A grassland vegetation state inversion method and system based on red edge singularity topological manifold solution and a storage medium

Abstract

The present application relates to the technical field of grassland monitoring, and discloses a grassland vegetation state inversion method and system based on red edge singularity topological manifold unwrapping and a storage medium, the method comprising: extracting singularity topological features from a red edge region, and constructing a red edge singularity topological space and a red edge curvature manifold; using spectral manifold unwrapping technology, separating vegetation signals and soil background signals in a nonlinear manner; according to the vegetation pure signals, establishing a topological mapping model of the red edge singularity topological space to the chlorophyll content; based on long-time sequence remote sensing data, extracting red edge manifold time sequence trajectories, and constructing a comprehensive physiological stress index with manifold geometric significance; in view of differences in red edge bands of different satellite sensors, constructing a spectral space alignment model; constructing a vegetation health state manifold classification atlas; and based on time sequence manifold monitoring data, constructing a manifold early warning mechanism. The present application can realize high-precision inversion and early identification of the chlorophyll content and physiological stress state of grassland vegetation.

Description

Technical Field

[0001] This invention relates to the field of grassland monitoring technology, specifically to a method, system, and storage medium for grassland vegetation state inversion based on red-edge singularity topological manifold untangling. Background Technology

[0002] In vegetation spectral characteristics, the red edge region (680-780 nm) represents a steep transition in vegetation reflectance from the red band absorption valley to the near-infrared high reflectance plateau. Its location, slope, and area are highly correlated with vegetation chlorophyll content, physiological state, and stress level. The red edge position undergoes a "blue shift" (shifting towards shorter wavelengths) as vegetation health declines, making it a sensitive indicator of vegetation physiological stress. However, current technologies for utilizing grassland vegetation spectral characteristics suffer from the following fundamental shortcomings: (1) The use of red edge features is crude. Existing methods mostly use a single red edge index for vegetation monitoring, which fails to fully explore the complete spectral information of the red edge region. The red edge region contains multiple feature points, forming a multi-dimensional feature space. A single index is difficult to fully characterize the physiological state of vegetation.

[0003] (2) The problem of mixed pixels has not been effectively solved. Grassland vegetation is mostly sparse, especially in desert steppe areas where the vegetation coverage is less than 30%. Each pixel often contains multiple land cover types such as vegetation, bare soil, litter, and gravel. Traditional pixel-based red edge feature extraction directly attributes mixed spectra to vegetation, resulting in a serious decrease in the accuracy of vegetation parameter inversion. Existing spectral unmixing methods are mostly based on linear assumptions, ignoring the nonlinear interaction between vegetation and soil.

[0004] (3) The quantitative relationship between red edge characteristics and physiological parameters is unclear. There is a physical correlation between the red edge position shift and the change in chlorophyll content, but the relationship is not a simple linear one due to interference from multiple factors such as leaf structure, water status, and soil background. Existing methods lack quantitative inversion models that can simultaneously consider multiple interference factors.

[0005] (4) The temporal information is not effectively coupled. The red edge characteristics of grassland vegetation change dynamically with the phenological period. The red edge analysis of a single period cannot distinguish between "physiological stress" and "normal phenological fluctuations". For example, the natural blue shift of the red edge position during the yellowing period is easily misjudged as degradation. Existing technology lacks a mechanism to couple the temporal characteristics of the red edge with phenological priors.

[0006] (5) Inconsistent spectra among sensors and differences in the red edge band settings of different satellite sensors make it difficult to transfer and apply inversion models trained on a single sensor, thus limiting the collaborative use of multi-source data.

[0007] Therefore, there is an urgent need for a method to invert grassland vegetation physiological parameters that can fully explore the deep spectral structure of the red edge, effectively unwrap the nonlinear components of mixed pixels, establish the topological mapping relationship between the red edge and physiological parameters, couple the temporal phenological priors, and achieve multi-sensor spectral spatial alignment. Summary of the Invention

[0008] This invention provides a grassland vegetation state inversion method based on red-edge singularity topological manifold unwrapping. By constructing a red-edge singularity topological space, developing spectral manifold nonlinear unwrapping technology, establishing a red-edge-chlorophyll topological mapping model, and coupling time-series phenological manifold priors, it achieves high-precision inversion and early identification of grassland vegetation chlorophyll content and physiological stress state.

[0009] Therefore, the present invention provides the following technical solution: A method for inverting the physiological state of grassland vegetation based on red-edge singularity topology and spectral manifold untangling, the method comprising: Step 1: Extract the topological features of singularities from the red-edge region and construct the topological space of the red-edge singularities and the red-edge curvature manifold; Step 2: Using spectral manifold unwrapping technology, the vegetation signal and soil background signal are nonlinearly separated to obtain the pure vegetation signal; Step 3: Based on the pure vegetation signal, establish a topological mapping model from the red-edge singularity topological space to the chlorophyll content to obtain the chlorophyll content; Step 4: Based on long-term remote sensing data, extract the red-edge manifold time-series trajectory and construct a comprehensive physiological stress index with manifold geometric significance; Step 5: Based on the differences in red-edge band settings for different satellite sensors, construct a spectral spatial alignment model to perform isomorphic mapping of multi-source data in manifold space; Step 6: Construct a manifold hierarchical map of vegetation health status; Step 7: Based on time-series manifold monitoring data, construct a manifold early warning mechanism.

[0010] Optionally, step 1 includes: Step 11: Resample the multi-source satellite data to a sub-nanometer spectral interval to construct a continuous red-edge spectral curve; Step 12: Introduce curvature theory from differential geometry to calculate the curvature values ​​of the red-edge spectral curve at each wavelength point. The calculation formula is: ; in Let red-edge spectral reflectance function, and These are its first and second derivatives, respectively; local maxima of curvature are taken as red-edge singularities, which include red-edge starting point singularities, red-edge inflection point singularities, red-edge ending point singularities, and red-edge shoulder point singularities. Each red-edge singularity is characterized by three parameters: wavelength position, curvature value, and curvature direction. Step 13: Calculate the topological relationships between red-edge singularities. The topological relationships between red-edge singularities include the topological parameters of each red-edge singularity and the topological relationship parameters between singularities. The topological parameters of each red-edge singularity include: wavelength position, curvature value, curvature direction, and singularity type. The topological relationship parameters between singularities include: singularity spacing, spectral arc length between singularities, integral of curvature change between singularities, average rate of curvature change between singularities, and spectral area between singularities. Based on the topological parameters of each red-edge singularity and the topological relationship parameters between singularities, construct a singularity topological relationship graph with singularities as nodes and topological relationships as edges. The adjacency matrix elements of the graph are composed of vectors consisting of the topological parameters of each red-edge singularity and the topological relationship parameters between singularities, forming the graph structure basis of the red-edge singularity topological space. Step 14: Map the red-edge spectral curve onto the curvature-wavelength phase space to form a red-edge curvature manifold. Each point on the manifold corresponds to the curvature state at a wavelength position. The topological structure of the manifold reflects the intrinsic geometric features of the red-edge spectrum. Extract the topological features of the red-edge curvature manifold, including: local curvature features, volume and boundary features, and connectivity features, to provide geometric support for the topological space of the red-edge singularity. Step 15: Nonlinearly fuse the topological parameters of each red-edge singularity, the topological relationship parameters between singularities, and the topological features of the red-edge curvature manifold with the original spectral bands to construct the red-edge singularity topological space; Based on the red-edge singularity topological space, organize the parameters of each red-edge singularity, the topological relationship parameters between singularities, and the topological features of the red-edge curvature manifold into a unified high-dimensional tensor form to construct the red-edge singularity topological space tensor.

[0011] Optionally, step 2 includes: Step 21: The spectrum of each pixel in the multi-source satellite data processed in Step 11 is regarded as a point in a high-dimensional spectral space. The spectral points of all pixels constitute a low-dimensional manifold embedded in the high-dimensional space. The isometric mapping algorithm in manifold learning is used to map the original spectral space to the intrinsic low-dimensional manifold space. Step 22: Based on the mapping locations of the field-measured endmember spectral library, identify vegetation endmember clusters, bare soil endmember clusters, and litter endmember clusters. According to the geodesic theory in Riemannian geometry, calculate the position coordinates of each pixel's spectral point in the manifold space, and solve for the geodesic distance d from the pixel's spectral point to each endmember cluster. i ; where the coordinates of the pixel spectral points in the manifold space are called vegetation manifold coordinates; Step 23: Construct a soft affiliation function based on geodesic distance and calculate the affiliation degree.a i To achieve nonlinear decomposition of pixel spectra among endmembers; attribution a i The calculation formula is: a i =exp(- d i 2 / s 2 ) / ∑ j exp(- d j 2 / s 2 ); in d i To reach the first i Geodesic distance of endmember clusters s The temperature parameter is used; the affiliation degree of the vegetation endmember cluster is recorded as the vegetation signal strength. Step 24: Calculate the vegetation signal separation and diffusion distance using a diffusion mapping algorithm on the manifold. as follows: ; in P The Markov transition probability matrix is ​​constructed based on geodesic distance. t The number of diffusion steps is used to enhance the contrast between endmembers through multiple diffusion iterations, thereby achieving fine separation of vegetation signals and soil signals. The degree of interaction between vegetation endmember clusters and soil endmember clusters during the separation process is denoted as the vegetation-soil nonlinear interaction intensity. Step 25: Based on the pixel-by-pixel vegetation manifold coordinates, vegetation signal intensity, and vegetation-soil nonlinear interaction intensity, generate the manifold reconstruction result of the pure vegetation signal spectrum.

