A radar image difference recognition method based on scattering center modeling and deep learning

Abstract

A radar image difference recognition method based on scattering center modeling and deep learning is proposed. This method utilizes a Gaussian scattering center model to parametrically model the target scattering source, extracting features such as position, amplitude, width, and direction. An automatic thresholding method based on mutual information is employed for image registration. Optimal rigid body transformation parameters are obtained through cross-threshold search and derivative-free optimization, effectively eliminating geometric errors caused by imaging offset. A difference map is generated using a logarithmic ratio operator, and high-confidence pseudo-label samples are obtained through hierarchical fuzzy C-means clustering. Simultaneously, virtual sample generation technology is combined to expand the training set. Finally, a wavelet-constrained convolutional neural network is constructed, incorporating dual-tree complex wavelet transform to enhance direction sensitivity, achieving accurate classification and diagnosis of scattering source changes. This invention significantly improves radar image registration accuracy, change detection robustness, and model generalization ability, making it suitable for applications such as stealth target performance evaluation, radar image detection, and target recognition.

Description

Technical Field

[0001] This invention relates to the field of radar image recognition, and in particular to a radar image difference recognition method based on scattering center modeling and deep learning, for accurately detecting changes in scattering sources before and after a stealth target. Background Technology

[0002] During the service life of stealth weapons and equipment, their surface materials, structural details (such as steps and gaps), surface coatings, and electromagnetic parameters gradually change due to daily wear and tear and environmental erosion. These changes can lead to degradation of scattering characteristics, thus affecting the equipment's stealth performance. Therefore, during the periodic inspection and maintenance of equipment, it is urgent to use radar two-dimensional imaging to quickly diagnose the target's condition, accurately locate potential defects, and provide maintenance personnel with a reliable basis for repair. Current technology typically compares the currently measured radar two-dimensional image with a baseline image of the equipment in good condition to identify changes such as the addition, enhancement, or reduction of scattering sources, thereby achieving a precise assessment of changes in stealth performance.

[0003] However, to reliably identify changes in scattering sources, key technical challenges such as image registration, noise interference, and detection of subtle changes must be addressed. Specifically, existing methods have the following main shortcomings: (1) Low image registration accuracy: Traditional registration methods often rely on a single feature (such as SIFT), which is prone to failure under conditions of strong noise, low contrast or local deformation of the target, resulting in inaccurate subsequent difference analysis; (2) Poor robustness of change detection: Conventional clustering methods (such as fuzzy C-means clustering) are sensitive to intermediate classes and are prone to misjudging noise or pseudo-changes as real changes; (3) Weak generalization ability of the model: Traditional convolutional neural networks are prone to losing detailed information during pooling, making it difficult to capture small changes in scattering sources and affecting detection accuracy.

[0004] To address the aforementioned issues, a comprehensive approach that balances physical modeling accuracy, registration robustness, and deep learning recognition capabilities to achieve high-precision detection of changes in scattering sources of stealth targets has become a pressing technical challenge for existing technologies. Summary of the Invention

[0005] This invention aims to propose a radar image difference recognition method based on scattering center modeling and deep learning. By organically combining Gaussian scattering center modeling, adaptive image registration based on mutual information, and wavelet-constrained deep learning, high-precision recognition of radar image differences can be achieved. To achieve this objective, the invention adopts the following technical solution: A radar image difference recognition method based on scattering center modeling and deep learning, characterized by comprising: Scattering center modeling step S110: A Gaussian scattering center model is used to parameterize the scattering source. The scattering center is characterized by two-dimensional spatial position coordinates, peak amplitude, two principal axis widths and azimuth angles. A quadratic parabolic surface is fitted to the local area of ​​the radar image to eliminate system interference. The six-dimensional parameters are solved using the least squares method. Automatic image registration step S120 based on mutual information: Amplitude normalization and quantization are performed on two images to be registered. A candidate threshold set is constructed and reconstructed. For each image pair corresponding to a candidate threshold, the rigid body transformation parameters that maximize mutual information are solved to complete accurate registration in a single threshold scenario. Finally, the globally optimal threshold and the corresponding transformation parameters are selected as the final matching result to achieve robust geometric alignment of radar images. Difference map generation and sample construction steps S130: An initial difference map is generated using the log ratio operator to enhance the visibility of the changed regions. High-confidence pseudo-labels are extracted by hierarchical fuzzy C-means clustering. Virtual sample augmentation technology is used to expand the size of the training set. Neural network change detection and visualization analysis step S140: A wavelet-constrained convolutional neural network is constructed to detect changes in the difference map. This network uses dual-tree complex wavelet transform to replace the traditional pooling operation. After the change detection is completed, the results are briefly visualized and statistically processed. By labeling the enhancement or reduction of the scattering center and superimposing it on the original image, the changed area is presented intuitively. At the same time, basic statistics are performed on the changes in the number and amplitude of the change sources. Combined with multi-temporal image data, the overall trend of the scattering source changes is observed, providing an auxiliary reference for stealth performance evaluation.

[0006] The present invention further discloses an electronic device, including a processor and a memory, which are connected by a bus. The memory stores instructions or programs suitable for the processor to execute. When the processor executes the instructions or programs, it implements the steps of the radar image difference recognition method based on scattering center modeling and deep learning described above.

