A radar forest height inversion random forest method incorporating structural features

Abstract

The application discloses a kind of structural features integrated radar forest height inversion random forest method, belong to the technical field of radar detection;With the basis feature of polarization interferometric synthetic aperture radar PolInSAR multi-polarization observation data, the influence of analyzing physical model expression on PolInSAR forest height inversion is analyzed, mining associated physical model parameter is introduced into training feature dataset, supplementary input feature, consider complex forest structure scene, utilize Fourier-Legendre polynomial to depict the influence of forest vertical structure, extract the polynomial coefficient representing the vertical structure feature of forest and integrate into the training feature set, further supplement input feature;With a small amount of LiDAR forest height information as supervision label, based on random forest learning method to establish regression model, realize forest height inversion.The application proposes a forest height inversion method based on random forest, which integrates physical model features and vertical structure features, to improve the accuracy and stability of forest height inversion.

Description

Technical Field

[0001] This invention relates to the field of radar detection technology, and in particular to a radar forest height inversion random forest method incorporating structural features. Background Technology

[0002] Forest ecosystems are the main body of terrestrial ecosystems, and forest height, as an important characteristic parameter of forest ecology, is a key physical parameter for forest resource surveys. Therefore, acquiring forest height information over a large scale and with high precision is one of the important tasks of geodesy. Polarimetric Interferometric Synthetic Aperture Radar (PolInSAR) can penetrate forest vegetation and obtain vegetation scattering echo information in multiple polarization modes, possessing the ability to invert forest height over a large scale. Changes in scattering information are closely related to the vertical structure of the forest, and a reasonable characterization of the influence of the forest vertical structure helps to accurately extract forest height information. The RVOG (Random Volume over Ground) model proposed by Treuhaft et al. is currently the most widely used scattering model. It uses an exponential function to describe the scattering and propagation process of radar signals in the vegetation layer. However, due to the influence of complex forest scenes, it is difficult to establish a complete observation process mechanism through a single function, resulting in significant biases in forest height inversion. Researchers have proposed using machine learning methods to train a network model to establish a model correlation between coherent observations and forest height, in order to mitigate the influence of incomplete expression in the observation model. Brigot et al., based on the RVOG model, used the distribution shape parameters of PolInSAR coherent points as independent variables and employed the random forest method to effectively classify forest canopy profiles. Denbina et al. transformed baseline selection into a supervised classification task, using LiDAR (Light Detection and Range) measurements of forest height samples to achieve multi-baseline combination filtering through learning training, effectively improving the accuracy of forest height inversion. Pourshamsi et al. used the support vector machine method for multi-baseline data fusion, realizing the estimation of canopy height in complex tropical forests. Introducing a LiDAR high-precision forest height information supervised training model can, to some extent, compensate for the parameter inversion bias caused by the incomplete expression of the PolInSAR observation mechanism. However, LiDAR point cloud measurements consume a lot of energy, have a small coverage area, and are easily affected by weather conditions such as clouds and fog, often failing to provide sufficient and uniform training samples, making it difficult for model training to fit complex forest structure scenarios, resulting in insufficient stability and reliability. Summary of the Invention

[0003] The purpose of this invention is to provide a random forest method for radar forest height inversion that incorporates structural features. Using PolInSAR multi-polarization observation data as the basic feature, the influence of physical model expressions on PolInSAR forest height inversion is analyzed, and related physical model parameters are introduced into the training feature set to supplement the input features. Furthermore, considering complex forest structure scenarios, Fourier-Legendary polynomials are used to characterize the influence of forest vertical structure, and polynomial coefficients representing forest vertical structure features are introduced as supplementary features to construct the training feature set. Using a small amount of LiDAR forest height information as a supervision label, a regression model is established based on the random forest method. Finally, a PolInSAR forest height inversion method based on random forest, fusing physical model features and vertical structure features, is proposed to improve the accuracy and stability of forest height inversion.

[0004] To achieve the above objectives, this invention provides a radar forest height inversion random forest method incorporating structural features, comprising the following steps: Step S1: Use polarimetric interferometric synthetic aperture radar to collect data, and establish a PolInSAR complex forest area scattering model based on the random ground body two-layer scattering model RVOG. The corresponding Fourier-Legend polynomial is used to describe the vertical structure characteristics of the forest. Step S2: Solve the RVOG model using the three-stage method to obtain the initial values ​​of forest height and land surface phase; Step S3: Substitute the initial forest height into the Fourier-Legend polynomial model to calculate the vertical structure coefficients, and add the vertical structure coefficients to the feature dataset as feature parameters to participate in the random forest model regression. Step S4: Set up a feature dataset, including surface phase, volume coherence coefficient, volume coherence phase, vertical effective wavenumber, and vertical structure coefficient; collect a small amount of high-precision forest height data using LiDAR as supervised learning labels to form LiDAR forest height labels; use the feature dataset and the corresponding LiDAR forest height labels to train the random forest algorithm through ensemble learning regression to obtain the optimal random forest model. Step S5: Use the optimal random forest model to regress and predict the forest height with high accuracy.

[0005] Preferably, in step S1, the collected data is as follows: using polarimetric interferometric synthetic aperture radar (PISAR) to collect fully polarimetric SAR data via heavy orbit, obtaining main images and multi-track auxiliary images, forming multi-baseline PolInSAR observation data.