[0012] Optionally, step 3 includes: Step 31: Introduce the PROSPECT leaf radiative transfer model to generate a reflectance lookup table covering the physiological parameter space of grassland vegetation, and obtain the continuous spectrum of the red edge region. The physiological parameters of grassland vegetation include chlorophyll content, dry matter content, equivalent water thickness, and leaf structure parameters. Step 32: For each continuous spectrum of the red-edge region in the reflectance lookup table, perform the red-edge singularity topological analysis of Step 1, extract the singularity topological feature vector, and construct the singularity topological feature library; combine the singularity topological feature library with the corresponding chlorophyll content to form a training dataset, and use the persistent cohomology method in topological data analysis to calculate the persistence graph of the red-edge singularity topological features in high-dimensional space, and identify the topological features most sensitive to chlorophyll changes. Step 33: Construct a topology mapping network based on the training dataset; the input of the topology mapping network is the topological feature vector of the singularity, and the output is the chlorophyll content; the loss function of the topology mapping network is designed as follows: L=L MSE + α ·L topo ; Where L MSE For the mean square error of chlorophyll inversion, L topo For topology preservation constraints, α To balance the weights; Step 34: After training the topology mapping network, obtain the topology mapping model from the red-edge singularity topology space to the chlorophyll content, invert the chlorophyll content pixel by pixel, and output the confidence region of the inversion result in the topology space as a geometric measure of the inversion uncertainty.

[0013] Optionally, step 4 includes: Step 41: For the vegetation pure signal of the 18 time series images of the year, perform the red edge curvature manifold construction of Step 1 for each period to obtain 18 time series manifolds. Each manifold is a set of points in an 8-dimensional embedding space. Connect the 18 manifolds in series on the time axis to construct a four-dimensional spatiotemporal manifold. Step 42: Using the dynamic time warping algorithm on the manifold, the temporal manifold trajectory of each pixel is aligned with the standard trajectory of the healthy reference area, and the manifold curvature distance between the trajectories is calculated. Step 43: Based on the manifold bending distance, three geometrically meaningful red-edge manifold trajectory parameters are decomposed, including trajectory offset component, trajectory twist component, and trajectory contraction component. The trajectory offset component reflects the drift of the overall position of the manifold, corresponding to the systematic change in chlorophyll content; the trajectory twist component reflects the deformation of the local shape of the manifold, corresponding to the abnormality of the red-edge curve shape; the trajectory contraction component reflects the reduction of the manifold scale, corresponding to the reduction of the red-edge dynamic range. Step 44: Nonlinearly fuse the three stress components on the manifold to construct a comprehensive physiological stress index.

[0014] Optionally, step 5 includes: Step 51: Obtain the spectral response functions of different satellite sensors, simulate the red-edge band response values ​​of each sensor based on the measured hyperspectral data, and construct a spectral pair dataset between sensors; Step 52: Introducing optimal transport theory, the source sensor spectral distribution is mapped to the target sensor spectral distribution via transport. The cost function of the transport mapping is measured by the Wasserstein distance between the spectra.

[0015] in, m and nThe spectral distributions of the source sensor and the target sensor are shown respectively. x Spectral distribution of the source sensor m The sample points in the vector represent the spectral reflectance vector of the source sensor. y Spectral distribution of the target sensor n The sample points in the vector represent the spectral reflectance vector of the target sensor. c for m and n The joint distribution of Γ( m , n Let be the set of all joint distributions; || xyz ‖express x and y The Euclidean distance between them; by solving the optimal transmission problem, a nonlinear mapping function from the source sensor spectral space to the target sensor spectral space is obtained; Step 53: Perform the red-edge singularity topological analysis of the transformed spectrum in Step 1 to verify the isomorphism of the transformed spectrum in the manifold space and ensure that the topological structure of the red-edge manifold remains unchanged before and after the transformation.

[0016] Optionally, step 6 includes: Step 61: Multidimensional information such as chlorophyll content, comprehensive physiological stress index, vegetation manifold coordinates, and red-edge manifold trajectory parameters are fused on the manifold features to construct a healthy state manifold. The healthy state manifold uses the health features of all pixels as a point set, and the geodesic distance between points reflects the similarity of health status. Step 62: Use a spectral clustering algorithm on the manifold to divide the health status manifold into several submanifolds, with each submanifold corresponding to a health level; Step 63: Compare the clustering results (i.e., sub-manifolds) with the health levels of ground quadrats, and propagate the quadrat levels to the entire manifold using the manifold label propagation algorithm to complete the health level assignment for all pixels; generate a vegetation health status manifold classification map, where each level corresponds to a connected region on the manifold, and the region boundary is defined by geodesics on the manifold. Step 64: Gradient flow analysis on the manifold is used to calculate the gradient direction field of the healthy manifold, identify the direction of the fastest degradation of the healthy state, generate a stress diffusion path map, and reveal the spatial propagation law of degradation.

[0017] Optionally, step 7 includes: Step 71: Extract the temporal manifold trajectory of each cell from the four-dimensional spatiotemporal manifold and project it onto the two-dimensional manifold visualization space to form a manifold trajectory map; Step 72: On the manifold trajectory map, anomaly detection algorithms on the manifold are used to identify outlier trajectories that deviate from the mainstream, periodic anomalies with loop structures in the trajectory, and abrupt anomalies that cause sudden breaks in the trajectory. Step 73: Mark the pixels corresponding to the abnormal trajectories as warning pixels, perform connectivity analysis on the warning pixels on the manifold, and identify the warning manifold sub-regions; Step 74: Determine the warning level based on the geometric characteristics of the warning sub-region on the manifold; Step 75: Map the early warning information back to geospatial space to generate a manifold early warning geographic map; generate differentiated decision recommendations based on manifold geometric features: areas with large curvature in the early warning sub-region are recommended for key intervention; areas with complex boundaries in the early warning sub-region are recommended for edge-priority treatment; and areas in the early warning sub-region that are far from the healthy mainstream shape are recommended for engineering repair.

[0018] A grassland vegetation physiological state inversion system based on red-edge singularity topology and spectral manifold untangling, the system comprising: Red-edge singularity topology building unit: Extract singularity topological features from red-edge regions to construct red-edge singularity topological space and red-edge curvature manifold; The nonlinear separation unit uses spectral manifold unwrapping technology to nonlinearly separate the vegetation signal from the soil background signal to obtain the pure vegetation signal; The topological mapping model construction unit establishes a topological mapping model from the red-edge singularity topological space to chlorophyll content based on the pure vegetation signal, and obtains the chlorophyll content. The comprehensive physiological stress index construction unit is based on long-term remote sensing data, extracting the red-edge manifold temporal trajectory to construct a comprehensive physiological stress index with manifold geometric significance; The spectral spatial alignment model construction unit sets differences in the red edge band of different satellite sensors to construct a spectral spatial alignment model and perform isomorphic mapping of multi-source data in manifold space. Manifold hierarchical map construction unit, constructing a manifold hierarchical map of vegetation health status; The manifold early warning mechanism construction unit constructs a manifold early warning mechanism based on time-series manifold monitoring data.

[0019] A computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to perform the steps of the grassland vegetation state inversion method based on red-edge singularity topological manifold untangling.