[0007] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the radar image difference recognition method based on scattering center modeling and deep learning described above.

[0008] In summary, the present invention has the following advantages: 1. Scattering center extraction: This invention uses six-dimensional parametric modeling of the Gaussian scattering center to accurately capture the core features such as the location and amplitude of the scattering source from a physical perspective. Combined with local parabolic fitting and least squares optimization, it ensures the accuracy and anti-interference of feature extraction, provides stable physical feature support for subsequent registration, and serves as the core comparison basis for difference detection. This avoids the limitations of traditional reliance on surface features and is conducive to the foundation of high-precision detection.

[0009] 2. Combining mutual information with a two-level structure optimizes registration results: Mutual information is used as a similarity metric, adapting to scenarios with strong noise and nonlinear grayscale changes in radar images, thus solving the problem of easy failure in traditional single-feature registration. By combining outer-layer threshold search with inner-layer derivative-free optimization, multiple imaging scenarios are covered, and rigid body transformation parameters are accurately solved, significantly improving registration accuracy and providing reliable geometrically aligned images for subsequent difference detection.

[0010] 3. Improved neural network and expanded detection sample: The difference map is enhanced by the log-ratio operator, and high-confidence samples are selected through hierarchical clustering. The sample size is then expanded to three times the original size using virtual samples, balancing training data quality and scale, and mitigating overfitting with small samples. The neural network introduces dual-tree complex wavelet transform to replace traditional pooling, preserving details and direction sensitivity. Combined with a dual-channel structure, it efficiently extracts features, accurately capturing subtle changes in scattering sources even at low signal-to-noise ratios. Its detection sensitivity and generalization ability are significantly superior to traditional methods.

[0011] 4. Multi-dimensional output to enhance engineering value: Through visualization, quantitative statistics, and trend analysis, multi-dimensional output results are provided. Color marking and transparency mapping make the changing areas intuitive and easy to understand. The quantification of core indicators provides an objective basis for performance evaluation, and multi-temporal trend analysis enables degradation early warning. Attached Figure Description

[0012] Figure 1 This is a flowchart of a radar image difference recognition method based on scattering center modeling and deep learning according to a specific embodiment of the present invention; Figure 2 The image shows the result of target scattering center extraction according to a specific embodiment of the present invention. The upper left is an image of the aircraft model without the ball attached, the upper right is the result after the scattering center is extracted, the lower left is an image of the aircraft model with the ball attached, and the lower right is the result after the scattering center is extracted. Figure 3 This is the image registration result according to a specific embodiment of the present invention; Figure 4 This is a flowchart of the difference diagram generation process according to a specific embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the generation of training samples according to a specific embodiment of the present invention; Figure 6This is a diagnostic result of changes in the scattering center according to a specific embodiment of the present invention. Detailed Implementation

[0013] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0014] This invention primarily involves: firstly, parametrically modeling the target scattering source using a Gaussian scattering center model to extract features such as position, amplitude, width, and direction; then, employing an automatic thresholding method based on mutual information for image registration, obtaining optimal rigid body transformation parameters through cross-threshold search and derivative-free optimization to effectively eliminate geometric errors caused by imaging offset; furthermore, generating a difference map using a logarithmic ratio operator and obtaining high-confidence pseudo-label samples through hierarchical fuzzy C-means clustering, while simultaneously expanding the training set using virtual sample generation technology; finally, constructing a wavelet-constrained convolutional neural network and fusing dual-tree complex wavelet transform to enhance directional sensitivity, achieving accurate classification and diagnosis of scattering source changes. This invention significantly improves radar image registration accuracy, change detection robustness, and model generalization ability, making it suitable for applications such as stealth target performance evaluation, radar image detection, and target recognition.

[0015] For details, see Figure 1 The flowchart of the radar image difference recognition method based on scattering center modeling and deep learning according to the present invention is shown, including the following steps: Scattering center modeling step S110: Changes in radar images essentially stem from changes in the target's scattering center (such as the addition, disappearance, amplitude increase / decrease, or positional shift of scattering sources). The scattering center is a localized region on the radar target that generates strong backscattering (such as equipment edges, gaps, or protrusions), and its radar echo can be approximated as the convolution of the target scatterer and the imaging system's impact response function. Therefore, this step mainly includes: A Gaussian scattering center model is used to parameterize the scattering source. The scattering center is characterized by two-dimensional spatial position coordinates, peak amplitude, two principal axis widths and azimuth angles. A quadratic parabolic surface is fitted to the local area of ​​the radar image to eliminate system interference. The six-dimensional parameters are solved using the least squares method.

[0016] This step is not only used for physical modeling of the scattering source, but also provides stable feature support for subsequent image registration, and lays a reliable comparative foundation for the final difference detection, making it easier to accurately identify the real changes in the scattering source.

[0017] Specifically, the steps include: Gaussian scattering center parameterization modeling sub-step S111: Based on the electromagnetic scattering mechanism and imaging system characteristics, two radar two-dimensional images of the target area are extracted, and a Gaussian scattering center model with six parameters including two-dimensional spatial position coordinates, peak amplitude, two principal axis widths and azimuth angles is constructed to characterize the spatial distribution and morphological characteristics of the scattering source.

