Three-dimensional pore reconstruction method and system based on rock image

Abstract

The present invention relates to the field of rock structure measurement, and disclosed are a three-dimensional pore reconstruction method and system based on a rock image, for use in solving the problem that using a machine learning method to reconstruct pores in a rock image requires relatively high mathematical or computer science expertise, involves high labor and economic costs, and is difficult to apply to small-scale rock pore reconstruction projects. The method comprises: step 1: grouping slice images of each rock sample into one set, and performing preprocessing; step 2: performing grayscale processing, histogram equalization and normalization processing on an image; step 3: using a Harris corner detection algorithm to perform corner detection, sorting Harris response values, selecting key points by setting the number of key points, and using a non-maximum suppression method to screen the selected key points; step 4: segmenting the boundaries of pores in the image by means of an adaptive threshold selection method, and extracting pore features; and step 5: using a marching cubes algorithm to construct a three-dimensional pore reconstruction model. The present invention is used for three-dimensional reconstruction of pores in a rock image.

Description

A 3D pore reconstruction method and system based on rock images Technical Field

[0001] The present invention relates to the technical field of rock structure measurement, and in particular to a method and system for three-dimensional pore reconstruction based on rock images. Background Art

[0002] Rock pores are the spaces or holes within a rock. They are typically formed by a variety of factors during rock formation and metamorphism, including sedimentation, dissolution, and the shrinkage of mineral crystals. The size, shape, and distribution of rock pores have a significant impact on the properties and uses of the rock.

[0003] When it comes to measurements related to rock pores, the main methods include electron microscopy scanning, nuclear magnetic resonance, CT scanning, etc., but they are not capable of reflecting the conditions of rock pores. Using neural network technology to process and analyze data helps to extract information about the pore structure. Machine learning and three-dimensional modeling rendering technology are usually used to restore and reconstruct the pores. The process of the method often includes cleaning, normalizing and processing the data to ensure data quality and consistency. When preparing a data set for machine learning training, it is necessary to select appropriate machine learning algorithms, such as convolutional neural networks, support vector machines, etc., and use labeled data sets for model training, which requires a lot of costs, involving hardware requirements, training time, data collection and labeling, etc. In addition, the operator needs to have proficiency in machine learning and relevant expertise, which makes some small-scale rock pore reconstruction projects difficult to undertake. Summary of the Invention

[0004] The technical problems to be solved by the present invention are:

[0005] The existing technology of reconstructing the pores of rock images through machine learning methods requires high mathematical or computer expertise, and has high labor and economic costs, making it difficult to apply to small-scale rock pore reconstruction projects. To this end, the present invention provides a three-dimensional pore reconstruction method and system based on rock images.

[0006] The present invention is to solve the above technical problems using the following technical solutions:

[0007] The present invention provides a method for three-dimensional pore reconstruction based on rock images, comprising the following steps:

[0008] Step 1: Slice the rock sample, collect microscopic images of the particles and pores of the rock sample slices, divide the slice images of each rock sample into a group, and pre-process the image data;

[0009] Step 2: First, grayscale the image, then remove image noise through median filtering, enhance image details and adaptability through histogram equalization, and finally map the image pixel values ​​to a specific range through normalization;

[0010] Step 3: Use the Harris corner detection algorithm to detect corners, sort the Harris response values, select key points by setting the number of key points, and further screen the selected key points using the non-maximum suppression method;

[0011] Step 4: Segment the boundaries of the image pores using an adaptive threshold selection method, extract pore features, assign different colors to the pores according to their different properties, and generate a pseudo-color image;

[0012] Step 5: Using the marching cubes algorithm, a three-dimensional reconstruction model of the pores of the grid structure is constructed based on the pseudo-color images of each group of slices.

