterer locations are determined, and based on each stable scatterer location, point coordinates and point type identifiers are obtained, where the point type identifier is the distributed scatterer monitoring point.

[0027] The beneficial effects of this invention are as follows:

[0028] 1. This invention introduces a Kolmogorov-Arnold network to learn and discriminate the scattering relationship between pixel pairs, replacing the approach of relying solely on empirical criteria such as amplitude dispersion and coherence threshold. This invention constructs a six-dimensional feature vector on landslide monitoring pixels, composed of amplitude fluctuations, interference continuity, and phase jumps. It generates twelve-dimensional paired features using a rule that combines component-wise summation with the order-independent absolute value of the difference, ensuring feature consistency when the input order of the same pixel pair is changed, and matching the symmetry of similar relationships. The Kolmogorov-Arnold network maps and fuses feature branches with different physical meanings through multiple sets of one-dimensional learnable functions, outputting a similar scattering score, explicitly quantifying the nonlinear similarity relationship between pixels, providing a callable edge weight basis for subsequent grouping and phase processing, and reducing the dependence on a single threshold screening point.

[0029] 2. This invention proposes a novel mechanism for generating and selecting similar pixel groups driven by a similar scattering correlation graph. It transforms the learned pixel similar scattering scores into graph structure edge weights, combining these with the spatial adjacency relationships of the pixel grid to jointly constrain the formation of similar pixel groups. Unlike simply performing statistical homogeneity checks within a fixed window, this invention uses a seed pixel as the center within a squeezed scatterer selection framework, expanding the search along spatially adjacent connections whose scores satisfy a first threshold. Connectivity constraints ensure the reachability and spatial continuity of similar pixel groups, avoiding the generation of disconnected sets that cross holes. Simultaneously, it statistically analyzes the scores of all pixel pairs within a group, constructing a consistency index derived from mapping the mean and dispersion of scores within the group. A second threshold is used to determine the validity of the pixel group, ensuring that the output valid similar pixel groups have a unified selection criterion in both similarity and intra-group stability, reducing the uncertainty propagation caused by uneven quality of homogeneous pixel sets.

[0030] 3. This invention proposes a comprehensive process for generating stable scatterer locations. It combines effective similar pixel groups with radar time-series observations for phase convergence. Convergence weights are determined based on similar scattering scores. After forming distributed scatterer monitoring points, the coordinates and type identifiers of the output points are determined by incorporating landslide boundary information. This invention uses seed pixels as a reference, reads similar scattering scores between pixels within a group and the reference pixel based on the correlation diagram, and obtains non-negative convergence weights through weight mapping and normalization. For each interferometric pair, the phase is converted to a unit complex number and weighted summed to obtain the phase angle, yielding a representative phase value within the group. Simultaneously, missing interferometric phase samples are assigned zero weights and normalized twice to ensure the feasibility and consistency of the convergence process under conditions of missing samples. By binding the sequence of phase representative values ​​within a group to the seed cell location and performing boundary determination, this method can automatically generate distributed scatterer points within the landslide body that can be directly used for temporal deformation calculation. It realizes a closed-loop process from cell feature construction, learning of similar relationships, spatial grouping, phase convergence to point output. Compared with the traditional process of first screening points and then empirically grouping or uniformly stacking, it is more in line with the joint needs of similar scattering discrimination and spatial constraints in vegetation cover landslide scenarios. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. 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.

[0032] Figure 1 This is a flowchart of an automatic identification method for stable scatterer locations based on a Kolmogorov-Arnold network according to an embodiment of the present invention.

[0033] Figure 2 This is a flowchart of radar timing observation construction in the automatic identification method for stable scatterer locations based on the Kolmogorov-Arnold network according to an embodiment of the present invention.

[0034] Figure 3 This is a flowchart of the monitoring pixel feature vector extraction in the automatic identification method of stable scatterer points based on Kolmogorov-Arnold network according to an embodiment of the present invention.

[0035] Figure 4 This is a flowchart illustrating the calculation of pixel-like scattering scores and the construction of a similar scattering association map in the automatic identification method for stable scatterer locations based on the Kolmogorov-Arnold network according to an embodiment of the present invention.

[0036] Figure 5 This is a flowchart of the screening and validity determination of similar pixel groups in the automatic identification method of stable scatterer points based on Kolmogorov-Arnold network according to an embodiment of the present invention.

[0037] Figure 6 This is a flowchart of phase convergence and distributed scatterer monitoring point generation in the automatic identification method of stable scatterer points based on Kolmogorov-Arnold network according to an embodiment of the present invention.

[0038] Figure 7 This is a comparison diagram of spatial coverage improvement in the automatic identification method for stable scatterer points based on the Kolmogorov-Arnold network according to an embodiment of the present invention.

[0039] Figure 8 This is an illustration of the effect of coverage heat in the automatic identification method for stable scatterer points based on the Kolmogorov-Arnold network according to an embodiment of the present invention.

[0040] Figure 9 This is a schematic diagram of complex-weighted convergence of phase units within a group in the automatic identification method for stable scatterer points based on the Kolmogorov-Arnold network according to an embodiment of the present invention.

[0041] Figure 10 This is a model diagram of the Kolmogorov-Arnold network in the automatic identification method of stable scatterer points based on the Kolmogorov-Arnold network according to an embodiment of the present invention. Detailed Implementation

[0042] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention.

[0043] According to an embodiment of the present invention, an automatic identification method for stable scatterer locations based on the Kolmogorov-Arnold network is proposed.

[0044] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 1 As shown, the automatic identification method for stable scatterer locations based on the Kolmogorov-Arnold network according to an embodiment of the present invention includes:

[0045] Step S1: Acquire boundary data of the vegetation cover landslide monitoring area and generate the landslide boundary; acquire interferometric synthetic aperture radar time-series observations of multi-temporal geometry;

[0046] Step S2: Based on the landslide boundary and radar time-series observations, determine the monitoring pixel points of the landslide body, and extract multi-dimensional interferometric phase features from the monitoring pixel points of the landslide body to obtain the monitoring pixel feature vector;

[0047] Step S3: Use order-independent combination rules to perform multi-dimensional pairing of the monitoring pixel feature vectors to generate multi-dimensional pixel pairing features. Input the multi-dimensional pixel pairing features into a pre-configured Kolmogorov network for calculation and analysis to obtain the pixel similar scattering score. Based on the pixel similar scattering score, generate a similar scattering correlation map.

[0048] Step S4: Based on the similar scattering correlation map and the squeeze scattering body point selection framework, filter the spatially adjacent pixels of each landslide body monitoring pixel point. If the similar scattering score of the pixel meets the first threshold parameter and the spatial connectivity constraint, a similar pixel group is obtained. Calculate the intra-group consistency index for the similar pixel group. If the intra-group consistency index meets the second threshold parameter, a valid similar pixel group is determined. If the intra-group consistency index does not meet the second threshold parameter, an invalid label is generated.

[0049] Step S5: Perform phase convergence on effective similar pixel groups and radar time-series observations, and determine the phase representative value within the group based on the phase convergence results and the similar scattering score of the pixels, and determine the distributed scatterer monitoring point based on the phase representative value within the group;

[0050] Step S6: Spatial inclusion determination is performed on the distributed scatterer monitoring points and landslide boundaries to obtain stable scatterer locations. Based on the stable scatterer locations, point coordinates and point type identifiers are generated to achieve the stability of automatic scatterer location identification.

[0051] In this optional embodiment, acquiring boundary data of the vegetation-covered landslide monitoring area and generating the landslide boundary; acquiring interferometric synthetic aperture radar (ISAR) time-series observations with multi-temporal geometry includes: acquiring boundary data of the vegetation-covered landslide monitoring area and performing boundary closure checks on the boundary data to obtain the landslide boundary; acquiring multi-temporal IAR single-view complex images based on the same satellite platform, orbital direction, imaging mode, and polarization conditions, and selecting one temporal phase as the master image to define the same observation geometry; registering the remaining temporal IAR single-view complex images to the pixel grid of the master image to generate the correspondence between the pixel grid and geographic coordinates; generating a first interferometric phase sequence based on a preset time baseline threshold and a vertical baseline threshold and incorporating them into an interferometric pair set, and calculating the multi-temporal amplitude sequence for each temporal image pixel by pixel; and generating radar time-series observations based on the first interferometric phase sequence and the multi-temporal amplitude sequence.

