Coal rock CT fracture fracture repair and connection method based on deep learning

Abstract

This invention discloses a deep learning-based method for repairing and connecting fractures in coal and rock CT images, belonging to the interdisciplinary fields of digital core image processing and mining rock physics. Addressing the common problems of non-physical fractures, topological disconnections, and loss of width information in coal and rock CT image segmentation using deep learning, this invention constructs a fully automated repair scheme involving fracture skeleton extraction and endpoint detection, distance and direction dual-constraint endpoint pairing, Bresenham line connection and adaptive width recovery, and greedy iterative global connectivity reconstruction. This invention can seamlessly integrate with various deep learning segmentation models, accurately connecting only the actual fracture locations to maximize the preservation of the original fracture network topology. Simultaneously, it can adaptively recover the actual fracture width at the fracture site, eliminating the bottleneck effect of manual intervention. The entire process requires no manual intervention and can process massive amounts of CT slices in batches, providing accurate basic data for 3D digital core reconstruction, seepage simulation, and coal and rock mechanical stability evaluation.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of digital core image processing and computational topology, specifically involving a method for intelligent repair and topological connection of fractures and breaks based on deep learning segmentation results in CT images of coal and rock industry, which falls under the category of integrated application of mining rock physics and computer vision. Background Technology

[0002] Accurate extraction of the internal fracture network of coal and rock is a crucial prerequisite for constructing digital cores and conducting seepage simulations and mechanical stability assessments. Industrial CT scanning technology provides a powerful tool for non-destructive acquisition of the microstructure of coal and rock. However, due to factors such as the resolution limitations of CT equipment, low contrast caused by the heterogeneity of coal and rock matrix density, and interference from mineral infilling, the original CT images often exhibit weak fracture grayscale and blurred boundaries, posing a significant challenge to accurate fracture extraction.

[0003] Currently, deep learning-based semantic segmentation algorithms (such as U-Net and DeepLabV3+) have been widely applied in coal and rock fracture extraction tasks. These methods learn deep features through a large number of labeled samples and can robustly identify the main fracture morphology. However, due to the limitations of the model's receptive field and the local characteristics of class activation mapping, severe non-physical fracture phenomena generally exist in the binarized segmentation results in low-contrast regions. That is, the originally spatially continuous fracture structure is misjudged as background in micro-locations, forming numerous isolated and short fracture segments. This directly leads to the distortion of the topological connectivity of the subsequently constructed three-dimensional fracture network and seriously underestimates key physical parameters such as coal and rock permeability.

[0004] Traditional post-processing methods typically employ morphological closing operations to close gaps, mathematically expressed as performing dilation and erosion sequentially on the binary image B: Where K is a structural element of fixed size. and These represent expansion and corrosion operations, respectively. This method has significant inherent drawbacks: fixed-scale structuring elements cannot adapt to fractures of varying widths; small-scale structuring elements struggle to close large gaps, while large-scale structuring elements easily cause erroneous adhesion between adjacent independent fractures, disrupting the original topology; furthermore, the closing operation cannot restore the original fracture width at the fracture location, resulting in repaired fractures retaining only single-pixel connections at the fracture point, creating a "bottleneck effect" that severely impacts the physical accuracy of subsequent seepage simulations; simultaneously, this method lacks constraints on fracture orientation, easily leading to lateral connections that violate physical laws.