[0018] Among them, the two-dimensional spatial position coordinates (x, y) describe the specific location of the scattering center in the radar image; Peak amplitude (A): Characterizes the backscattering intensity of the scattering source and is directly related to the electromagnetic scattering characteristics of the target; The two principal axis widths (σ1, σ2) describe the diffusion range of the scattering center in the two orthogonal principal axis directions, reflecting the geometry of the scattering source; Direction angle (θ): Characterizes the angle between the coordinate system formed by the two principal axes and the image coordinate system, reflecting the spatial orientation of the scattering source.

[0019] Therefore, this sub-step transforms the abstract scattering source into a quantifiable and computable set of parameters, providing a mathematical basis for subsequent fitting and optimization.

[0020] See Figure 2 The image shows an exemplary result of scattering center extraction according to the present invention, wherein the upper left is an image of the airplane model without the ball attached, the upper right is the result after scattering center extraction, the lower left is an image of the airplane model with the ball attached, and the lower right is the result after scattering center extraction.

[0021] Local parabolic fitting sub-step S112: The actual measurement system is affected by multiplicative noise and additive noise. However, in each resolution cell of the radar image, the target backscattering plays a dominant role, and the multiplicative noise effect can be ignored. The additive noise can be suppressed through subsequent filtering. Therefore, the Gaussian model is transformed into a quadratic parabolic form, which facilitates parameter fitting and local maximum detection.

[0022] The sub-step is as follows: for the local neighborhood (such as a 3×3 or 5×5 window) of each pixel in the measured radar image, fit it with a quadratic parabolic equation and extract the polynomial coefficients; The fitting results are used to determine whether there is a local maximum in the neighborhood (the local maximum point is the potential scattering center, because it corresponds to the strong echo region of the scattering source). If a local maximum exists, the initial position, amplitude, width, and orientation angle of the potential scattering center can be inferred from the parabolic fitting coefficients.

[0023] This sub-step can initially screen out candidate scattering centers, while eliminating convolution distortion caused by the system's impulse response and improving the basic accuracy of parameter extraction.

[0024] Sub-step S113 for optimizing scattering parameters: This sub-step is used to correct the parameter errors of the initial fitting, ensure the accuracy of the scattering center parameters, and meet the accuracy requirements of subsequent registration and change detection.

[0025] The specific sub-step is as follows: To improve modeling accuracy, a system of nonlinear equations was constructed based on the Hessian matrix, and the least squares method was used for iterative solution to optimize the six-dimensional parameters of the scattering center. The optimization objectives were to reduce the peak position error to less than 0.5 pixels and the relative error of the width parameter to less than 3%.

[0026] This sub-step corrects the initial parameters of the potential scattering center to high-precision, high-reliability final parameters, providing stable physical features for subsequent image registration.

[0027] Automatic image registration step S120 based on mutual information: Due to unavoidable attitude changes and measurement errors during radar imaging, subsequent difference detection will be severely hampered without precise registration. To achieve high-precision geometric alignment between two radar 2D imaging datasets, this invention employs an automatic thresholding image registration method based on mutual information (MI). Mutual information measures the statistical dependence between the grayscale distributions of two images, exhibiting robustness across imaging conditions and amplitude scale variations, making it particularly suitable for radar images in scenarios with high noise and significant nonlinear grayscale changes. This method utilizes a two-level structure of "outer threshold search + inner derivative-free optimization" to automatically select the optimal threshold and solve for rigid body transformation parameters, thereby obtaining the most robust registration result.

[0028] Therefore, this step includes: Amplitude normalization and quantization are performed on the two images to be registered. A candidate threshold set is constructed and reconstructed. For each image pair corresponding to the candidate threshold, the rigid body transformation parameters that maximize mutual information are solved to complete the accurate registration in the single threshold scenario. Finally, the globally optimal threshold and the corresponding transformation parameters are selected as the final matching result to achieve robust geometric alignment of radar images.

[0029] This step eliminates geometric biases in radar images, unifies image scale, constructs multi-threshold scenes, optimizes inner-layer parameters, and filters outer-layer thresholds to achieve high-precision geometric alignment between two radar images (reference image: baseline state image; floating image: state image to be detected). This eliminates interference from attitude changes and measurement errors for subsequent difference detection, ensuring that the generated difference image accurately reflects the true changes in the scattering source, rather than spurious changes caused by geometric biases.

[0030] Specifically, this step includes the following sub-steps: Amplitude normalization and quantization processing sub-step S121: For two radar images to be registered, i.e., reference images With floating chart Linear amplitude normalization is performed to reduce the impact of differences in dimensions and dynamic range, and the data is quantized to a fixed gray level, such as 256 gray levels, to obtain quantized image data, providing a unified gray space basis for subsequent registration processing.

[0031] This sub-step is used to ensure that the two images are consistent in "scale standard" to avoid misregistration due to differences in amplitude range.

[0032] Automatic threshold set construction and image reconstruction sub-step S122: This sub-step addresses the threshold sensitivity of radar images by covering different imaging states with multiple threshold scenarios, thus avoiding registration errors caused by a single threshold. Different thresholds filter out scattering signals of varying intensities in the image (high thresholds retain strong scattering signals, while low thresholds retain more detailed signals). Constructing a multi-threshold set allows for traversing various signal filtering scenarios, ensuring that the registration results are not limited by a single threshold.