[0013] Furthermore, the image data is preprocessed as described in step 1, including cropping and scaling the image, and smoothing each set of images using Gaussian filtering to remove high-frequency noise. The specific calculation method is:

[0014] Among them I smooth (x,y) is the smoothed intensity at pixel (x,y) after Gaussian filtering, k is the size of the filter, w(i,j) is the weight given to the pixel at the relative position in the filter, x i 、x j represents the spatial distance between pixels, i and j are the pixel distances relative to the filter center, and σ0 is the standard deviation of the pixels;

[0015] Furthermore, the calculation method of the histogram equalization in step 2 is:

[0016] Where s is the grayscale of the image after histogram equalization, r is the grayscale of the original image, and P(r) is the probability density of the random variable r, that is:

[0017] Where μ is the mean of the pixels and σ is the standard deviation of the pixels, that is:

[0018] Where M and N are the height and width of the image, r ij is the grayscale value at pixel (i, j).

[0019] Furthermore, in the histogram equalization process, 50% of the pixel values ​​of the image are set to be less than 128, and 25% of the pixel values ​​are set to be less than 64, so that the histogram grayscale levels of the image are dispersed from being concentrated in a small part of the grayscale levels to having a certain coverage in all grayscale levels.

[0020] Furthermore, the normalized calculation method in step 2 is:

[0021] Where x' is the pixel value after normalization, x is the pixel value before normalization, and x max Represents the maximum pixel value, x min Represents the minimum pixel value.

[0022] Furthermore, step three includes the following process:

[0023] First, the gradient of each pixel in the image obtained in step 2 is calculated using a first-order gradient operator. Then, the Harris corner detection algorithm is used to detect corners. Specifically, the pixel gradient matrix image is traversed through a local window, and the curvature C of the pixel is calculated using the Hessian matrix, that is:

[0024] Where trace(M) is the trace of the gradient matrix, det(M) is the determinant of the gradient matrix;

[0025] For each pixel in the image, calculate its local feature response value, set a threshold for the local feature response value, and the pixel points above the threshold are corner points;

[0026] Finally, the Harris response values ​​are sorted, and key points are selected by setting the number of key points; and the non-maximum suppression method is used to further screen the selected key points.

[0027] Furthermore, step 4 includes the following process:

[0028] The boundaries of the image pores are segmented by the adaptive threshold selection method, that is, an optimal grayscale threshold is determined to divide the image into foreground and background, and the inter-class variance of the segmented foreground and background is calculated to maximize the variance of the two classes after segmentation. The specific calculation method is:

[0029] σbetween2(t) is the variance after segmentation, t is the threshold, P(t) and are the probabilities of foreground and background at threshold t, μ(t) and is the average gray value of the foreground and background;

[0030] The shape, size, and distribution characteristics of the pores are extracted, and different colors are assigned to the pores according to their different properties to generate a pseudo-color image.

[0031] Furthermore, step five includes the following process:

[0032] The generated pseudo-color image is divided into multiple grid voxels, the voxel grid is converted into a three-dimensional grid with surface information, the voxel data is converted into vertices and faces of the grid, and the voxels are fitted with a surface; the density and grayscale information of each voxel are obtained, and a histogram of the voxel data is drawn based on the voxel information to determine the range of pore scalar values; using the marching cube algorithm, an isosurface of the three-dimensional structure of the rock pores is generated within the determined range of pore scalar values, and the entire set of pseudo-color images is integrated to form a three-dimensional reconstructed model of the pores, which simultaneously presents the characteristics of shape and color.

[0033] Furthermore, step five also includes: using a VTK rendering window to achieve real-time interaction and visualization of the pore three-dimensional reconstructed model.

[0034] A three-dimensional pore reconstruction system based on rock images has a program module corresponding to the steps of any of the above technical solutions, and executes the steps of the above three-dimensional pore reconstruction method based on rock images when running.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention provides a method and system for three-dimensional pore reconstruction based on rock images. The method uses grayscale, median filtering, histogram equalization, and normalization to improve image quality and minimize noise. Key features in the image are extracted through operations such as threshold segmentation and corner detection. The Harris corner detection algorithm is innovatively improved so that feature points can be automatically sorted according to their response level. The improved algorithm exhibits excellent performance in the feature point matching stage, thereby efficiently obtaining the number of custom feature points. Finally, the marching cubes algorithm is introduced to perform high-precision restoration of the rock pore structure.

