Polarimetric SAR image classification method based on riemann-euclidean dual domain fusion

Abstract

The application discloses a polarimetric SAR image classification method based on Riemann-Euclidean dual domain fusion, and steps are as follows: step 1, data preprocessing and HPD matrix validity check; step 2, local geometric features of complex HPD manifold convolution are extracted, local feature aggregation on the Riemann manifold is realized based on complex weighted Frisch mean, always keeping the output as a legal HPD matrix, and hierarchical polarized scattering local features are extracted; step 3, global features of the Riemann-Euclidean dual domain are enhanced, and through a dual domain conversion mechanism, deep fusion of manifold local features and Euclidean global features is realized; and step 4, global classification decision and model output, long-range dependence between modeling features is realized through global attention interaction, and the probability distribution of the ground object category is output. The application belongs to the technical field of polarimetric synthetic aperture radar image processing and machine learning, and can significantly improve the ground object classification accuracy of the polarimetric SAR image.

Description

Technical Field

[0001] This invention belongs to the field of polarimetric synthetic aperture radar image processing and machine learning technology, and relates to a polarimetric SAR image classification method based on Riemann-Euclidean dual-domain fusion. Background Technology

[0002] Polarimetric SAR image classification is one of the core tasks in polarimetric synthetic aperture radar (PolSAR) remote sensing image classification processing. Its core data representation is the complex HPD covariance matrix, which naturally belongs to the Riemannian manifold space and contains key information about the polarimetric scattering amplitude and phase of the target. Traditional polarimetric SAR image classification methods are mostly based on Euclidean space design, vectorizing the HPD matrix, extracting its real part, or decoupling its real and imaginary parts before inputting it into a deep learning model. This processing method directly destroys the inherent Riemannian geometry of the HPD matrix and loses the correlation information of the polarimetric scattering phase, resulting in a significant decrease in feature discrimination ability. In heterogeneous regions, the classification accuracy is insufficient for practical applications. Even if some methods introduce polarimetric target decomposition to extract artificial features, they cannot capture high-dimensional semantic information, are sensitive to speckle noise, and are difficult to adapt to the classification needs of complex terrain scenes.

[0003] To preserve the geometric properties of the HPD matrix, researchers have proposed polarimetric SAR classification methods based on SPD / HPD manifolds. These methods linearize manifold features through Riemannian metrics and log-exponential mappings, extracting local features on the Riemannian manifold and effectively addressing the problem of geometric structure destruction. However, these methods can only capture scattering features in the local neighborhood of pixels and cannot model the global spatial context of the image, exhibiting significant locality limitations. Some methods attempt to fuse Riemannian and Euclidean space features, but often employ simple feature concatenation methods, failing to achieve deep collaborative learning of dual-domain features. Furthermore, manifold convolutions generally use real weights, failing to fully utilize the phase information of polarimetric scattering and making it difficult to accurately distinguish phase-dependent scattering structures such as dihedrals and dipoles. In addition, existing manifold deep learning methods are prone to destroying the positive definiteness and Hermitian symmetry of the HPD matrix during kernel function mapping and feature aggregation. Moreover, global feature modeling often uses fully connected layers, resulting in poor generalization ability and a tendency to overfit on small-sample polarimetric SAR datasets.

[0004] In summary, existing polarimetric SAR image classification methods suffer from problems such as geometric structure destruction, insufficient utilization of phase information, poor dual-domain feature fusion, insufficient local-global feature synergy, and low training stability, making it difficult to balance the preservation of the geometric characteristics of the HPD matrix with the learning ability of deep features. Summary of the Invention

[0005] The purpose of this invention is to provide a polarimetric SAR image classification method based on Riemann-Euclidean dual-domain fusion, which solves the problems of existing technologies such as destruction of HPD matrix geometry, loss of phase information, inefficiency of dual-domain feature fusion, and insufficient local-global feature coordination. At the same time, it ensures the numerical stability of model training and improves the accuracy and generalization ability of polarimetric SAR image land cover classification.

[0006] The technical solution adopted in this invention is a polarimetric SAR image classification method based on Riemann-Euclidean dual-domain fusion, implemented according to the following steps:

[0007] Step 1: Data preprocessing and HPD matrix validity verification; Step 2: Extract local geometric features of complex HPD manifold convolution, aggregate local features on the Riemannian manifold based on complex weighted Frescher mean, always keep the output as a valid HPD matrix, and extract hierarchical polarization scattering local features; Step 3: Enhance the global features of the Riemann-Euclidean dual domain by using a dual-domain transformation mechanism to achieve deep fusion of local features of the manifold and global features of Euclidean. Step 4, Global Classification Decision and Model Output: Through global attention interaction modeling of long-range dependencies between features, the probability distribution of land cover categories is output.

