Highway pavement crack real-time identification method and system based on millimeter wave radar

Abstract

The invention relates to a highway pavement crack real-time identification method and system based on a millimeter-wave radar, and relates to the technical field of disease detection. The millimeter-wave radar is cooperated with an optical sensor, continuous scanning is performed on a pavement through the millimeter-wave radar, and multi-dimensional features are extracted for primary perception and probability determination; when a suspicious area is identified, an optical sensor is triggered to carry out high-precision image confirmation and crack identification, and finally crack information is output through decision fusion. Large-range and low-power-consumption primary perception is performed through the millimeter wave radar, and the optical sensor is triggered to perform high-precision imaging analysis on a specific area only when radar feature analysis shows that the crack possibility exists. The coarse-to-fine collaborative strategy effectively overcomes the limitation of a single sensor technology, high-precision pavement disease detection is realized, and the crack suspicion can be identified from the physical level first by directly capturing the electromagnetic wave physical property change caused by the crack.

Description

Technical Field

[0001] This invention relates to the field of highway pavement inspection technology, specifically to a method and system for real-time identification of highway pavement cracks based on millimeter-wave radar. Background Technology

[0002] Current technologies for detecting cracks in highway pavements largely rely on optical sensors and image processing techniques. These methods acquire pavement images using high-definition cameras and utilize computer vision algorithms for crack identification. However, optical detection methods are severely limited by ambient lighting and weather conditions. In low-visibility situations such as at night, in strong shadows, or during rain, snow, fog, or haze, image quality deteriorates sharply, leading to a significant reduction in recognition accuracy or even rendering the method inoperable. This makes it difficult to meet the urgent need for all-weather detection in highway maintenance.

[0003] Optical sensor technology is highly dependent on the environment, severely limited by ambient light and weather conditions. For example, in low-light scenarios such as nighttime or dusk, insufficient image brightness leads to blurred crack outlines, making feature extraction difficult. In rainy, snowy, foggy, or dusty weather, reduced visibility results in noise, glare, or occlusion in the image, significantly reducing recognition accuracy or even causing it to fail. Under strong shadow conditions, drastic changes in local light and dark on the road surface can easily be confused with crack features, leading to missed detections or false alarms. Furthermore, interference factors such as stains, shadows, and asphalt aggregates on the road surface are similar in characteristics to real cracks in two-dimensional images, easily causing misjudgments and resulting in a high false alarm rate.

[0004] Traditional image processing technologies consume enormous computational resources and have low efficiency because pure image processing methods typically require full-image analysis of a large number of high-resolution images, involving steps such as image preprocessing, feature extraction, and classification. In real-time vehicle detection scenarios, full-image processing consumes significant computational resources and storage space, leading to processing delays and making it difficult to achieve real-time response at high speeds. The high data transmission and processing load of high-resolution images increases system power consumption and hardware costs, limiting the feasibility of large-scale deployment. Furthermore, the low recognition efficiency makes real-time vehicle detection difficult to achieve. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for real-time identification of road surface cracks based on millimeter-wave radar. The system continuously scans the road surface using millimeter-wave radar. First, the echo signal is preprocessed in terms of range and Doppler dimensions, and micro-Doppler features and polarization scattering features are extracted to form a high-dimensional feature vector. The millimeter-wave radar performs large-area, low-power initial sensing, triggering optical detection only in suspicious areas, forming a coarse-to-fine collaborative strategy that effectively overcomes the limitations of a single sensor and achieves high-precision detection in all weather conditions. Subsequently, the electromagnetic wave characteristic changes caused by cracks are directly analyzed from a physical perspective, reducing dependence on the optical environment and significantly enhancing robustness under adverse conditions such as nighttime, rain, and fog. A primary classification model is used to calculate the probability of crack existence; when the probability exceeds a threshold, the area is identified as a region of interest and the optical sensor is triggered. Finally, the system integrates the optical results with geographic location information to output crack records and uses a feedback learning mechanism to continuously optimize the primary classification model, thereby continuously reducing the false alarm rate and improving the identification accuracy, thus solving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for real-time identification of road surface cracks based on millimeter-wave radar includes the following steps:

[0008] Step 1: Radar signal preprocessing: The road surface is continuously scanned by millimeter-wave radar, echo signals are received, and range and Doppler dimensions are preprocessed.