[0020] This invention provides a method and system for grassland vegetation state inversion based on red-edge singularity topological manifold unwrapping. It relates to hyperspectral remote sensing and vegetation physiological and ecological monitoring technologies, specifically a method for assessing grassland vegetation health status based on red-edge singularity topological structure analysis, spectral manifold nonlinear unwrapping, and deep physiological parameter inversion. This method is applicable to grassland vegetation chlorophyll content monitoring, early identification of physiological stress, diagnosis of degradation levels, and assessment of restoration effectiveness. Compared with existing technologies, this invention introduces differential geometry, topological data analysis, manifold learning, and optimal transport theory into the field of grassland vegetation spectral monitoring for the first time. It constructs a novel theoretical framework and technical system from red-edge singularity topology to spectral manifold unwrapping, achieving a paradigm shift in grassland vegetation physiological state inversion from "feature engineering" to "geometric deep learning." Breaking through the limitations of traditional parameterization methods, it achieves a geometrical representation of the red-edge spectrum for the first time through red-edge singularity topological space and red-edge curvature manifold, upgrading red-edge information from discrete parameters to a continuous topological structure, increasing the amount of feature information by more than 15 times, and exhibiting natural robustness to noise. A red-edge-chlorophyll topological mapping model was established, transforming the inversion problem into a preserving mapping in the topological space. The inversion accuracy reached R² of 0.93, and the output provided a geometrically meaningful confidence region, offering an interpretable measure of uncertainty for the inversion results. A hierarchical map of healthy manifolds was constructed, transforming health levels into connected regions on the manifold. This represents the first time a spatially continuous representation of healthy states has been achieved. Gradient flow analysis revealed stress diffusion paths, providing a novel perspective for studying the laws governing degradation propagation. Attached Figure Description

[0021] 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 described below. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart of a grassland vegetation state inversion method based on red-edge singularity topological manifold untangling in a specific embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of a grassland vegetation physiological state inversion system based on red-edge singularity topology and spectral manifold unentanglement in a specific embodiment of the present invention. Detailed Implementation

[0023] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0024] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0025] like Figure 1 As shown, Figure 1 This is a flowchart of a grassland vegetation state inversion method based on red-edge singularity topological manifold untangling in a specific embodiment of the present invention. The grassland vegetation state inversion method based on red-edge singularity topological manifold untangling includes: Step S1: Construct the red-edge singularity topological space and the red-edge curvature manifold.

[0026] Based on the spectral characteristics of grassland vegetation, singularity topological features are extracted from the red-edge region to construct a red-edge singularity topological space and a red-edge curvature manifold. Specifically, this includes: Step 11: Resample the multi-source satellite data to a sub-nanometer spectral interval (e.g., 0.5 nanometer interval) to construct a continuous red-edge spectral curve.

[0027] Step 12: Introduce curvature theory from differential geometry to calculate the curvature value of the red-edge spectral curve at each wavelength point. The curvature calculation formula is as follows: ; in Let red-edge spectral reflectance function, and These are its first and second derivatives, respectively. Local maxima of curvature are identified as red-edge singularities based on the curvature calculation formula. These singularities include red-edge starting point singularities, red-edge inflection point singularities, red-edge ending point singularities, red-edge shoulder point singularities, etc., each singularity is determined by its wavelength position. l i curvature value k i Curvature direction d i The three parameters (curvature change trend) characterize this.

[0028] Step 13: Calculate the topological relationships between red-edge singularities. These relationships include the topological parameters of each red-edge singularity and the topological relationship parameters between the singularities. The topological parameters of each red-edge singularity include: Wavelength position: The wavelength position (nm) of the singularity; Curvature value: The magnitude of curvature at a singularity, reflecting the degree of spectral bending; Curvature direction: The direction of curvature change is determined by the sign of the second derivative, which distinguishes between convex and concave singularities; Singularity types: There are four types, including red edge starting point singularity, red edge inflection point singularity, red edge ending point singularity, and red edge shoulder point singularity, which are encoded by enumeration values; The topological relationship parameters between singularities include: Singularity spacing: the wavelength interval (nm) between two singularities; Spectral arc length between singularities: the length of the curve between two points along the spectral curve; Integral of curvature change between singularities: the cumulative change in curvature value between two points; Average rate of change of curvature between singularities: the average rate of change of curvature per unit wavelength; Spectral area between singularities: the area enclosed by the spectral curve and the wavelength axis; Based on the above parameters, a singularity topology graph is constructed with singularities as nodes and topological relationships as edges. The adjacency matrix elements of the graph consist of vectors composed of the aforementioned relationship parameters. Specifically, 12-Victokay topological parameters and 8-Victokay relationship parameters are extracted to construct the singularity topology graph. For each red-edge singularity, three parameters are extracted: wavelength position, curvature value, and curvature direction. A total of four singularities are identified (red-edge starting point singularity, red-edge inflection point singularity, red-edge ending point singularity, and red-edge shoulder point singularity), yielding the 12-Victokay topological parameters. The relationship parameters between singularities include four types: singularity spacing, spectral arc length between singularities, integral of curvature change between singularities, and average rate of curvature change between singularities. The mean and variance of these parameters are calculated for each singularity pair to obtain the 8-Victokay relationship parameters. Finally, a singularity topology graph is constructed with singularities as nodes and topological relationships as edges.

[0029] Step 14: Map the red-edge spectral curve to the curvature-wavelength phase space to form a red-edge curvature manifold. Each point on the manifold corresponds to the curvature state at a wavelength position. The topological structure of the manifold reflects the intrinsic geometric characteristics of the red-edge spectrum. Extractable topological features of the red-edge curvature manifold include, but are not limited to, the following: local curvature features (geodesic curvature and its statistics at each point on the manifold, such as mean, variance, skewness, and kurtosis), manifold volume and boundary features (occupied volume, boundary length, and compactness of the manifold in the curvature-wavelength phase space), and manifold connectivity features (distribution characteristics of geodesic distances between any two points on the manifold, including average geodesic distance, maximum geodesic distance, and dispersion). In a preferred embodiment of the present invention, 6-dimensional red-edge curvature manifold topological features are actually extracted, specifically: Betti number (2-dimensional, including β0 and β1), persistence graph features (2-dimensional, taking the persistence values ​​of the two topological features with the highest persistence), local curvature mean of the manifold (1-dimensional), and manifold volume to boundary ratio (1-dimensional). This 6-dimensional feature set balances computational efficiency and topological representation capability, and is a preferred implementation of the present invention, but it is not an exhaustive limitation on the extractable features.

[0030] Step 15: The 12-Vicchi point topological parameters and 8-Vicchi point relationship parameters extracted in Step 13, along with the 6-dimensional curvature manifold topological features extracted in Step 14, are nonlinearly fused with the original spectral bands to construct a red-edge singularity topological space. Based on this space, all the aforementioned feature parameters are organized into a unified high-dimensional tensor form to construct the red-edge singularity topological space tensor. The red-edge singularity topological space tensor is a high-dimensional tensor (e.g., 71-dimensional) that unifies the organization of all pixels, all bands, and multiple types of features, and is a data structure oriented towards batch computation.

[0031] Step S2: Separation of vegetation-soil nonlinear components based on spectral manifold unwrapping.

[0032] To address the mixed pixel problem caused by sparse grassland vegetation cover, a spectral manifold unwrapping technique was developed to achieve nonlinear separation of vegetation signals from soil background signals. Specifically, this includes: Step 21: The spectrum of each pixel in the multi-source satellite data processed in Step 11 is considered as a point in a high-dimensional spectral space. The spectral points of all pixels constitute a low-dimensional manifold embedded in the high-dimensional space. Different mixing ratios of vegetation and soil cause the spectral points to be distributed in different regions of this manifold, forming a complex manifold structure. Using the isometric mapping algorithm in manifold learning, the original spectral space is mapped to the intrinsic low-dimensional manifold space (8-dimensional), so that the geodesic distance on the manifold approximately corresponds to the physical similarity of the spectrum.

[0033] Step 22: In the low-dimensional manifold space, spectral points of different endmember types (vegetation, soil, litter) aggregate to form different manifold clusters, while the spectral points of mixed pixels are distributed in the manifold connection regions between clusters. Based on the mapping positions of the field-measured endmember spectral library, vegetation endmember clusters, bare soil endmember clusters, and litter endmember clusters are identified. According to the geodesic theory in Riemannian geometry, the position coordinates of each pixel's spectral point in the manifold space are calculated, and the geodesic distance d from the pixel's spectral point to each endmember cluster is solved. i ; where the position coordinates of the pixel spectral points in the manifold space are called vegetation manifold coordinates.

[0034] Step 23: Construct a soft attribution function based on geodesic distance to achieve nonlinear decomposition of the pixel spectrum among endmembers. (Attribution) a i The calculation formula is: a i =exp(- d i 2 / s 2 ) / ∑ j exp(- dj 2 / s 2 ); in d i To reach the first i Geodesic distance of endmember clusters s The temperature parameter is the median of all geodesic distances. The attribution vector serves as the nonlinear decomposition coefficients of the pixel among its endmembers.

[0035] Step 24: Using a diffusion mapping algorithm on the manifold, construct the vegetation signal separation and diffusion distance. Dt ( i , j )as follows: ; in P The Markov transition probability matrix is ​​constructed based on geodesic distance. t This represents the number of diffusion steps. Represents the transition matrix P go through t After the first step of evolution, from the first i The probability distribution vector of starting from one point and reaching all other points; The L2 norm (Euclidean norm) is the square root of the sum of the squares of the differences between two vectors. By enhancing the contrast between endmembers through multiple diffusion iterations, fine separation of vegetation and soil signals is achieved.

[0036] Step 25: Output the per-pixel vegetation manifold coordinates, vegetation signal intensity, and vegetation-soil nonlinear interaction intensity to generate the manifold reconstruction result of the pure vegetation signal spectrum.

[0037] Step S3: Construct the red-edge-chlorophyll topological mapping model and invert physiological parameters.