[0005] Current research and development focuses primarily on optimizing the structure of deep learning segmentation models themselves, with very little research on post-processing repair schemes for fractures after segmentation. Existing schemes often suffer from low automation, poor topological fidelity, and an inability to adaptively recover fracture widths, failing to meet the demands of batch processing of massive amounts of coal and rock CT slices and high-precision reconstruction of 3D digital cores. Therefore, there is an urgent need for an automated post-processing repair method that intelligently identifies fracture locations, accurately matches fracture endpoints, and adaptively recovers fracture widths from the binarized images extracted by deep learning. This method would address the core issues of fracture fragmentation, topological disconnection, and loss of width information in existing deep learning segmentation results for coal and rock CT images, ensuring the physical continuity and geometric fidelity of the 3D fracture network. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a deep learning-based method for repairing and connecting fractures in coal and rock CT scans. This method can automatically detect the location of fracture endpoints in a binary fracture map, accurately distinguish fracture endpoints and intersections, establish reasonable endpoint pairing relationships based on spatial distance and directional constraints to avoid non-physical erroneous connections, adaptively restore the original fracture width of the fracture connection region, eliminate the artificial bottleneck effect, ensure the accuracy of subsequent physical parameter calculations, and seamlessly integrate with various deep learning segmentation models.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a method for repairing and connecting coal and rock fractures based on deep learning CT, comprising the following core steps: Step 1: Extraction and Endpoint Detection of the Crack Skeleton S11. Probability map of coal and rock CT fracture prediction output by the deep learning segmentation model. Binarization is performed using a preset threshold T to obtain the initial binary image of the fracture. Where 1 represents the fracture prospect and 0 represents the matrix background; S12. A parallel iterative morphological thinning algorithm is used to refine the initial fracture binary image. Perform iterative erosion to extract the centerline image of the crack skeleton with a single pixel width. This ensures the connectivity, single-pixel integrity, and centrality of the refined skeleton. S13. Axial view of the fracture skeleton Above, calculate each foreground pixel. Eight-neighbor crossover number Counting the pixels with the neighboring foreground pixels, clockwise. Agreement Crossover number N c The calculation formula is: Simultaneously calculate the neighborhood foreground pixel count If satisfied and If so, then the pixel is determined to be a skeleton endpoint; if If the intersection point is marked as an intersection point and protected, all endpoint coordinates are stored in a set. .

[0008] Step 2: Endpoint pairing based on distance and orientation constraints: S21. Calculate the Euclidean distance between all pairs of endpoints in the endpoint set E, and construct a symmetric distance matrix. ,in The adaptive search radius R is set based on the CT image resolution. max Only those with a distance less than or equal to R max endpoint pairs (i.e.) ) included in the candidate set; S22. For each endpoint, use the eight-connected region growing method to trace back along the skeleton with a fixed step size L, extract the skeleton chain code sequence, and use principal component analysis or linear regression to fit the local tangent direction vector. S23. For endpoint pairs in the candidate set, perform direction consistency verification based on the preset maximum allowable deflection angle, and retain only endpoint pairs that simultaneously meet the direction consistency condition as valid pairs. Specifically, for candidate endpoint pairs... Define the connection vector as Set the maximum allowable deflection angle θ max A pair is considered valid only if all of the following conditions are met: in, As the endpoint Starting from a point, a unit vector pointing in the direction of the extension of the fracture skeleton at that point represents the fracture trend at that endpoint. As the endpoint Starting from a point, it is a unit vector pointing in the direction of extension of the fracture skeleton.

[0009] Step 3, Bresenham Line Connection and Adaptive Width Restoration: S31. For validly paired endpoint pairs The Bresenham linear rasterization algorithm is used to generate a sequence of discrete pixel coordinates as the initial connection path. The Bresenham algorithm uses integer recursive decision parameters to generate a pixel set that approximates the ideal line. Its core recursive formula is: in , C is a constant related to the initial point.

[0010] S32, Based on original coal and rock CT grayscale images Adaptive width restoration of the connected region: Calculate the connected path The normal vector of each point on (It is obtained by rotating the connection vector by 90°), and the location of drastic gradient change in the grayscale image along the positive and negative directions of the normal vector is used as the true boundary of the crack. Grayscale morphological dilation is performed using a structuring element that adaptively matches the local crack width, and a grayscale morphological dilation operator is defined. For connection paths Local neighborhood image patches centered on each point The size of the structural element K is adaptively matched with the width of the local crack. By performing a logical OR operation between the expanded binary boundary template and the original binary image, the gap filling and width restoration are completed.

[0011] Step 4: Iterative Repair and Global Connectivity Reconstruction S41. A greedy iterative strategy is used to achieve global repair: First, the endpoint set and effective distance matrix of the current crack binary map are calculated. The minimum value index is used to locate the effective paired endpoints with the shortest effective distance. The connection and width restoration operation in step three is performed to update the crack binary map. The endpoint set is updated and the connected endpoints are removed. If the connecting line intersects with the existing skeleton, the intersection point is recalculated and the endpoint set is updated. The above process is repeated until the minimum effective distance is greater than Rmax or there are no effective paired endpoints that meet the direction constraints. S42. After the iteration terminates, output the repaired binary fracture map, which fully preserves the topological connectivity and original width features of the fracture network.