[0009] Step 2, Feature Extraction: Extract micro-Doppler features and polarization scattering features from the preprocessed radar data and combine them into a high-dimensional feature vector;

[0010] Step 3: Calculation and Judgment: Calculate the probability of the existence of the crack based on the high-dimensional feature vector. When the probability exceeds a preset threshold, it is determined to be a region of interest.

[0011] Step 4, Optical Conversion and Region Calibration: Based on the coordinate information of the region of interest, guide the optical sensor to capture the corresponding road surface area image block;

[0012] Step 5: Crack Calculation and Identification: Perform semantic segmentation on the captured image blocks to identify cracks and analyze their type and severity level;

[0013] Step 6, Decision Fusion and Output: Fusion of optical recognition results and geographic location information to generate crack records and output them. At the same time, the confirmation results are fed back to the calculation and judgment steps to optimize the model.

[0014] Preferably, for step one, the range dimension processing is to convert the signal from the time domain to the range domain using a fast Fourier transform to separate the target echo;

[0015] The Doppler processing is used to suppress stationary clutter and sense phase changes caused by cracks through second-dimensional fast Fourier analysis.

[0016] Preferably, regarding step two, the micro-Doppler feature is obtained by performing high-precision tracking of the phase of the radar echo signal, analyzing its subtle fluctuations over time, and capturing time-frequency features through short-time Fourier transform.

[0017] The polarization scattering characteristics are obtained by analyzing the amplitude and relative phase of the echo signals from different polarization channels to calculate the polarization ratio or polarization entropy parameter.

[0018] Preferably, for step three, the calculation and judgment steps use a support vector machine as the primary classification model, and the preset threshold value range is 0.6-0.7.

[0019] Simultaneously, by combining the distance and angle information from the radar, the two-dimensional coordinates of the suspicious area in the vehicle coordinate system are calculated.

[0020] Preferably, in step four, optical transformation and region calibration establish a mapping relationship between the radar coordinate system and the optical sensor pixel coordinate system through pre-calibrated spatial transformation parameters, converting the radar coordinates into specific pixel positions in the optical image.

[0021] Preferably, for step five, the crack calculation and identification uses a U-Net network with an encoder-decoder structure for semantic segmentation, outputs a crack segmentation mask, and performs post-processing on the segmented crack pixel clusters to calculate the direction and width of the skeleton lines and determine the crack type.

[0022] Preferably, for step six, the generated crack record includes crack outline, type, length and width, latitude and longitude coordinates and timestamp;

[0023] The feedback learning mechanism associates the result of each optical confirmation with the radar feature vector at the time of triggering to form training samples for optimizing the primary classification model.

[0024] A real-time road surface crack identification system based on millimeter-wave radar, used to implement a method for real-time identification of road surface cracks based on millimeter-wave radar, comprising:

[0025] Millimeter-wave radar is used to continuously scan the road surface. It transmits frequency-modulated continuous waves to the road surface at a high repetition frequency and simultaneously receives radar echo signals from the road surface. The radar echo signals are collected in real time and sent to the preprocessing module.

[0026] Optical sensors are used to acquire optical images of the road surface;

[0027] The preprocessing module is used to perform range dimension and Doppler dimension processing on radar echo signals;

[0028] The feature extraction module is used to extract micro-Doppler features, polarization scattering features, scattering intensity features and geometric distribution features from the preprocessed data. The extracted feature values ​​are combined into a high-dimensional feature vector.

[0029] The calculation and judgment module is used to perform weighted calculation and nonlinear transformation based on the high-dimensional feature vector transmitted by the feature extraction module, calculate the probability value of the credibility of the crack in the current area and determine whether it is an area of ​​interest, and determine whether to trigger the optical collaborative recognition process.

[0030] The image processing module is used to convert the precise coordinate information provided by the millimeter-wave radar and the precise mapping relationship between the radar coordinate system and the camera pixel coordinate system into the specific pixel position and area range in the high-definition camera image, and to extract the image block of the specific area.