[0008] The beneficial effects of this invention are as follows: It employs Riemannian-Euclidean dual-domain fusion modeling, utilizing both the geometric structure of the HPD manifold and the global modeling capabilities of Euclidean space to fully exploit the scattering phase information and spatial context features of polarimetric SAR images; by optimizing the feature fusion method of complex-weighted Fréchet mean manifold convolution and Transformer global attention, it learns polarimetric features that possess both local geometric properties and global discriminative capabilities, improving feature differentiation and recognition; it combines Riemannian manifold geometric operations with deep learning, fully utilizing the automatic feature learning capabilities of deep networks; furthermore, the method employs multiple numerical stabilization mechanisms and a lightweight classification decision architecture, effectively ensuring the stability of end-to-end model training and reducing the risk of overfitting, resulting in a significant improvement in classification accuracy. Experiments show that compared to traditional Euclidean methods, single-manifold methods, and real-weighted manifold methods, the method of this invention can significantly improve the classification accuracy of polarimetric SAR images. Attached Figure Description

[0009] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a false color image of the fully polarimetric SAR of the Xian region in Embodiment 1 of the present invention; Figure 3 This is a diagram showing the effect obtained using the existing DFGCN method in Example 1; Figure 4This is a diagram showing the effect obtained using the existing HybridCVnet method in Example 1; Figure 5 This is a diagram showing the effect obtained by using the method of the present invention in Example 1; Figure 6 This is a fully polarimetric SAR pseudocolor image of the Flevoland region from Embodiment 2 of the present invention; Figure 7 yes Figure 6 Corresponding class label reference diagram; Figure 8 This is a diagram showing the effect obtained using the existing DFGCN method in Example 2; Figure 9 This is a diagram showing the effect obtained by using the method of the present invention in Example 2; Figure 10 This refers to the confusion matrix for classifying fully polarimetric SAR images of the Xian area using the existing HybridCVnet method in Example 3; Figure 11 This is the confusion matrix for classifying fully polarimetric SAR images of the Xian area using the method of the present invention in Example 3. Detailed Implementation

[0010] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0011] Reference Figure 1 The polarimetric SAR image classification method based on Riemann-Euclidean dual-domain fusion of the present invention is implemented according to the following steps: Step 1, data preprocessing and HPD matrix validity verification, the specific process is as follows: 1.1) Acquire polarimetric SAR image data and extract the 3×3 complex covariance matrix corresponding to each pixel in the image. This matrix is ​​the core representation of polarimetric SAR data and contains key information on the amplitude and phase of the target polarimetric scattering. 1.2) The extracted 3×3 complex covariance matrix is ​​validated for legality, with a focus on verifying two core properties: first, Hermitian symmetry, checking whether the 3×3 complex covariance matrix satisfies the condition that it is equal to its conjugate transpose, i.e., the diagonal elements are real numbers and the off-diagonal elements are conjugate complex numbers; second, positive definiteness, checking whether all eigenvalues ​​of the 3×3 complex covariance matrix are positive real numbers, ensuring that for any non-zero vector, the product of the vector's conjugate transpose and the matrix is ​​greater than 0. 1.3) Correction processing for complex covariance matrices that do not satisfy the HPD matrix properties: through... The operation forces Hermitian symmetry, where X refers to the 3×3 complex covariance matrix to be corrected; This indicates that the conjugate transpose operation is performed on the X matrix; the eigenvalues ​​less than 1e-6 are pruned to the lower bound and adjusted to above 1e-6 to avoid the values ​​approaching 0; let I be the identity matrix, add 1e-8×I for regularization to enhance the matrix's positive definiteness and robustness, and finally obtain all legal complex number HPD matrices that meet the conditions. 1.4) Use a 7×7 spatial neighborhood window to extract local features of each pixel, sample the original image data at a ratio of 15% to generate a training sample set, and divide the sampled samples into a training set and a validation set at a ratio of 3:7 to ensure that the samples of each category are evenly distributed. This completes the data preprocessing.