[0012] Furthermore, in step S11, the preset threshold T is preferably 0.5; in step S12, the parallel iterative morphological thinning algorithm is preferably the ZhangSuen fast parallel thinning algorithm; in step S21, the adaptive search radius R... max The maximum crack width is preferably 5 to 10 times; the fixed step size L for reverse tracking in step S22 is preferably 5 to 8 pixels; the maximum allowable deflection angle in step S23 is preferably 30°.

[0013] Compared with existing morphological closing operations and manual interactive repair methods, the present invention has the following advantages: 1. This invention uses precise identification of skeleton endpoints and distance-direction dual constraint pairing to connect only the locations of actual physical fractures, effectively avoiding erroneous adhesion between adjacent independent fractures, preserving the original fracture network topology to the maximum extent, resulting in high topology fidelity, and solving the core defect of poor topology fidelity in traditional methods.

[0014] 2. This invention utilizes adaptive morphological dilation guided by the original CT grayscale image to accurately restore the true crack opening at the fracture location, completely eliminating the artificial bottleneck effect caused by single-pixel connections in traditional methods, and ensuring the physical accuracy of subsequent seepage simulation and mechanical parameter calculation. Experimental verification shows that the average width relative error of the repaired area is less than 0.8 pixels.

[0015] 3. The entire process of this invention requires no manual interaction or parameter adjustment. It can process massive CT slice sequences in batches. In a GPU environment, the processing time for a single slice is only about 0.3 seconds, providing an efficient and robust post-processing solution for three-dimensional digital core reconstruction.

[0016] 4. As an independent post-processing module, this invention can be seamlessly integrated with various mainstream deep learning segmentation models such as U-Net and DeepLabV3+. It is not only applicable to coal and rock CT images, but can also be widely extended to fracture image repair scenarios of various rock types such as shale and granite, and has strong compatibility and applicability.

[0017] 5. Validation results on 5,500 coal and rock CT test images show that after repair by this method, the number of isolated connected components in the fracture network is reduced by an average of 67%, which greatly improves the physical continuity of the fracture network. Attached Figure Description

[0018] Figure 1 This is an overall flowchart of the method described in this invention.

[0019] Figure 2 This is a schematic diagram of the process of refining the fracture skeleton and detecting the endpoints described in this invention.

[0020] Figure 3 This is a schematic diagram of the Bresenham linear connection and grayscale expansion width recovery process described in this invention.

[0021] In the figure: 1-Binarized image of fracture, 2-Crack skeleton extraction, 3-Automatic detection of crack endpoints, 4-Calculation of endpoint distance matrix, 5-Batch processing of crack endpoints, 6-Endpoint connection and crack expansion, 6-1-Binarized image before endpoint connection, 6-2-Fracture gap, 6-3-Bresenham connector, 6-4-Skeleton endpoints, 6-5-Grayscale morphological expansion, 6-6-Binarized image after endpoint connection. Detailed Implementation

[0022] The present invention will be further described below.

[0023] Example 1: This example demonstrates the batch fracture repair of medium- and high-density bituminous coal industrial CT scan sections. The specific implementation process is as follows: Sample and Data Preparation: The sample used in this embodiment is anthracite coal from a certain coal seam. 1200 consecutive slices were obtained through industrial CT scanning, with an image resolution of 1024×1024 pixels, a pixel physical size of 10μm / pixel, and a maximum crack width of 4 pixels. The U-Net deep learning segmentation model was used to segment cracks in all slices, outputting a crack prediction probability map for each slice.

[0024] S1. Crack skeleton extraction and endpoint detection: S11. The predicted probability map output by the U-Net model is binarized using a threshold of T=0.5 to obtain an initial fracture binary map, where pixel value 1 represents the fracture foreground and 0 represents the coal and rock matrix background.

[0025] S12. The ZhangSuen fast parallel thinning algorithm is used to iteratively erode the initial binary image of the crack. Conditional judgment is performed on the eight neighborhoods of each foreground pixel, and non-skeleton pixels are peeled off layer by layer to finally obtain the central axis image of the crack skeleton with a single pixel width. This ensures that the center position of the skeleton coincides with the center position of the original crack and does not change the connectivity of the original crack.