[0038] Based on the pure vegetation signals separated in step S2, a topological mapping model from the red-edge singularity topological space to chlorophyll content is established. Specifically, this includes: Step 31: Introduce the PROSPECT leaf radiative transfer model to generate a reflectance lookup table covering the physiological parameter space of grassland vegetation. The parameter settings cover the entire physiological range of chlorophyll content, dry matter content, equivalent water thickness, and leaf structure parameters.

[0039] Step 32: For each spectrum in the lookup table, perform the singularity topology analysis from step S1 to extract its singularity topology feature vector and construct a singularity topology feature library. The singularity topology feature vector is a feature extracted from a single spectrum, with low dimensionality (e.g., 31 or 50 dimensions), and is a component of the "spatial tensor".

[0040] The singularity topological feature library and the corresponding chlorophyll content are used to form a training dataset. The persistent cohomology method in topological data analysis is used to calculate the persistence graph of the singularity topological features in high-dimensional space and identify the topological features most sensitive to chlorophyll changes.

[0041] In one embodiment, singularity topological analysis is performed on each spectrum in the lookup table using step S1 to extract 31-dimensional topological features and construct a singularity topological feature library. The persistent cohomology method in topological data analysis is used to calculate the simplex evolution process of the singularity topological features in 31-dimensional space, generating a persistence map. Each point in the persistence map represents a topological feature, with its x-axis representing the appearance threshold and its y-axis representing the disappearance threshold. The distance of the point from the diagonal reflects the persistence of the feature. The 50 most persistent topological features are selected as the topological invariants most sensitive to chlorophyll changes.

[0042] Step 33: Using the training dataset constructed in Step 32, construct a topology mapping network; the network input is the singularity topology feature vector extracted in Step 32, and the output is the chlorophyll content; the network loss function is designed as follows: L=L MSE + α ·L topo ; Where L MSE For the mean square error of chlorophyll inversion, L topo This includes topology-preserving constraints (compiling the difference in persistence graphs between the input feature space and the output space). α To balance the weights.

[0043] Step 34: After training, the red-edge-chlorophyll topological mapping model is obtained, which can invert chlorophyll content pixel by pixel and output the confidence region of the inversion result in the topological space as a geometric measure of inversion uncertainty.

[0044] Step S4: Construct the temporal red-edge manifold trajectory and physiological stress index.

[0045] Based on long-term remote sensing data, the temporal trajectory of the red-edge manifold is extracted to construct a physiological stress index with manifold geometric significance. Specifically, this includes: Step 41 involves sequentially constructing the red-edge curvature manifold from step S1 for the pure vegetation signals of the 18 annual time-series images, resulting in 18 time-series manifolds, each a set of points in an 8-dimensional embedding space. These 18 manifolds are then concatenated along the time axis to construct a four-dimensional spatiotemporal manifold with dimensions of 8 (manifold coordinates) × 18 (time) × H (image height) × W (image width), where H and W represent the number of pixels in the north-south and east-west directions, respectively. This manifold comprehensively depicts the evolutionary trajectory of the red-edge features of grassland vegetation in the time dimension.

[0046] Step 42: Using the dynamic time warping algorithm on the manifold, the temporal manifold trajectory of each pixel is aligned with the standard trajectory of the healthy reference area, and the manifold curvature distance between the trajectories is calculated.

[0047] Step 43: Based on the manifold bending distance, three stress components with geometric significance are decomposed: the trajectory offset component reflects the drift of the overall position of the manifold, corresponding to the systematic change of chlorophyll content; the trajectory twist component reflects the deformation of the local shape of the manifold, corresponding to the abnormality of the red edge curve morphology; and the trajectory contraction component reflects the reduction of the manifold scale, corresponding to the reduction of the red edge dynamic range.

[0048] Step 44: Nonlinearly fuse the three stress components on the manifold to construct a comprehensive physiological stress index. This index has a clear manifold geometric meaning and can effectively distinguish between "physiological stress" and "normal phenological fluctuations".

[0049] Step S5: Multi-sensor spectral spatial alignment and manifold isomorphic mapping.

[0050] To address the differences in red-edge band settings among different satellite sensors, a spectral spatial alignment model is constructed to achieve isomorphic mapping of multi-source data in manifold space. Specifically, this includes: Step 51: Obtain the spectral response functions of different satellite sensors (such as Sentinel-2, GF-6, and Landsat-8 / 9). The spectral response function describes the sensor's response sensitivity to incident radiation of different wavelengths and is a weighted distribution function of each band of the sensor in the wavelength dimension. Simulate the red-edge band response values ​​of each sensor based on measured hyperspectral data to construct a dataset of spectral pairs between sensors.

[0051] Spectral response function Generally, the following conditions are met:

[0052] Sensor No. The simulated reflectance of the band is:

[0053] in To measure hyperspectral reflectance, For the first Spectral response function of the band.

[0054] In the formula, λ: wavelength variable, in nanometers (nm), representing the continuous wavelength coordinates of the spectrum; λmin, λmax: The lower and upper limits of the wavelength range covered by the k-th band of the sensor, in nanometers (nm). R(λ): Measured hyperspectral reflectance, which is the dimensionless reflectance value at wavelength λ, usually obtained by ground or field spectrometer measurement; R k (λ): The spectral response function of the sensor in the k-th band, describing the sensor's response sensitivity to incident radiation at wavelength λ, satisfying the normalization condition ∫R k (λ)dλ=1, unit is nm - ¹(if integrated in terms of wavelength) or dimensionless (if expressed in terms of relative response); ρ k The simulated reflectance of the sensor in the k-th band is a dimensionless value, representing the overall reflectance of ground objects in that band. ρ(λ): Continuous hyperspectral reflectance function, which has the same meaning as R(λ) and the two can be used interchangeably; ∫: Integral symbol, indicating integration over wavelength λ within the wavelength range [λmin, λmax].

[0055] Step 52: Introducing optimal transport theory, the source sensor spectral distribution is mapped to the target sensor spectral distribution via transport. The cost function of the transport mapping is measured by the Wasserstein distance between the spectra.

[0056] in, m and n The spectral distributions of the source sensor and the target sensor are shown respectively. x Spectral distribution of the source sensor m The sample points in the vector represent the spectral reflectance vector of the source sensor. y Spectral distribution of the target sensor n The sample points in the vector represent the spectral reflectance vector of the target sensor. c for m and n The joint distribution of Γ( m , n Let be the set of all joint distributions; || xyz ‖express x and y The Euclidean distance between them is determined; by solving the optimal transmission problem, a nonlinear mapping function from the spectral space of the source sensor to the spectral space of the target sensor is obtained. Applying this mapping function to the red-edge spectrum of the source sensor yields a converted spectrum consistent with the spectral distribution of the target sensor.

[0057] Step 53: Input the transformed spectrum into the singularity topology analysis in step S1 to verify its isomorphism in the manifold space, ensuring that the topological structure of the red-edge manifold remains unchanged before and after the transformation. Using the Sentinel-2 red-edge manifold as a reference, establish isomorphic mappings from the GF-6 and Landsat red-edge manifolds to the reference manifold, realizing a unified expression of multi-source red-edge features in the manifold space.

[0058] In one embodiment, the Wasserstein distance between the transformed features and the concurrent Sentinel-2 features decreased from 0.42 to 0.09. Manifold isomorphism testing showed that the persistence graph correlation coefficient of the manifolds before and after the transformation was greater than 0.94, indicating that the topological structure remained intact. Using the Sentinel-2 red-edge manifold as a reference, an isomorphic mapping library of GF-6 and Landsat red-edge manifolds was established. Multi-sensor collaboration increased the effective monitoring frequency across the entire region from 18 periods / year to 36 periods / year, achieving clear-sky observations every 10 days.

[0059] The red-edge band settings (center wavelength, bandwidth, and spectral response function) of different satellite sensors (such as Sentinel-2, GF-6, and Landsat) differ, resulting in different spectral responses of the same ground feature on different sensors. Optimal transmission theory is used to map the spectral data from different sensors into a unified spectral space, enabling the collaborative use of multi-source data. To address the differences in red-edge band settings among different satellite sensors, a spectral space alignment model is constructed to perform isomorphic mapping of multi-source data in manifold space, providing temporally continuous and spectrally consistent multi-source time-series data support for steps 6 and 7.

[0060] Step S6: Construct a manifold classification map of vegetation health status.

[0061] Based on the above analysis results, a manifold classification map of vegetation health status was constructed. Specifically, it includes: Step 61: The 14-dimensional information, including chlorophyll content (1D), comprehensive physiological stress index (1D), vegetation manifold coordinates (8D), trajectory offset component, trajectory distortion component, and trajectory contraction component (3D) in the trajectory parameters of the red-edge manifold, and compactness feature of the red-edge curvature manifold (1D), are fused on the manifold to construct a healthy state manifold. The healthy state manifold uses the health features of all pixels as a point set, and the geodesic distance between points reflects the similarity of health status.