[0033] Specifically, considering the sensitivity of radar data to thresholds, a set of discrete candidate thresholds, i.e., threshold set, is set according to the amplitude distribution of radar images. At each threshold, amplitude thresholding / reconstruction operations are performed on the quantized reference image and floating image to generate corresponding normalized image versions to cover different imaging states from strong noise suppression to detail preservation.

[0034] In one specific embodiment, a set of candidate thresholds is constructed. For each candidate threshold The quantized images were processed separately. , Perform amplitude thresholding / reconstruction operations to generate images at the corresponding thresholds. and This provides input data for subsequent registration calculations under different thresholds.

[0035] Therefore, this sub-step provides multiple sets of input data to ensure the robustness of the registration results under different signal screening scenarios.

[0036] Mutual information-driven rigid body registration steps S123: This step is used to solve for the rigid body transformation parameters that maximize mutual information for each candidate threshold image pair, thus completing accurate registration in single-threshold scenarios.

[0037] Specifically, a two-dimensional transformation is used to register the image, mutual information is used as the similarity measure, and the transformation parameters and threshold set are jointly optimized. Under each threshold, the Powell derivative-free optimization method is used to alternately perform one-dimensional line search in the three parameter directions of translation and rotation, with the goal of maximizing mutual information to solve for the optimal rigid body transformation parameters, until the gain of mutual information is lower than the set threshold or the parameter change tends to stabilize.

[0038] This sub-step belongs to the inner layer optimization, which realizes accurate registration in the single threshold scenario and provides the correspondence of "threshold-optimal parameter-maximum mutual information" for the outer layer threshold screening.

[0039] In one specific embodiment, a two-dimensional rigid body transformation is used for image registration. The transformation form is as follows: (1) in, Represents the pixel position of the image, transformation parameters , , These are the horizontal and vertical translation amounts, respectively. For rotation angle, For rotation matrix, Translation vector .

[0040] To evaluate the registration effect, mutual information was used as a similarity metric, and the transformation parameters were adjusted accordingly. With threshold set The above joint optimization, the objective function is as follows: (2) in, To be the optimal threshold, These are the optimal rigid body transformation parameters. Indicating in the candidate threshold set Select the threshold that maximizes the function value. , Indicates all rigid body transformation parameters Select the parameter that maximizes the function value. , These are the original two-dimensional radar images. , At the threshold The image obtained by amplitude thresholding / reconstruction, Indicates to Perform rigid body transformation The image obtained later, Mutual information is used to measure the degree of information coupling between two images.

[0041] The definition of mutual information is: (3) in: , Images , The gray distribution entropy, For image , The joint gray-level distribution entropy is calculated. This formula quantifies the statistical dependence of the gray-level distributions of two images by subtracting the joint entropy from the sum of the individual image entropies (the larger the value, the higher the registration accuracy). To avoid interference from boundary padding values ​​in the calculation results, mutual information is only statistically analyzed within the overlapping regions of the images; simultaneously, a minimal smoothing term is added to the probability estimation to avoid... This leads to numerical instability issues.

[0042] Since the mutual information pairs are not differentiable and are often accompanied by noise disturbances in radar images, this invention employs Powell's derivative-free optimization method for parameter search. Starting from the initial parameters, the method sequentially moves along the translation... With rotation The method employs a one-dimensional line search, generating new synthetic search directions through "displacement differences" and iteratively updating them until the mutual information gain falls below a set threshold or the parameter changes stabilize. This method requires no gradient information, is simple to implement, and is suitable for non-convex, non-differentiable objective functions such as mutual information.

[0043] Cross-threshold model selection sub-step S124: Since different thresholds correspond to different signal screening scenarios, their optimal mutual information value reflects the registration effect under that scenario. By selecting the threshold and transformation parameters corresponding to the global maximum mutual information value, the optimal registration result covering multiple scenarios can be obtained. This sub-step avoids the limitations of a single threshold through outer-layer search, and obtains the most robust registration result through cross-threshold screening, ensuring that subsequent difference detection is not affected by geometric bias.

[0044] Specifically, the maximum mutual information value corresponding to all candidate thresholds is collected, all maximum mutual information values ​​are compared, and the threshold corresponding to the maximum mutual information value is selected as the optimal threshold. The corresponding rigid body transformation parameter is used as the global optimal transformation parameter. The global optimal transformation parameter is applied to the original floating map to generate the registered floating map, thus completing the final registration of the two radar images, i.e., geometric alignment.

[0045] For details, see Figure 3 An example image registration result is shown.

[0046] In one specific embodiment, for each candidate threshold , For candidate threshold set The first in There are 1 candidate thresholds, and their corresponding values ​​at the threshold are recorded. The optimal mutual information value that can be achieved is... Choose the threshold that maximizes mutual information as the optimal threshold: (4) in, To determine the final optimal threshold, select the "corresponding optimal mutual information value" from all candidate thresholds. The maximum threshold, and the corresponding registration parameters. Substitute the rigid body transformation to generate the final registration result, thus achieving the registration of the two radar images.

[0047] Difference map generation and sample construction steps S130: Reliable change detection can only be performed after image registration is completed.