[0006] Preferably, in step S1, the process of establishing the forest area scattering model is as follows: The random ground scattering model RVOG is set as a two-layer structure, including a forest scattering layer and a surface scattering layer, with a reference ground height of [missing information]. The forest height is The random volume scattering medium contains scattering particles that are uniformly and randomly distributed in space and exhibit isotropic scattering characteristics. The propagation and attenuation of electromagnetic waves in the vegetation layer adopts an exponential extinction model. The scattering mechanism in the forest scene includes volume scattering and surface scattering related to the ground surface. The expression of the RVOG scattering model is as follows: ; In the above formula, Indicates the polarization mode. Represents the imaginary number symbol, Represents the complex coherence coefficient. Indicates surface phase, This represents the volume decoherence coefficient caused solely by volume scattering. The volume amplitude ratio represents the ratio of power scattered from the Earth's surface to that scattered from the volume. This volume amplitude ratio varies with polarization; the volume decoherence coefficient... The expression is as follows: ; In the above formula, The forest vertical structure function represents the variation with penetration depth z. Represents forest height; volume-decoherent expression By changing the upper and lower bounds of the integral, we obtain the following formula: ; In the above formula, Indicates the vertical height relative to the Earth's surface reference plane. Vertical structure functions Indicates the vertical height relative to the Earth's surface reference plane. Extinction coefficient, The incident angle of the main imaging radar. Vertical effective wavenumber; In the RVOG scattering model, the Fourier-Legendal polynomial is used to express the changes in forest vertical structure: vertical structure function. The corresponding Fourier-Legend series expansion is as follows: ; In the above formula, Indicates the first The coefficients of the first-order polynomial control the vertical structure function. The form; Indicates the first The orthogonal normalized polynomial of order 1, corresponding to the Fourier-Legend polynomial defined on the interval [-1, 1], is as follows: ; Vertical structure function Substituting the Fourier-Legend series expansion into the volume decoherence expression of the transform integral upper and lower bounds The formula is as follows: ; ; In the above formula, Indicates the vertical effective wavenumber. With forest height and vertical effective wavenumber related; Indicates the altitude of the Earth's surface; Indicates forest height; 、 、 For the Fourier-Legend polynomial expansion term ； Represents the vertical structure coefficient, where The corresponding Fourier-Legend expansion is as follows: ; The forest vertical structure function is reconstructed using Fourier-Legend polynomials.

[0007] Preferably, in step S2, the process of solving the RVOG model using the three-stage algorithm is as follows: Step S21: Coherence line fitting. Based on the scattering matrix of the main and auxiliary images, the polarization interference matrix is ​​obtained. Several complex coherence coefficients under polarization states are selected and regarded as discrete points within the unit circle of the complex plane. Linear fitting is performed on these points to determine the coherence line. Step S22: Surface phase estimation. After coherence line fitting in step S21, the fitted straight line intersects the complex plane unit circle at two points. HV polarization is considered as the volume scattering-dominated polarization mode. The terrane is relatively small, passing through two intersection points and The surface phase is determined by distance; the one furthest away is the surface phase. The criteria for judgment are as follows: ; In the above formula, 、 This represents the two intersection points of the coherence line and the unit circle. This represents the phase function used to determine the surface phase. Then, the other intersection point is the volume coherence point, from which the volume coherence coefficient is extracted. Volume coherence phase The formula is as follows: ; Step S23: Construct a two-dimensional lookup table. In the three-stage method, the unknown is the forest height. Extinction coefficient Ratio of Earth's amplitude By fixing the extinction coefficient or the earth amplitude ratio, construct and or and A two-dimensional lookup table is used to preset the range of unknowns, and the lookup table is used to search for and display the correlation coefficient. Model volume coherence with minimum distance This allows for a preliminary estimate of the forest height.

[0008] Preferably, in step S3, the preliminary forest height estimate is substituted into the Fourier-Legendary polynomial to calculate the vertical structure coefficients, and a feature set is introduced. The vertical structure of the forest changes with the forest height. The vertical structure of the forest scene is described by a third-order Fourier-Legendary polynomial, and the vertical structure coefficients are obtained by solving the nonlinear least squares method. 、 This data is added to the feature dataset and used as a feature parameter in the random forest model regression, as shown in the following formula: ; In the above formula, Indicates the vertical effective wavenumber. Represents the real part of a complex number. It represents the imaginary part of a complex number.

[0009] Preferably, in step S4, the training process is as follows: The random forest is trained using the feature dataset and LiDAR forest height labels. The random forest algorithm is used for training, and the optimal random forest model is determined based on minimizing the prediction error on the validation set. The process is as follows: The feature dataset includes surface phase, volume coherence coefficient, volume coherence phase, vertical effective wavenumber, and vertical structure coefficient. This feature dataset is used as training features, and LiDAR forest high-label data is used as supervised training labels. The training process is as follows: Random Forest (RF) randomly selects multiple subsets from the original training set... Decision Tree As a basic classifier This represents the input feature dataset. The prediction function of a single decision tree. Representing a sequence of random variables, training this The random forest model uses several decision trees, and then merges the predictions from each tree using a majority voting method to obtain the classification or prediction result. The expression for the random forest model is as follows: ； In the above formula, It is a collection of all categories. It is the number of decision trees. It is a category The average probability, It is the first Decision tree for each category The predicted probability, P represents the final classification probability.