[0012] Step 2: Extract local geometric features from complex HPD manifold convolution. Aggregate local features on the Riemannian manifold using complex weighted Fréchet mean, ensuring the output remains a valid HPD matrix. Extract hierarchical polarimetric scattering local features. The original complex weights of the convolution kernel are normalized in magnitude and preserved in phase. The normalized magnitude is combined with the original phase to generate valid complex weights, achieving joint learning of polarization feature magnitude and phase. Then, the Fréchet mean is calculated recursively. Finally, HPD regularization is applied to ensure that the output always satisfies the HPD property. The specific process is as follows: 2.1) Construct two cascaded complex HPD manifold convolutional layers. The first layer is set to have 1 input channel and 8 output channels, and the second layer is set to have 8 input channels and 16 output channels. The kernel size of both layers is 3×3, the stride is 1, and the kernel weights are initialized to complex number type. The real and imaginary parts are initialized using Xavier uniform distribution to ensure the rationality of the initial weights. 2.2) Perform complex modulation processing on the convolution kernel weights: calculate the amplitude of each weight. , The magnitude of the i-th original complex weight parameter in the convolution kernel is normalized using the softmax function, resulting in: ,in, Let be the magnitude of the i-th original complex weight in the convolution kernel. The scaling factor is set to 10 to ensure a balanced contribution from different features; the original phase of the weights is preserved, ultimately generating valid complex weights. ,in, The phase angle of the i-th original complex weight in the convolution kernel; The imaginary unit; 2.3) Perform feature aggregation within the local receptive field window: Using a 7×7 neighborhood as the unit, iteratively aggregate the pixel-level 3×3 complex HPD covariance matrix within the window, after validity verification and correction, using the complex weighted Fréchet mean. Initialize the aggregation mean to the identity matrix I, and perform fusion calculation on each matrix within the window. The fusion formula is as follows: , in, It is the first t The aggregate mean of the next iteration. For the next HPD matrix to be aggregated, It is the modulated complex weight; 2.4) Three regularization measures are implemented during the aggregation process to ensure the HPD characteristics of the output matrix: upper and lower bounds are pruned on the modulated eigenvalues, limiting them to the range [1e-3, 1e3]; the aggregation result is then subjected to... The operation forces Hermitian symmetry to be maintained; 1e-3×I small unit matrix regularization is added to the matrix operation to enhance positive definiteness and robustness; and hierarchical local manifold features from basic scattering features to high-level discriminative features are extracted step by step through multi-layer convolution.

[0013] From this point on, the obtained polarization information features are used for subsequent dual-domain feature enhancement.

[0014] Step 3: Enhance the global features of the Riemann-Euclidean dual-domain model. Through a dual-domain transformation mechanism, achieve deep fusion of local features of the manifold and global features of Euclidean model, thus overcoming the locality limitations of manifold convolution. The specific process is as follows: 3.1) First stage, low-dimensional feature enhancement: Logarithmic mapping is performed on the low-dimensional HPD features output by the first layer of manifold convolution, and matrix eigenvalue decomposition is used. ,calculate The expression is as follows: , Where Y represents the low-dimensional HPD feature matrix output by the first layer of manifold convolution; This indicates that a Riemann logarithmic mapping is performed on the HPD feature matrix Y; , , These are the three eigenvalues ​​of the HPD feature matrix Y after eigenvalue decomposition; U represents the eigenvector matrix of the HPD feature matrix Y after eigenvalue decomposition. The superscript H represents the conjugate transpose of the eigenvector matrix U, and the superscript H indicates the conjugate transpose operation of the matrix. The manifold features are mapped to the Euclidean tangent space; the real and imaginary parts of the mapped features are separated and flattened, and concatenated into an 18-dimensional feature vector; a global Transformer extractor is constructed, including a feature projection layer, a positional encoding module, and a two-layer Transformer encoder. A multi-head self-attention mechanism is used to capture the global spatial context. After the features are restored to 18 dimensions via residual connections and projection layers, the result is calculated using exponential mapping. , in, This represents the tangent space matrix obtained by mapping 18-dimensional eigenvectors in Euclidean space after global feature enhancement by Transformer; This indicates that a Riemann exponent mapping is performed on the tangent space matrix Z to achieve the transformation from Euclidean features to Riemannian manifold features; , , These represent the three eigenvalues ​​after eigenvalue decomposition of the tangent space matrix Z; This represents the eigenvector matrix after the eigenvalue decomposition of the tangent space matrix Z; This represents the conjugate transpose of the eigenvector matrix V, with the superscript H indicating the conjugate transpose operation; Map back to the manifold space and feed it into the second manifold convolution; 3.2) Second stage, high-dimensional feature enhancement: For the high-dimensional HPD features output by the second layer manifold convolution, repeat the logarithmic mapping and feature vectorization operation in step 3.1); use the global Transformer extractor with the same configuration as the first stage to perform global feature enhancement, focusing on modeling the long-range dependencies of deep features and focusing on the global scattering difference patterns of easily confused ground objects; The enhanced 18-dimensional Euclidean features in the second stage are no longer mapped back to the manifold but are directly retained for subsequent classification decisions, achieving deep collaboration between local manifold features and global Euclidean features.