[0048] This step uses the log-ratio operator to generate an initial difference map to enhance the visibility of the changed regions and strengthen the distinction between real changes and noise. Then, high-confidence pseudo-labels are extracted through hierarchical fuzzy C-means clustering to provide reliable training samples for the deep learning model. Virtual sample augmentation technology is used to expand the size of the training set, thereby effectively alleviating the overfitting problem caused by small samples.

[0049] This series of processes provides the neural network with high-quality, low-noise, and sufficient training data, laying the foundation for subsequent change detection.

[0050] This step specifically includes the following sub-steps: Difference map generation and enhancement sub-step S131: This sub-step transforms the pixel differences between the two registered images into a visual and distinguishable difference map, while enhancing the recognition of subtle changes and suppressing spurious changes caused by noise.

[0051] Specifically, this includes: using a logarithmic ratio operator to calculate the initial difference map between the registered reference map and the floating map, and enhancing the contrast of the change area through nonlinear compression, with the pixel value range limited to [-3,3] to improve the recognizability of subtle changes.

[0052] In an optional embodiment, the logarithmic ratio operator is formulated as follows: (5) in, and These are two two-dimensional images to be compared. As a reference two-dimensional image, For comparison with two-dimensional images. Size and The same initial difference plot, Represents the natural logarithm. This method improves the distinguishability between changing and invariant classes. The process for generating the difference graph is as follows: Figure 4 As shown.

[0053] This sub-step transforms abstract image differences into intuitive difference maps, amplifying the signal intensity of real scattering source changes and providing clear input data for subsequent clustering.

[0054] Pre-classification sub-step S132: Traditional FCM clustering directly divides the difference map into two categories: "changed" and "unchanged". It is easy to misjudge the intermediate ambiguous areas (noise or weak pseudo-changes) as real changes. This sub-step reduces the proportion of intermediate classes and improves the reliability of samples by using two-level clustering and threshold screening.

[0055] Specifically, the basic fuzzy C-means (FCM) algorithm is used to initially divide the difference map into changed and unchanged classes, obtaining preliminary classification results. The FCM algorithm is then applied again to the difference map after the preliminary classification, dividing it into 5 subclasses. A confidence threshold is set, for example, 80%, and samples with confidence scores below the threshold are removed. The remaining 5 subclasses are sorted by average value and merged into 3 classes. The clustering parameters are adjusted to reduce the proportion of the intermediate class, for example, by compressing it to 15%, and finally, three pseudo-labels are obtained, representing the unchanged, changed, and intermediate classes, respectively.

[0056] This sub-step effectively reduces the proportion of intermediate class pixels, improving the reliability of training samples. It selects pseudo-label samples with high confidence changes and those that haven't changed for training the neural network, providing "clean" training data for the deep learning model and preventing the model from learning incorrect features. The intermediate classes are then further classified by the trained neural network.

[0057] Virtual sample enhancement sub-step S133: This sub-step generates virtual samples by linearly interpolating high-confidence pseudo-label samples. This preserves the characteristic patterns of the original samples while significantly expanding the training set size. It addresses the overfitting problem caused by the scarcity of real-world variation samples in radar image difference recognition scenarios, improving the model's generalization ability and stability.

[0058] Specifically, linear interpolation is performed on samples of the same category to expand the training set size to 2-4 times that of the original data, such as 3 times, to alleviate the problem of overfitting with small samples and improve model stability.

[0059] In one specific embodiment, after extracting a 3×3 block from the image, a neighborhood window is used as a training sample block, and edge pixels are padded with zeros to preserve boundary information. To expand the training set, a virtual sample generation strategy is adopted: (6) in, These are two pseudo-labeled training samples from the same category after clustering. It is an interval A random weight is applied within the sample. The generated virtual samples inherit the original class labels. A diagram illustrating the training sample generation is shown below. Figure 5 As shown.

[0060] Neural network change detection and visualization analysis step S140: After obtaining high-quality training samples, this step is used to generate a complete radar image difference recognition report through detection, visualization, statistics, and trend analysis, directly meeting the core needs of application scenarios such as stealth target performance evaluation and radar image detection.

[0061] Specifically, a wavelet-constrained convolutional neural network is constructed to detect changes in the difference map. This network uses dual-tree complex wavelet transform to replace traditional pooling operations, enhancing the sensitivity to changes in directional features and weak scattering sources, thereby achieving accurate identification of changed regions. After completing the change detection, the invention performs brief visualization and statistical processing on the results. By labeling the enhancement or weakening of scattering centers and superimposing them onto the original image, the changed regions are presented intuitively. At the same time, basic statistics are performed on the changes in the number and amplitude of change sources. Combined with multi-temporal image data, the overall trend of scattering source changes is observed, providing auxiliary reference for stealth performance evaluation.

[0062] This step includes the following sub-steps: Wavelet-constrained neural network diagnostic sub-step S141: A dual-channel input wavelet constrained neural network (CWNN) is constructed, replacing traditional pooling operations with dual-tree complex wavelet transform (DT-CWT) in the network structure. Wavelet domain features are directly integrated into the convolutional neural network (CNN), allowing the network to retain directional and phase information while downsampling. This enhances directional sensitivity and change detection capabilities. Efficient feature extraction is achieved by combining multi-layer deep separable convolutions. The CWNN is jointly trained using high-confidence pseudo-labeled samples and virtual samples to improve generalization ability. Intermediate samples are input into the network for testing. Finally, the clustering results of FCM and the classification results of CWNN are jointly processed to generate a change image containing both changing and invariant classes, achieving precise localization and display of changes in the scattering center.