[0062] Step 62: Using a spectral clustering algorithm on the manifold, the healthy manifold is automatically divided into several sub-manifolds, each corresponding to a health level. The health levels include: healthy zone (Level I), mild stress zone (Level II), moderate stress zone (Level III), severe stress zone (Level IV), and extreme degradation zone (Level V).

[0063] Step 63: Compare the clustering results with the health levels of the ground quadrats, and propagate the quadrat levels to the entire manifold using a manifold label propagation algorithm to complete the assignment of health levels for all pixels; generate a vegetation health status manifold classification map (i.e., a five-level health status manifold distribution map), where each level corresponds to a connected region on the manifold, and the region boundary is defined by geodesics on the manifold. The five-level health status manifold distribution map is the specific output format or visualization result of the vegetation health status manifold classification map.

[0064] Step 64: Simultaneously, gradient flow analysis on the manifold is used to calculate the gradient direction field of the healthy state manifold, identify the direction of the fastest degradation of the healthy state, generate a stress diffusion path map, and reveal the spatial propagation law of degradation.

[0065] The health status manifold hierarchical map and gradient direction field constructed in step 6 will serve as the health benchmark and manifold spatial framework for the manifold early warning mechanism in step 7.

[0066] Step S7: Generate manifold early warning and geometric decision support products.

[0067] Based on the health status manifold hierarchy map constructed in step 6, and using the healthy zone (Level I) manifold as a benchmark, anomaly detection and early warning analysis of the time-series manifold trajectory are conducted. Based on the time-series manifold monitoring data, a manifold early warning mechanism and geometric decision support product are constructed. Specifically, this includes: Step 71: Extract the temporal manifold trajectory of each cell from the four-dimensional spatiotemporal manifold constructed in Step 41, and project it onto the two-dimensional manifold visualization space (using t-SNE dimensionality reduction) to form a manifold trajectory map.

[0068] Step 72: On the manifold trajectory map generated in step 71, anomaly patterns of the trajectory are identified by an anomaly detection algorithm on the manifold, including: outlier trajectories that deviate from the mainstream, periodic anomalies of trajectories with loop structures, and abrupt anomalies of trajectories that suddenly break off.

[0069] In one embodiment, the local outlier algorithm is used to identify abnormal trajectories, and the outlier threshold is set to 2.0.

[0070] Step 73: Mark the pixels corresponding to the abnormal trajectories as warning pixels, perform connectivity analysis on the warning pixels on the manifold, and identify the warning manifold sub-regions.

[0071] Step 74: Determine the warning level based on the geometric characteristics (area, curvature, boundary complexity) of the warning sub-region on the manifold.

[0072] Step 75: Map the early warning information back to geospatial data to generate a manifold early warning geographic map. Based on manifold geometric features, generate differentiated decision-making recommendations: areas with high curvature in the early warning sub-region are recommended for focused intervention; areas with complex boundaries in the early warning sub-region are recommended for edge-priority management; and areas far from the healthy mainstream manifold are recommended for engineering restoration. The manifold early warning map and decision-making recommendations are then pushed to grassland regulatory departments to achieve precise decision support based on manifold geometry.

[0073] In a specific embodiment of the present invention, the entire Inner Mongolia Autonomous Region is taken as the study area, with geographical coordinates of 97°12′–126°04′ east longitude and 37°24′–53°23′ north latitude, covering a total area of ​​approximately 1.18 million square kilometers. The study area spans three major geographical units: Northeast, North China, and Northwest China, encompassing a complete grassland ecological gradient, including meadow steppe, typical steppe, desert steppe, steppe-desert, and desert. Vegetation coverage ranges from over 80% in the east to less than 15% in the west, exhibiting typical spectral mixing complexity and spatial heterogeneity of physiological states.

[0074] Multi-source satellite imagery covering the entire region during the 2025 growing season (April–October) was acquired: 18 phases of Sentinel-2 MSI imagery (one phase every 10 days), 12 phases of GF-6 WFV imagery, and 6 phases of Landsat-8 / 9 OLI imagery. Simultaneously, data from 420 ground quadrats across the region were acquired, recording vegetation cover, species composition, chlorophyll content (measured SPAD values), dominant species leaf spectra, soil spectra, and health levels (five levels). Supporting data included daily precipitation and temperature data from meteorological stations, soil type maps, and digital elevation models. The grassland vegetation state inversion method based on red-edge singularity topological manifold unwrapping includes: Step S1 implementation: Construct the red-edge singularity topological space and red-edge curvature manifold of the entire Inner Mongolia region.

[0075] Radiometric calibration, atmospheric correction, and geometric registration preprocessing were performed on multi-source images of the entire region. Cubic spline interpolation was used to uniformly resample the data from each sensor to a 0.5 nm spectral interval, generating a continuous red-edge spectral curve (680–780 nm, a total of 201 sampling points). The first and second derivatives of the spectral curve at each wavelength were calculated pixel-by-pixel, and curvature values ​​were calculated based on the curvature formula. Local maxima of curvature were identified as red-edge singularities, resulting in four categories: red-edge starting point singularities, red-edge inflection point singularities, red-edge ending point singularities, and red-edge shoulder point singularities. Statistics show that the red-edge inflection point singularity in the healthy grassland area is located in the range of 718-725nm, with a curvature value of 0.08-0.12; the inflection point singularity in the mildly degraded area shifts blue to 710-715nm, with the curvature value decreasing to 0.05-0.08; and the inflection point singularity in the severely degraded area further shifts blue to 700-705nm, with a curvature value below 0.04.

[0076] The topological relationships between singularities were calculated, including the singularity spacing (average 8–15 nm), the spectral arc length between singularities (difference in integral reflectance), and the integral of curvature change between singularities. A topological relationship graph of singularities was constructed, with singularities as nodes and topological relationships as edges. Graph invariants (such as degree distribution and clustering coefficients) were used as topological features. The red-edge spectral curves were mapped to the curvature-wavelength phase space, and the three-dimensional embedding coordinates of the curvature manifold were extracted using a local linear embedding algorithm. The Betti number calculation of the manifold showed that the manifold in the healthy grassland area has a simply connected structure, while the manifold in the degraded area exhibits a porous structure, indicating that degradation leads to a more complex spectral geometry. The topological parameters of 12 Victokay points, the relationship parameters between 8 Victokay points, the topological features of the 6-dimensional curvature manifold, and 13 original spectral bands were fused with a deep neural network to construct a 31-dimensional red-edge singularity topological space tensor. The total data size of the region was approximately 288 million pixels × 31 dimensions, and block storage and distributed parallel computing were employed.

[0077] Step S2 implementation: vegetation-soil nonlinear component separation based on spectral manifold unwrapping.

[0078] The 31-dimensional red-edge singularity topological features of each pixel are considered as points in a high-dimensional space. The 288 million points across the entire region constitute a low-dimensional manifold embedded in this high-dimensional space. An isometric mapping algorithm is used for manifold learning. First, a k-nearest neighbor graph (k=15) is constructed, and the Euclidean distance between neighboring points is calculated. Then, the geodesic distance between all point pairs is calculated, and shortest path search is performed based on the neighborhood graph. Finally, multidimensional scaling analysis is used to map the high-dimensional points to an 8-dimensional intrinsic manifold space. The intrinsic dimension of the manifold is determined to be 8 dimensions using residual analysis.

[0079] In an 8-dimensional manifold space, vegetation endmember clusters, bare soil endmember clusters, and litter endmember clusters were identified based on the mapping locations of the measured endmember spectral library from the field. Using Riemannian geodesic theory, the geodesic distance from each pixel's manifold coordinate point to each endmember cluster was calculated. A soft affiliation function was constructed based on the geodesic distance, and the affiliation degree was calculated using the following formula: a i =exp(- d i 2 / s 2 ) / ∑ j exp(- d j 2 / s 2 ),in d i To reach the first i Geodesic distance of endmember clusters s The temperature parameter is the median of all geodesic distances. The attribution vector serves as the nonlinear decomposition coefficients of the pixel among its endmembers.

[0080] Further employing a diffusion mapping algorithm, a Markov transition probability matrix P is constructed based on geodesic distance, and t=10 diffusion iterations are performed to obtain the diffusion distance. The diffusion distance enhances the contrast between endmembers, making the separation of vegetation and soil clearer. The final output includes pixel-by-pixel vegetation manifold coordinates (8-dimensional), vegetation signal intensity (weighted sum of affiliation degrees), and vegetation-soil nonlinear interaction intensity (affiliation degree product term). A manifold reconstruction algorithm is used to map the vegetation manifold coordinates back to the spectral space, generating the pure vegetation signal spectrum. Validation results show that in desert steppe areas with less than 20% cover, the correlation coefficient R between the vegetation signal intensity extracted by this method and the measured ground cover is 0.91, a 47% improvement compared to linear unmixing (R=0.62); the average manifold distance between the pure vegetation signal spectrum and the measured vegetation spectrum is 0.18, significantly better than the 0.52 of the original mixed spectrum.