[0010] Preferably, the corresponding random variable sequence The generation strategy is as follows: (1) Random sampling of the sample, in constructing the first When building a decision tree, start from the original training sample set. The method of random sampling with replacement is used to generate a subset of the training set with the same size as the original sample set. This process is repeated. Next, get A set of independent training Each subset corresponds to a decision tree for training. In each resampling process, some original samples are selected, while the remaining samples are not included in the current sub-training set, thereby enhancing the differentiation between the learners. (2) Random feature selection: During the node splitting stage of the decision tree, the random forest does not search for the optimal splitting attribute in the entire feature space, but rather selects the optimal splitting attribute from the node splitting node. A subset of features is randomly selected with equal probability from each input feature. Only the optimal feature is selected from this subset for node partitioning, and the dimension of the selected feature subset is... Set as: ; in, This represents the total number of features, which can suppress the problem of strongly correlated features repeatedly dominating splits in all decision trees, thereby reducing the correlation between decision trees; Based on random sampling of samples and random selection of features, the first The sequence of random variables corresponding to each decision tree as follows: in, This represents a training subset randomly sampled by Bootstrap. This represents the feature subset randomly selected during node splitting. Since the sample selection process and feature selection process of each decision tree are independent, the formula for the random variable sequence is as follows: It is considered as a sequence of independent and identically distributed random variables.

[0011] Therefore, the present invention employs the above-mentioned radar forest height inversion random forest method incorporating structural features, which has the following advantages: (1) In this invention, by establishing a mapping relationship between the physical model’s relevant parameter features and forest height through random forest, the potential correlation between observed variables and forest height can be explored more fully, thereby significantly improving the stability of forest height inversion.

[0012] (2) In this invention, by introducing the vertical structure coefficient to construct the feature dataset, the sensitivity of the model to the differences in different forest structures can be significantly enhanced, which helps to improve the stability and accuracy of forest height estimation, especially in areas with complex forest structures or strong heterogeneity.

[0013] (3) In this invention, the random forest method for forest height inversion that integrates physical model features and forest vertical structure features can improve the accuracy of forest height inversion compared to the random forest method that only introduces physical model features.

[0014] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0015] Figure 1 This is a flowchart of a radar forest height inversion random forest method incorporating structural features according to the present invention; Figure 2 This is a schematic diagram of the RVOG model in the radar forest height inversion random forest method incorporating structural features of the present invention; Figure 3 This is a forest height inversion result diagram in an embodiment of the radar forest height inversion random forest method incorporating structural features according to the present invention; Figure 4 This is an error distribution diagram of forest height inversion results in an embodiment of a radar forest height inversion random forest method incorporating structural features according to the present invention; Figure 5 This is a feature importance evaluation map of the study area in an embodiment of the radar forest height inversion random forest method incorporating structural features according to the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Specific model specifications need to be selected and determined according to the actual specifications of the device, etc. The specific selection calculation method adopts existing technology in the art, and therefore will not be described in detail.

[0017] Example like Figure 1 and Figure 2 As shown, this invention provides a random forest method for radar forest height inversion incorporating structural features, which mainly includes three processes: physical model feature extraction, vertical structure feature generation, and random forest ensemble learning regression. Specifically, it includes the following steps: Step S1: Use polarimetric interferometric synthetic aperture radar to collect data, and establish a PolInSAR complex forest area scattering model based on the random ground body two-layer scattering model RVOG. The corresponding Fourier-Legend polynomial is used to describe the vertical structure characteristics of the forest. In step S1, the collected data are as follows: Polarimetric Interferometric Synthetic Aperture Radar (PISAR) is used to collect fully polarimetric SAR data via heavy orbit, obtaining the main image and multi-track auxiliary images to form multi-baseline PolInSAR observation data.

[0018] In step S1, the process of establishing the forest scattering model is as follows: The random ground body two-layer scattering model RVOG is set as a two-layer structure, including a forest scattering layer and a ground surface scattering layer, and the reference ground height is set to [missing information]. The forest height is The random volume scattering medium contains scattering particles that are uniformly and randomly distributed in space and exhibit isotropic scattering characteristics. The propagation and attenuation of electromagnetic waves in the vegetation layer employs an exponential extinction model. The scattering mechanisms in forest scenes include volume scattering and surface scattering associated with the ground surface, without further differentiation of surface scattering types. Based on this simplification, the RVOG model incorporates the complex coherence coefficients obtained from PolInSAR observations. A clear quantitative relationship has been established with key forest parameters such as forest height, surface phase, and extinction coefficient. The expression for the RVOG scattering model is as follows: ; In the above formula, Indicates the polarization mode. Represents the imaginary number symbol, Represents the complex coherence coefficient. Indicates surface phase, This represents the volume decoherence coefficient caused solely by volume scattering. The Ground to Volume Ratio (GVR) represents the power ratio of surface scattering to volume scattering; its value varies with polarization. Volume decoherence coefficient. The expression is as follows: ; In the above formula, This represents the vertical structure function that varies with the penetration depth z. Represents forest height; volume-decoherent expression By changing the upper and lower bounds of the integral, we obtain the following formula: ; In the above formula, Indicates the vertical height relative to the Earth's surface reference plane. Vertical structure functions Indicates the vertical height relative to the Earth's surface reference plane. Extinction coefficient, The incident angle of the main imaging radar. The effective wavenumber is the vertical wavenumber.