[0026] S13. On the central axis diagram of the fracture skeleton, for each foreground pixel P, mark its eight neighboring pixels clockwise as follows: Agreement Calculate the crossover number Simultaneously count the number of foreground pixels in the neighborhood. If satisfied and If the pixel is determined to be a skeleton endpoint; The intersection points are marked and protected, and finally all endpoint coordinates are stored in the endpoint set E.

[0027] S2. Endpoint pairing based on distance and orientation constraints: S21. Based on the pixel size and maximum crack width of the CT image in this embodiment, set an adaptive search radius R. max =20 pixels (5 times the maximum crack width), calculate the Euclidean distance of all endpoint pairs in the endpoint set E, construct a symmetric distance matrix, and only include endpoint pairs with a distance of less than 20 pixels into the candidate set.

[0028] S22. For each endpoint, the eight-connected region growing method is used to trace back along the skeleton with a fixed step size of L=5 pixels to extract the corresponding skeleton chain code sequence, and the local tangent direction vector of the skeleton segment is fitted by linear regression.

[0029] S23. Set the maximum allowable deflection angle θ max =25°, for endpoint pairs in the candidate set Define the connection vector as Calculate the angle between the tangent direction vectors of the two endpoints and the connecting vector. Only when both angles are less than or equal to 25° is the endpoint pair considered a valid pair, thus avoiding erroneous connections that violate the fracture orientation.

[0030] S3, Bresenham Line Connection and Adaptive Width Recovery: S31. For validly paired endpoints, the Bresenham linear rasterization algorithm is used to generate a discrete pixel coordinate sequence that approximates an ideal straight line through integer recursive decision parameters, which serves as the initial connection path between the two endpoints.

[0031] S32. For each pixel on the connection path, rotate the connection vector by 90° to obtain the normal vector of that point. Search for locations with drastic grayscale gradient changes in the original CT grayscale image along both positive and negative directions of the normal vector, using these locations as the true upper and lower boundaries of the crack. Based on the detected local crack width, adaptively match the size of the circular structuring element K to perform grayscale morphological dilation on the connection path. Perform a logical OR operation between the dilated binary boundary template and the original crack binary image to complete the filling of the fracture gap and the restoration of the original crack width, avoiding the bottleneck effect caused by single-pixel connections.

[0032] S4. Iterative Repair and Global Connectivity Reconstruction: A greedy iterative strategy is used to perform global repair: The effective distance matrix of the current crack binary image is constructed based on NumPy vectorization operations. The effective paired endpoints with the shortest effective distance are located using the argmin minimum index function. The connection and width restoration operations of the paired endpoints are completed first, and the crack binary image is updated. Then, the endpoint set is updated, and the two endpoints that have been connected are removed. If the newly added connection line intersects with the existing skeleton, the intersection point is recalculated and the endpoint set is updated. The above iterative process is repeated until the current minimum effective distance is greater than 20 pixels, or there are no effective paired endpoints that meet the direction constraints, at which point the iteration terminates.

[0033] Implementation Results: This embodiment successfully performed batch repair on 1200 coal and rock CT slices. The average processing time per slice in a GPU environment was 0.28 seconds, with no manual intervention required throughout the entire process. After repair, the number of isolated connected components in the fracture network decreased by an average of 69%, the average relative error of the repaired area was 0.72 pixels, there was no erroneous adhesion between adjacent fractures, and the original fracture topology and width characteristics were fully preserved, providing high-precision basic data for subsequent 3D digital core reconstruction.

[0034] Example 2: This example demonstrates the repair of fractures in high-resolution Micro-CT scan sections of low-rank, low-density lignite. It addresses extreme scenarios involving low contrast, well-developed micro-fractures, and more severe fracture phenomena. The specific implementation process is as follows: Sample and Data Preparation: The sample used in this embodiment is a lignite sample from a certain region. This sample has well-developed pores and fractures, low matrix density, and extremely low grayscale contrast between fractures and matrix in CT images. Micro-fractures are prone to large-scale fractures. 800 consecutive slices were obtained through Micro-CT scanning, with an image resolution of 2048×2048 pixels, a pixel physical size of 2μm / pixel, a maximum fracture width of 8 pixels, and micro-fractures (width <2 pixels) accounting for more than 60%. The DeepLabV3+ deep learning segmentation model was used to segment fractures in all slices, and a fracture prediction probability map for each slice was output.