[0052] Specifically, such as Figure 8 As shown, a point density heat map layer is superimposed on the same base map and boundary. The color from light to dark indicates that the coverage is from low to high. Traditional methods result in scattered and fragmented heat maps, with large areas of low coverage existing inside the landslide body. The method of this invention has continuous heat maps that extend to the vegetation coverage area, resulting in better coverage uniformity. This indicates that the invention can form more continuous spatial sampling, improving the integrity and stability of landslide deformation inversion. The boundary data of the vegetation-covered landslide monitoring area is obtained and denoted as B. B includes a sequence of geographic coordinate points used to describe the outer contour of the landslide body. The coordinate points in B are connected in a predetermined order to form a boundary line, and a closure check is performed on the boundary line. When the first and last points of the boundary line do not coincide, the coordinates of the first point are appended as the coordinates of the last point to achieve closure. A topological consistency check is performed on the closed boundary line, deleting duplicate points and correcting self-intersection segments to obtain a closed polygonal boundary, denoted as P. P is used as the landslide body boundary for the pixel-level spatial inclusion determination in the above steps. Multi-temporal interferometric synthetic aperture radar single-look complex images were acquired under the same satellite platform, orbital orientation, imaging mode, and polarization conditions. The set of multi-temporal single-look complex images is denoted as {S}. t}, where t is the phase index, S t Each pixel is a complex echo, and one phase is selected as the master image, denoted as S. r and with S r Define the same observation geometry G such that the multi-temporal amplitude sequence and the interferometric phase sequence required in the above steps have consistent spatial indices within the same pixel grid. For each image S... t Perform registration to align with the master image S r The pixel grid is used to obtain the registered image. The registration process includes: estimating the row and column offsets between the main image and the secondary image within a preset matching window based on the magnitude map, and resampling the secondary image according to the offsets to achieve pixel-level alignment, with the main image S... r The pixel grid is taken as the pixel grid Ω, and the correspondence between Ω and geographic coordinates is established based on the orbital parameters and imaging geometry. The correspondence is denoted as M. M is used to map geographic coordinates to pixel row and column indices, or to map pixel row and column indices to geographic coordinates. Through M, the landslide boundary P can be projected onto Ω, thereby ensuring that the above steps can screen landslide monitoring pixel points that fall into the landslide boundary in radar time-series observation.

[0053] like Figure 2 As shown, the time interval between any two time phases is calculated based on the acquisition time of each time phase, and the time interval is denoted as D. ij Based on the orbital parameters, the vertical baseline in the landslide monitoring area is calculated for any two time phases, and the vertical baseline is denoted as L. ij Set the preset time baseline threshold T d With vertical baseline threshold T b When D ij Satisfy T d And L ij Satisfy T b At that time, the time relative (i,j) is included in the set of interference pairs Π. For each interference pair (i,j), conjugate multiplication is performed pixel by pixel on the pixel grid Ω to obtain the complex interference number. The interference phase is then extracted from the complex interference number to obtain the interference phase sequence {ϕ}. k} (i.e., the first interferometric phase sequence), where k is the interferometric pair index. For each temporal image, the modulus of the complex echo is calculated pixel by pixel to obtain the amplitude value, forming a multi-temporal amplitude sequence {A}. t}, where A t To be with S t The corresponding amplitude diagram will be {ϕ k} and {A t Align and combine the pixels according to the grid Ω to form the radar time series observation R. R provides a unified input for the amplitude fluctuation characteristics, interferometric continuity characteristics and phase jump characteristics of the above steps, and provides a data basis under the same observation geometry for the above steps to construct pixel pairing characteristics and calculate the pixel similar scattering score of the Kolmogorov-Arnold network.

[0054] In this optional embodiment, landslide monitoring pixel points are determined based on landslide boundaries and radar time-series observations. Multidimensional interferometric phase features are extracted from these monitoring pixel points to obtain monitoring pixel feature vectors. This includes: projecting the landslide boundary onto the pixel grid and performing spatial inclusion determination based on the correspondence between the landslide boundary, pixel grid, and geographic coordinates; assigning unique pixel indices to the determined landslide boundary pixels to obtain landslide monitoring pixel points; extracting multi-temporal amplitude sequences from the landslide monitoring pixel points using radar time-series observations as input values ​​for amplitude fluctuation features; constructing multidimensional interferometric phase features based on amplitude fluctuation features, interferometric continuity features, and phase jump features; and calculating two components of the amplitude fluctuation features from the multi-temporal amplitude sequences to obtain the amplitude mean of the first component and the amplitude dispersion of the second component. The indicators are as follows: A second interferometric phase sequence is extracted from each landslide monitoring pixel using radar time-series observations. An interferometric marker is generated for each interferometric phase sample based on a preset interferometric threshold parameter. Two components of the interference continuity feature are calculated for the interferometric marker, yielding the number of effective interferometric samples for the first component and the longest continuous effective length for the second component. A phase jump threshold parameter is used to determine the phase difference sequence jump, resulting in interferometric phase samples for adjacent time phases. Two components of the phase jump determination feature are calculated for the interferometric phase samples of adjacent time phases, yielding the number of jumps in the first component that satisfy the phase jump threshold parameter and the median of the phase difference amplitude in the second component that satisfies the phase jump threshold parameter. The components are then organized according to amplitude fluctuation characteristics, interference continuity characteristics, and phase jump characteristics to obtain the monitoring pixel feature vector.

[0055] Specifically, the landslide boundary P, the pixel grid Ω, and the corresponding relationship M are read. M is used to project the landslide boundary P onto the geographic coordinate coverage area of ​​the pixel grid Ω. Spatial inclusion determination is performed on the center point coordinates of each pixel in Ω. When the center point coordinates of a pixel fall within the landslide boundary P, the pixel is included in the landslide monitoring pixel point set, denoted as U. A unique pixel index u is assigned to each landslide monitoring pixel point, where u is used to locate the amplitude and phase samples of that pixel in radar time-series observations. The radar time-series observation R obtained from the above steps is read, and for each landslide monitoring pixel point u, a multi-temporal amplitude sequence is extracted from R according to the temporal phase index. This multi-temporal amplitude sequence is denoted as A. u , where A u It consists of multiple temporal amplitude samples, each derived from the amplitude image pixel value corresponding to u, serving as the input for calculating amplitude fluctuation characteristics. For each landslide monitoring pixel u, the amplitude sequence A is used. u The input consists of two components for calculating the amplitude fluctuation characteristics. The first component is defined as the amplitude mean m. u Using A uThe second component is obtained by averaging all amplitude samples within the range, and is defined as the amplitude dispersion index d. u First calculate A u The standard deviation s of all amplitude samples u Then the standard deviation s u Divide by the mean amplitude m u Get d u When m u Less than the preset minimum amplitude threshold parameter T a At that time, m u Replace with T a Participate in d u Calculations are performed to ensure that the amplitude dispersion index can be calculated stably.