[0015] Step 4, Global Classification Decision and Model Output: This step models the long-range dependencies between features through global attention interaction, outputting the probability distribution of land cover categories. The specific process is as follows: 4.1) Perform global average pooling on the enhanced high-dimensional Euclidean features in the second stage, separate the real and imaginary parts of the features and flatten them respectively, and concatenate the two parts of the features into a unified feature vector of 16×3×3×2=288 dimensions to achieve the fusion and integration of dual-domain features. 4.2) Constructing a global classification network: Construct a classification network containing two Transformer encoder layers. Input features are transformed into 128-dimensional feature vectors through projection layers. The long-range dependencies between features are modeled through a multi-head self-attention mechanism, replacing the traditional fully connected layers and improving the model's feature discrimination ability. After the long-range dependencies are modeled by the Transformer encoder, two fully connected layers are connected, with ReLU activation function and Dropout layer added in between to prevent the model from overfitting. 4.3) Classification output: The output of the fully connected layer is normalized by the softmax activation function to obtain the probability distribution of the land cover category corresponding to each pixel. The dimension corresponding to the maximum probability is selected as the final classification result of the pixel, thus completing the accurate classification of multiple different land cover such as water, grassland, buildings and forests in the polarimetric SAR image.

[0016] Step 4 yields the final classification result.

[0017] Example 1 I. Classification criteria are as follows: 1) In the classification experiment, a 512×512 polarimetric SAR image data of a certain area was selected, and the 3×3 complex HPD covariance matrix corresponding to each pixel was extracted. The land features to be classified included three typical polarimetric SAR land features: water, grassland, and buildings. 2) In the classification experiment, a 7×7 spatial neighborhood window was used to extract the local features of each pixel. The original image data was randomly sampled at a ratio of 15% to generate a training sample set. The sampled samples were divided into a training set and a validation set at a ratio of 3:7 to ensure that the samples of each category were evenly distributed. 3) In the classification experiment, the core parameters of the model were set as follows: two layers of cascaded complex HPD manifold convolutional layers (number of input channels 1→8→16, kernel size 3×3, stride 1), the global feature extraction module adopted 2 layers of Transformer encoder, 4 attention heads, and the classification feature projection dimension was 128. 4) The experiment was built on the PyTorch framework, with GPU acceleration for training. The batch size was 128, the training epochs were 200, the optimizer was Adam, the initial learning rate was 0.001, and the learning rate adopted an adaptive decay strategy.

[0018] II. Following the steps described above in the method of this invention, the following steps shall be implemented: Step 1: Data preprocessing and HPD matrix validity verification. Input the complex covariance matrix of the polarimetric SAR data and verify whether the matrix satisfies the HPD property.

[0019] Step 2, local geometric feature extraction from complex HPD manifold convolution: Local feature aggregation on the Riemannian manifold is achieved based on complex weighted Fréchet mean, ensuring the output remains a valid HPD matrix. Hierarchical polarization scattering local features are extracted, specifically as follows: The original complex weights of the convolution kernel are normalized in magnitude and preserved in phase. The normalized magnitude is combined with the original phase to generate valid complex weights, realizing the joint learning of polarization feature magnitude and phase. Then, the weighted Fréchet mean is calculated recursively. Finally, HPD regularization is used to ensure that the output always meets the HPD characteristics. Step 3: Global feature enhancement of Riemann-Euclidean dual domains. Through the dual domain transformation mechanism, the deep fusion of local features of the manifold and global features of Euclidean is achieved, which makes up for the locality limitation of manifold convolution.

[0020] Step 4, Global Classification Decision and Model Output: Through global attention interaction modeling of long-range dependencies between features, the probability distribution of land cover categories is output.