[0035] S1. Crack skeleton extraction and endpoint detection: S11. The predicted probability map output by the DeepLabV3+ model is binarized using a threshold T=0.5 to obtain the initial binary map of the crack.

[0036] S12. To address the skeleton noise problem caused by low contrast in lignite images, a 3×3 morphological opening operation is first performed on the initial binary image to remove isolated noise points. Then, ZhangSuen's fast parallel thinning algorithm is used for iterative erosion to extract the central axis image of the crack skeleton with a single pixel width, thus avoiding false endpoints caused by noise points.

[0037] S13. Using the same eight-neighbor cross-number algorithm as in Example 1, identify skeleton endpoints and cross-points, protect cross-points, store all endpoint coordinates in endpoint set E, and remove isolated single-pixel endpoints generated only by noise.

[0038] S2. Endpoint pairing based on distance and orientation constraints: S21. To address the characteristic of larger fracture gaps in the micro-fractures of lignite, an adaptive search radius R is set. max =60 pixels (7.5 times the maximum crack width), calculate the Euclidean distance of all endpoint pairs, construct a symmetric distance matrix, and only include endpoint pairs with a distance of less than 60 pixels into the candidate set.

[0039] S22. To address the issue of large fluctuations in the orientation of micro-cracks, the reverse tracing step size L is adjusted to 8 pixels. For each endpoint, 8 pixels are traced in reverse along the skeleton to extract the skeleton chain code sequence. Principal component analysis is used to fit the local tangent direction vector to improve the anti-interference capability of the orientation calculation.

[0040] S23, Simultaneously set the maximum permissible deflection angle θ max The angle was adjusted to 30° to suit the geological characteristics of lignite fractures, which exhibit significant fluctuations in fracture orientation. This ensures effective pairing of genuine, curved fractures while avoiding incorrect connections. A directional consistency check was performed on candidate endpoint pairs; only pairs were considered valid if the angles between the tangent directions of both endpoints and the connection vector were less than or equal to 30°.

[0041] S3, Bresenham Line Connection and Adaptive Width Recovery: S31. For validly paired endpoints, the Bresenham line algorithm is used to generate the initial connection path.

[0042] S32. To address the ambiguous fracture boundaries in lignite, during the width recovery step, the average grayscale gradient is calculated using a 5×3 neighborhood window for the normal vector direction of each point on the connection path. This accurately locates the true fracture boundary and avoids boundary detection errors caused by grayscale noise. Based on the detected local fracture width, the size of the structuring element K is adaptively matched, and grayscale morphological dilation is performed on the connection path. The dilated boundary template is then logically ORed with the original binary image to complete the fracture gap filling and width recovery.

[0043] S4. Iterative Repair and Global Connectivity Reconstruction: Using the same greedy iterative strategy as in Example 1, the shortest effective pairing endpoints are connected first. After each round of connection, the binary crack map and endpoint set are updated. The iteration continues until the minimum effective distance is greater than 60 pixels, or there are no effective pairing endpoints that meet the directional constraints. The repaired binary crack map is then output.

[0044] Implementation Results: This embodiment successfully restored 800 micro-CT slices of lignite, with an average processing time of 0.32 seconds per slice. It effectively solved the problem of large-scale fractures in low-contrast images. After restoration, the number of isolated connected components in the fracture network decreased by an average of 72%, and the average relative error of the restored area was 0.78 pixels. No false connections or erroneous adhesions were observed. The true interconnected structure of the internal micro-fracture network of lignite was successfully restored, providing accurate data support for the study of the seepage characteristics of low-rank coal.