[0037] This method uses computer vision technology to process images, significantly reducing costs, shortening neural network training time, and lowering hardware requirements, enabling efficient processing of small-scale rock pore reconstruction projects. This method achieves low-cost rock image pore reconstruction without requiring advanced math or computer science expertise, significantly reducing labor and economic costs, and has proven to be fully applicable to small-scale rock pore reconstruction projects.

[0038] The method of the present invention enables high-resolution three-dimensional image reconstruction, providing a new perspective for geological research and bringing enormous potential to fields such as resource development and environmental protection. Simulation experiments and practical applications have verified the claimed technical effectiveness and practicality of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] FIG1 is a flow chart of a method for three-dimensional pore reconstruction based on rock images in an embodiment of the present invention;

[0040] FIG2 is a partial rock image used in the pore identification method according to an embodiment of the present invention;

[0041] FIG3 is a schematic diagram of grayscale conversion of a rock image in an embodiment of the present invention;

[0042] FIG4 is a flow chart of Harris feature extraction in an embodiment of the present invention;

[0043] FIG5 is a schematic diagram of a basic model of a moving cube in an embodiment of the present invention;

[0044] FIG6 is a histogram equalization diagram of a rock image in an embodiment of the present invention;

[0045] FIG7 is a feature extraction diagram using the Harris algorithm in an embodiment of the present invention;

[0046] FIG8 is a schematic diagram of image segmentation according to an embodiment of the present invention;

[0047] FIG9 is a schematic diagram of pore feature point extraction in an embodiment of the present invention;

[0048] FIG10 is a schematic diagram of pore results in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] In the description of the present invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of the present invention are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly specifying the number of the technical features indicated. Therefore, a feature specified as "first," "second," or "third" may explicitly or implicitly include one or more of such features.

[0050] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0051] Specific embodiment 1: As shown in FIG1 , the present invention provides a method for 3D pore reconstruction based on rock images, comprising the following steps:

[0052] Step 1: Slice the rock sample, collect microscopic images of the particles and pores of the rock sample slices, divide the slice images of each rock sample into a group, and pre-process the image data;

[0053] Step 2: First, grayscale the image, then remove image noise through median filtering, enhance image details and adaptability through histogram equalization, and finally map the image pixel values ​​to a specific range through normalization;

[0054] Step 3: Use the Harris corner detection algorithm to detect corners, sort the Harris response values, select key points by setting the number of key points, and further screen the selected key points using the non-maximum suppression method;

[0055] Step 4: Segment the boundaries of the image pores using an adaptive threshold selection method, extract pore features, assign different colors to the pores according to their different properties, and generate a pseudo-color image;

[0056] Step 5: Using the marching cubes algorithm, a three-dimensional reconstruction model of the pores of the grid structure is constructed based on the pseudo-color images of each group of slices.

[0057] In step 1 of this implementation plan, rock thin section images are collected and thin sections of different sizes are prepared to meet specific needs. The rock thin sections are prepared into thin sections with a size of 10 mm*10 mm. Subsequently, these thin sections are scanned over a large range of the entire field of view using a Zeiss EVO15 scanning electron microscope to obtain microscopic rock images that clearly show the rock particles and pores, as shown in Figure 2.

[0058] The grayscale processing in step 2 of this implementation preserves the brightness information of the rock sample while reducing data complexity. This is achieved using a simple average calculation, ensuring that the grayscale value of each pixel in the image is equal to the average of its red, green, and blue channel values. The median filter replaces the value of each pixel with the median of the pixel values ​​within its neighborhood window, suppressing noise while preserving detail. The odd numbers in the window are arranged in order of magnitude, and the number at the center is used as the processing result, smoothing the image while preserving edge information. Median filtering does not use a linear weighted average, but directly selects the median. Compared to linear filtering, median filtering is more effective at preserving edge information while removing noise. This makes pixel values ​​at the edge less susceptible to smoothing. Furthermore, it does not rely on the statistical properties of the image, making it relatively robust when processing different types of rock images.