[0031] The parsing module is used to identify, segment, and post-process cracks in image patches, determine the crack type, and assess the severity level.

[0032] The fusion and feedback module is used to bind crack information with precise geographical location, generate crack records, and transmit crack records to the human-computer interaction interface, cloud maintenance management platform, and local database respectively.

[0033] Preferably, the preprocessing module performs distance dimension processing through Fast Fourier Transform and Doppler dimension processing through second-dimensional Fast Fourier Analysis.

[0034] Preferably, the fusion and feedback module further includes a feedback learning mechanism, which is configured such that, regardless of whether the crack is confirmed as a real one or a false alarm, each confirmation result is associated with the feature vector extracted by the millimeter-wave radar at that time, forming a labeled training sample. The accumulated training samples are used to retrain or fine-tune the primary classification model, so that the initial judgment capability of the millimeter-wave radar can continuously improve itself as the usage time increases, forming a closed-loop system that becomes smarter with use.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] 1. This invention utilizes millimeter-wave radar for large-scale, low-power initial sensing. Only when radar feature analysis indicates the possibility of cracks is the optical sensor triggered to perform high-precision imaging analysis on a specific area. This coarse-to-fine collaborative strategy effectively overcomes the limitations of single-sensor technology, achieving all-weather, high-precision road surface defect detection, while reducing the overall computational load and energy consumption of the system and improving detection efficiency.

[0037] 2. The innovation of this invention lies in the feature extraction method of the millimeter-wave radar channel. The system does not rely on generating high-resolution radar images, but focuses on extracting multi-dimensional features that can characterize the physical nature of cracks from the radar data cube. It directly captures the changes in electromagnetic wave physical properties caused by cracks, and can identify suspected cracks from a physical level even under poor optical conditions. This provides a reliable triggering basis for optical confirmation and enhances the robustness of the system in complex environments such as night, rain, and fog.

[0038] 3. This invention also designs a closed-loop feedback learning mechanism. The result of each optical confirmation will be associated with the radar feature vector that triggered it, forming a new training sample for continuous optimization of the primary classification model. This allows the millimeter-wave radar's initial judgment capability to continuously evolve with the increase of usage time, possessing self-learning ability, gradually adapting to different road conditions, effectively reducing the false alarm rate, improving the recognition accuracy, and forming a virtuous cycle of becoming smarter with use. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the system architecture of the present invention;

[0040] Figure 2 This is a schematic diagram of the system flow of the present invention. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] To address the problems of current highway inspection systems that rely on optical detection, are limited by ambient light conditions, have low processing efficiency, and high false alarm rates, please refer to [link to relevant documentation]. Figure 1-2 This embodiment provides the following technical solution:

[0043] A real-time identification system for road surface cracks based on millimeter-wave radar is proposed. The entire system is deployed on a road inspection vehicle. The system uses the satellite positioning of the inspection vehicle to attach precise latitude and longitude coordinates and timestamps to all identification results. The identification process of road surface cracks through this system includes radar signal preprocessing, feature extraction, calculation and judgment, optical conversion and regional calibration, crack calculation and identification, and decision fusion and output.

[0044] I. Radar Signal Preprocessing Stage

[0045] After the system is started, the detection vehicle begins to travel along the highway.

[0046] The vehicle-mounted millimeter-wave radar begins to continuously scan the road surface, transmitting frequency-modulated continuous waves to the road surface at a high repetition frequency, and simultaneously receiving radar echo signals from the road surface. The radar echo signals are collected in real time and sent to the preprocessing module for preprocessing.

[0047] The first step in preprocessing is to perform range dimension processing, which uses Fast Fourier Transform to convert the signal from the time domain to the range domain, thereby distinguishing target echoes at different distances. The purpose is to separate road surface reflection echoes from other irrelevant background echoes.

[0048] The second step of preprocessing is to perform Doppler processing. Through second-dimensional fast Fourier analysis, the frequency differences caused by the relative motion between the vehicle and the road surface are distinguished. This step can effectively suppress stationary clutter and initially detect phase changes caused by microstructures such as cracks.