[0045] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A coal rock CT fracture fracture repair and connection method based on deep learning, characterized by, Includes the following steps: Step 1: Fracture skeleton extraction and endpoint detection: The coal and rock CT fracture prediction probability map output by the deep learning segmentation model is binarized to obtain the initial fracture binary map; then, the centerline map of the fracture skeleton with a single pixel width is extracted. On the graph, the endpoints and intersections of the fracture skeleton are identified by calculating the number of eight neighboring intersections, and the coordinates of all endpoints are stored in the endpoint set. Step 2: Endpoint pairing based on distance and direction constraints: Calculate the Euclidean distance between all endpoint pairs in the endpoint set E, construct a symmetric distance matrix, and set an adaptive search radius R. max Only those with a distance less than R max The endpoint pairs are included in the candidate set; for each endpoint, a fixed step size L is traced in reverse along its skeleton to extract the skeleton chain code sequence and fit the local tangent direction vector; for the endpoint pairs in the candidate set, the direction consistency is checked based on the preset maximum allowable deflection angle, and only the endpoint pairs that simultaneously meet the direction consistency condition are retained as valid pairings. Step 3, Bresenham Line Connection and Adaptive Width Recovery: For validly paired endpoints, the Bresenham line rasterization algorithm is used to generate the initial connection path; based on the original coal and rock CT grayscale image, adaptive width recovery is performed on the initial connection path: the normal vector of each point on the connection path is calculated, and the location of drastic gradient change in the grayscale image along the positive and negative directions of the normal vector is searched as the true boundary of the fracture. Grayscale morphological dilation is performed using a structuring element that adaptively matches the local fracture width. The dilated binary boundary template is logically ORed with the initial fracture binary image to complete the fracture gap filling and fracture width recovery. Step 4: Iterative Repair and Global Connectivity Reconstruction: A greedy iterative strategy is used to perform global repair, and the repaired binary crack map is output.

2. The method of claim 1, wherein, In step one, the preset threshold T for binarizing the predicted probability map is 0.

5. After binarization, a pixel value of 1 represents the crack foreground and 0 represents the matrix background.

3. The method of claim 1, wherein, In step one, a parallel iterative morphological thinning algorithm is used to iteratively erode the initial binary image of the crack to extract the central axis image of the crack skeleton with a single pixel width. The parallel iterative morphological thinning algorithm is the ZhangSuen fast parallel thinning algorithm. This algorithm performs conditional judgment on the eight neighbors of the boundary pixels and peels off non-skeleton pixels layer by layer to ensure the connectivity, single-pixelity and centrality of the skeleton after thinning.

4. The method of claim 1, wherein, In step one, the eight-neighbor crossover number is calculated as follows: for each foreground pixel on the axis map in the crack skeleton , its eight-neighbor pixels are denoted clockwise as , conventionally , the intersection number N c The formula for calculating is: Simultaneously calculate the neighborhood foreground pixel count If satisfied and If so, then the pixel is determined to be a skeleton endpoint; if If it is, then mark it as an intersection and protect it.

5. The method according to claim 1, characterized in that, In the second step, the adaptive search radius R max According to the CT image resolution, the value is 5-10 times of the maximum fissure width; the fixed step length L of the reverse tracking is 5-8 pixels.

6. The method according to claim 1, characterized in that, In step two, the method for determining the directional consistency condition is as follows: For candidate endpoint pairs Define the connection vector as Set the maximum allowable deflection angle θ max A pair is considered valid only if all of the following conditions are met: in, As the endpoint Starting from a point, it is a unit vector pointing in the direction of extension of the fracture skeleton where it is located; As the endpoint Starting from a point, it is a unit vector pointing in the direction of extension of the fracture skeleton.

7. The method according to claim 6, characterized in that, the maximum allowed deflection angle θ max of 30°.

8. The method according to claim 1, characterized in that, In step three, the normal vector of each point on the connecting path is obtained by rotating the connecting vector by 90°.

9. The method according to claim 1, characterized in that, Step four specifically involves: calculating the endpoint set and effective distance matrix of the current fracture binary graph; locating the effective paired endpoints with the shortest effective distance using the minimum index; performing the connection and width restoration operation of step three and updating the fracture binary graph; updating the endpoint set and removing connected endpoints; and recalculating the intersection point and updating the endpoint set if the connecting line intersects with the existing skeleton. Repeat the iterative process until the minimum effective distance is greater than R. max If there are no valid paired endpoints that satisfy the directional constraints, output a binarized crack map showing the repaired crack.

10. The method according to claim 1, characterized in that, The method, as a post-processing module, seamlessly integrates with U-Net and DeepLabV3+ deep learning semantic segmentation models, and is suitable for crack repair in CT images of coal, shale, and granite.

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