Target recognition-based new reclamation GPR image space obstacle detection method and device
By combining dual-frequency ground-penetrating radar and the YOLO-SGISAC model, underground obstacles in newly reclaimed farmland can be efficiently identified, solving the problem of low efficiency in traditional detection methods and achieving rapid and accurate obstacle location.
Patent Information
- Application Number
- CN202511213808.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-28
- Publication Date
- 2025-12-12
- Estimated Expiration
- 2045-08-28
AI Technical Summary
Existing technologies are insufficient for efficiently identifying obstacles in the underground space of newly reclaimed farmland, which affects crop yields. Furthermore, traditional detection methods are inefficient, time-consuming, and labor-intensive.
Signals were acquired using a 400-900MHz dual-frequency ground-penetrating radar. After filtering and image enhancement, a YOLO-SGISAC target detection model was constructed to detect and identify obstacles in GPR images. The center coordinates of the target box were corrected by combining the soil dielectric constant.
It enables efficient identification of spatial obstacles in newly reclaimed farmland under non-technical conditions, quickly locates and resolves the mapping relationship from pixel level to the target's real coordinates, and improves detection efficiency.
Smart Images

Figure CN120703720B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of target detection technology, and in particular to a method and apparatus for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition. The method involves acquiring and processing ground-penetrating radar (GPR) scanning data using GPR post-processing software, and then inputting the data into the YOLO-SGISAC target detection model to achieve the detection and recognition of spatial obstacles in GPR images of newly reclaimed farmland. Background Technology
[0002] Land reclamation and consolidation are among the main ways to increase arable land area and alleviate the conflict between population and land. With the vigorous development of land reclamation and consolidation projects and their subsequent management, quality testing of newly reclaimed arable land has become a necessary task. However, current land consolidation projects still rely heavily on traditional testing methods, such as core drilling for verification, which suffers from problems such as randomness, low efficiency, and high time and labor costs. During land reclamation, excessively high levels of underground structural targets in newly reclaimed arable land significantly impact crop yields; relevant national standards have clear regulations regarding the content of underground structural targets. Summary of the Invention
[0003] The purpose of this invention is to overcome the shortcomings of the prior art and, in view of the current situation where non-technical personnel find it difficult to identify underground obstacles in newly reclaimed farmland using GPR images, provide a method and device for detecting spatial obstacles in farmland using GPR images based on target recognition.
[0004] To achieve the above objectives, the technical solution of the present invention includes the following steps: a method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition, the method comprising the following steps:
[0005] S1: Detection signals of the underground structure of newly reclaimed farmland obtained based on ground-penetrating radar;
[0006] S2: Filter the detection signal to obtain a GPR image that highlights edge details;
[0007] S3: Perform direct wave and background DC signal filtering operations on the GPR image;
[0008] S4: Perform image enhancement on the filtered GPR image to obtain diverse GPR spatial obstacle feature images;
[0009] S5: Label the diverse GPR spatial obstacle feature images to construct a spatial obstacle GPR image dataset;
[0010] S6: Construct a single-head target recognition network model YOLO-SGISAC that integrates serial path dynamic deformable convolution, supervise the training of the spatial obstacle GPR image dataset, and perform farmland underground obstacle detection based on the trained model. At the same time, output the center coordinates of the target box and correct the center coordinates of the target box by the soil dielectric constant.
[0011] Furthermore, in step S1, the ground penetrating radar is a 400-900MHz dual-frequency ground penetrating radar, with the sampling frequency of both channel one and channel two set to 10GHz, the number of sampling points to 512, and the sampling interval to 2cm, and the relevant detection tasks are carried out in range mode.
[0012] Furthermore, in step S2, bandpass filtering is used at 400 and 900 MHz to extract image edges and texture details and suppress smooth areas; at the same time, the high cutoff frequencies are 600 MHz and 1350 MHz respectively; and the low cutoff frequencies are 200 MHz and 450 MHz respectively.