[0056] For each landslide monitoring pixel u, the interferometric phase sequence is extracted from the radar time-series observation R, and the interferometric phase sequence is denoted as Φ. u (i.e., the second interference phase sequence), Φ u Each sample corresponds to an interferometric pair index k. A one-to-one correspondence is established between the interferometric pair index k and the interferometric pair set Π constructed in the above steps, so that each k corresponds to one interferometric pair (i... k ,j k ), where i k With j k Let Φ be the two-phase index of the interference pair, and Φ u The interferometric phase sample with index k is derived from the interferometric pair (i k ,j k To generate interferometric markers, for each k, a discriminant q at u is calculated that reveals the interferometric quality. u,k Discriminant q u,k Using the preset coherence window size parameter W c The coherence coefficient is obtained by calculating within a limited local window, and S is used in the calculation. ik (p), the acquired multi-temporal single-view complex image set {S t Read, participate in the calculation The obtained registered image is read from the image and the specific calculation is as follows:

[0057] ;

[0058] In the formula, q u,k W represents the discriminant of landslide monitoring pixel u on interferometric pair index k. u This indicates a window centered at u, defined by a preset coherence window size parameter W. c A defined set of cell indices within a local window, where p represents W. u Cell index within, S ik (p) represents the complex echo at pixel p of the first temporal single-view complex image corresponding to index k of the interferometric pair. This represents the complex echo after the second temporal single-view complex image corresponding to index k of the interferometer is registered to the pixel grid of the main image. The complex conjugate operation is represented by |⋅|, and the modulus operation is represented by i. k With j k This represents the two phase indices corresponding to the interferometric pair index k, and q u,k With the preset interference threshold parameter T i Comparison, when q u,k Satisfy T i Time-dependent generation of interferometric marker g u,k For it to be valid, when q u,k Not satisfied with T i Time-dependent generation of interferometric marker g u,k The invalid sample is marked as missing, and the corresponding interferometric phase sample is marked as missing. For each landslide monitoring pixel u, the interferometric label sequence {g} can be generated. u,k The two components of the continuous interferometric feature are calculated. The first component is defined as the number of effective interferometric samples, n. u Statistical analysis of all k. u,k To obtain the number of valid occurrences, the second component is defined as the longest consecutive valid length l. u First, according to the acquisition time sequence of the interference pairs, {g} u,k Sort the data, then count the length of the longest consecutive valid segment to obtain l. u For each landslide monitoring pixel u, two components of the phase transition characteristic are calculated based on the transition determination result. The first component is defined as the transition number c. u The number of samples that are identified as jumps is obtained by statistical analysis. The second component is defined as the median jump amplitude h. u The median of the phase difference amplitudes of all phase transitions determined to be transitions is obtained when the number of transitions is c. u When h is zero, u Set to zero, and set the m value of the amplitude fluctuation characteristic to zero. u With d u n, the continuous characteristics of interference u With l u c of phase jump characteristics u with h u The monitoring pixel feature vectors are organized in the order of amplitude fluctuation characteristics, interference continuity characteristics, and phase jump characteristics, such as... Figure 3 As shown, the feature vector of the monitored pixel is denoted as F. u F u To fix the six-dimensional structure, it is used to generate twelve-dimensional pixel pairing features in the above steps, inputting them into the Kolmogorov-Arnold network to calculate the pixel homogeneous scattering score.

[0059] In this optional embodiment, the process of determining the phase difference sequence for jumps using a preset phase jump threshold parameter to obtain interference phase samples of adjacent time phases includes: filtering interference pairs composed of adjacent acquisition times from the interference pair set to obtain an adjacent interference pair set; obtaining an adjacent interference phase sequence based on each landslide monitoring pixel point and reading the corresponding interference phase samples from the adjacent interference pair set; calculating the phase difference of adjacent samples in the adjacent interference phase sequence according to the acquisition time order to obtain a phase difference sequence; calculating the phase difference amplitude for each phase difference sample in the phase difference sequence and performing a jump determination on the phase difference amplitude using the preset phase jump threshold parameter; if the phase difference amplitude meets the preset phase jump threshold parameter, it is determined to be a jump; and obtaining interference phase samples of adjacent time phases of the jump information based on the jump determination result.

[0060] Specifically, to obtain interferometric phase samples of adjacent time phases, firstly, interferometric pairs consisting of adjacent acquisition times are selected from the set of interferometric pairs to form an adjacent set of interferometric pairs, denoted as Π. a For each landslide monitoring pixel u, in Π a The corresponding interference phase samples are read to form an adjacent interference phase sequence. and to The phase difference between adjacent samples is calculated sequentially according to the acquisition time to obtain the phase difference sequence ΔΦ. u For ΔΦ u For each phase difference sample, the phase difference amplitude is calculated, and a preset phase jump threshold parameter T is used. p Perform a transition determination when the phase difference amplitude satisfies T p It is determined to be a jump.

[0061] In this optional embodiment, multi-dimensional pairing of monitoring pixel feature vectors is performed using order-independent combination rules to generate multi-dimensional pixel pairing features. These features are then input into a pre-configured Kolmogorov network for computation and analysis to obtain pixel-like scattering scores. Based on these scores, a similar scattering correlation map is generated, including: determining a preset search window size parameter for each landslide monitoring pixel point in the landslide monitoring pixel point set, and filtering other landslide monitoring pixel points falling within the preset search window to obtain pixel pairs; reading the monitoring pixel feature vectors for each pixel pair and pairing them to obtain pixel pairing features; calculating the absolute values ​​of the component-wise sum and differences between the six corresponding components using order-independent combination rules to obtain twelve-dimensional pixels; pairing features of the twelve-dimensional pixels using a fixed component order method; and inputting the monitoring pixel feature vectors into the order-preserving method of the twelve-dimensional pixel pairing features based on the pairing results. The process is as follows: The twelve-dimensional pixel pairing features are input into the input layer of the Kolmogorov network. The twelve-dimensional pixels are then divided into three input groups using feature amplitude fluctuation, interference continuity, and phase jump features. These three input groups are then input into three parallel sub-layers of the feature grouping mapping layer. Neurons in the Kolmogorov network connect these three parallel sub-layers and configure one-dimensional learnable functions. The outputs of each one-dimensional learnable function are summed to obtain the outputs of the three parallel sub-layers. The outputs of these three parallel sub-layers are then input into the feature fusion layer. Neurons in the Kolmogorov network fuse these outputs to obtain fused features. The fused features are then input into a single output neuron of the output layer to generate pixel-specific scattering scores. Based on preset score normalization parameters, the pixel-specific scattering scores are limited to a preset range. Landslide monitoring pixels are used as nodes, and pixel-specific scattering scores are used as edge weight pairs. Connections are established using these pixel pairs to obtain a similar scattering correlation graph.

[0062] Specifically, the landslide monitoring pixel set U obtained from the above steps is read, and the row and column indices in the pixel grid Ω are read for each landslide monitoring pixel u in U. The preset search window size parameter W is set. s W s To define the coverage area of ​​a square search window centered at u, for each landslide monitoring cell u, other landslide monitoring cells whose row and column indices fall within the search window are filtered out within U, resulting in a candidate set N. u And the ordered pair (u,v) is treated as a pixel pair, where v is N. u For landslide monitoring pixels, when u and v appear repeatedly, a pixel index sorting rule is used to retain only pixel pairs where the u index is less than the v index to avoid duplicate pairings. For each pixel pair (u,v), two monitoring pixel feature vectors F are read. u With F v Fu With F v All are fixed six-dimensional structures obtained from the above steps. The six components correspond in order to the mean amplitude m, amplitude dispersion index d, number of effective interference samples n, longest continuous effective length l, number of jumps c, and median jump amplitude h. A twelve-dimensional pixel pairing feature is generated using order-independent combination rules. The twelve-dimensional pixel pairing feature is denoted as X. u,v Generate X u,v First, sum the six corresponding components one by one to obtain six sum components. Then, subtract the six corresponding components one by one and take the absolute value to obtain six difference components. Finally, concatenate the six sum components and the six difference components in a fixed order to form X. u,v , to exchange F u With F v When inputting in sequence, X u,v Maintain consistency. For example... Figure 10 As shown, X u,v The twelve components are sequentially input into the input layer of the Kolmogorov-Arnold network K. The input layer contains twelve input neurons, which are divided into three groups of inputs according to their physical meaning: amplitude fluctuation feature group. For the four components corresponding to m and d, the interference continuity feature set The four components corresponding to n and l, the phase transition feature group For the four components corresponding to c and h, components with different physical meanings are directed to their respective branches. The three sets of inputs are then fed into three parallel sub-layers of the feature grouping mapping layer, denoted as follows: , , Each parallel sublayer consists of multiple Kolmogorov-Arnold neurons. Each Kolmogorov-Arnold neuron includes an input connection set, a set of connection functions, and a summation unit. The input connection set receives the scalar output from the previous layer. The set of connection functions consists of multiple sets of one-dimensional learnable functions that correspond one-to-one with the input connections. Each one-dimensional learnable function maps a single scalar to a single scalar. The summation unit sums the outputs of each one-dimensional learnable function to obtain the output of the Kolmogorov-Arnold neuron. Based on this structure, the three parallel sublayers respectively... , , Performing group mapping yields three sets of sub-layer outputs, denoted as follows: , , .