[0059] Specific implementation scheme 2: Preprocess the image data as described in step 1, including cropping and scaling the image, and use Gaussian filtering to smooth each group of images to remove high-frequency noise. The specific calculation method is:

[0060] Among them I smooth (x,y) is the smoothed intensity at pixel (x,y) after Gaussian filtering, k is the size of the filter, w(i,j) is the weight given to the pixel at the relative position in the filter, x i 、x j represents the spatial distance between pixels, i and j are the pixel distances relative to the filter center, and σ0 is the standard deviation of the pixels.

[0061] Specific implementation scheme three: As shown in FIG6 , the calculation method of the histogram equalization in step 2 is:

[0062] Where s is the grayscale of the image after histogram equalization, r is the grayscale of the original image, and P(r) is the probability density of the random variable r, that is:

[0063] Where μ is the mean of the pixels and σ is the standard deviation of the pixels, that is:

[0064] Where M and N are the height and width of the image, r ij is the grayscale value at pixel (i, j). The rest of this embodiment is the same as the second embodiment.

[0065] In this implementation, histogram equalization first stretches and compresses the brightness level of the image, and then controls the grayscale values ​​of the pixels according to the histogram, so that the pixels vary between black and white, making the relatively concentrated grayscale more widely distributed. This belongs to the point operation range, and r and s represent the normalized original image grayscale and the image grayscale after histogram equalization, respectively. That is, any r in the interval [0,1] can produce a corresponding s through the transformation function T(r), and the formula is: s=T(r)

[0066] Specific embodiment 4: During the histogram equalization process, 50% of the image's pixel values ​​are set to be less than 128, and 25% of the pixel values ​​are set to be less than 64. This disperses the image's histogram grayscale levels from being concentrated in a small number of grayscale levels to having a certain coverage across all grayscale levels. This improves the brightness resolution and helps more accurately represent brightness variations in the image. This embodiment is otherwise identical to specific embodiment 3.

[0067] Specific implementation scheme 5: The normalized calculation method in step 2 is:

[0068] Where x' is the pixel value after normalization, x is the pixel value before normalization, and x max Represents the maximum pixel value, x min The rest of this embodiment is the same as the fourth embodiment.

[0069] This implementation ensures that the pixel values ​​of the image are within the same range, ensures the consistency of scale, and improves the generalization ability.

[0070] Specific implementation plan six: As shown in Figures 4 and 7, step three includes the following process:

[0071] First, the gradient of each pixel in the image obtained in step 2 is calculated using a first-order gradient operator. Then, the Harris corner detection algorithm is used to detect corners. Specifically, the pixel gradient matrix image is traversed through a local window, and the curvature C of the pixel is calculated using the Hessian matrix, that is:

[0072] Where trace(M) is the trace of the gradient matrix, det(M) is the determinant of the gradient matrix;

[0073] For each pixel in the image, calculate its local feature response value, set a threshold for the local feature response value, and the pixel points above the threshold are corner points;

[0074] Finally, the Harris response values ​​are sorted and key points are selected by setting the number of key points. The result is shown in FIG9 . The non-maximum suppression method is then used to further screen the selected key points. The rest of this embodiment is the same as the specific embodiment five.

[0075] In this embodiment, a local window is moved on the image to determine whether there is a significant change in the grayscale. If the grayscale values ​​within the window (on the gradient map) have significant changes, then there is a corner point in the area where the window is located. By building a model, the center of a window is located at a position (x, y) in the grayscale image. The grayscale value of the pixel at this position is I(x, y). If the window moves a small displacement u and v in the x and y directions respectively to a new position (x+u, y+v), I(x+u, y+v)-I(x, y), that is, the change in grayscale value caused by the window movement, is the feature to be extracted.