[0049] II. Feature Extraction Stage

[0050] After the initial processing of the radar signal is completed, the feature extraction and analysis stage of the millimeter-wave radar channel is entered. This stage is performed by the feature extraction module. This module does not form a high-resolution radar image, but extracts multi-dimensional features that can characterize the physical nature of the crack from the radar data cube. The multi-dimensional features include micro-Doppler features and polarization scattering features.

[0051] The first step is to extract micro-Doppler features, performing high-precision phase tracking of the radar echo signal and analyzing its subtle fluctuations over time. Because cracks disrupt the continuity and smoothness of the road surface, they cause distortion in the reflected wavefront. This distortion manifests as a unique phase nonlinearity under vehicle motion, appearing as specific sidelobes or spectral broadening on the time-frequency plot. These subtle time-frequency features are captured using short-time Fourier transform.

[0052] Secondly, polarization scattering characteristics are extracted. If the radar has dual-polarization or full-polarization capabilities, it analyzes the amplitude and relative phase of the echo signals from different polarization channels. As a linear anisotropic structure, cracks respond differently to electromagnetic waves of different polarizations compared to a uniform road surface, exhibiting enhancement of cross-polarization components or alterations in depolarization effects. The system calculates polarization characteristic parameters, including polarization ratio and polarization entropy. Finally, this module also extracts the target's scattering intensity and geometric distribution characteristics.

[0053] All these extracted feature values ​​are combined into a high-dimensional feature vector for subsequent intelligent judgment.

[0054] III. Calculation and Judgment Stage

[0055] The high-dimensional feature vector is fed into the calculation and judgment module by the feature extraction module for real-time inference and calculation. This module uses a pre-trained primary classification model, which is a lightweight support vector machine model. The model performs weighted calculation and nonlinear transformation on the input high-dimensional feature vector, and finally outputs a probability value between 0 and 1. This probability value represents the confidence that there is a crack in the current radar illumination area.

[0056] Simultaneously, by combining the distance and angle information from the radar, the two-dimensional coordinates of the suspicious area in the vehicle coordinate system are calculated. If the calculated probability value exceeds a preset threshold (0.6-0.7), the area is determined to be an area of ​​interest, and the optical collaborative recognition process is immediately triggered.

[0057] IV. Optical Conversion and Region Calibration Stage

[0058] Once the area of ​​interest is identified, the calculation and judgment module sends an alarm signal containing the coordinates of the suspicious area to the image processing module.

[0059] The image processing module uses the precise coordinate information provided by the millimeter-wave radar and calls the pre-calibrated spatial transformation parameters between the millimeter-wave radar and the high-definition camera. The spatial transformation parameters are obtained through joint calibration to establish a precise mapping relationship between the radar coordinate system and the camera pixel coordinate system. Using this mapping relationship, the coordinate information of the suspicious area provided by the radar is converted into the specific pixel position and area range in the high-definition camera image in real time.

[0060] Extracting a specific area from a video frame captured by a high-definition camera and then analyzing and processing only that area instead of the entire image can greatly save computing resources.

[0061] V. Crack Calculation and Identification Stage

[0062] Image patches are transmitted to the parsing module, which uses a conventional encoder-decoder semantic segmentation network U-Net. The encoder consists of multiple convolutional and pooling layers to extract multi-level features from the input image patches, while the decoder uses upsampling and skip connections.

[0063] The parsing module restores the feature map to its original image size and classifies each pixel, outputting a segmentation mask of the same size as the input image. On this mask, background pixels are marked as 0, and crack pixels are marked as 1. This method can finely delineate the meandering shape of cracks and effectively distinguish cracks from interfering factors such as road stains, shadows, and asphalt aggregate.

[0064] Finally, the segmented crack pixel clusters are post-processed to calculate the direction and width of their skeleton lines, automatically determine whether the cracks are horizontal, vertical, or mesh-like cracks, and assess their severity level.