[0021] III. The classification content and results analysis are as follows: Table 1 compares the results of Example 1 using the method of the present invention with other methods in the prior art.

[0022] Figure 2 A pseudo-color map of the fully polarimetric SAR in the Xian region; Figure 3 The classification results of the existing DFGCN method on the fully polarimetric SAR image of the Xian area are shown, with a classification accuracy of 89.10%. Figure 4 The classification result obtained by the existing HybridCVnet technology has a classification accuracy of 94.56%. Figure 5 This is the classification result of the fully polarimetric SAR image of the Xian area using the method of this invention (hereinafter referred to as Proposed), with a classification accuracy of 94.74%. It can be seen that... Figure 4 It will produce a lot of noise and cannot effectively suppress noise, while according to Figure 5 The method of the present invention shown can obtain more consistent classification results and has better performance. In the classification results, grassland, buildings, and other land cover categories are accurately identified, the boundaries between categories are clear, and the classification accuracy reaches 94.74%; the Kappa coefficient is 91.84%.

[0023] Example 2 I. Classification criteria are as follows: 1) In the classification experiment, polarimetric SAR image data of size 300×270 in Flevoland region were selected, and the 3×3 complex HPD covariance matrix corresponding to each pixel was extracted; 2) In the classification experiment, a 7×7 spatial neighborhood window was used to extract the local features of each pixel. The original image data was randomly sampled at a ratio of 15% to generate a training sample set. The sampled samples were divided into a training set and a validation set at a ratio of 3:7 to ensure that the samples of each category were evenly distributed. 3) In the classification experiment, the core parameters of the model were set as follows: two layers of cascaded complex HPD manifold convolutional layers (number of input channels 1→8→16, kernel size 3×3, stride 1), the global feature extraction module adopted 2 layers of Transformer encoder, 4 attention heads, and the classification feature projection dimension was 128. 4) The experiment was built on the PyTorch framework, with GPU acceleration for training. The batch size was 128, the training epochs were 200, the optimizer was Adam, the initial learning rate was 0.001, and the learning rate adopted an adaptive decay strategy.

[0024] II. The steps and processes described above in the method of the present invention are as follows, with specific steps and processes referred to in Example 1.

[0025] III. The classification content and results are as follows: Figure 6 This is a pseudocolor SAR image of the Flevoland region with full polarization, represented using the Pauli base as the RGB three-channel color representation. Figure 7 for Figure 6 The corresponding class label reference diagram shows that the white area has no reference class label. Therefore, the method of the present invention does not consider the classification results of the white area. In the reference diagram, the Flevoland region is divided into 6 categories. Figure 8 The image shows the classification results obtained by the existing technology, with a classification accuracy of 95.9%. Figure 9 This is a classification result image obtained after processing the Flevoland region's fully polarimetric SAR image using the method of this invention. The classification accuracy is 96.8%. It can be seen that... Figure 8 This method will result in many noise points and cannot effectively suppress noise, while the method of this invention can obtain more consistent classification results.

[0026] Example 3 I. Classification criteria are as follows: 1) In the classification experiment, a 512×512 polarimetric SAR image data of a certain area was selected, and the 3×3 complex HPD covariance matrix corresponding to each pixel was extracted. The land features to be classified included three typical polarimetric SAR land features: water, grassland, and buildings. 2) In the classification experiment, a 9×9 spatial neighborhood window was used to extract the local features of each pixel. The original image data was randomly sampled at a ratio of 15% to generate a training sample set. The sampled samples were divided into a training set and a validation set at a ratio of 3:7 to ensure that the samples of each category were evenly distributed. 3) In the classification experiment, the core parameters of the model were set as follows: two layers of cascaded complex HPD manifold convolutional layers (number of input channels 1→8→16, kernel size 3×3, stride 1), the global feature extraction module adopted 2 layers of Transformer encoder, 4 attention heads, and the classification feature projection dimension was 128. 4) The experiment was built on the PyTorch framework, with GPU acceleration for training. The batch size was 128, the training epochs were 200, the optimizer was Adam, the initial learning rate was 0.001, and the learning rate adopted an adaptive decay strategy.

[0027] II. The steps and procedures described above in the method of the present invention are as described in Example 1.