[0076] This implementation uses recall, accuracy, and F1 score to evaluate the effectiveness of the Harris corner detection algorithm:

[0077] Among them, True Positives represents the number of correctly detected corner points, and False Negatives represents the number of corner points that actually exist but are not detected.

[0078] In this embodiment, the gradient of each pixel in the image is calculated by a first-order gradient operator, and then the corner detection is performed using the Harris corner detection algorithm, which can achieve higher accuracy and recall rate.

[0079] Specific implementation plan seven: As shown in Figure 8, step four includes the following process:

[0080] The boundaries of the image pores are segmented by the adaptive threshold selection method, that is, an optimal grayscale threshold is determined to divide the image into foreground and background, and the inter-class variance of the segmented foreground and background is calculated to maximize the variance of the two classes after segmentation. The specific calculation method is:

[0081] σbetween2(t) is the variance after segmentation, t is the threshold, P(t) and are the probabilities of foreground and background at threshold t, μ(t) and is the average gray value of the foreground and background;

[0082] The shape, size, and distribution characteristics of the pores are extracted, and different colors are assigned to the pores according to their different properties to generate a pseudo-color image.

[0083] Specific implementation plan eight: As shown in Figure 5, step five includes the following process:

[0084] The generated pseudo-color image is divided into multiple grid voxels, the voxel grid is converted into a three-dimensional grid with surface information, the voxel data is converted into mesh vertices and faces, and surface fitting is performed on the voxels. Density and grayscale information for each voxel are obtained, and a histogram of the voxel data is plotted using this information to determine the range of pore scalar values. Using the marching cubes algorithm, isosurfaces of the three-dimensional structure of the rock pores are generated within the determined range of pore scalar values. The entire set of pseudo-color images is then integrated to form a three-dimensional reconstructed model of the pores, simultaneously presenting both shape and color characteristics. This embodiment is otherwise identical to Specific Embodiment 7.

[0085] Specific implementation scheme nine: Step five also includes: using the VTK rendering window to achieve real-time interaction and visualization of the pore 3D reconstruction model; the result is shown in Figure 10. The rest of this implementation scheme is the same as the specific implementation scheme eight.

[0086] Specific implementation scheme ten: A three-dimensional pore reconstruction system based on rock images, which has a program module corresponding to the steps of any of the above-mentioned specific implementation schemes, and executes the steps in the above-mentioned three-dimensional pore reconstruction method based on rock images during operation.

[0087] The present invention proposes a method (algorithm) for three-dimensional pore reconstruction based on rock images, which is the underlying technical core of the present invention. Various products can be derived based on the algorithm.

[0088] Based on the method proposed in the present invention, a three-dimensional pore reconstruction system based on rock images is developed using a programming language. The system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned three-dimensional pore reconstruction method based on rock images during operation.

[0089] The developed system (software) computer program is stored on a computer-readable storage medium. The computer program is configured to implement the steps of the above-described rock image-based 3D pore reconstruction method when invoked by a processor. This materializes the present invention on a carrier, becoming a computer program product.