[0063] In this optional embodiment, , , The input feature fusion layer is used to perform fusion mapping on the outputs of the three sub-layers through at least one Kolmogorov-Arnold neuron to obtain the fused feature, denoted as Z. u,v To explicitly define the computational link between grouping and fusion mapping to directly executable scalar operations, the following fusion mapping is used to calculate Z. u,v The outputs of the three parallel sub-layers are input into the feature fusion layer, and the neurons in the Kolmogorov network are used to fuse and map the outputs of the three parallel sub-layers. The formula for calculating the fused features is as follows:

[0064] ;

[0065] In the formula, Z u,v Represents the fusion feature of pixel pairs; X u,v,j J represents the j-th component value of the 12-dimensional pixel pairing feature; j represents the input component index; J b This represents the set of input component indices corresponding to branch b; b represents the branch identifier. Let q be a one-dimensional learnable function of the Kolmogorov-Arnold neurons of branch b in the feature grouping mapping layer on the input connection j. This indicates the number of Kolmogorov-Arnold neurons in branch b; R represents a one-dimensional learnable function in the feature fusion layer that receives the output of the q-th group mapping of branch b and connects it to the t-th Kolmogorov-Arnold neuron in the feature fusion layer; t represents the neuron index in the feature fusion layer; f This indicates the number of Kolmogorov-Arnold neurons in the feature fusion layer; denoted as a one-dimensional learnable function corresponding to the t-th Kolmogorov-Arnold neuron in the feature fusion layer; amp represents the amplitude fluctuation feature branch; cont represents the interference continuous feature branch; jump represents the phase jump feature branch.

[0066] like Figure 4 As shown, the fused feature Z u,v The unnormalized value of the isoscattering score of a single output neuron in the input-output layer is denoted as . The output neuron follows the Kolmogorov-Arnold neuron structure, configuring a one-dimensional learnable function for the input connections and summing the output of the one-dimensional learnable function to obtain the output neuron. Using preset score normalization parameters to Mapped to pixel-like scattering score s u,v The preset score normalization parameters include the normalization lower bound S. min With the normalized upper bound Smax Normalization should first be performed on the following: Execution based on S min With S max The linear scaling is then applied, followed by lower and upper bound truncation of the scaling result, so that s u,v Limited to a range of zero to one, the parameters of the Kolmogorov-Arnold network K are obtained by training on a pre-set training sample set, which consists of known pairs of pixels of the same type and pairs of pixels of different types. A similar scattering correlation map is constructed using landslide monitoring pixels as nodes, denoted as G. a G a Let the set of nodes be U. For each pixel pair (u,v) obtained in the above steps, in G... a Establish connecting edges and score pixel-like scattering s u,v Assigning values ​​to edge weights, thus making G a The similarity between monitoring pixels of the landslide body is explicitly expressed in the form of edge weights, and is used as the input map called in the squeeze scattering body point selection framework in the above steps.

[0067] In this optional embodiment, based on the similar scattering correlation diagram and the squeeze scatterer point selection framework, spatially adjacent pixels are screened for each landslide monitoring pixel. If the similar scattering score of a pixel satisfies the first threshold parameter and the spatial connectivity constraint, a similar pixel group is obtained. A consistency index within the similar pixel group is calculated. If the consistency index within the group satisfies the second threshold parameter, a valid similar pixel group is determined; if the consistency index within the group does not satisfy the second threshold parameter, an invalid label is generated. This includes: taking each landslide monitoring pixel as the center, determining a set of spatially adjacent pixels in the pixel grid according to a preset adjacency type parameter, where the adjacency type parameter limits the spatial adjacency relationship to four-adjacency or eight-adjacency; reading the corresponding edge weights in the similar scattering correlation diagram for the set of spatially adjacent pixels to obtain the similar scattering score of the pixel, and excluding spatially adjacent pixels whose similar scattering scores do not satisfy the first threshold parameter; using the landslide monitoring pixel as a seed node, and... The retained spatially adjacent pixels are expanded for search based on the pixel grid connectivity. During the expansion search, propagation only occurs along connections where the pixel-like scattering scores satisfy the first threshold parameter. Spatial connectivity constraints are determined based on the expanded search pixel set. Based on these constraints, the pixel set and the seed node are determined to belong to the same connected component in the pixel grid. Based on the pixel set determined by spatial connectivity constraints, similar pixel groups are obtained. Using the similar scattering scores in the similar scattering association graph, all pixel pairs within the similar pixel group are statistically analyzed to obtain the mean score and the dispersion of the score within the group. According to a preset consistency mapping parameter, the mean score and the dispersion of the score within the group are mapped and calculated to obtain the consistency index within the group. The consistency index within the group is compared with the second threshold parameter. If the consistency index within the group satisfies the second threshold parameter, a valid similar pixel group is determined; otherwise, an invalid marker is generated.

[0068] Specifically, such as Figure 5 As shown, the set of landslide monitoring pixels U and the pixel grid Ω obtained in the above steps are read, and the row and column indices (r) of each landslide monitoring pixel u in U are read in Ω. u ,c u Set the preset adjacency type parameter P. n P n Used to define spatial adjacency relationships as four-adjacency or eight-adjacency, when P n When limited to four adjacent nodes, with (r u ,c u Construct four candidate adjacent positions in Ω with ) as the center. The row and column indices of the candidate adjacent positions are (r) and (r, r) respectively. u -1,c u ), (r u +1,c u ), (r u ,cu -1), (r) u ,c u +1), and remove candidate adjacent positions that exceed the range of Ω, when P n When limited to eight adjacencies, four diagonal candidate adjacencies are added to the four-adjacency candidate adjacency positions. The row and column indices of the four diagonal candidate adjacency positions are (r... u -1,c u -1), (r) u -1,c u +1), (r) u +1,c u -1), (r) u +1,c u +1), and remove candidate adjacent positions that exceed the range of Ω. For each candidate adjacent position, search within U according to the row and column indices to find whether there is a corresponding landslide monitoring pixel point, thus obtaining the set of spatially adjacent pixel points. ,in Each element in the array satisfies P with u. n Landslide monitoring pixels with defined spatial adjacency relationships. Read the similar scattering correlation map G obtained from the above steps. a and in Read G one by one within the range a The edge weight between node u and node v is used as the pixel-like scattering score s u,v , where v is Spatial adjacent pixels within G, when G a When there is no connecting edge between node u and node v, the pixel-like scattering score s of the pixel pair is calculated. u,v Set the threshold to zero, set the first threshold parameter T1, and set the pixel-like scattering score s. u,v Spatial adjacent pixel points v that do not meet the first threshold parameter T1 By excluding the adjacent elements, we obtain the filtered set of adjacencies. This allows adjacent connections entering the extended search to simultaneously possess spatial adjacency constraints and similar scattering score constraints.