[0013] Further, in step S2, the filtering process is as follows:
[0014] (1) Read the ground-penetrating radar signal data, convert it into txt format, and then convert it into two-dimensional data format;
[0015] (2) Reading the two-dimensional data Perform a two-dimensional discrete Fourier transform to obtain frequency domain data. The formula is as follows:
[0016]
[0017] in, and These represent the number of sampling points in the horizontal and vertical directions, respectively. , , , This represents the total number of sampling points. , Corresponding to the spatial domain and Frequency components in the direction, , For complex numbers; this transformation will change the image in the spatial domain. Convert to frequency domain This enables filtering operations on images in the frequency domain;
[0018] (3) Generate a frequency grid and calculate the distance from each frequency point to the frequency origin. The formula is as follows:
[0019]
[0020] In the frequency domain, to construct a filter, it is necessary to calculate each frequency point. to the frequency origin The distance;
[0021] (4) Constructing a filter: Constructing a bandpass filter by using the high and low cutoff frequencies of different channels of the dual-frequency ground penetrating radar. ,in and These are the distances corresponding to the low and high cutoff frequencies of the bandpass filter, respectively.
[0022] (5) Image in the frequency domain With bandpass filter Multiply to obtain the filtered frequency domain image. The result is then subjected to a two-dimensional inverse discrete Fourier transform to obtain the spatial domain filtered image. The formula is as follows:
[0023]
[0024] This transformation converts the filtering result in the frequency domain back to the spatial domain, resulting in the final filtered image.
[0025] Further, in step S3, the GPR image is filtered for direct waves and other DC interference signals. First, the direct waves are filtered out using an averaging removal method. The ground-penetrating radar data is read, converted into txt format, and then converted into two-dimensional data form, assuming a data matrix. Size is Calculate the average value of each row. , The formula is as follows:
[0026]
[0027] The above formula yields the data matrix for removing direct waves. , ,in Representing the OK The value of the column, Represents the first [number] after filtering OK The values of the columns are then applied to the entire matrix based on the weight matrix. Perform median filtering;
[0028] The weighted median is calculated using their respective weights to obtain the weighted set of elements. Subsequently Take the median to get a new value. .
[0029] Further, in step S4, the filtered GPR image is enhanced. First, the image is read, and if the image has a transparency channel, it is removed, converted to a grayscale image, and then converted to double precision type. The pixel values of the grayscale image are then mapped to the range of -32767 to +32767. Subsequently, the selected region features are enhanced with different intensities using MATLAB library functions. Finally, the pixel values after gain processing and range limiting are remapped to the range of 0 to 255.
[0030] Further, in step S5, labels are created for the enhanced GPR spatial obstacle feature images. The label category is "Anomalous areas" and the label is in YOLO format. The label dataset is randomly divided into training set, validation set and test set in a ratio of 7:2:1 for model training and testing.
[0031] Further, in step S6, the target detection network model consists of a backbone network, a neck network, and a detection head. The backbone network comprises 11 stages, including standard convolutional blocks, feature fusion modules, GS convolutional blocks, downsampling layers, inner convolution operators, spatial pyramid pooling layers, and a PSA attention mechanism. The neck network comprises 6 stages, including upsampling layers, feature splicing layers, feature fusion modules, and skip connections and serially dynamic deformable feature fusion modules in stages 4, 6, and 11 of the backbone network. Target detection is performed using a single detection head, and the network outputs the center coordinates of the target bounding box.
[0032] The aforementioned serial dynamic deformable feature fusion module replaces the standard convolution in the first stage of the bottleneck structure of the feature fusion module with a serpentine dynamic convolution and the standard convolution in the second stage with a linear deformable convolution, thus fusing the convolutions of the two with different dimensions and scale of concern into the feature fusion module.
[0033] Further, in step S7, the target box center coordinates are corrected using the soil dielectric constant based on the detection results. YOLO outputs the target box center coordinates as follows: The formula is as follows:
[0034]
[0035]
[0036] Where S is the number of grids. and The coordinates of the top-left corner of the grid cell. and This further refines the target's position within the grid cells;
[0037] Pixel-level mapping to true depth is used for coordinate correction, mapping GPR image pixels to the true temporal window depth. The formula is as follows:
[0038]
[0039] Where T is the preset time window depth, and the corrected... The coordinates are:
[0040]
[0041] in, At the speed of light, is the relative permittivity of the soil.
[0042] On the other hand, the present invention also provides a spatial obstacle detection device for newly reclaimed farmland GPR images based on target recognition, including a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it implements the aforementioned spatial obstacle detection method for newly reclaimed farmland GPR images based on target recognition.