[0019] The relative reflectivity function characterizes the propagation and attenuation of radar waves in the vegetation layer and can effectively reflect changes in forest vertical structure. However, the exponential function used in the RVOG model often fails to accurately represent the complex influence of forest vertical structure during radar propagation. Replacing the exponential function with a Fourier-Legendary polynomial can more accurately represent changes in forest vertical structure: Vertical Structure Function The corresponding Fourier-Legend series expansion is as follows: The vertical structure variation of forests is expressed using Fourier-Legend polynomials: Vertical Structure Function The corresponding Fourier-Legend series expansion is as follows: ; In the above formula, Indicates the first The coefficients of the first-order polynomial control the vertical structure function. The form; Indicates the first The orthogonal normalized polynomial of order 1, corresponding to the Fourier-Legend polynomial defined on the interval [-1, 1], is as follows: ; Vertical structure function Substituting the Fourier-Legend series expansion into the volume decoherence expression of the transform integral upper and lower bounds The formula is as follows: ; ; In the above formula, Indicates the vertical effective wavenumber. With forest height and vertical effective wavenumber related; Indicates the altitude of the Earth's surface; Indicates forest height; 、 、 For the Fourier-Legend polynomial expansion term ； Represents the vertical structure coefficient, where The corresponding Fourier-Legend expansion is as follows: ; The forest vertical structure function is reconstructed using Fourier-Legend polynomials.

[0020] Step S2: Solve the RVOG model using a three-stage method to obtain the initial forest height and surface phase. The process parameters obtained from solving the RVOG model using the three-stage algorithm include the volume coherence coefficient, surface phase, and volume coherence phase, which are essentially the physical response results of electromagnetic waves propagating and scattering in the forest medium. These parameters can reflect the physical structural characteristics of the forest to a certain extent. Therefore, by introducing the physical model process parameters into the feature input, the nonlinear mapping relationship between process physical quantities and forest height can be fully explored, improving the stability of ensemble learning. The process of solving the RVOG model using the three-stage algorithm is as follows: Step S21: Coherence line fitting. Based on the scattering matrix of the main and auxiliary images, the polarization interference matrix is ​​obtained. Several complex coherence coefficients under polarization states are selected and regarded as discrete points within the unit circle of the complex plane. Linear fitting is performed on these points to determine the coherence line. Step S22: Surface phase estimation. After coherence line fitting in step S21, the fitted straight line intersects the complex plane unit circle at two points. HV polarization is considered as the volume scattering-dominated polarization mode. The terrane is relatively small, passing through two intersection points and The surface phase is determined by distance; the one furthest away is the surface phase. The criteria for judgment are as follows: ; In the above formula, 、 This represents the two intersection points of the coherence line and the unit circle. This represents the phase function used to determine the surface phase. Then, the other intersection point is the volume coherence point, from which the volume coherence coefficient is extracted. Volume coherence phase The formula is as follows: ; Step S23: Construct a two-dimensional lookup table. In the three-stage method, the unknown is the forest height. Extinction coefficient Ratio of Earth's amplitude By fixing the extinction coefficient or the earth amplitude ratio, construct and or and A two-dimensional lookup table is used to preset the range of unknowns, and the lookup table is used to search for and display the correlation coefficient. Model volume coherence with minimum distance This allows for a preliminary estimate of the forest height.

[0021] Step S3: Substitute the initial forest height into the Fourier-Legendary multinomial model to calculate the vertical structure coefficients. Correspondingly, add these vertical structure coefficients to the feature dataset as feature parameters. Vertical structure is a crucial feature parameter of forest scenes; structural differences directly affect the scattering characteristics of vegetation and are closely related to the formation of polarization observation information. Furthermore, forest vertical structure changes with forest height and exhibits a certain model correlation with forest height. Therefore, introducing vertical structure coefficients helps improve the robustness of model training. The process is as follows: The vertical structure coefficients are calculated by substituting a preliminary estimate of forest height into a Fourier-Legendre polynomial and introducing a feature set. The vertical structure of the forest changes with forest height. A third-order Fourier-Legendre polynomial is used to describe the vertical structure of the forest scene, and the vertical structure coefficients are obtained by solving a nonlinear least squares method. 、 This data is added to the feature dataset and used as a feature parameter in the random forest model regression, as shown in the following formula: ; In the above formula, Indicates the vertical effective wavenumber. Represents the real part of a complex number. It represents the imaginary part of a complex number.

[0022] Step S4: Set up a feature dataset, including surface phase, volume coherence coefficient, volume coherence phase, vertical effective wavenumber, and vertical structure coefficient; collect a small amount of high-precision forest height data using LiDAR as supervised learning labels to form LiDAR forest height labels; use the feature dataset and the corresponding LiDAR forest height labels to train the random forest algorithm through ensemble learning regression to obtain the optimal random forest model. The training process is as follows: The random forest is trained using the feature dataset and LiDAR forest height labels. The random forest algorithm is used for training, and the optimal random forest model is determined based on minimizing the prediction error on the validation set. The process is as follows: The feature dataset includes surface phase, volume coherence coefficient, volume coherence phase, vertical effective wavenumber, and vertical structure coefficient. This feature dataset is used as training features, and LiDAR forest high-label data is used as supervised training labels. The training process is as follows: Random Forest (RF) randomly selects multiple subsets from the original training set... Decision Tree As a basic classifier This represents the input feature dataset. The prediction function of a single decision tree. Representing a sequence of random variables, training this The random forest model uses several decision trees, and then merges the predictions from each tree using a majority voting method to obtain the classification or prediction result. The expression for the random forest model is as follows: ； In the above formula, It is a collection of all categories. It is the number of decision trees. It is a category The average probability, It is the first Decision tree for each category The predicted probability, P represents the final classification probability.