[0028] III. The classification content and results are as follows: Figure 10 The confusion matrix diagram is generated using the existing HybridCVnet method. Figure 11 This is the confusion matrix diagram of the fully polarimetric SAR image of the Xian area obtained by the method of this invention. It can be seen that... Figure 11 The fewer misclassifications will result, indicating that the method of the present invention can obtain more consistent classification results.

[0029] Example 4 I. Classification criteria are as follows: 1) In the classification experiment, a 512×512 polarimetric SAR image data of a certain area was selected, and the 3×3 complex HPD covariance matrix corresponding to each pixel was extracted. The land features to be classified included three typical polarimetric SAR land features: water, grassland, and buildings. 2) In the classification experiment, an 11×11 spatial neighborhood window was used to extract the local features of each pixel. The original image data was randomly sampled at a ratio of 15% to generate a training sample set. The sampled samples were divided into a training set and a validation set at a ratio of 3:7 to ensure that the samples of each category were evenly distributed. 3) In the classification experiment, the core parameters of the model were set as follows: two layers of cascaded complex HPD manifold convolutional layers (number of input channels 1→8→16, kernel size 3×3, stride 1), the global feature extraction module adopted 2 layers of Transformer encoder, 4 attention heads, and the classification feature projection dimension was 128. 4) The experiment was built on the PyTorch framework, with GPU acceleration for training. The batch size was 128, the training epochs were 200, the optimizer was Adam, the initial learning rate was 0.001, and the learning rate adopted an adaptive decay strategy.

[0030] II. The steps and processes described above in the method of the present invention are as follows, and other steps and processes are as described in Example 1.

[0031] III. The classification content and results are as follows: The method of this invention enables accurate classification of different land features such as water bodies, grasslands, and buildings, and can obtain better classification results.

[0032] Example 5 I. Classification criteria are as follows: 1) In the classification experiment, the 3×3 complex HPD covariance matrix corresponding to each pixel was extracted from the 300×270 polarimetric SAR image data of Flevoland region. 2) In the classification experiment, a 9×9 spatial neighborhood window was used to extract the local features of each pixel. The original image data was randomly sampled at a ratio of 15% to generate a training sample set. The sampled samples were divided into a training set and a validation set at a ratio of 3:7 to ensure that the samples of each category were evenly distributed. 3) In the classification experiment, the core parameters of the model were set as follows: two layers of cascaded complex HPD manifold convolutional layers (number of input channels 1→8→16, kernel size 3×3, stride 1), the global feature extraction module adopted 2 layers of Transformer encoder, 4 attention heads, and the classification feature projection dimension was 128. 4) The experiment was built on the PyTorch framework, with GPU acceleration for training. The batch size was 128, the training epochs were 200, the optimizer was Adam, the initial learning rate was 0.001, and the learning rate adopted an adaptive decay strategy.

[0033] II. The steps and processes described above in the method of the present invention are as follows, and other steps and processes are as described in Example 1.

[0034] III. The classification content and results are as follows: The method of this invention can achieve accurate classification of various land features and obtain better classification results.

[0035] Example 6 I. Classification criteria are as follows: 1) In the classification experiment, the 3×3 complex HPD covariance matrix corresponding to each pixel was extracted from the 300×270 polarimetric SAR image data of Flevoland region. 2) In the classification experiment, an 11×11 spatial neighborhood window was used to extract the local features of each pixel. The original image data was randomly sampled at a ratio of 15% to generate a training sample set. The sampled samples were divided into a training set and a validation set at a ratio of 3:7 to ensure that the samples of each category were evenly distributed. 3) In the classification experiment, the core parameters of the model were set as follows: two layers of cascaded complex HPD manifold convolutional layers (number of input channels 1→8→16, kernel size 3×3, stride 1), the global feature extraction module adopted 2 layers of Transformer encoder, 4 attention heads, and the classification feature projection dimension was 128. 4) The experiment was built on the PyTorch framework, with GPU acceleration for training. The batch size was 128, the training epochs were 200, the optimizer was Adam, the initial learning rate was 0.001, and the learning rate adopted an adaptive decay strategy.

[0036] II. The steps and processes described above in the method of the present invention are as follows, and other steps and processes are as described in Example 1.

[0037] III. The classification content and results are as follows: The method of this invention can achieve accurate classification of various land features and obtain better classification results.