[0043] Compared with existing technologies, the method for detecting spatial obstacles in farmland GPR images in this invention has the following advantages:
[0044] (1) The present invention adopts the improved YOLO-SGISAC target detection algorithm to achieve efficient spatial obstacle recognition without the need for relevant technical personnel;
[0045] (2) It solves the mapping relationship from pixel level to the actual coordinates of the target, and realizes fast target localization. Attached Figure Description
[0046] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0047] Figure 1 This is a logic block diagram of the spatial obstacle detection method for newly reclaimed farmland based on GPR images with target recognition, according to an embodiment of this application.
[0048] Figure 2 This is a logic block diagram of the filtering process in an embodiment of this application.
[0049] Figure 3 This is a structural diagram of the improved YOLO-SGISAC model according to an embodiment of this application.
[0050] Figure 4 This is a block diagram of the improved serial dynamic deformable feature fusion module in the YOLO-SGISAC model of this application embodiment.
[0051] Figure 5 This is a block diagram of the improved bottleneck structure in the YOLO-SGISAC model of this application embodiment.
[0052] Figure 6 This is a schematic diagram of the spatial obstacle detection device for newly reclaimed farmland GPR images based on YOLO-SGISAC, according to an embodiment of this application. Detailed Implementation
[0053] To more clearly illustrate the technical problems, technical solutions, and beneficial effects of this application, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.
[0054] The following detailed explanation illustrates the specific implementation methods:
[0055] This embodiment discloses a method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition. For example... Figure 1 As shown, it includes the following steps:
[0056] S1: The optimal frequency for both Channel 1 and Channel 2 of the 400-900MHz dual-frequency ground-penetrating radar is set to 10GHz, the optimal number of sampling points is 512, and the optimal sampling interval is 2cm, in order to acquire underground GPR scan images of farmland.
[0057] S2: Bandpass filtering is used at 400MHz and 900MHz to extract image edges and texture details and suppress smoothed areas. High cutoff frequencies are 600MHz and 1350MHz respectively; low cutoff frequencies are 200MHz and 450MHz respectively. See the logic block diagram. Figure 2 As shown, the filtering process is as follows: (1) Read the ground-penetrating radar data, convert it into txt format, and then convert it into two-dimensional data format; (2) Process the read two-dimensional data... Perform a two-dimensional discrete Fourier transform to obtain frequency domain data. The formula is as follows:
[0058]
[0059] in, and These represent the number of sampling points in the horizontal and vertical directions, respectively. , , ( (for complex numbers) , This represents the total number of sampling points. , Corresponding to the spatial domain and The frequency component of the direction. This transformation will change the image in the spatial domain. Convert to frequency domain This allows us to perform filtering operations on the image in the frequency domain; (3) Generate a frequency grid and calculate the distance from each frequency point to the frequency origin. The formula is as follows:
[0060]
[0061] In the frequency domain, to construct a filter, it is necessary to calculate each frequency point. to the frequency origin (4) Construct a filter by using the high and low cutoff frequencies of different channels of the dual-frequency ground-penetrating radar to construct a bandpass filter. ,in and These are the distances corresponding to the low and high cutoff frequencies of the bandpass filter, respectively. In this invention, their values are 400 and 900 MHz. Bandpass filtering is used to extract image edges and texture details and suppress smooth areas. Meanwhile, the high cutoff frequencies are 600 MHz and 1350 MHz, respectively; and the low cutoff frequencies are 200 MHz and 450 MHz, respectively. (5) The image in the frequency domain With bandpass filter Multiply to obtain the filtered frequency domain image. The result is then subjected to a two-dimensional inverse discrete Fourier transform to obtain the spatial domain filtered image. The formula is as follows:
[0062]
[0063] This transformation converts the filtering result in the frequency domain back to the spatial domain, resulting in the filtered image we ultimately need.
[0064] S3: Filter the GPR image for direct waves and other DC interference signals. First, filter out the direct waves using an averaging removal method. Read the ground-penetrating radar data, convert it to txt format, and then convert it to a two-dimensional data format, assuming a data matrix. Size is Calculate the average value of each row. , The formula is as follows:
[0065]
[0066] The above formula yields the data matrix for removing direct waves. , ,in Representing the OK The value of the column, Represents the first [number] after filtering OK The values of the columns are then used to perform median filtering on the entire matrix. This invention defines a new weight matrix. Its size is 3 3. The domain is the same (traditional median filtering), the central element of the weight matrix The weight is 2, and the weight of other domain elements is 1. The weighted median is calculated using the weights, resulting in the weighted set of elements. Subsequently Take the median to get a new value. .