[0063] In an optional embodiment, DT-CWT decomposes the convolutional layer output into eight subbands, including two low-frequency subbands and six directional high-frequency subbands: (7) The pooling layer output is the average of two low-frequency subbands: (8) The CWNN structure consists of three convolutional layers, two wavelet pooling layers, and one fully connected output layer. The input is a 28×28 image patch, and the output is the classification result of the variable class and the invariant class.

[0064] This sub-step solves the problem that traditional neural networks have difficulty capturing subtle changes in scattering sources, enabling high-precision change recognition in noisy and low signal-to-noise ratio scenarios.

[0065] For details, see Figure 6 The diagram illustrates the diagnostic results of scattering center changes according to a specific embodiment of the present invention. The upper left and upper right are aircraft models with filters applied at different locations. The middle left is a two-dimensional image of the upper left aircraft model, referred to as the reference two-dimensional image. The middle right is a two-dimensional image of the upper right aircraft model, referred to as the comparison two-dimensional image. The lower left is a variation diagram, showing the changes in the two two-dimensional images. The greater the magnitude of the change, the darker the color. The lower right is a difference diagram, which marks the position of the change relative to the reference two-dimensional image and the value of enhancement or reduction on the comparison two-dimensional image.

[0066] The results demonstrate that the method of this invention can accurately identify the scattering center variation region caused by the attachment of filter material. The dark areas in the variation diagram are highly consistent with the actual attachment positions, indicating that the mutual information registration and wavelet-constrained neural network of this invention can effectively suppress background noise and spurious changes, highlighting the changes in the true scattering source. Furthermore, the quantitative annotations of enhanced and weakened scattering in the difference diagram clearly reflect the changing trends of scattering intensity, providing an intuitive and reliable basis for stealth performance evaluation.

[0067] Sub-step S142 of the visualization analysis of changed areas: This step overlays the changes in the scattering center onto the original radar image, determines the type of change and color markings by comparing parameters, and transforms the abstract classification results into an intuitive and interpretable image, helping analysts quickly locate the changed area and determine the type of change (enhancement, weakening, addition, disappearance).

[0068] Specifically, by comparing the six-dimensional parameters (position, amplitude, etc.) of the scattering center in the reference image and the registered floating image, the type of change is determined by the position offset and amplitude change. When the amplitude offset and amplitude change exceed the threshold, it is determined to be a newly added or disappeared scattering source. When only the amplitude change exceeds the threshold and there is no significant position offset, it is identified as enhanced or weakened scattering. Different colors are used to represent enhanced or weakened sources. The confidence level of the change is mapped by transparency, a change layer is generated and superimposed on the original radar image to generate the final visualization result, which intuitively presents the spatial distribution and change attributes of the changed area.

[0069] In an optional embodiment, when the spatial offset of the scattering center exceeds 3 pixels and the amplitude change exceeds 3dB, it is determined as a "new scattering source" or a "disappeared scattering source"; when the amplitude change exceeds 3dB but the position does not shift significantly, it is determined as an "enhanced scattering source" or a "weakened scattering source". Color marking is performed according to the direction of amplitude change, with enhanced sources displayed in red and weakened sources displayed in blue.

[0070] This sub-step improves the interpretability of the results, reduces the difficulty for analysts to interpret them, and enables rapid location and qualitative judgment of areas of change.

[0071] Quantitative statistical sub-step S143 for sources of change: Quantitative analysis of the changed areas is performed, outputting specific statistical indicators, including the number of newly added or disappeared scattering sources, the average amplitude change value, and the spatial distribution density. This, combined with the target structure model, identifies whether the changed areas are located in critical locations. This provides quantitative indicator support for stealth performance evaluation.

[0072] The statistical results of this sub-step can be used to construct a change index matrix, providing data support for subsequent performance evaluation, condition monitoring and maintenance decisions, and further enhancing the system's sensitivity to and diagnostic capabilities for minor changes.

[0073] Trend analysis sub-step S144: This sub-step is used for trend analysis based on multi-temporal radar image sequences to achieve dynamic monitoring of the state evolution of stealth targets.

[0074] Specifically, by registering and detecting changes in images acquired at different times, a time-series change atlas is constructed, change indicators are extracted and trend models are performed, and by combining the spatial location and magnitude of the change areas, the rising, falling or abrupt change patterns of the change trend are identified to determine whether there are potential areas where stealth performance degrades.

[0075] This step can be used to model the time dimension by combining historical image sequences.

[0076] The analysis results can be used to generate trend charts and early warning prompts, providing technical support for the formulation of maintenance strategies and life prediction of stealth equipment.

[0077] The present invention further discloses an electronic device, including a processor and a memory, which are connected by a bus. The memory stores instructions or programs suitable for the processor to execute. When the processor executes the instructions or programs, it implements the steps of the radar image difference recognition method based on scattering center modeling and deep learning described above.

[0078] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the radar image difference recognition method based on scattering center modeling and deep learning described above.