[0069] Using landslide monitoring cell u as the seed node, an extended search is used to generate a candidate set of similar cells C in the cell grid Ω. u During initialization, u is added to C. u Then add u to the queue to be expanded, perform loop processing on the queue to be expanded, retrieve the current cell point p from the queue, and according to the preset adjacency type parameter P n Construct a set of spatially adjacent pixels of p in Ω, and then filter the set of spatially adjacent pixels of p in U. For each spatially adjacent pixel q, read the similar scattering correlation map G. a The pixel-like scattering scores s of p and q p,qWhen G a When there are no connecting edges in s p,q Set to zero only if s p,q The first threshold parameter T1 is satisfied and q has not yet been added to C. u When q is added to C u And add q to the queue to be expanded, and propagate only along the connections where the pixel-like scattering scores satisfy the first threshold parameter T1 during the expansion search process, so that the candidate set of pixels of the same type C is expanded. u From the same type of scattering correlation graph G a The generation process is driven by maintaining spatial adjacency with the cell grid Ω. This applies to candidate sets of similar cells C. u Perform spatial connectivity constraint determination; the object of spatial connectivity constraint determination is C. u P in the cell grid Ω n Limited connectivity, starting from the seed node u, exists only in set C. u Press P inside n By performing connected component traversal based on the defined spatial adjacency relations, a subset D of pixels belonging to the same connected component as u is obtained. u When D u With C u When they are consistent, determine C. u Determined by spatial connectivity constraints, and using C u Forming a group of pixels of the same type, denoted as C. u When D u With C u When inconsistent, determine C u Failed to pass the spatial connectivity constraint determination, and with D u Replace C u Obtain the same type of pixel group G u This ensures that pixels of the same type satisfy the spatial connectivity constraint that the seed node can reach.

[0070] For the same type of pixel group G u All pixel pairs in the same type of scattering correlation map G a The pixel-like scattering scores in the dataset are statistically analyzed to obtain the mean score and the dispersion of the score within each group. Specifically, G is enumerated. u For any two distinct pixels (p, q) within the region, read G. a The corresponding edge weight is used as the pixel-like scattering score s p,q When G a When there are no connecting edges in s p,q Set to zero, and set all s p,q Summing and dividing by the number of pixel pairs yields the mean score within a group, denoted as . The dispersion of scores within a group is denoted as , The calculation uses each sp,q and The square of the difference, the average of all squared differences, and the square root are used to obtain the result. It can be directly calculated from scalar samples of scattering scores of pixels of the same type. The mean score within a group is calculated based on preset consistency mapping parameters. Within-group score dispersion Mapped to an intra-group consistency index, the preset consistency mapping parameters include the mean gain parameter. Dispersion penalty parameter With consistency bias parameter B c The intragroup consistency index is calculated using the following mapping: In the formula, I u Indicates the consistency index within the group; This represents the average score within the group; The within-group score dispersion; This is the mean gain parameter; B is the dispersion penalty parameter. c Here, I is the consistency bias parameter; exp(⋅) is the natural exponential function, which is mapped to make I... u Follow Increase and increase and follow Increases and decreases, and I u Limit it to the range of zero to one. Set a second threshold parameter T2 to set the group consistency index I. u Compared with the second threshold parameter T2, when I u When the second threshold parameter T2 is satisfied, the same type of pixel group G is determined. u For a valid group of pixels of the same type, when I u When the second threshold parameter T2 is not met, for the same type of pixel group G u Invalid markers are generated so that valid similar pixel groups output by the squeeze scatterer point selection frame can be directly used as input constraints for intra-group phase convergence by the above steps.

[0071] In this optional embodiment, phase convergence is performed on effective similar pixel groups and radar time-series observations. Based on the phase convergence results and pixel similar scattering scores, the phase representative value within the group is determined. The distributed scatterer monitoring point is determined based on the phase representative value within the group. This includes: using radar time-series observations, extracting the interference phase sequence of each pixel within each effective similar pixel group; using the seed node of the effective similar pixel group as the reference pixel, and reading the pixel similar scattering score between each pixel within the group and the reference pixel according to the similar scattering association map; converting the pixel similar scattering score into a non-negative phase convergence weight using a preset weight mapping parameter, and normalizing the phase convergence weight; converting the interference phase sample into a unit complex number representation; weighting the phase convergence weight, converting the weighted convergence result into a phase value, and obtaining the phase representative value sequence within the group; associating the phase representative value sequence within the group with the pixel position of the seed node, and determining the distributed scatterer monitoring point based on the association result.

[0072] Specifically, the radar timing observation R obtained from the above steps and the effective similar pixel groups output from the above steps are read, and each effective similar pixel group is denoted as G. u Where u is the seed node corresponding to the valid class of pixels, and G u It consists of multiple landslide monitoring pixels p, for each Extract the interference phase sequence from R according to the interference pair index k, and denote the interference phase sequence as Φ. p And simultaneously read the interference-capable marker g generated in the above steps. p,k , where g p,k Used to indicate whether the interference phase sample at the interferometric pair index k of pixel point p is valid. This is used to determine whether the valid class of pixels G is valid. u The corresponding seed node u is the reference pixel. The homogeneous scattering correlation map G obtained from the above steps is read. a For each Read G a The edge weight between node p and node u is used as the pixel-like scattering score s p,u When G a When there are no connecting edges in s, p,u Set to zero, and set the preset weight mapping parameter P. w P w Including the power exponent parameter K w With lower bound bias parameter B w For each s p,u Perform the following weight mapping process: First, set s p,u The execution range is truncated to obtain a truncation value. If the truncation value is less than zero, it is set to zero; if the truncation value is greater than one, it is set to one. Then, K is calculated from the truncation value. w The exponent is obtained by raising the power to the power of B, and then the exponent is combined with B. wAdding them together yields the unnormalized phase convergence weights. ,make It is a nonnegative scalar, for all Normalization is performed to obtain the phase convergence weight w p Normalization adopts the method of normalizing each Divide by all Summation of all When the summation is zero, the w corresponding to the reference pixel u will be... u Set the weights to one and reset the weights of the remaining pixels to zero, so that the weights can be directly used for weighted pooling. Then, set the phase representative value sequence within the group. The position of a seed node u is bound to its cell location, which is determined by its row and column indices (r) in the cell grid Ω. u ,c u ) indicates that (r u ,c u )and The data are collectively recorded as a single distributed scatterer monitoring point, denoted as D. u Repeat the above steps for all valid pixels of the same type to output the set of distributed scatterer monitoring points, such as... Figure 6 As shown, the set of distributed scatterer monitoring points is denoted as D, where each element of D consists of a seed node pixel position and its corresponding intra-group phase representative value sequence.

[0073] In this optional embodiment, the interferometric phase samples are converted into unit complex number representations; and the phase convergence weights are weighted and converged, and the weighted convergence result is converted into phase values ​​to obtain a sequence of phase representative values ​​within the group. This includes: performing phase convergence for each interferometric pair index within the effective same-type pixel group; based on each pixel within the effective same-type pixel group, reading the interferometric phase sample corresponding to the interferometric pair index in the interferometric phase sample set corresponding to the pixel; converting the read interferometric phase samples into unit complex number representations, and calculating the cosine value of the interferometric phase sample as the real part of the unit complex number, and calculating the sine value of the interferometric phase sample as the imaginary part of the unit complex number to obtain the unit complex number of the interferometric phase sample value; judging the state of the interferable marker and the integrity of the interferometric phase samples; if the interferable marker is invalid or the interferometric phase sample is missing, resetting the phase convergence weight of the corresponding pixel under the interferometric pair index to zero; When the interferometric mark is in an effective state, the phase convergence weight under the interferometric pair index is assigned the weight of the normalized non-negative phase convergence after conversion by the preset weight mapping parameters; the phase convergence weights under all interferometric pair indices are subjected to secondary normalization, and the sum of the effective phase convergence weights under the same interferometric pair index is the preset value; if the denominator of the secondary normalization is zero, all unit complex numbers corresponding to the reference pixel under the interferometric pair index are weighted and summed to obtain the weighted convergence result; where the weight of each unit complex number is the phase convergence weight under the corresponding interferometric pair index; the weighted convergence result is converted into a phase value, the real and imaginary parts of the weighted convergence result are read, and the phase angle of the weighted convergence result is obtained by using the two-parameter arctangent operation, and the phase angle is recorded as the in-group phase representative value; the in-group phase representative values ​​corresponding to all interferometric pair indices are sorted according to the index order to obtain the in-group phase representative value sequence.