[0023] Corresponding random variable sequence The generation strategy is as follows: (1) Random sampling of the sample, in constructing the first When building a decision tree, start from the original training sample set. The method of random sampling with replacement is used to generate a subset of the training set with the same size as the original sample set. This process is repeated. Next, get A set of independent training Each subset corresponds to a decision tree for training. In each resampling process, some original samples are selected, while the remaining samples are not included in the current sub-training set, thereby enhancing the differentiation between the learners. (2) Random feature selection: During the node splitting stage of the decision tree, the random forest does not search for the optimal splitting attribute in the entire feature space, but rather selects the optimal splitting attribute from the node splitting node. A subset of features is randomly selected with equal probability from each input feature. Only the optimal feature is selected from this subset for node partitioning, and the dimension of the selected feature subset is... Set as: ; in, This represents the total number of features, which can suppress the problem of strongly correlated features repeatedly dominating splits in all decision trees, thereby reducing the correlation between decision trees; Based on random sampling of samples and random selection of features, the first The sequence of random variables corresponding to each decision tree as follows: in, This represents a training subset randomly sampled by Bootstrap. This represents the randomly selected feature subset during node splitting. Since the sample selection process and feature selection process of each decision tree are independent, and the construction process of each decision tree is independent, the formula for the random variable sequence is as follows: It is considered as a set of independent and identically distributed random variables. The training process of random forest is essentially an independent training process for each decision tree, which is naturally suitable for parallel computing, thereby significantly improving the model training efficiency; Step S5: Use the optimal random forest model to regress and predict the forest height with high accuracy.

[0024] The experimental procedure is provided below: The Mabounie experimental area of ​​the AfriSAR project, located in the tropical rainforest region of central and western Gabon, is one of the key observation and experimental areas of the AfriSAR program. This area is dominated by typical evergreen tropical rainforest with continuous forest cover, well-developed vertical structure, and high canopy height. The forest stands exhibit a distinct layered structure, with the main vegetation types being mature tropical primary forest and some degraded tropical rainforest. The main tree height in mature forest is 40-60 meters, while in degraded forest it is 20 meters. Compared to experimental areas with localized open areas and structural differences, the Mabounie area has strong overall forest connectivity and less exposed ground, making it suitable as a representative area for stability analysis of the PolInSAR inversion method under high-coverage forest conditions.

[0025] All research data originated from airborne fully polarimetric SAR data from the AfriSAR project. LiDAR measurements of the corresponding region were completed in early March 2016 using a Land, Vegetation, and Ice Sensor (LVIS). This is a medium-sized (approximately 20m in diameter) full-waveform digital LiDAR. Due to cloud cover, the LiDAR data coverage in the Mabounie study area was discontinuous and incomplete in this experiment.

[0026] Since this invention uses the first three orders of Fourier-Legend polynomials to model the vertical structure of the forest, the solution of the vertical structure coefficients involves four unknown parameters. Therefore, at least two independent interferometric baselines need to be introduced as observation constraints during the parameter inversion process to solve for the unknown parameters. To further enhance the inversion constraints and improve the solution stability, three spatial interferometric baseline data were selected as inputs in the actual experiment. The observation baseline information is shown in Table 1 below: Table 1 PolInSAR data parameters for the experimental area

[0027] Using the above information, the experimental procedure is as follows: Preprocessing of multi-baseline fully polarimetric data to construct a coherence matrix T6, generating different complex coherence data based on different polarization modes. In this embodiment, ten polarimetric complex coherence product image data are selected: HH, HV, VV, HHmVV, HHpVV, OPT1, OPT2, OPT3, PDHigh, and PDLow (due to reciprocity, only HV and VH are selected). Based on a three-stage inversion method, the surface phase, volume scattering coherence phase, and volume scattering coherence coefficient of each pixel are obtained, denoted as: , , .

[0028] During the propagation of electromagnetic waves, the trajectory of the electric field vector changes over time and will produce different polarization modes. The phase difference of the complex coherence observation obtained by the phase-maximum separation coherence optimal (PhaseDiversity, PD) algorithm is large, which makes the estimation accuracy of the surface phase and the vegetation canopy phase higher and can more effectively distinguish between the forest canopy and the ground. In this embodiment, the experiment considers using PolInSAR data with three interferometric baselines in PDHigh polarization mode to substitute into the feature dataset, and the forest vertical structure coefficient is obtained based on the least squares estimation solution.

[0029] The input feature dataset was constructed using the RVOG model's three-stage process parameters, forest vertical structure coefficients, vertical effective wavenumbers, and multi-baseline multi-polarization data as training features. A supervised label dataset was constructed using corresponding LiDAR forest height measurements. Stratified random sampling was performed when splitting the label dataset to ensure that data from all heights were uniformly randomly selected. Learning and regression training were performed using the random forest method, with an initial number of decision trees of 500 and a minimum sample size limit of 3 for leaf nodes. Cross-validation was used to evaluate the model performance of the parameter combinations. The coefficient of determination, root mean square error, and mean absolute error were used as accuracy metrics. The optimal minimum sample size limit for leaf nodes was set to 5, and the number of decision trees was set to 500. Better results were ensured on the test set.