[0067] S4: Enhance the GPR image after the secondary filtering. The algorithm pseudocode is shown in Table 1. First, read the image. If the image has an alpha channel (transparency channel), remove it, convert it to a grayscale image, and then convert it to double-precision type. This is done to avoid data overflow and improve calculation accuracy in subsequent pixel value mapping and calculation processes, because transparency information is usually not needed in subsequent processing, and unifying the image to grayscale format facilitates processing. Further, map the pixel values of the grayscale image to the range of -32767 to +32767. Then, use MATLAB library functions to enhance the selected region features with different intensities. Finally, remap the pixel values after gain processing and range limiting to the range of 0 to 255. This is because image display devices typically use the pixel value range of 0 to 255 to represent color intensity, so it is necessary to convert the processed pixel values back to this range for correct image display.
[0068] Table 1
[0069]
[0070] S5: Label the enhanced GPR spatial obstacle feature images. All labels are categorized as "Anomalous areas" and are in YOLO format. The labeled dataset is randomly divided into training, validation, and test sets in a 7:2:1 ratio for model training and testing.
[0071] S6: The YOLO-SGISAC single-detection-head target recognition network model, which integrates dynamic deformable convolutional paths and fused concatenated paths, mainly consists of a backbone network, a neck network, and a detection head. The network structure diagram is shown below. Figure 3 As shown, the backbone network consists of 11 stages: standard convolutional blocks, feature fusion module C2f, GS convolutional blocks, downsampling layers, inner convolution operators, spatial pyramid pooling layers, and PSA attention mechanisms. The neck network consists of 6 stages: upsampling layers, feature splicing layers, feature fusion module C2f, and skip connections and cascaded dynamic deformable feature fusion modules in stages 4, 6, and 11 of the backbone network. This invention proposes to use a single detection head for target detection. The structure diagram of the cascaded dynamic deformable feature fusion module is shown below. Figure 4 As shown. This invention replaces the standard convolution in the first stage of the serially dynamically deformable bottleneck module in the feature fusion module C2f with a serpentine dynamic convolution, and replaces the standard convolution in the second stage with a linear deformable convolution. This fuses the convolutions of different dimensions and scale concerns into the feature fusion module C2f. Its structure diagram is shown below. Figure 5 As shown in the image. Finally, the coordinates of the center of the target bounding box are output via the network.
[0072] S7: The target bounding box center coordinates are corrected using the soil dielectric constant based on the detection results. YOLO outputs the target bounding box center coordinates as follows: The formula is as follows:
[0073]
[0074]
[0075] Where S is the number of grids. and The coordinates of the top-left corner of the grid cell. and This further refines the target's position within the grid cells. In this invention, the YOLO image size is 512*512, and the radar image also uses 512 points. This invention proposes a coordinate correction method that maps pixel-level data to true depth, mapping GPR image pixels to the true time window depth. The formula is as follows:
[0076]
[0077] Where T is the preset time window depth, and the corrected... The coordinates are:
[0078]
[0079] in, At the speed of light, is the relative permittivity of the soil.
[0080] Corresponding to the aforementioned embodiment of a spatial obstacle detection method for newly reclaimed farmland GPR images based on target recognition, the present invention also provides an embodiment of a spatial obstacle detection device for newly reclaimed farmland GPR images based on target recognition.
[0081] See Figure 6 The present invention provides a spatial obstacle detection device for newly reclaimed farmland GPR images based on target recognition, comprising a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement a spatial obstacle detection method for newly reclaimed farmland GPR images based on target recognition as described in the above embodiment.
[0082] The embodiment of the spatial obstacle detection device for newly reclaimed farmland based on GPR images provided by this invention can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented through software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 2 The diagram shown is a hardware structure diagram of any device with data processing capabilities, which is an obstacle detection device for newly reclaimed farmland based on GPR images provided by the present invention. (Except for...) Figure 2 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.
[0083] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.
[0084] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.
[0085] This invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements a spatial obstacle detection method for newly reclaimed farmland GPR images based on target recognition, as described in the above embodiments.
[0086] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device of any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units and external storage devices of any data processing device. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.
[0087] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition.
[0088] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.