[0074] Specifically, such as Figure 9 As shown, within the same pixel group, the phase direction (unit complex number) is indicated by arrows, and the arrow line width represents the weight mapped from the same-group score. Missing phases are represented by gray or dashed lines and assigned zero weight. After weighted complex summation within the group and taking the phase angle, the representative phase is output at the seed pixel. This invention demonstrates how grouping of similar pixels and weighted convergence suppresses the effects of noise and missing data, resulting in more robust phase estimation and more reliable DS points. For the effective same-group pixel G... u Phase convergence is performed on each interferometer index k. Read Φ p The interferometric phase sample with index k is denoted as ϕ. p,k , will ϕ p,k Convert z to the unit complex number representation p,k When calculating cos(ϕ) p,k As z p,k Calculate the real part of sin(ϕ). p,k As z p,kThe imaginary part is obtained, thus yielding an amplitude of one and a phase angle of ϕ. p,k The complex number z p,k When the interferometric marker g p,k Invalid or ϕ p,k When a pixel is missing, its phase convergence weight under the interferometric pair index k is reset to zero, thus obtaining the effective weight w under the interferometric pair index k. p,k When the interferometric marker g p,k When it is valid, w p,k Assign the value obtained from the above steps to w. p For all w p,k Perform a second normalization to sum the effective weights under the same interferometric pair index k to one. When the denominator of the second normalization is zero, reset the weight of reference pixel u under that interferometric pair index k to one and reset its residual weight to zero. Then, apply the same method to all... z p,k The weighted summation is performed to obtain the weighted convergence result, which is denoted as . , where each z p,k The weight is w p,k ,Will When converting to phase, read The real and imaginary parts are obtained by using a two-parameter arctangent operation. The phase angle is used as the representative value of the phase within the group, and the representative value of the phase within the group is denoted as... All interference pairs corresponding to index k Organized in index order into a sequence of phase representative values ​​within a group, the sequence of phase representative values ​​within a group is denoted as... .

[0075] In this optional embodiment, spatial inclusion determination is performed on the distributed scatterer monitoring points and landslide boundaries to obtain stable scatterer locations. Based on the stable scatterer locations, point coordinates and point type identifiers are generated to achieve the stability of automatic scatterer point identification. This includes: for each distributed scatterer monitoring point, reading the location information of the bound landslide monitoring pixel in the pixel grid, and determining the corresponding geographic coordinates of the distributed scatterer monitoring point based on the mapping relationship between the pixel grid and geographic coordinates; unifying the geographic coordinates of the point and the landslide boundary to the same coordinate reference, and performing spatial inclusion determination; if the geographic coordinates of the point fall within the landslide boundary range, it is determined to be included; if the geographic coordinates of the point do not fall within the landslide boundary range, it is determined not to be included; for the distributed scatterer monitoring points that are determined to be included in the spatial inclusion determination, stable scatterer locations are determined, and based on each stable scatterer location, point coordinates and point type identifiers are obtained, wherein the point type identifier is the distributed scatterer monitoring point.

[0076] Specifically, the distributed scatterer monitoring point set D output from the above steps, the pixel grid Ω obtained from the above steps, and the correspondence between the pixel grid and geographic coordinates M are read. For each distributed scatterer monitoring point D within D... u Read the pixel position (r) of the landslide body monitoring pixel point bound to it in Ω. u ,c u ), where r u For row index, c u As a column index, determine the point coordinates (x) based on M. u ,y u When M is provided in affine parameter form, read the coordinates of the top left corner (x0, y0) and the pixel resolutions Δx and Δy, and then (r u ,c u Converted to pixel center in geographic coordinate system (x) u ,y u When M is provided in the form of a lookup table, press (r) directly. u ,c u Read the cell center (x) from the lookup table. u ,y u ), will (x u ,y u Recorded as distributed scatterer monitoring point D u The coordinates of the point; read the landslide boundary P obtained in the above steps, and set the coordinates of the point (x) u ,y u When the landslide boundary P is placed under the same coordinate reference as M, spatial inclusion determination is performed. If the landslide boundary P is already at the geographic coordinate reference corresponding to M, the landslide boundary P is directly used in the determination. The landslide boundary P is represented as a sequence of polygon vertices arranged in order. , where N P Let N be the number of vertices, and let N be the number of vertices. P Connecting to vertex 1 forms a closed boundary, for each point's coordinates (x... u ,y u ) Perform ray casting determination: using (x u ,y u Construct a semi-infinite ray starting from point P and proceeding along the positive x-axis, traversing every edge of boundary P ((x...). i ,y i ),(x i+1 ,y i+1 When the edge satisfies y i =y i+1 When the edge is determined to be a horizontal edge, its intersection count is skipped. This applies when the edge satisfies min(y) i ,y i+1 ) <y u ≤max(y i ,yi+1 When determining if an edge crosses the ray height and enters the intersection calculation, an asymmetric open / closed interval is used to avoid double counting when the ray passes through a vertex. For edges entering the intersection calculation, linear interpolation is used to calculate the intersection between the edge and the horizontal line y=y. u The x-coordinate of the intersection point is denoted as . And press: ; Perform calculations, if >x u Then, this edge is recorded as a valid intersection, and the number of valid intersections is denoted as m. u When m u Determine the point coordinates (x) when the x is odd. u ,y u Falling into the landslide boundary P and being denoted as spatial inclusion is considered inclusion, when m u Determine the point coordinates (x) when the number is even. u ,y u If the point does not fall within the landslide boundary P and is marked as spatially contained, it is considered not contained. u ,y u If a point is located on any boundary edge, the spatial inclusion determination will be directly set to inclusion, and the determination of that point will end. For example... Figure 7 As shown in the figure, the red line represents the landslide boundary, and the points are stable scatterer locations that can be used for InSAR monitoring. Traditional threshold screening results in sparse locations and significant gaps in vegetated areas. The method of this invention produces denser and more uniform locations within the landslide body. Local magnification shows that even in vegetated areas, effective points are formed, demonstrating that this invention significantly improves monitoring coverage and usability in scenarios with scarce PS (photometric data). Distributed scatterer monitoring points D are spatially included. u Determine the location of the stable scatterer and output its coordinates and type identifier. Specifically, for each point satisfying the condition D... u Output its point coordinates (x) u ,y u ), and output the point type identifier. ,in Take the distributed scatterer monitoring points with fixed identifier values, and organize all output results into a set S of stable scatterer points. Each element of S contains (x u ,y u )and This is used for the unified calling and display of stable scatterer locations in the future.

[0077] According to another embodiment of the present invention, an automatic identification system for stable scatterer locations based on Kolmogorov-Arnold networks is also provided, comprising:

[0078] The boundary and data acquisition module is used to acquire boundary data of the vegetation-covered landslide monitoring area and generate the landslide boundary; and to acquire interferometric synthetic aperture radar time-series observations of multi-temporal geometry.

[0079] Pixel feature extraction is used to determine the monitoring pixel points of the landslide body based on the landslide body boundary and radar time-series observations, and to extract multi-dimensional interferometric phase features from the monitoring pixel points of the landslide body to obtain the monitoring pixel feature vector;

[0080] The same-type scattering calculation module is used to perform multi-dimensional pairing of the feature vectors of the monitored pixels using order-independent combination rules, generate multi-dimensional pixel pairing features, and input the multi-dimensional pixel pairing features into a pre-configured Kolmogorov network for calculation and analysis to obtain the same-type scattering score of the pixel. Based on the same-type scattering score of the pixel, a same-type scattering correlation map is generated.

[0081] The pixel group validity determination module is used to filter spatially adjacent pixel points for each landslide monitoring pixel point based on the same type scattering correlation map and the squeeze scattering body point selection framework. If the same type scattering score of the pixel meets the first threshold parameter and the spatial connectivity constraint, the same type pixel group is obtained. The module also calculates the intra-group consistency index for the same type pixel group. If the intra-group consistency index meets the second threshold parameter, the same type pixel group is determined to be valid. If the intra-group consistency index does not meet the second threshold parameter, an invalid mark is generated.