[0079] In summary, the present invention has the following advantages: 1. Scattering center extraction: This invention uses six-dimensional parametric modeling of the Gaussian scattering center to accurately capture the core features such as the location and amplitude of the scattering source from a physical perspective. Combined with local parabolic fitting and least squares optimization, it ensures the accuracy and anti-interference of feature extraction, provides stable physical feature support for subsequent registration, and serves as the core comparison basis for difference detection. This avoids the limitations of traditional reliance on surface features and is conducive to the foundation of high-precision detection.

[0080] 2. Combining mutual information with a two-level structure optimizes registration results: Mutual information is used as a similarity metric, adapting to scenarios with strong noise and nonlinear grayscale changes in radar images, thus solving the problem of easy failure in traditional single-feature registration. By combining outer-layer threshold search with inner-layer derivative-free optimization, multiple imaging scenarios are covered, and rigid body transformation parameters are accurately solved, significantly improving registration accuracy and providing reliable geometrically aligned images for subsequent difference detection.

[0081] 3. Improved neural network and expanded detection sample: The difference map is enhanced by the log-ratio operator, and high-confidence samples are selected through hierarchical clustering. The sample size is then expanded to three times the original size using virtual samples, balancing training data quality and scale, and mitigating overfitting with small samples. The neural network introduces dual-tree complex wavelet transform to replace traditional pooling, preserving details and direction sensitivity. Combined with a dual-channel structure, it efficiently extracts features, accurately capturing subtle changes in scattering sources even at low signal-to-noise ratios. Its detection sensitivity and generalization ability are significantly superior to traditional methods.

[0082] 4. Multi-dimensional output to enhance engineering value: Through visualization, quantitative statistics, and trend analysis, multi-dimensional output results are provided. Color marking and transparency mapping make the changing areas intuitive and easy to understand. The quantification of core indicators provides an objective basis for performance evaluation, and multi-temporal trend analysis enables degradation early warning.

[0083] This invention features a high degree of automation throughout the entire process, requiring no manual intervention. It is suitable for batch processing needs and can be widely applied in fields such as stealth target performance evaluation. It provides comprehensive technical support for equipment maintenance and has strong engineering practicality.

[0084] Obviously, those skilled in the art will understand that the various units or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device, or alternatively, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by the computing device. Alternatively, they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0085] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection of the present invention as defined by the submitted claims.

Claims

1. A radar image difference recognition method based on scattering center modeling and deep learning, characterized in that, include: Scattering center modeling step S110: A Gaussian scattering center model is used to parameterize the scattering source. The scattering center is characterized by two-dimensional spatial position coordinates, peak amplitude, two principal axis widths and azimuth angles. A quadratic parabolic surface is fitted to the local area of ​​the radar image to eliminate system interference. The six-dimensional parameters are solved using the least squares method. Automatic image registration step S120 based on mutual information: Amplitude normalization and quantization are performed on two images to be registered. A candidate threshold set is constructed and reconstructed. For each image pair corresponding to a candidate threshold, the rigid body transformation parameters that maximize mutual information are solved to complete accurate registration in a single threshold scenario. Finally, the globally optimal threshold and the corresponding transformation parameters are selected as the final matching result to achieve robust geometric alignment of radar images. Difference map generation and sample construction steps S130: An initial difference map is generated using the log ratio operator to enhance the visibility of the changed regions. High-confidence pseudo-labels are extracted by hierarchical fuzzy C-means clustering. Virtual sample augmentation technology is used to expand the size of the training set. Neural network change detection and visualization analysis step S140: A wavelet-constrained convolutional neural network is constructed to detect changes in the difference map. This network uses dual-tree complex wavelet transform to replace the traditional pooling operation. After the change detection is completed, the results are briefly visualized and statistically processed. By labeling the enhancement or reduction of the scattering center and superimposing it on the original image, the changed area is presented intuitively. At the same time, basic statistics are performed on the changes in the number and amplitude of the change sources. Combined with multi-temporal image data, the overall trend of the scattering source changes is observed, providing an auxiliary reference for stealth performance evaluation.

2. The radar image difference recognition method according to claim 1, characterized in that: The scattering center modeling step S110 includes: Gaussian scattering center parameterization modeling sub-step S111: Based on the electromagnetic scattering mechanism and imaging system characteristics, two radar two-dimensional images of the target area are extracted, and a Gaussian scattering center model with six parameters including two-dimensional spatial position coordinates, peak amplitude, two principal axis widths and azimuth angles is constructed to characterize the spatial distribution and morphological characteristics of the scattering source. Local parabolic fitting sub-step S112: For the local neighborhood of each pixel in the measured radar image, a quadratic parabolic equation is used for fitting, and polynomial coefficients are extracted. The fitting results are used to determine whether there is a local maximum in the neighborhood. If there is a local maximum, the preliminary position, amplitude, width and orientation parameters of the potential scattering center are inferred from the parabolic fitting coefficients. Sub-step S113 for optimizing scattering parameters: A system of nonlinear equations was constructed based on the Hessian matrix, and the least squares method was used for iterative solution to optimize the six-dimensional parameters of the scattering center.

3. The radar image difference recognition method according to claim 2, characterized in that: In the sub-step S113 of optimizing the scattering parameters, the optimization objective is to have a peak position error of less than 0.5 pixels and a relative error of less than 3% for the width parameter.