[0065] VI. Decision Integration and Output Stage

[0066] This stage is performed by the fusion and feedback module, which binds the optically confirmed crack information with the precise geographic location information initially provided by the radar channel to generate a complete crack record. The crack record includes at least the specific outline, type, estimated length and width, latitude and longitude coordinates, and discovery timestamp of the crack.

[0067] All crack records are displayed in real time on the in-vehicle human-machine interface and simultaneously stored in a local database, and are periodically or in real time transmitted to the cloud maintenance management platform.

[0068] In addition, a feedback learning mechanism was designed in this stage. The feedback learning mechanism is set up so that each confirmation result is associated with the feature vector extracted by the millimeter-wave radar at that time, regardless of whether it is confirmed as a real crack or a false alarm, and forms a labeled training sample. These samples are accumulated and used to retrain or fine-tune the primary classification model, so that the initial judgment capability of the millimeter-wave radar can continuously improve itself as the usage time increases, forming a closed-loop system that becomes smarter with use.

[0069] Working Principle: This invention relates to a real-time road surface crack identification system based on millimeter-wave radar. Deployed on a detection vehicle, the system continuously detects road surfaces through vehicle movement. The system first uses millimeter-wave radar to transmit frequency-modulated continuous waves to the road surface and receives the echo signals for preprocessing. Preprocessing includes range-dimensional processing, which uses Fast Fourier Transform to convert the signal to the range domain to separate target echoes, and Doppler-dimensional processing, which analyzes frequency differences to suppress stationary clutter and detect phase changes caused by cracks. In the feature extraction stage, the system extracts multi-dimensional features from the radar data, including micro-Doppler features and polarization scattering features. Micro-Doppler features capture the time-frequency changes caused by cracks by analyzing phase fluctuations, while polarization scattering features identify crack structures using differences in different polarization channels. These features are combined into a high-dimensional feature vector for subsequent determination.

[0070] The calculation and judgment phase employs a primary classification model to perform real-time inference on feature vectors and output crack probability values. If the probability exceeds a preset threshold, the system identifies it as a region of interest and triggers optical collaborative recognition. The optical conversion phase maps radar coordinates to camera pixel coordinates and extracts image patches of suspicious areas to conserve resources. The crack recognition phase uses a semantic segmentation network to analyze the image patches, outputting a crack segmentation mask to distinguish cracks from interference factors and calculate crack type and level. Finally, the decision fusion phase binds the optical results with geographic location information, generating and outputting crack records. Simultaneously, the system accumulates samples through a feedback learning mechanism, continuously optimizing the primary classification model to achieve self-improvement.

[0071] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0072] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention.

Claims

1. A method for real-time identification of road surface cracks based on millimeter-wave radar, characterized in that, Includes the following steps: Step 1: Radar signal preprocessing: The road surface is continuously scanned by millimeter-wave radar to receive echo signals, and range dimension preprocessing and Doppler dimension preprocessing are performed. Step 2, Feature Extraction: Extract micro-Doppler features and polarization scattering features from the preprocessed radar data and combine them into a high-dimensional feature vector; Step 3: Calculation and Judgment: Calculate the probability of the existence of the crack based on the high-dimensional feature vector. When the probability exceeds a preset threshold, it is determined to be a region of interest. Step 4, Optical Conversion and Region Calibration: Based on the coordinate information of the region of interest, guide the optical sensor to capture the corresponding road surface area image block; Step 5: Crack Calculation and Identification: Perform semantic segmentation on the captured image blocks to identify cracks and analyze their type and severity level; Step 6, Decision Fusion and Output: Fusion of optical recognition results and geographic location information to generate crack records and output them. At the same time, the confirmation results are fed back to the calculation and judgment steps to optimize the model.

2. The method for real-time identification of road surface cracks based on millimeter-wave radar according to claim 1, characterized in that, Range-dimensional processing uses Fast Fourier Transform to convert the signal from the time domain to the range domain in order to separate the target echo; The Doppler preprocessing is performed by using second-dimensional fast Fourier analysis to suppress stationary clutter and detect phase changes caused by cracks.