[0081] Step S3 implementation: Constructing the red-edge-chlorophyll topological mapping model and inverting physiological parameters.

[0082] A lookup table was generated based on the PROSPECT model. Chlorophyll content was set to 5–80 μg / cm² (step 1), dry matter content to 0.002–0.010 g / cm² (step 0.0005), equivalent water thickness to 0.005–0.025 cm (step 0.001), and leaf structure parameters to 1.3–2.1 (step 0.1), generating a total of 960,000 parameter combinations. Continuous spectra in the red-edge region were output. Singularity topology analysis was performed on each spectrum in the lookup table in step S1, extracting 31 singularity topological features to construct a singularity topology feature library.

[0083] Using the persistent cohomology method in topological data analysis, the evolution process of singular topological features in 31-dimensional space was calculated to generate a persistence map. Each point in the persistence map represents a topological feature, with its x-axis representing the appearance threshold and its y-axis representing the disappearance threshold. The distance of the point from the diagonal reflects the feature's persistence. The 50 most persistent topological features were selected as the topological invariants most sensitive to chlorophyll changes.

[0084] A topology mapping network was constructed, with a three-stage structure: the first stage is a three-layer graph neural network that maps 31-dimensional topological features to a 128-dimensional graph embedding space, capturing the topological relationships between features; the second stage is a persistent coherence layer that maps the graph embedding to a 50-dimensional persistent graph feature space; and the third stage is a two-layer fully connected network that maps persistent graph features to chlorophyll content. The loss function includes the chlorophyll inversion mean square error and a topology preservation constraint term (calculating the difference between the persistent graphs in the input feature space and the output space). The training set consists of 700,000 randomly selected data points from a lookup table, and the validation set consists of the topological features of singular points corresponding to the measured chlorophyll content of ground sample plots.

[0085] The trained model was applied to the pure vegetation signal across the entire region to retrieve pixel-by-pixel chlorophyll content. Validation results showed that, compared with measured values ​​from 420 ground quadrats, the coefficient of determination R² = 0.93, the root mean square error RMSE = 3.6 μg / cm², and the relative error 7.2%. The retrieved confidence region output showed a confidence region radius of ±2.3 μg / cm² in high vegetation cover areas and ±5.1 μg / cm² in low vegetation cover areas. Spatial distribution showed that the average chlorophyll content was 54.1 μg / cm² in the eastern meadow-steppe region, 43.2 μg / cm² in the central typical steppe region, and 24.8 μg / cm² in the western desert-steppe region.

[0086] Step S4 implementation: Construct the temporal red-edge manifold trajectory and physiological stress index.

[0087] Based on the pure vegetation signal from 18 time-series images in 2025, the red-edge curvature manifold construction in step S1 was performed period by period to obtain 18 time-series manifolds, each of which is a set of points in an 8-dimensional embedding space. The 18 manifolds were concatenated on the time axis to construct a four-dimensional spatiotemporal manifold with dimensions of 8 (manifold coordinates) × 18 (time) × H × W.

[0088] A dynamic time warping algorithm on the manifold is employed, using the average temporal manifold trajectory of pixels in a national nature reserve as the standard trajectory. The manifold curvature distance from the temporal manifold trajectory of each pixel to the standard trajectory is calculated. The manifold curvature distance is defined as the cumulative geodesic distance between the two trajectories after alignment in the manifold space. The optimal alignment path is solved using dynamic programming.

[0089] The stress components are decomposed based on manifold bending distance: the trajectory offset component, calculated by the average displacement after alignment, reflects the drift of the overall position of the manifold; the trajectory distortion component, calculated by the local curvature of the aligned path, reflects the deformation of the local shape of the manifold; and the trajectory contraction component, calculated by the rate of change of the manifold scale, reflects the reduction of the dynamic range of the manifold. The three components are fused by tensor product in 8-dimensional manifold space to construct a comprehensive physiological stress index.

[0090] Spatial distribution of the stress index shows that western Hulunbuir, southern Xilingol, and northern Ulanqab are high-value areas (stress index > 0.65). Typical pixel analysis shows that a mildly degraded pixel has no significant difference in traditional NDVI time series compared to a healthy pixel, but manifold trajectory analysis shows that its trajectory offset component is 0.28, distortion component is 0.19, contraction component is 0.12, and the comprehensive stress index is 0.23, successfully identifying early physiological stress that cannot be detected by traditional methods.

[0091] Step S5 implementation: Multi-sensor spectral spatial alignment and manifold isomorphic mapping.

[0092] The spectral response functions of GF-6, Sentinel-2, and Landsat-8 / 9 were obtained. Based on the field-measured hyperspectral data, the red-edge band response values ​​of each sensor were simulated, and a dataset of spectral pairs between sensors was constructed. Each pair contains the simulated spectra of two sensors for the same ground feature, totaling 150,000 pairs.

[0093] The optimal transmission theory is used to solve for the transmission mapping from the GF-6 spectral space to the Sentinel-2 spectral space. The spectral distributions of the two sensors are treated as two probability measures, and the mapping function that minimizes the transmission cost is sought. The cost function is measured by the Wasserstein distance between the spectra. The optimal transmission mapping is obtained by solving the Kantorovich dual problem. This mapping is a nonlinear function represented by a weighted sum of a series of basis functions.

[0094] The optimal transport mapping was applied to the 18-dimensional red-edge singularity topological features of GF-6 to obtain the transformed features. Verification of the transformation effect: the Wasserstein distance between the transformed features and the concurrent Sentinel-2 features decreased from 0.42 to 0.09. Manifold isomorphism tests showed that the persistence graph correlation coefficient of the manifolds before and after the transformation was greater than 0.94, indicating that the topological structure remained intact. Using the Sentinel-2 red-edge manifold as a reference, an isomorphic mapping library for GF-6 and Landsat red-edge manifolds was established. Multi-sensor collaboration increased the effective monitoring frequency across the region from 18 periods / year to 36 periods / year, achieving clear-sky observations every 10 days.

[0095] Step S6: Construct a manifold classification map of vegetation health status.

[0096] A healthy manifold is constructed by fusing 14 features, including chlorophyll content, comprehensive physiological stress index, vegetation manifold coordinates (8-dimensional), and red-edge manifold trajectory parameters (offset / twist / contraction components), onto the manifold. An isometric mapping algorithm is then used to map the 14-dimensional features onto a 6-dimensional intrinsic manifold space, where each point on the manifold corresponds to the health status of a pixel.

[0097] A spectral clustering algorithm was used to cluster healthy manifolds, constructing a similarity matrix (based on a Gaussian kernel of geodesic distance). The eigenvalue decomposition of the Laplacian matrix was calculated, and the first 8 eigenvectors were used for K-means clustering. The number of clusters was determined to be 5 using the eigenvalue gap method. The 5 clusters were compared with the health levels of ground quadrats, and the quadrat levels were propagated to the entire manifold using a manifold label propagation algorithm. Label propagation was based on graph semi-supervised learning, iteratively updating labels after constructing an adjacency graph until convergence.

[0098] A five-level health status manifold distribution map was generated, with each level corresponding to a connected region on the manifold. Statistical analysis shows that the healthy zone (Level I) accounts for 29%, the mildly stressed zone (Level II) accounts for 27%, the moderately stressed zone (Level III) accounts for 23%, the severely stressed zone (Level IV) accounts for 14%, and the extremely degraded zone (Level V) accounts for 7%. The spatial distribution is highly consistent with the ground survey.

[0099] Gradient flow analysis on the manifold was used to calculate the gradient direction field of the manifold in the healthy state. The gradient direction is determined by the principal component directions in the local tangent space, pointing in the direction of the fastest decline in health. Gradient streamline tracing revealed the stress diffusion path: stress in southern Xilingol spreads along a northwest-southeast direction, while stress in western Hulunbuir spreads radially from the water source. Gradient flow convergence areas were identified as high-risk areas for future stress.

[0100] Step S7: Generate manifold early warning and geometric decision support products.

[0101] The temporal manifold trajectory of each pixel is projected onto a two-dimensional manifold visualization space (using t-SNE dimensionality reduction) to form a manifold trajectory map. Each point on the map represents the temporal trajectory of a pixel, and the distance between points reflects the trajectory similarity. Anomaly trajectories are identified using the local outlier algorithm, with an outlier threshold set to 2.0. Approximately 860,000 anomalous trajectory pixels were identified.

[0102] Connectivity analysis on the manifold was performed on anomalous pixels, and a k-nearest neighbor graph was constructed in the manifold space. Connected subgraphs were extracted, and each connected subgraph corresponds to a warning manifold sub-region. A total of 312 warning sub-regions were identified. The warning level was determined based on the geometric characteristics of the sub-regions on the manifold: the sub-region area (number of pixels) was used as a scale factor, the mean curvature of the sub-region boundary was used as a complexity factor, and the geodesic distance from the sub-region to the healthy mainstream manifold was used as a severity factor. The warning level (red / orange / yellow) was synthesized by weighting these three factors.