Claims

1. A polarimetric SAR image classification method based on Riemann-Euclidean dual domain fusion, characterized in that, Follow these steps: Step 1: Data preprocessing and HPD matrix validity verification; Step 2: Extract local geometric features of complex HPD manifold convolution, aggregate local features on the Riemannian manifold based on complex weighted Frescher mean, always keep the output as a valid HPD matrix, and extract hierarchical polarization scattering local features; Step 3: Enhance the global features of the Riemann-Euclidean dual domain by using a dual-domain transformation mechanism to achieve deep fusion of local features of the manifold and global features of Euclidean. Step 4, Global Classification Decision and Model Output: Through global attention interaction modeling of long-range dependencies between features, the probability distribution of land cover categories is output.

2. The polarimetric SAR image classification method based on Riemann-Euclidean dual domain fusion according to claim 1, characterized in that, In step 1, the specific process is as follows: 1.1) Acquire polarimetric SAR image data and extract the 3×3 complex covariance matrix corresponding to each pixel in the image. This matrix is ​​the core representation of polarimetric SAR data and contains key information on the amplitude and phase of the target polarimetric scattering. 1.2) The extracted 3×3 complex covariance matrix is ​​validated for legality, with a focus on verifying two core properties: first, Hermitian symmetry, checking whether the 3×3 complex covariance matrix satisfies the condition that it is equal to its conjugate transpose, i.e., the diagonal elements are real numbers and the off-diagonal elements are conjugate complex numbers; second, positive definiteness, checking whether all eigenvalues ​​of the 3×3 complex covariance matrix are positive real numbers, ensuring that for any non-zero vector, the product of the vector's conjugate transpose and the matrix is ​​greater than 0. 1.3) Correcting the complex covariance matrix that does not meet the HPD matrix property: through Operation forces to achieve Hermite symmetry, X refers to the 3x3 complex covariance matrix to be corrected; Indicates the conjugate transpose operation on the X matrix; the lower bound of the eigenvalue less than 1e-6 is clipped to 1e-6 or above to avoid numerical approach to 0; set I as the unit matrix, add 1e-8xI for regularization to enhance the robustness of matrix positive definiteness, and finally get all legal complex HPD matrices that meet the conditions; 1.4) Use a 7×7 spatial neighborhood window to extract local features of each pixel, generate a training sample set, and divide the training set and validation set.

3. The polarimetric SAR image classification method based on Riemann-Euclidean dual domain fusion according to claim 2, characterized in that, In step 1.4), the original image data is sampled at a ratio of 15% to generate a training sample set, and the sampled samples are divided into a training set and a validation set at a ratio of 3:

7.

4. The polarimetric SAR image classification method based on Riemann-Euclidean dual domain fusion according to claim 1, characterized in that, In step 2, specifically: the original complex weights of the convolution kernel are normalized in magnitude and phase preserved. The normalized magnitude is combined with the original phase to generate valid complex weights, realizing the joint learning of polarization feature magnitude and phase. Then, the recursive weighted Fréchet mean is calculated. Finally, HPD regularization is used to ensure that the output always satisfies the HPD characteristics.

5. The polarimetric SAR image classification method based on Riemann-Euclidean dual domain fusion according to claim 1, characterized in that, Step 2, the specific process is as follows: 2.1) Construct two cascaded complex HPD manifold convolutional layers. The first layer is set to have 1 input channel and 8 output channels, and the second layer is set to have 8 input channels and 16 output channels. The kernel size of both layers is 3×3, the stride is 1, and the kernel weights are initialized to complex number type. The real and imaginary parts are initialized using Xavier uniform distribution to ensure the rationality of the initial weights. 2.2) Complex modulation processing on the convolution kernel weights: calculate the amplitude of each weight , is the i-th original complex weight parameter in the convolution kernel, and the amplitude is normalized by the softmax function to obtain , is the amplitude of the i-th original complex weight in the convolution kernel, is a scaling factor; the original phase of the weight is retained to finally generate a legal complex weight: , is the phase angle of the i-th original complex weight in the convolution kernel; is the imaginary unit; 2.3) Perform feature aggregation within the local receptive field window: Using a 7×7 neighborhood as the unit, iteratively aggregate the pixel-level 3×3 complex HPD covariance matrix within the window, after validity verification and correction, using the complex weighted Fréchet mean. Initialize the aggregation mean to the identity matrix I, and perform fusion calculation on each matrix within the window. The fusion formula is as follows: ， wherein, is the aggregated mean of the first t iterations, is the HPD matrix to be aggregated next, is the modulated complex weight; 2.4) Three regularization measures are implemented during the aggregation process to ensure the HPD characteristics of the output matrix: upper and lower bounds are pruned on the modulated eigenvalues, limiting them to the range [1e-3, 1e3]; the aggregation result is then subjected to... The operation forces Hermitian symmetry to be maintained; 1e-3×I small unit matrix regularization is added to the matrix operation to enhance positive definiteness and robustness; and hierarchical local manifold features from basic scattering features to high-level discriminative features are extracted step by step through multi-layer convolution.