[0082] The distributed scatterer determination module is used to perform phase convergence on effective similar pixel groups and radar time-series observations, and determine the phase representative value within the group based on the phase convergence results and the similar scattering score of the pixel, and determine the distributed scatterer monitoring point based on the phase representative value within the group;

[0083] The stable scatterer identification module is used to determine the spatial inclusion of distributed scatterer monitoring points and landslide boundaries to obtain stable scatterer locations. Based on the stable scatterer locations, it generates point coordinates and point type identifiers to achieve the stability of automatic scatterer location identification.

[0084] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An automatic identification method for stable scatterer locations based on Kolmogorov-Arnold networks, characterized in that, include: Acquire boundary data of the monitoring area of ​​vegetation-covered landslides and generate landslide boundaries; Acquire time-series observations from interferometric synthetic aperture radar with multi-temporal geometry; Based on landslide boundary and radar time-series observations, the monitoring pixel points of the landslide body are determined, and multidimensional interferometric phase features are extracted from the monitoring pixel points of the landslide body to obtain the monitoring pixel feature vector; The monitoring pixel feature vectors are paired in multiple dimensions using order-independent combination rules to generate multi-dimensional pixel pairing features. These features are then input into a pre-configured Kolmogorov network for calculation and analysis to obtain pixel-like scattering scores. Based on these scores, a similar scattering correlation map is generated. Based on the similar scattering correlation map and the squeeze scattering body point selection framework, spatially adjacent pixels are screened for each landslide monitoring pixel point. If the similar scattering score of a pixel satisfies the first threshold parameter and the spatial connectivity constraint, a similar pixel group is obtained. The intra-group consistency index is calculated for the similar pixel group. If the intra-group consistency index satisfies the second threshold parameter, a valid similar pixel group is determined. If the intra-group consistency index does not satisfy the second threshold parameter, an invalid label is generated. Phase convergence is performed on effective similar pixel groups and radar time-series observations. Based on the phase convergence results and the similar scattering scores of pixels, the phase representative value within the group is determined, and the distributed scatterer monitoring point is determined according to the phase representative value within the group. Spatial inclusion determination is performed on the monitoring points of distributed scatterers and the boundaries of landslide bodies to obtain stable scatterer locations. Based on the stable scatterer locations, point coordinates and point type identifiers are generated to achieve the stability of automatic identification of scatterer locations. The process of using order-independent combination rules to perform multi-dimensional pairing of monitored pixel feature vectors to generate multi-dimensional pixel pairing features, and inputting these features into a pre-configured Kolmogorov network for calculation and analysis to obtain pixel-like scattering scores, and generating a similar scattering correlation map based on these scores, includes: For each landslide monitoring pixel in the set of landslide monitoring pixels, determine the preset search window size parameters, and filter out other landslide monitoring pixels that fall into the preset search window to obtain pixel pairs; The monitoring pixel feature vectors are read for each pixel pair and paired to obtain pixel pair features. The absolute values ​​of the component sum and the difference between the component sum and the component sum are calculated for each of the six corresponding components using the order-independent combination rule to obtain twelve-dimensional pixels. The twelve-dimensional pixels are then paired using a fixed component order method. Based on the pairing results, the order of the monitoring pixel feature vectors input to the twelve-dimensional pixel pair features is kept consistent. The twelve-dimensional pixel pairing features are input into the input layer of the Kolmogorov network, and the twelve-dimensional pixel pairing features are divided into three groups of inputs using the feature amplitude fluctuation feature, interference continuity feature and phase jump feature. The three sets of inputs are respectively input into the three parallel sub-layers of the feature grouping mapping layer. The neurons in the Kolmogorov network are used to connect the three parallel sub-layers and configure one-dimensional learnable functions. The outputs of each one-dimensional learnable function are summed to obtain the outputs of the three parallel sub-layers. The outputs of the three parallel sub-layers are input into the feature fusion layer, and the neurons in the Kolmogorov network are used to fuse and map the outputs of the three parallel sub-layers to obtain the fused features. The individual output neurons of the fused feature input-output layer generate pixel-like scattering scores, and the pixel-like scattering scores are limited to a preset range according to preset score normalization parameters. By using the monitoring pixels of the landslide body as nodes and the scattering scores of the same type of pixels as edge weight pairs, and establishing connections using the pixel pairs, a scattering correlation map is obtained. The process involves inputting the outputs of three parallel sub-layers into a feature fusion layer, and using neurons in a Kolmogorov network to perform a fusion mapping on the outputs of the three parallel sub-layers. The formula for calculating the fused features is as follows: ； In the formula, Z u,v Represents the fusion feature of pixel pairs; X u,v,j J represents the j-th component value of the 12-dimensional pixel pairing feature; j represents the input component index; J b This represents the set of input component indices corresponding to branch b; b represents the branch identifier. Let q be a one-dimensional learnable function of the Kolmogorov-Arnold neurons of branch b in the feature grouping mapping layer on the input connection j. This indicates the number of Kolmogorov-Arnold neurons in branch b; R represents a one-dimensional learnable function in the feature fusion layer that receives the output of the q-th group mapping of branch b and connects it to the t-th Kolmogorov-Arnold neuron in the feature fusion layer; t represents the neuron index in the feature fusion layer; f This indicates the number of Kolmogorov-Arnold neurons in the feature fusion layer; denoted as a one-dimensional learnable function corresponding to the t-th Kolmogorov-Arnold neuron in the feature fusion layer; amp represents the amplitude fluctuation feature branch; cont represents the interference continuous feature branch; jump represents the phase jump feature branch.

2. The method for automatic identification of stable scatterer locations based on Kolmogorov-Arnold networks according to claim 1, characterized in that, The process of acquiring boundary data of the vegetation-covered landslide monitoring area and generating the landslide boundary; and acquiring multi-temporal geometric interferometric synthetic aperture radar time-series observations includes: Obtain boundary data of the vegetation cover landslide monitoring area, and perform boundary closure checks on the boundary data of the vegetation cover landslide monitoring area to obtain the landslide boundary; Based on the same satellite platform, orbital direction, imaging mode and polarization conditions, multi-temporal interferometric synthetic aperture radar single-look complex images are acquired, and one temporal phase is selected as the master image to define the same observation geometry; The remaining temporal interferometric synthetic aperture radar single-view complex images are registered to the pixel grid of the main image to generate the correspondence between the pixel grid and the geographic coordinates. Based on the preset time baseline threshold and vertical baseline threshold and included in the interferometric pair set, the first interferometric phase sequence is generated, and the multi-temporal amplitude sequence is obtained by calculating each pixel of each temporal image; Radar timing observations are generated based on the first interferometric phase sequence and the multi-temporal amplitude sequence.

3. The method for automatic identification of stable scatterer locations based on Kolmogorov-Arnold networks according to claim 1, characterized in that, The method, based on landslide boundary and radar time-series observations, determines landslide monitoring pixel points and extracts multidimensional interferometric phase features from these monitoring pixel points to obtain monitoring pixel feature vectors, including: Based on the correspondence between the landslide boundary and the pixel grid and geographic coordinates, the landslide boundary is projected onto the pixel grid and spatial inclusion is determined. A unique pixel index is assigned to the determined landslide boundary pixels to obtain the landslide monitoring pixel points. Multi-temporal amplitude sequences were extracted from monitoring pixel points of the landslide body using radar time-series observations, and used as input values ​​for amplitude fluctuation characteristics; Based on amplitude fluctuation characteristics, interference continuity characteristics, and phase jump characteristics, multidimensional interference phase characteristics are constructed. The amplitude fluctuation characteristics of the multi-temporal amplitude sequence are calculated using two components, resulting in the mean amplitude of the first component and the amplitude dispersion index of the second component. The second interferometric phase sequence is extracted from each monitoring pixel point of the landslide body using radar time-series observation, and an interferometric marker is generated for each interferometric phase sample based on the preset interferometric threshold parameter; The two components of the interference continuity feature of the interferometric mark are calculated to obtain the effective number of interference samples of the first component and the longest continuous effective length of the second component. The phase difference sequence is judged by using a preset phase jump threshold parameter to obtain interference phase samples of adjacent time phases; Two components of the phase jump determination feature are calculated for the interferometric phase samples of adjacent time phases. The number of jumps that satisfy the phase jump threshold parameter of the first component and the median of the phase difference amplitude that satisfy the phase jump threshold parameter of the second component are obtained. The components are then organized according to the amplitude fluctuation feature, the interferometric continuity feature and the phase jump feature to obtain the monitoring pixel feature vector.