4. The radar image difference recognition method according to claim 1, characterized in that: The automatic image registration step S120 based on mutual information includes: Amplitude normalization and quantization processing sub-step S121: For the two radar images to be registered, namely the reference image and the floating image, linear amplitude normalization is performed, and then quantized to a fixed gray level; Automatic threshold set construction and image reconstruction sub-step S122: Based on the amplitude distribution of the radar image, a set of discrete candidate thresholds, i.e., the threshold set, is set, and amplitude thresholding / reconstruction operations are performed on the quantized reference image and the floating image under each threshold to generate the corresponding normalized image version, so as to cover different imaging states from strong noise suppression to detail preservation; Mutual information-driven rigid body registration steps S123: Two-dimensional transformation is used for image registration, mutual information is used as the similarity measure, and joint optimization is performed on the transformation parameters and threshold set. Under each threshold, Powell's derivative-free optimization method is used to alternately perform one-dimensional line search in the three parameter directions of translation and rotation, with the goal of maximizing mutual information to solve for the optimal rigid body transformation parameters, until the gain of mutual information is lower than the set threshold or the parameter change tends to stabilize. Cross-threshold model selection sub-step S124: Collect the maximum mutual information value corresponding to all candidate thresholds, compare all the maximum mutual information values, select the threshold corresponding to the maximum mutual information value as the optimal threshold, and use the corresponding rigid body transformation parameter as the global optimal transformation parameter. Apply the global optimal transformation parameter to the original floating map to generate the registered floating map, and complete the final registration of the two radar images, i.e. geometric alignment.

5. The radar image difference recognition method according to claim 4, characterized in that: In the amplitude normalization and quantization processing sub-step S121, the number of gray levels is fixed at 256.

6. The radar image difference recognition method according to claim 1, characterized in that: The difference map generation and sample construction step S130 includes: Difference map generation and enhancement sub-step S131: The initial difference map is calculated using the log ratio operator between the registered reference map and the floating map, and the contrast of the change area is enhanced by nonlinear compression. The pixel value range is limited to [-3,3] to improve the recognizability of subtle changes. Pre-classification sub-step S132: The basic fuzzy C-means FCM algorithm is used to initially divide the difference map into changed and unchanged classes, obtaining preliminary classification results. The FCM algorithm is applied again to the difference map after preliminary classification, dividing it into 5 subclasses. A confidence threshold is set, and samples with confidence scores below the threshold are removed. The remaining 5 subclasses are sorted by average value and merged into 3 classes. The clustering parameters are adjusted to reduce the proportion of the intermediate class, and finally three pseudo-labels are obtained, representing the unchanged, changed, and intermediate classes, respectively. Virtual sample enhancement sub-step S133: Linear interpolation is performed on samples of the same category to expand the training set to several times the size of the original data, thus alleviating the problem of overfitting with small samples.

7. The radar image difference recognition method according to claim 6, characterized in that: In the pre-classification sub-step S132, the confidence threshold is 80%, and the proportion of the intermediate class is 15%. In the virtual sample enhancement sub-step S133, the training set size is expanded to 2-4 times that of the original data.

8. The radar image difference recognition method according to claim 1, characterized in that: The neural network change detection and visualization analysis step S140 includes: Wavelet-constrained neural network diagnostic sub-step S141: A dual-channel input wavelet constrained neural network is constructed. In the network structure, dual-tree complex wavelet transform (DT-CWT) replaces the traditional pooling operation, and wavelet domain features are directly integrated into the convolutional neural network (CNN). This allows the network to retain directional and phase information while downsampling. Combined with multi-layer deep separable convolution, efficient feature extraction is achieved. The wavelet constrained neural network is jointly trained with high-confidence pseudo-label samples and virtual samples. Intermediate samples are used to input the network for testing. Finally, the clustering results of FCM and the classification results of CWNN are jointly processed to generate a change image containing both change and invariant classes, achieving accurate localization and display of changes in the scattering center. Sub-step S142 of the visualization analysis of changed areas: By comparing the six-dimensional parameters of the scattering center in the reference image and the registered floating image, the type of change is determined by position offset and amplitude change. When the amplitude offset and amplitude change exceed the threshold, it is determined to be a newly added or disappeared scattering source. When only the amplitude change exceeds the threshold and there is no significant position offset, it is identified as enhanced or weakened scattering. Different colors are used to represent enhanced or weakened sources. The confidence level of the change is mapped by transparency, a change layer is generated and superimposed on the original radar image to generate the final visualization result. Quantitative statistical sub-step S143 for sources of change: The changes in the region are quantitatively analyzed, and specific statistical indicators are output, including the number of new or disappearing scattering sources, the average amplitude change value, and the spatial distribution density. The changes are then combined with the target structure model to identify whether the changes are located in critical areas. Trend analysis sub-step S144: Images acquired at different times are registered and change detected to construct a time series change atlas. Change indicators are extracted and trend models are performed. By combining the spatial location and magnitude of change in the change area, the rising, falling or abrupt change patterns of the change trend are identified, and it is determined whether there are potential areas where stealth performance degrades.

9. An electronic device comprising a processor and a memory, the processor and the memory being connected via a bus, the memory storing instructions or programs executable by the processor, characterized in that: When the processor executes instructions or programs, it implements the steps of the radar image difference recognition method based on scattering center modeling and deep learning as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the radar image difference recognition method based on scattering center modeling and deep learning as described in any one of claims 1-8.

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