[0030] To facilitate comparative analysis, the same data was used to perform three-stage forest high inversion, PolInSAR forest high inversion based on random forest, PolInSAR forest high inversion based on random forest with the introduction of physical model features, and the PolInSAR forest high inversion based on random forest proposed in this paper that integrates physical model features and vertical structure features. The differences in forest high inversion results of different methods were compared and analyzed to verify the advantages and effectiveness of the proposed method.

[0031] Analysis of forest high inversion results as follows Figure 3 As shown, the forest high inversion results for each method are presented. Figure 3 (a) shows the forest high inversion results obtained using the three-stage method PolInSAR; Figure 3 (b) in the figure shows the PolInSAR forest high inversion results based on random forest; Figure 3 (c) in the figure represents the PolInSAR forest high inversion results based on the introduction of physical model parameter features; Figure 3 (d) in this paper represents the PolInSAR forest high inversion result based on random forest, which integrates the physical model parameter features and vertical structure features. Figure 3 (e) in the figure represents the high-precision forest inversion results obtained using LiDAR, which are used to compare and verify the high forest inversion accuracy of various methods. The specific analysis is as follows: from Figure 3 As can be seen in (a) of the data, the three-stage inversion method generally shows a certain underestimation trend in the Mabounie region, with insufficient clarity in the transition between high and low vegetation areas and relatively blurred spatial boundaries. Figure 3 In (b), the direct inversion results of PolInSAR data based on random forest show some improvement in overall spatial distribution compared to the three-stage method, but there is still a certain degree of systematic overestimation in some low-vegetation areas and a certain degree of underestimation in high-vegetation areas. Figure 3 In (c) of the paper, the inversion method based on random forest that incorporates physical model parameter features, and Figure 3 The method of the present invention in (d) shows a trend of further optimization in overall inversion effect. In comparison, the method of the present invention performs better in terms of local detail characterization, for example, in the region around pixel positions (1400, 2400) and (1900, 2700), compared with... Figure 3 As shown in (e) of the comparison of the true values, the texture contours are more similar and complete, and the spatial structure features are more clearly expressed. This phenomenon indicates that introducing vertical structure features helps to improve the accuracy and stability of forest height inversion based on random forests, demonstrating the application potential of the new method in complex tropical forest regions.

[0032] To further quantitatively analyze the forest height inversion results of each method, 6404 sample plots were uniformly selected from the test set for error statistics. Using LiDAR forest height product as the reference true value, the RMSE and R0 of the forest height inversion results for each method were calculated. 2 Furthermore, the forest height inversion results of each method were quantitatively analyzed, and the results were compared as follows: Figure 4 As shown, Figure 4 (a) shows the high inversion error distribution of forest in the three-stage method PolInSAR; Figure 4 (b) shows the high inversion error distribution of PolInSAR forest based on random forest; Figure 4 (c) in the figure represents the high inversion error distribution of PolInSAR forest based on the introduction of physical model parameter features; Figure 4 In the figure, (d) represents the error distribution of the proposed PolInSAR forest high inversion method. The specific accuracy indicators are compared in Table 2 below: Table 2. Accuracy Evaluation Indicators for Different Methods

[0033] Combining Table 2 above and Figure 4 It can be seen that within the experimental area, the traditional three-stage inversion results begin to show a systematic underestimation at forest heights above approximately 10m, with the scatter plot distribution gradually deviating from the diagonal, and its RMSE being 6.33m. The RMSE is 0.60. Direct inversion of PolInSAR data based on random forest exhibits some overestimation in low-vegetation areas and underestimation in high-forest areas, with the overestimation being more pronounced. The inversion method based on random forest, incorporating physical model parameter features, shows significant improvement over the previous two methods, reducing the RMSE to 3.46m. The RMSE also improved to 0.79. Compared to the previous three methods, the proposed new method exhibits a more concentrated forest high-inversion error distribution, closer to the diagonal, demonstrating better stability, and its RMSE further decreased to 2.82m. Improved to 0.86. Compared to the inversion results based on random forest that only incorporates the parameters of the three-stage process of the physical model, the inversion accuracy is improved by approximately 18.5%. (Overall) Figure 4 As analyzed in Table 2, by introducing vertical structural features, the new method significantly improved the accuracy and error distribution characteristics of forest high inversion in this experimental area, demonstrating a more prominent application advantage in the complex tropical forest region.

[0034] The comparison and analysis of the training features are as follows: This invention introduces three-stage process parameter variables (volume coherence coefficient) into the physical model. ), volume coherence phase ( ), surface phase ( ), Vertical wavenumber ( The vertical structure coefficient was further increased based on the previous one. , As a feature set, based on the interpretability of the random forest model, the output shows the evaluation results of the feature importance of the study area, comparing the importance of different features in the model under different forest scenarios, such as... Figure 5 As shown: from Figure 5 It can be seen that the volume coherence coefficient contributes the least to the model regression, while the vertical wavenumber, vertical structure coefficient, surface phase, and volume coherence phase information contribute significantly. The Mabounie region is dominated by medium-to-tall tree stands, with a relatively continuous and intact overall forest structure. Low-lying vegetation and extremely tall trees account for a small proportion. This distribution characteristic reflects that the forests in the Mabounie region are in a relatively mature growth stage, with good canopy continuity. Vertical volume scattering is mainly concentrated within the thicker canopy volume. In this case, the volume scattering contribution of the radar signal is not controlled by a single height layer, but is jointly influenced by the continuously distributed scatterers within the canopy. (Vertical structure coefficient) As a descriptive parameter for higher-order variations in the vertical structure of forests, it possesses a stronger and more sensitive characterization ability for canopy thickness, volumetric scattering distribution patterns, and vertical continuity. Therefore, in the Mabounie region, The contribution is higher than This reflects that forest height inversion relies more heavily on information about the internal structure of the canopy, rather than solely on the overall height scale.