6. The polarimetric SAR image classification method based on Riemann-Euclidean dual-domain fusion according to claim 5, characterized in that, In step 2.2), the scaling factor is set to 10.

7. The method of claim 1, wherein the method is a method of polarimetric SAR image classification based on Riemann-Euclidean dual domain fusion. Step 3, the specific process is as follows: 3.1) First stage, low-dimensional feature enhancement: Perform a logarithmic mapping on the low-dimensional HPD features output by the first layer manifold convolution, and calculate the expression of the following matrix eigenvalue decomposition The expression is as follows:​ ， wherein Y represents a low-dimensional HPD feature matrix of the first layer manifold convolution output; represents a Riemann logarithm mapping on the HPD feature matrix Y; , , are respectively three eigenvalues of the HPD feature matrix Y after eigenvalue decomposition; U represents an eigenvector matrix of the HPD feature matrix Y after eigenvalue decomposition; represents a conjugate transpose of the eigenvector matrix U, and the superscript H represents a conjugate transpose operation of a matrix. The manifold features are mapped to the Euclidean tangent space; the real and imaginary parts of the mapped features are separated and flattened, and concatenated into an 18-dimensional feature vector; a global Transformer extractor is constructed, including a feature projection layer, a positional encoding module, and a two-layer Transformer encoder. A multi-head self-attention mechanism is used to capture the global spatial context. After the features are restored to 18 dimensions via residual connections and projection layers, the result is calculated using exponential mapping. ， in, This represents the tangent space matrix obtained by mapping 18-dimensional eigenvectors in Euclidean space after global feature enhancement by Transformer; This indicates that a Riemann exponent mapping is performed on the tangent space matrix Z to achieve the transformation from Euclidean features to Riemannian manifold features; , , These represent the three eigenvalues ​​after eigenvalue decomposition of the tangent space matrix Z; This represents the eigenvector matrix after the eigenvalue decomposition of the tangent space matrix Z; This represents the conjugate transpose of the eigenvector matrix V, with the superscript H indicating the conjugate transpose operation; Map back to the manifold space and feed it into the second manifold convolution; 3.2) Second stage, high-dimensional feature enhancement: For the high-dimensional HPD features output by the second layer manifold convolution, repeat the logarithmic mapping and feature vectorization operation in step 3.1); use the global Transformer extractor with the same configuration as the first stage to perform global feature enhancement, focusing on modeling the long-range dependencies of deep features and focusing on the global scattering difference patterns of easily confused ground objects; The enhanced 18-dimensional Euclidean features in the second stage are no longer mapped back to the manifold but are directly retained for subsequent classification decisions, achieving deep collaboration between local manifold features and global Euclidean features.

8. The polarimetric SAR image classification method based on Riemann-Euclidean dual-domain fusion according to claim 1, characterized in that, Step 4, the specific process is as follows: 4.1) Perform global average pooling on the enhanced high-dimensional Euclidean features in the second stage, separate the real and imaginary parts of the features and flatten them respectively, and concatenate the two parts of the features into a unified feature vector of 16×3×3×2=288 dimensions to achieve the fusion and integration of dual-domain features. 4.2) Constructing a global classification network: Construct a classification network containing two Transformer encoder layers. Input features are transformed into 128-dimensional feature vectors through projection layers. The long-range dependencies between features are modeled through a multi-head self-attention mechanism, replacing the traditional fully connected layers and improving the model's feature discrimination ability. After the long-range dependencies are modeled by the Transformer encoder, two fully connected layers are connected, with ReLU activation function and Dropout layer added in between to prevent the model from overfitting. 4.3) Classification output: The output of the fully connected layer is normalized by the softmax activation function to obtain the probability distribution of the land cover category corresponding to each pixel. The dimension corresponding to the maximum probability is selected as the final classification result of the pixel, thus completing the accurate classification of multiple different land cover such as water, grassland, buildings and forests in the polarimetric SAR image.

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