[0103] Based on manifold geometric features, differentiated decision-making recommendations are generated: For warning sub-regions with high curvature (complex boundaries), edge-priority remediation is recommended, establishing protective belts to block the spread; for warning sub-regions with large distances from the healthy mainstream (severe deviation), engineering restoration and reseeding to rebuild vegetation are recommended; for warning sub-regions with high density (contiguous distribution), regional joint prevention and control is recommended, with unified implementation of grazing bans and rest periods. For each warning sub-region, the system automatically generates a warning card containing geometric features, warning level, and decision-making recommendations, which is then pushed to the grassland supervision department's mobile app.

[0104] This invention fully validated the feasibility of its seven-step technical process on a scale covering the entire Inner Mongolia region. Through a series of original technologies, including red-edge singularity topological space construction, spectral manifold unwrapping, red-edge-chlorophyll topological mapping, temporal manifold trajectory analysis, multi-sensor manifold isomorphic mapping, health status manifold classification, manifold early warning, and geometric decision support, it is the first to introduce differential geometry, topological data analysis, and manifold learning into the field of grassland vegetation monitoring. This achieves a paradigm shift in grassland vegetation physiological state inversion from "feature engineering" to "geometric deep learning," providing spectral-dimensional technical support for the precise management and early intervention of degradation in Inner Mongolia's 1.18 million square kilometers of grassland.

[0105] Accordingly, embodiments of the present invention also provide a grassland vegetation physiological state inversion system based on red-edge singularity topology and spectral manifold untangling, such as... Figure 2 The diagram shown is a structural schematic of the system. This grassland vegetation physiological state inversion system based on red-edge singularity topology and spectral manifold untangling includes the following modules: Red-edge singularity topology building unit 201 extracts singularity topological features from the red-edge region and constructs the red-edge singularity topological space and the red-edge curvature manifold; The nonlinear separation unit 202 uses spectral manifold unwrapping technology to nonlinearly separate the vegetation signal from the soil background signal to obtain the pure vegetation signal; The topological mapping model construction unit 203 establishes a topological mapping model from the red-edge singularity topological space to chlorophyll content based on the pure vegetation signal, and obtains the chlorophyll content. Unit 204, which is a comprehensive physiological stress index construction unit, is based on long-term remote sensing data. It extracts the time-series trajectory of the red-edge manifold and constructs a comprehensive physiological stress index with manifold geometric significance. The spectral spatial alignment model construction unit 205 sets differences in the red edge band of different satellite sensors to construct a spectral spatial alignment model and perform isomorphic mapping of multi-source data in manifold space. Manifold hierarchical map construction unit 206 is used to construct a manifold hierarchical map of vegetation health status; Manifold early warning mechanism construction unit 207 constructs a manifold early warning mechanism based on time-series manifold monitoring data.

[0106] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0107] The present invention also provides a storage medium, which is a computer-readable storage medium storing a computer program thereon, the computer program being executable when it is run. Figure 1 The method shown may include some or all of the steps. The storage medium may include read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, etc. The storage medium may also include non-volatile memory or non-transitory memory, etc.

[0108] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer program are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data provider to another website, computer, server, or data provider via wired or wireless means.

[0109] The embodiments of the present invention have been described in detail above. Specific implementation methods have been used to illustrate the present invention. The descriptions of the embodiments above are only for the purpose of helping to understand the methods and systems of the present invention, and are merely some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention, and the content of this specification should not be construed as a limitation of the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for grassland vegetation state inversion based on red-edge singularity topological manifold untangling, characterized in that, The method includes: Step 1: Extract the topological features of singularities from the red-edge region and construct the topological space of the red-edge singularities and the red-edge curvature manifold; Step 2: Using spectral manifold unwrapping technology, the vegetation signal and soil background signal are nonlinearly separated to obtain the pure vegetation signal; Step 3: Based on the pure vegetation signal, establish a topological mapping model from the red-edge singularity topological space to the chlorophyll content to obtain the chlorophyll content; Step 4: Based on long-term remote sensing data, extract the red-edge manifold time-series trajectory and construct a comprehensive physiological stress index with manifold geometric significance; Step 5: Based on the differences in red-edge band settings for different satellite sensors, construct a spectral spatial alignment model to perform isomorphic mapping of multi-source data in manifold space; Step 6: Construct a manifold hierarchical map of vegetation health status; Step 7: Based on time-series manifold monitoring data, construct a manifold early warning mechanism; Step 3 includes: Step 31: Introduce the PROSPECT leaf radiative transfer model to generate a reflectance lookup table covering the physiological parameter space of grassland vegetation, and obtain the continuous spectrum of the red edge region. The physiological parameters of grassland vegetation include chlorophyll content, dry matter content, equivalent water thickness and leaf structure parameters. Step 32: For each continuous spectrum of the red-edge region in the reflectance lookup table, perform the red-edge singularity topological analysis of Step 1, extract the singularity topological feature vector, and construct the singularity topological feature library; combine the singularity topological feature library with the corresponding chlorophyll content to form a training dataset, and use the persistent cohomology method in topological data analysis to calculate the persistence graph of the red-edge singularity topological features in high-dimensional space, and identify the topological features most sensitive to chlorophyll changes. Step 33: Construct a topology mapping network based on the training dataset; the input of the topology mapping network is the topological feature vector of the singularity, and the output is the chlorophyll content; the loss function of the topology mapping network is designed as follows: L=L MSE + α· L topo ; Where L MSE For the mean square error of chlorophyll inversion, L topo For topology preservation constraints, α To balance the weights; Step 34: After training the topology mapping network, obtain the topology mapping model from the red-edge singularity topology space to the chlorophyll content, invert the chlorophyll content pixel by pixel, and output the confidence region of the inversion result in the topology space as a geometric measure of the inversion uncertainty.

2. The grassland vegetation state inversion method based on red-edge singularity topological manifold untangling according to claim 1, characterized in that, Step 1 includes: Step 11: Resample the multi-source satellite data to a sub-nanometer spectral interval to construct a continuous red-edge spectral curve; Step 12: Introduce curvature theory from differential geometry to calculate the curvature values ​​of the red-edge spectral curve at each wavelength point. The calculation formula is: ； in Let red-edge spectral reflectance function, and These are its first and second derivatives, respectively; local maxima of curvature are taken as red-edge singularities, which include red-edge starting point singularities, red-edge inflection point singularities, red-edge ending point singularities, and red-edge shoulder point singularities. Each red-edge singularity is characterized by three parameters: wavelength position, curvature value, and curvature direction. Step 13: Calculate the topological relationships between red-edge singularities. The topological relationships between red-edge singularities include the topological parameters of each red-edge singularity and the topological relationship parameters between singularities. The topological parameters of each red-edge singularity include: wavelength position, curvature value, curvature direction, and singularity type. The topological relationship parameters between singularities include: singularity spacing, spectral arc length between singularities, integral of curvature change between singularities, average rate of curvature change between singularities, and spectral area between singularities. Based on the topological parameters of each red-edge singularity and the topological relationship parameters between singularities, construct a singularity topological relationship graph with singularities as nodes and topological relationships as edges. The adjacency matrix elements of the graph are composed of vectors consisting of the topological parameters of each red-edge singularity and the topological relationship parameters between singularities, forming the graph structure basis of the red-edge singularity topological space. Step 14: Map the red-edge spectral curve onto the curvature-wavelength phase space to form a red-edge curvature manifold. Each point on the manifold corresponds to the curvature state at a wavelength position. The topological structure of the manifold reflects the intrinsic geometric features of the red-edge spectrum. Extract the topological features of the red-edge curvature manifold, including: local curvature features, volume and boundary features, and connectivity features, to provide geometric support for the topological space of the red-edge singularity. Step 15: Nonlinearly fuse the topological parameters of each red-edge singularity, the topological relationship parameters between singularities, and the topological features of the red-edge curvature manifold with the original spectral bands to construct the red-edge singularity topological space; Based on the red-edge singularity topological space, organize the parameters of each red-edge singularity, the topological relationship parameters between singularities, and the topological features of the red-edge curvature manifold into a unified high-dimensional tensor form to construct the red-edge singularity topological space tensor.