4. The method for automatic identification of stable scatterer locations based on Kolmogorov-Arnold networks according to claim 3, characterized in that, The step of using a preset phase jump threshold parameter to determine the phase difference sequence and obtain interference phase samples of adjacent time phases includes: By filtering the set of interference pairs that consist of adjacent acquisition times, a set of adjacent interference pairs is obtained; Based on the monitoring pixel points of each landslide body, and by reading the corresponding interference phase samples from the set of adjacent interference pairs, the adjacent interference phase sequence is obtained; The phase difference between adjacent samples is calculated sequentially according to the acquisition time order of the adjacent interference phase sequences to obtain the phase difference sequence; For each phase difference sample in the phase difference sequence, the phase difference amplitude is calculated, and a jump determination is performed on the phase difference amplitude using a preset phase jump threshold parameter. If the phase difference amplitude meets the preset phase jump threshold parameter, it is determined to be a jump. Based on the jump determination results, interference phase samples of adjacent time phases of the jump information are obtained.

5. The method for automatic identification of stable scatterer locations based on Kolmogorov-Arnold networks according to claim 1, characterized in that, The process involves filtering spatially adjacent pixels for each landslide monitoring pixel based on the similar scattering correlation map and the squeeze scatterer point selection framework. If the similar scattering score of a pixel satisfies the first threshold parameter and the spatial connectivity constraint, a similar pixel group is obtained. Furthermore, an intra-group consistency index is calculated for each similar pixel group. If the intra-group consistency index satisfies the second threshold parameter, a valid similar pixel group is determined. If the intra-group consistency index does not satisfy the second threshold parameter, an invalid marker is generated, including: Using each landslide monitoring pixel as the center, a set of spatially adjacent pixels is determined in the pixel grid according to the preset adjacency type parameters. The adjacency type parameters limit the spatial adjacency relationship to four-adjacency or eight-adjacency. Read the corresponding edge weights in the similar scattering correlation graph of the set of spatially adjacent pixels to obtain the similar scattering score of the pixels, and exclude spatially adjacent pixels whose similar scattering scores do not meet the first threshold parameter. Using the landslide monitoring pixel points as seed nodes, the remaining spatially adjacent pixel points are expanded and searched according to the pixel grid connectivity. During the expansion search, propagation only occurs along the connections where the pixel scattering scores of the same type satisfy the first threshold parameter. Spatial connectivity constraint determination is performed on the cell set based on the extended search. Based on the spatial connectivity constraint conditions, it is determined that the cell set and the seed node belong to the same connected component in the cell grid. Based on the cell set determined by the spatial connectivity constraint, the same type of cell group is obtained. By using the scattering scores of pixels in the scattering correlation map, statistics are performed on all pixel pairs within the same pixel group to obtain the mean score and the dispersion of the score within the group. Based on the preset consistency mapping parameters, the mean score within the group and the dispersion of the score within the group are mapped and calculated to obtain the consistency index within the group. The intragroup consistency index is compared with the second threshold parameter. If the intragroup consistency index meets the second threshold parameter, a valid class of pixels is determined. If the intragroup consistency index does not meet the second threshold parameter, an invalid label is generated.

6. The method for automatic identification of stable scatterer locations based on Kolmogorov-Arnold networks according to claim 1, characterized in that, The process of performing phase convergence on effective similar pixel groups and radar time-series observations, determining the representative phase value within the group based on the phase convergence results and the similar scattering score of the pixels, and determining the distributed scatterer monitoring points based on the representative phase value within the group includes: Using radar time-series observations, the interference phase sequence of each pixel within each effective group of the same type is extracted; Based on the seed node of the effective similar pixel group as the reference pixel, and according to the similar scattering association map, the similar scattering score of each pixel in the group and the reference pixel is read; the similar scattering score of the pixel is converted into non-negative phase convergence weight using the preset weight mapping parameters, and the phase convergence weight is normalized. The interferometric phase samples are converted into unit complex number representations; and the phase convergence weights are weighted and converged, and the weighted convergence results are converted into phase values ​​to obtain a sequence of representative phase values ​​within the group. The phase representative value sequence within the group is associated with the pixel location of the seed node, and the monitoring point of the distributed scatterer is determined based on the association result.

7. The method for automatic identification of stable scatterer locations based on Kolmogorov-Arnold networks according to claim 6, characterized in that, The interference phase samples are converted into unit complex number representations; The phase convergence weights are then weighted and converged, and the weighted convergence result is converted into phase values ​​to obtain a sequence of representative phase values ​​within the group, including: Phase convergence is performed on each interferometric pair index within the valid class of pixels. Based on each pixel within the valid class of pixels, the interferometric phase sample corresponding to the interferometric pair index in the interferometric phase sample set corresponding to the pixel is read. The read interference phase sample is converted into a unit complex number representation, and the cosine value of the interference phase sample is calculated as the real part of the unit complex number, and the sine value of the interference phase sample is calculated as the imaginary part of the unit complex number, so as to obtain the unit complex number of the interference phase sample value. The state of the interferometric marker and the integrity of the interferometric phase sample are judged. If the interferometric marker is invalid or the interferometric phase sample is missing, the phase convergence weight of the corresponding pixel under the interferometric pair index is reset to zero. When the interferometric marker is valid, the phase convergence weight under the interferometric pair index is assigned the weight of the normalized non-negative phase convergence after conversion by the preset weight mapping parameter. The phase convergence weights under all interferometric pairs are normalized twice, and the sum of the effective phase convergence weights under the same interferometric pair index is a preset value. If the denominator of the quadratic normalization is zero, the weighted sum of all unit complex numbers corresponding to the reference pixel under the interferometric pair index is performed to obtain the weighted convergence result; where the weight of each unit complex number is the phase convergence weight under the corresponding interferometric pair index. The weighted convergence result is converted into a phase value. The real and imaginary parts of the weighted convergence result are read, and the phase angle of the weighted convergence result is obtained by using a two-parameter arctangent operation. The phase angle is recorded as the representative phase value within the group. The in-group phase representative values ​​corresponding to all interferometric pairs are sorted according to the index order to obtain the in-group phase representative value sequence.

8. The method for automatic identification of stable scatterer locations based on Kolmogorov-Arnold networks according to claim 1, characterized in that, The process of spatially containing the distributed scatterer monitoring points and the landslide boundary to obtain stable scatterer locations, and generating point coordinates and point type identifiers based on these stable scatterer locations to achieve stable automatic identification of scatterer locations, includes: For each distributed scatterer monitoring point, the location information of the bound landslide monitoring cell point in the cell grid is read, and the geographic coordinates of the point corresponding to the distributed scatterer monitoring point are determined according to the mapping relationship between the cell grid and geographic coordinates. Unify the geographic coordinates of the points and the boundary of the landslide body to the same coordinate benchmark, and perform spatial inclusion relationship determination; if the geographic coordinates of the points fall within the boundary of the landslide body, they are determined to be included; if the geographic coordinates of the points do not fall within the boundary of the landslide body, they are determined to be not included. For distributed scatterer monitoring points that are included in the spatial inclusion, the location of stable scatterer points is determined, and the point coordinates and point type identifier are obtained based on each stable scatterer point, where the point type identifier is a distributed scatterer monitoring point.

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