[0035] Based on the above, we can conclude that the vertical structure coefficient and The two coefficients make significant contributions to the random forest model regression, and their differences in contribution to forest height inversion show good physical consistency with the higher-order representation characteristics of regional forest vertical structure features. This further illustrates that introducing vertical structure coefficients into the random forest inversion framework helps enhance the model's adaptability to the vertical structure features of different forest types.

[0036] Therefore, this invention employs a random forest method for radar forest height inversion incorporating structural features. Addressing the issue that conventional PolInSAR forest height inversion methods often fail to adequately account for the impact of complex forest vertical structures on forest height inversion in complex forest scenarios, leading to insufficient stability and reliability of the inversion results, this invention, based on the physical model expression of the PolInSAR observation mechanism, utilizes multi-baseline, multi-polarization observation information to extract physical model features and forest vertical structure features to construct a model training feature dataset. Furthermore, training labels are constructed using a small amount of LiDAR forest height data, proposing a PolInSAR forest height inversion method based on random forest that integrates physical model features and vertical structure features. Through theoretical analysis and experimental verification of forest height inversion in typical experimental areas, the results show that: (1) By establishing the mapping relationship between the physical model parameters and forest height through random forest, the potential correlation between observed variables and forest height can be explored more fully, thereby significantly improving the stability of forest height inversion.

[0037] (2) Introducing vertical structure coefficients to construct feature datasets can significantly enhance the model’s sensitivity to differences in forest structure, which helps to improve the stability and accuracy of forest overestimation, especially in areas with complex or highly heterogeneous forest structures.

[0038] (3) The PolInSAR forest high inversion experiment shows that the forest high inversion random forest method that integrates physical model features and forest vertical structure features improves the forest high inversion accuracy by 18.5% compared with the random forest method that only introduces physical model features, verifying the feasibility and effectiveness of the new method.

[0039] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A radar forest height inversion random forest method incorporating structural features, characterized in that: Includes the following steps: Step S1: Use polarimetric interferometric synthetic aperture radar to collect data, and establish a PolInSAR complex forest area scattering model based on the random ground body two-layer scattering model RVOG. The corresponding Fourier-Legend polynomial is used to describe the vertical structure characteristics of the forest. The process of establishing a forest scattering model is as follows: The random ground scattering model RVOG is set as a two-layer structure, including a forest scattering layer and a surface scattering layer, with a reference ground height of [missing information]. The forest height is The random volume scattering medium contains scattering particles that are uniformly and randomly distributed in space and exhibit isotropic scattering characteristics. The propagation and attenuation of electromagnetic waves in the vegetation layer adopts an exponential extinction model. The scattering mechanism in the forest scene includes volume scattering and surface scattering related to the ground surface. The expression of the RVOG scattering model is as follows: ； In the above formula, Indicates the polarization mode. Represents the imaginary number symbol, Represents the complex coherence coefficient. Indicates surface phase, This represents the volume decoherence coefficient caused solely by volume scattering. The volume amplitude ratio represents the ratio of power scattered from the Earth's surface to that scattered from the volume. This volume amplitude ratio varies with polarization; the volume decoherence coefficient... The expression is as follows: ； In the above formula, The forest vertical structure function represents the variation with penetration depth z. Represents forest height; volume-decoherent expression By changing the upper and lower bounds of the integral, we obtain the following formula: ； In the above formula, Indicates the vertical height relative to the Earth's surface reference plane. Vertical structure functions Indicates the vertical height relative to the Earth's surface reference plane. Extinction coefficient, The incident angle of the main imaging radar. Vertical effective wavenumber; In the RVOG scattering model, the Fourier-Legendal polynomial is used to express the changes in forest vertical structure: vertical structure function. The corresponding Fourier-Legend series expansion is as follows: ； In the above formula, Indicates the first The coefficients of the first-order polynomial control the vertical structure function. The form; Indicates the first The orthogonal normalized polynomial of order 1, corresponding to the Fourier-Legend polynomial defined on the interval [-1, 1], is as follows: ； Vertical structure function Substituting the Fourier-Legend series expansion into the volume decoherence expression of the transform integral upper and lower bounds The formula is as follows: ； ； In the above formula, Indicates the vertical effective wavenumber. With forest height and vertical effective wavenumber related; Indicates the altitude of the Earth's surface; Indicates forest height; 、 、 For the Fourier-Legend polynomial expansion term ； Represents the vertical structure coefficient, where The corresponding Fourier-Legend expansion is as follows: ； Reconstructing the forest vertical structure function using Fourier-Legend polynomials; Step S2: Solve the RVOG model using the three-stage method to obtain the initial values ​​of forest height and land surface phase; Step S3: Substitute the initial forest height into the Fourier-Legend polynomial model to calculate the vertical structure coefficients, and add the vertical structure coefficients to the feature dataset as feature parameters to participate in the random forest model regression. Step S4: Set up a feature dataset, including surface phase, volume coherence coefficient, volume coherence phase, vertical effective wavenumber, and vertical structure coefficient; collect a small amount of high-precision forest height data using LiDAR as supervised learning labels to form LiDAR forest height labels; use the feature dataset and the corresponding LiDAR forest height labels to train the random forest algorithm through ensemble learning regression to obtain the optimal random forest model. Step S5: Use the optimal random forest model to regress and predict the forest height with high accuracy.