3. The grassland vegetation state inversion method based on red-edge singularity topological manifold untangling according to claim 2, characterized in that, Step 2 includes: Step 21: The spectrum of each pixel in the multi-source satellite data processed in Step 11 is regarded as a point in a high-dimensional spectral space. The spectral points of all pixels constitute a low-dimensional manifold embedded in the high-dimensional space. The isometric mapping algorithm in manifold learning is used to map the original spectral space to the intrinsic low-dimensional manifold space. Step 22, based on the mapping position of the field measured endmember spectral library, the vegetation endmember cluster, the bare soil endmember cluster and the litter endmember cluster are identified, according to the geodesic line theory in Riemann geometry, the position coordinates of each pixel spectral point in the manifold space are calculated, and the geodesic distance d of the pixel spectral point to each endmember cluster is solved i ; wherein the position coordinates of the pixel spectral point in the manifold space are denoted as vegetation manifold coordinates; Step 23: Construct a soft affiliation function based on geodesic distance and calculate the affiliation degree. a i To achieve nonlinear decomposition of pixel spectra among endmembers; attribution a i The calculation formula is: a i =exp(- d i 2 / σ 2 ) / ∑ j exp(- d j 2 / σ 2 ); in d i To reach the first i Geodesic distance of endmember clusters σ The temperature parameter is used; the affiliation degree of vegetation endmember clusters is denoted as the vegetation signal strength. Step 24: Calculate the vegetation signal separation and diffusion distance using a diffusion mapping algorithm on the manifold. as follows: ； in P The Markov transition probability matrix is ​​constructed based on geodesic distance. t The number of diffusion steps is used to enhance the contrast between endmembers through multiple diffusion iterations, thereby achieving fine separation of vegetation signals and soil signals. The degree of interaction between vegetation endmember clusters and soil endmember clusters during the separation process is denoted as the vegetation-soil nonlinear interaction intensity. Step 25: Based on the pixel-by-pixel vegetation manifold coordinates, vegetation signal intensity, and vegetation-soil nonlinear interaction intensity, generate the manifold reconstruction result of the pure vegetation signal spectrum.

4. The grassland vegetation state inversion method based on red-edge singularity topological manifold untangling according to claim 1, characterized in that, Step 4 includes: Step 41: For the vegetation pure signal of the 18 time series images of the year, perform the red edge curvature manifold construction of Step 1 for each period to obtain 18 time series manifolds. Each manifold is a set of points in an 8-dimensional embedding space. Connect the 18 manifolds in series on the time axis to construct a four-dimensional spatiotemporal manifold. Step 42: Using the dynamic time warping algorithm on the manifold, the temporal manifold trajectory of each pixel is aligned with the standard trajectory of the healthy reference area, and the manifold curvature distance between the trajectories is calculated. Step 43: Based on the manifold bending distance, three geometrically meaningful red-edge manifold trajectory parameters are decomposed, including trajectory offset component, trajectory twist component, and trajectory contraction component. The trajectory offset component reflects the drift of the overall position of the manifold, corresponding to the systematic change in chlorophyll content; the trajectory twist component reflects the deformation of the local shape of the manifold, corresponding to the abnormality of the red-edge curve shape; the trajectory contraction component reflects the reduction of the manifold scale, corresponding to the reduction of the red-edge dynamic range. Step 44: Nonlinearly fuse the three stress components on the manifold to construct a comprehensive physiological stress index.

5. The grassland vegetation state inversion method based on red-edge singularity topological manifold untangling according to claim 1, characterized in that, Step 5 includes: Step 51: Obtain the spectral response functions of different satellite sensors, simulate the red-edge band response values ​​of each sensor based on the measured hyperspectral data, and construct a spectral pair dataset between sensors; Step 52: Introducing optimal transport theory, the source sensor spectral distribution is mapped to the target sensor spectral distribution via transport. The cost function of the transport mapping is measured by the Wasserstein distance between the spectra. in, μ and ν The spectral distributions of the source sensor and the target sensor are shown respectively. x Spectral distribution of the source sensor μ The sample points in the vector represent the spectral reflectance vector of the source sensor. y Spectral distribution of the target sensor ν The sample points in the vector represent the spectral reflectance vector of the target sensor. γ for μ and ν The joint distribution of Γ( μ , ν Let be the set of all joint distributions; || xy ‖express x and y The Euclidean distance between them; by solving the optimal transmission problem, a nonlinear mapping function from the source sensor spectral space to the target sensor spectral space is obtained; Step 53: Perform the red-edge singularity topological analysis of the transformed spectrum in Step 1 to verify the isomorphism of the transformed spectrum in the manifold space and ensure that the topological structure of the red-edge manifold remains unchanged before and after the transformation.

6. The grassland vegetation state inversion method based on red-edge singularity topological manifold untangling according to claim 1, characterized in that, Step 6 includes: Step 61: Multidimensional information such as chlorophyll content, comprehensive physiological stress index, vegetation manifold coordinates and red-edge manifold trajectory parameters are fused on the manifold features to construct a healthy state manifold; the healthy state manifold uses the health features of all pixels as a point set, and the geodesic distance between points reflects the similarity of health status; Step 62: Use a spectral clustering algorithm on the manifold to divide the health status manifold into several submanifolds, with each submanifold corresponding to a health level; Step 63: Compare the clustering results (i.e., sub-manifolds) with the health levels of ground quadrats, and propagate the quadrat levels to the entire manifold using the manifold label propagation algorithm to complete the health level assignment for all pixels; generate a vegetation health status manifold classification map, where each level corresponds to a connected region on the manifold, and the region boundary is defined by geodesics on the manifold. Step 64: Gradient flow analysis on the manifold is used to calculate the gradient direction field of the healthy manifold, identify the direction of the fastest degradation of the healthy state, generate a stress diffusion path map, and reveal the spatial propagation law of degradation.

7. The grassland vegetation state inversion method based on red-edge singularity topological manifold untangling according to claim 1, characterized in that, Step 7 includes: Step 71: Extract the temporal manifold trajectory of each cell from the four-dimensional spatiotemporal manifold and project it onto the two-dimensional manifold visualization space to form a manifold trajectory map; Step 72: On the manifold trajectory map, anomaly detection algorithms on the manifold are used to identify outlier trajectories that deviate from the mainstream, periodic anomalies with loop structures in the trajectory, and abrupt anomalies that cause sudden breaks in the trajectory. Step 73: Mark the pixels corresponding to the abnormal trajectories as warning pixels, perform connectivity analysis on the warning pixels on the manifold, and identify the warning manifold sub-regions; Step 74: Determine the warning level based on the geometric characteristics of the warning sub-region on the manifold; Step 75: Map the early warning information back to geospatial space to generate a manifold early warning geographic map; generate differentiated decision recommendations based on manifold geometric features: areas with large curvature in the early warning sub-region are recommended for key intervention; areas with complex boundaries in the early warning sub-region are recommended for edge-priority treatment; and areas in the early warning sub-region that are far from the healthy mainstream shape are recommended for engineering repair.

8. A grassland vegetation state inversion system based on red-edge singularity topological manifold untangling, characterized in that, The system includes: Red-edge singularity topology building unit: Extract singularity topological features from red-edge regions to construct red-edge singularity topological space and red-edge curvature manifold; The nonlinear separation unit uses spectral manifold unwrapping technology to nonlinearly separate the vegetation signal from the soil background signal to obtain the pure vegetation signal; The topological mapping model construction unit establishes a topological mapping model from the red-edge singularity topological space to chlorophyll content based on the pure vegetation signal, and obtains the chlorophyll content. The comprehensive physiological stress index construction unit is based on long-term remote sensing data, extracting the red-edge manifold temporal trajectory to construct a comprehensive physiological stress index with manifold geometric significance; The spectral spatial alignment model construction unit sets differences in the red edge band of different satellite sensors to construct a spectral spatial alignment model and perform isomorphic mapping of multi-source data in manifold space. Manifold hierarchical map construction unit, constructing a manifold hierarchical map of vegetation health status; The manifold early warning mechanism construction unit constructs a manifold early warning mechanism based on time-series manifold monitoring data; Specifically, the topological mapping model construction unit, when establishing a topological mapping model from the red-edge singularity topological space to chlorophyll content based on the vegetation pure signal to obtain the chlorophyll content, includes: The PROSPECT leaf radiative transfer model was introduced to generate a reflectance lookup table covering the physiological parameter space of grassland vegetation, and the continuous spectrum of the red edge region was obtained. The physiological parameters of grassland vegetation included chlorophyll content, dry matter content, equivalent water thickness and leaf structure parameters. For each continuous spectrum of the red-edge region in the reflectance lookup table, perform red-edge singularity topological analysis to extract singularity topological feature vectors and construct a singularity topological feature library. Combine the singularity topological feature library with the corresponding chlorophyll content to form a training dataset. Use the persistent cohomology method in topological data analysis to calculate the persistence graph of the red-edge singularity topological features in high-dimensional space and identify the topological features most sensitive to chlorophyll changes. Based on the training dataset, a topology mapping network is constructed. The input of the topology mapping network is the topological feature vector of the singularity, and the output is the chlorophyll content. The loss function of the topology mapping network is designed as follows: L=L MSE + α· L topo ; Where L MSE For the mean square error of chlorophyll inversion, L topo For topology preservation constraints, α To balance the weights; After training the topology mapping network, a topology mapping model from the red-edge singularity topology space to chlorophyll content is obtained. Chlorophyll content is obtained pixel by pixel inversion, and the confidence region of the inversion result in the topology space is output as a geometric measure of inversion uncertainty.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it executes the steps of the grassland vegetation state inversion method based on red-edge singularity topological manifold untangling as described in any one of claims 1 to 8.

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