3. The method for real-time identification of road surface cracks based on millimeter-wave radar according to claim 1, characterized in that, For step two, the micro-Doppler feature is used to analyze the subtle fluctuations in the phase of the radar echo signal over time by performing high-precision tracking, and the time-frequency features are captured by short-time Fourier transform. The polarization scattering characteristics are obtained by analyzing the amplitude and relative phase of the echo signals from different polarization channels to calculate the polarization ratio or polarization entropy parameter.

4. The method for real-time identification of road surface cracks based on millimeter-wave radar according to claim 1, characterized in that, For step three, the calculation and judgment steps use support vector machines as the primary classification model, and the preset threshold value range is 0.6-0.

7. Simultaneously, by combining the distance and angle information from the radar, the two-dimensional coordinates of the suspicious area in the vehicle coordinate system are calculated.

5. The method for real-time identification of road surface cracks based on millimeter-wave radar according to claim 1, characterized in that, For step four, optical transformation and region calibration establish a mapping relationship between the radar coordinate system and the optical sensor pixel coordinate system through pre-calibrated spatial transformation parameters, converting the radar coordinates into specific pixel positions in the optical image.

6. The method for real-time identification of road surface cracks based on millimeter-wave radar according to claim 1, characterized in that, For step five, the crack calculation and recognition uses a U-Net network with an encoder-decoder structure for semantic segmentation, outputs a crack segmentation mask, and performs post-processing on the segmented crack pixel clusters to calculate the direction and width of the skeleton lines and determine the crack type.

7. The method for real-time identification of road surface cracks based on millimeter-wave radar according to claim 1, characterized in that, For step six, the generated crack record includes crack outline, type, length and width, latitude and longitude coordinates and timestamp; The feedback learning mechanism associates the result of each optical confirmation with the radar feature vector at the time of triggering to form training samples for optimizing the primary classification model.

8. A real-time identification system for highway pavement cracks based on millimeter-wave radar, used to implement the real-time identification method for highway pavement cracks based on millimeter-wave radar as described in any one of claims 1-7, characterized in that, include: Millimeter-wave radar is used to continuously scan the road surface. It transmits frequency-modulated continuous waves to the road surface at a high repetition frequency and simultaneously receives radar echo signals from the road surface. The radar echo signals are collected in real time and sent to the preprocessing module. Optical sensors are used to acquire optical images of the road surface; The preprocessing module is used to perform range-dimensional preprocessing and Doppler-dimensional preprocessing on radar echo signals. The feature extraction module is used to extract micro-Doppler features, polarization scattering features, scattering intensity features and geometric distribution features from the preprocessed data. The extracted feature values ​​are combined into a high-dimensional feature vector. The calculation and judgment module is used to perform weighted calculation and nonlinear transformation based on the high-dimensional feature vector transmitted by the feature extraction module, calculate the probability value of the credibility of the crack in the current area and determine whether it is an area of ​​interest, and determine whether to trigger the optical collaborative recognition process. The image processing module is used to convert the precise coordinate information provided by the millimeter-wave radar and the precise mapping relationship between the radar coordinate system and the camera pixel coordinate system into the specific pixel position and area range in the high-definition camera image, and to extract the image block of the specific area. The parsing module is used to identify, segment, and post-process cracks in image patches, determine the crack type, and assess the severity level. The fusion and feedback module is used to bind crack information with precise geographical location, generate crack records, and transmit crack records to the human-computer interaction interface, cloud maintenance management platform, and local database respectively.

9. A real-time identification system for highway pavement cracks based on millimeter-wave radar according to claim 8, characterized in that, The preprocessing module performs distance dimension processing through Fast Fourier Transform and Doppler dimension processing through second-dimensional Fast Fourier Analysis.

10. A real-time identification system for highway pavement cracks based on millimeter-wave radar according to claim 8, characterized in that, The fusion and feedback module also includes a feedback learning mechanism, which is set up so that, regardless of whether it is confirmed as a real crack or a false alarm, the result of each confirmation is associated with the feature vector extracted by the millimeter-wave radar at that time, and a labeled training sample is formed. The accumulated training samples are used to retrain or fine-tune the primary classification model.

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