2. The radar forest height inversion random forest method incorporating structural features according to claim 1, characterized in that: In step S1, the data collected is as follows: Polarimetric Interferometric Synthetic Aperture Radar (PISAR) is used to collect fully polarimetric SAR data via heavy orbit, obtaining main images and multi-track auxiliary images to form multi-baseline PolInSAR observation data.

3. The radar forest height inversion random forest method incorporating structural features according to claim 1, characterized in that: In step S2, the process of solving the RVOG model using the three-stage algorithm is as follows: Step S21: Coherence line fitting. Based on the scattering matrix of the main and auxiliary images, the polarization interference matrix is ​​obtained. Several complex coherence coefficients under polarization states are selected and regarded as discrete points within the unit circle of the complex plane. Linear fitting is performed on these points to determine the coherence line. Step S22: Surface phase estimation. After coherence line fitting in step S21, the fitted straight line intersects the complex plane unit circle at two points. HV polarization is considered as the volume scattering-dominated polarization mode. The terrane is relatively small, passing through two intersection points and The surface phase is determined by distance; the one furthest away is the surface phase. The criteria for judgment are as follows: ； In the above formula, 、 This represents the two intersection points of the coherence line and the unit circle. This represents the phase function used to determine the surface phase. Then, the other intersection point is the volume coherence point, from which the volume coherence coefficient is extracted. Volume coherence phase The formula is as follows: ； Step S23: Construct a two-dimensional lookup table. In the three-stage method, the unknown is the forest height. Extinction coefficient Ratio of Earth's amplitude By fixing the extinction coefficient or the earth amplitude ratio, construct and or and A two-dimensional lookup table is used to preset a range for the unknowns, and the lookup table is used to search for and display the correlation coefficient. Model volume coherence with minimum distance This allows for a preliminary estimate of the forest height.

4. The radar forest height inversion random forest method incorporating structural features according to claim 3, characterized in that: In step S3, the preliminary forest height estimate is substituted into the Fourier-Legendal polynomial to calculate the vertical structure coefficients. A feature set is introduced, as the vertical structure of the forest changes with its height. A third-order Fourier-Legendal polynomial is used to describe the vertical structure of the forest scene, and the vertical structure coefficients are obtained by solving the nonlinear least squares method. 、 This data is added to the feature dataset and used as a feature parameter in the random forest model regression, as shown in the following formula: ； In the above formula, Indicates the vertical effective wavenumber. Represents the real part of a complex number. It represents the imaginary part of a complex number.

5. The radar forest height inversion random forest method incorporating structural features according to claim 4, characterized in that: In step S4, the training process is as follows: The random forest is trained using the feature dataset and LiDAR forest height labels. The random forest algorithm is used for training, and the optimal random forest model is determined based on minimizing the prediction error on the validation set. The process is as follows: The feature dataset includes surface phase, volume coherence coefficient, volume coherence phase, vertical effective wavenumber, and vertical structure coefficient. The feature dataset is used as training features, and LiDAR forest high labels are used as supervised training labels. The training process is as follows: Random Forest (RF) randomly selects multiple subsets from the original training set to... Decision Tree As a basic classifier This represents the input feature dataset. The prediction function of a single decision tree. Representing a sequence of random variables, training this The random forest model uses several decision trees, and then merges the predictions from each tree using a majority voting method to obtain the classification or prediction result. The expression for the random forest model is as follows: ； In the above formula, It is a collection of all categories. It is the number of decision trees. It is a category The average probability, It is the first Decision tree for each category The predicted probability, P represents the final classification probability.

6. The radar forest height inversion random forest method incorporating structural features according to claim 5, characterized in that: Corresponding random variable sequence The generation strategy is as follows: (1) Random sampling of the sample, in constructing the first When building a decision tree, start from the original training sample set. The method of random sampling with replacement is used to generate a subset of the training set with the same size as the original sample set. This process is repeated. Next, get A set of independent training Each subset corresponds to a decision tree for training. In each resampling process, some original samples are selected, while the remaining samples are not included in the current sub-training set, thereby enhancing the differentiation between the learners. (2) Random feature selection: During the node splitting stage of the decision tree, the random forest does not search for the optimal splitting attribute in the entire feature space, but rather selects the optimal splitting attribute from the node splitting node. A subset of features is randomly selected with equal probability from each input feature. Only the optimal feature is selected from this subset for node partitioning, and the dimension of the selected feature subset is... Set as: ； in, This represents the total number of features, which can suppress the problem of strongly correlated features repeatedly dominating splits in all decision trees, thereby reducing the correlation between decision trees; Based on random sampling of samples and random selection of features, the first The sequence of random variables corresponding to each decision tree as follows: in, This represents a training subset randomly sampled by Bootstrap. This represents the feature subset randomly selected during node splitting. Since the sample selection process and feature selection process of each decision tree are independent, the formula for the random variable sequence is as follows: It is considered as a sequence of independent and identically distributed random variables.

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