Claims
1. A method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition, characterized in that, The method includes the following steps: S1: Detection signals of the underground structure of newly reclaimed farmland obtained based on ground-penetrating radar; S2: Filter the detection signal to obtain a GPR image that highlights edge details; S3: Perform direct wave and background DC signal filtering operations on the GPR image; S4: Perform image enhancement on the filtered GPR image to obtain diverse GPR spatial obstacle feature images; S5: Label the diverse GPR spatial obstacle feature images to construct a spatial obstacle GPR image dataset; S6: Construct a single-head target recognition network model YOLO-SGISAC that integrates serial path dynamic deformable convolution, supervise the training of the spatial obstacle GPR image dataset, and perform farmland underground obstacle detection based on the trained model. At the same time, output the center coordinates of the target box and correct the center coordinates of the target box by the soil dielectric constant.
2. The method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition as described in claim 1, characterized in that: In step S1, the ground penetrating radar is a 400-900MHz dual-frequency ground penetrating radar. The sampling frequency of both channel one and channel two is set to 10GHz, the number of sampling points is 512, the sampling interval is 2cm, and the relevant detection tasks are carried out in range mode.
3. The method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition as described in claim 1, characterized in that: In step S2, bandpass filtering is used at 400 and 900 MHz to extract image edges and texture details and suppress smooth areas; at the same time, the high cutoff frequencies are 600 MHz and 1350 MHz respectively; and the low cutoff frequencies are 200 MHz and 450 MHz respectively.
4. The method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition as described in claim 1, characterized in that: In step S2, the filtering process is as follows: (1) Read the ground-penetrating radar signal data, convert it into txt format, and then convert it into two-dimensional data format; (2) Perform a two-dimensional discrete Fourier transform on the read two-dimensional data to obtain frequency domain data, and perform filtering operation on the image in the frequency domain; (3) Generate a frequency grid and calculate the distance from each frequency point to the frequency origin; (4) Construct a filter by using the high and low cutoff frequencies of different channels of the dual-frequency ground penetrating radar to construct a bandpass filter; (5) Multiply the frequency domain image with the bandpass filter to obtain the filtered frequency domain image. Then perform a two-dimensional inverse discrete Fourier transform on the result to obtain the spatial domain filtered image. Convert the frequency domain filtering result back to the spatial domain to obtain the final filtered image.
5. The method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition as described in claim 1, characterized in that: In step S3, the GPR image is filtered for direct waves using the average removal method and for background DC signals using the median filtering method.
6. The method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition as described in claim 1, characterized in that: In step S4, the filtered GPR image is enhanced. First, the image is read, and if the image has a transparency channel, it is removed, converted to a grayscale image, and then converted to double precision type. The pixel values of the grayscale image are further mapped to the range of -32767 to +32767. Then, the selected region features are enhanced with different intensities using MATLAB library functions. Finally, the pixel values after gain processing and range limiting are remapped to the range of 0 to 255.
7. The method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition as described in claim 1, characterized in that: In step S5, labels are created for the enhanced GPR spatial obstacle feature images. The label category is "Anomalous areas" and the label is in YOLO format. The label dataset is randomly divided into training set, validation set and test set in a ratio of 7:2:1 for model training and testing.
8. The method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition as described in claim 1, characterized in that: In step S6, the target recognition network model consists of a backbone network, a neck network, and a detection head. The backbone network comprises 11 stages, including standard convolutional blocks, feature fusion modules, GS convolutional blocks, downsampling layers, inner convolution operators, spatial pyramid pooling layers, and a PSA attention mechanism. The neck network comprises 6 stages, including upsampling layers, feature splicing layers, feature fusion modules, and skip connections and serial dynamic deformable feature fusion modules in stages 4, 6, and 11 of the backbone network. A single detection head is used for target detection, and the network outputs the center coordinates of the target bounding box. The aforementioned serial dynamic deformable feature fusion module replaces the standard convolution in the first stage of the bottleneck structure of the feature fusion module with a serpentine dynamic convolution and the standard convolution in the second stage with a linear deformable convolution, thus fusing the convolutions of the two with different dimensions and scale of concern into the feature fusion module.
9. The method for detecting spatial obstacles in GPR images of newly reclaimed farmland based on target recognition as described in claim 1, characterized in that: In step S6, based on the center coordinates of the target bounding box in the YOLO output detection result, the position of the target within the grid cell is obtained, the GPR image pixels are mapped to the real time window depth, and the center coordinates of the target bounding box are corrected by the soil dielectric constant.
10. A spatial obstacle detection device for newly reclaimed farmland based on GPR images using target recognition, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements a spatial obstacle detection method for newly reclaimed farmland GPR images based on target recognition, as described in any one of claims 1-9.
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