[0090] Various implementations of the systems and techniques described herein can be realized in digital electronic circuitry, integrated circuitry, dedicated ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include being implemented in one or more computer programs that are executable and / or interpreted on a programmable system comprising at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0091] The computer programs (also referred to as programs, software, software applications, or code) of the present invention include machine instructions for a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., a magnetic disk, an optical disk, a memory, a programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0092] Although the present invention is disclosed as above, the scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A 3D pore reconstruction method based on rock images, characterized in that: The steps include: Step 1: Slice the rock sample, collect microscopic images of the particles and pores of the rock sample slices, divide the slice images of each rock sample into a group, and pre-process the image data; Step 2: First, grayscale the image, then remove image noise through median filtering, enhance image details and adaptability through histogram equalization, and finally map the image pixel values ​​to a specific range through normalization; The calculation method of the histogram equalization is: Where s is the grayscale of the image after histogram equalization, r is the grayscale of the original image, and P(r) is the probability density of the random variable r, that is: Where μ is the mean of the pixels and σ is the standard deviation of the pixels, that is: Where M and N are the height and width of the image, r ij is the grayscale value at pixel (i, j); Step 3: Use the Harris corner detection algorithm to detect corners, sort the Harris response values, select key points by setting the number of key points, and further screen the selected key points using the non-maximum suppression method; the process includes the following: First, the gradient of each pixel in the image obtained in step 2 is calculated using a first-order gradient operator. Then, the Harris corner detection algorithm is used to detect corners. Specifically, the pixel gradient matrix image is traversed through a local window, and the curvature C of the pixel is calculated using the Hessian matrix, that is: Where trace(H) is the trace of the gradient matrix, det(H) is the determinant of the gradient matrix; For each pixel in the image, calculate its local feature response value, set a threshold for the local feature response value, and the pixel points above the threshold are corner points; Finally, the Harris response values ​​are sorted, and key points are selected by setting the number of key points; and the non-maximum suppression method is used to further screen the selected key points; Step 4: Segment the boundaries of the image pores using an adaptive threshold selection method, extract pore features, assign different colors to the pores according to their different properties, and generate a pseudo-color image; Step 5: Using the marching cubes algorithm, a three-dimensional reconstruction model of the pores of the grid structure is constructed based on the pseudo-color images of each group of slices.

2. The method for 3D pore reconstruction based on rock images according to claim 1, characterized in that: The image data is preprocessed as described in step 1, including cropping and scaling the image, and each set of images is smoothed using Gaussian filtering to remove high-frequency noise. The specific calculation method is: Among them I smooth (x,y) is the smoothed intensity at pixel (x,y) after Gaussian filtering, k is the size of the filter, w(i,j) is the weight given to the pixel at the relative position in the filter, x i 、y j represents the spatial distance between pixels, i and j are the pixel distances relative to the filter center, and σ0 is the standard deviation of the pixels.

3. The method for 3D pore reconstruction based on rock images according to claim 2, characterized in that: In the histogram equalization process, 50% of the pixel values ​​of the image are set to be less than 128, and 25% of the pixel values ​​are set to be less than 64, so that the histogram grayscale levels of the image are dispersed from being concentrated in a small part of the grayscale levels to having a certain coverage in all grayscale levels.

4. The method for 3D pore reconstruction based on rock images according to claim 3, characterized in that: The normalized calculation method in step 2 is: Where x' is the pixel value after normalization, x is the pixel value before normalization, and x max Represents the maximum pixel value, x min Represents the minimum pixel value.

5. The method for 3D pore reconstruction based on rock images according to claim 4, characterized in that: Step 4 includes the following process: The boundaries of the image pores are segmented by the adaptive threshold selection method, that is, an optimal grayscale threshold is determined to divide the image into foreground and background, and the inter-class variance of the segmented foreground and background is calculated to maximize the variance of the two classes after segmentation. The specific calculation method is: σbetween2(t) is the variance after segmentation, t is the threshold, P(t) and are the probabilities of foreground and background at threshold t, μ(t) and is the average gray value of the foreground and background; The shape, size, and distribution characteristics of the pores are extracted, and different colors are assigned to the pores according to their different properties to generate a pseudo-color image.

6. The method for 3D pore reconstruction based on rock images according to claim 5, characterized in that: Step 5 includes the following process: The generated pseudo-color image is divided into multiple grid voxels, the voxel grid is converted into a three-dimensional grid with surface information, the voxel data is converted into vertices and faces of the grid, and the voxels are fitted with a surface; the density and grayscale information of each voxel are obtained, and a histogram of the voxel data is drawn based on the voxel information to determine the range of pore scalar values; using the marching cube algorithm, an isosurface of the three-dimensional structure of the rock pores is generated within the determined range of pore scalar values, and the entire set of pseudo-color images is integrated to form a three-dimensional reconstructed model of the pores, which simultaneously presents the characteristics of shape and color.

7. The method for 3D pore reconstruction based on rock images according to claim 6, characterized in that: Step five also includes: using the VTK rendering window to achieve real-time interaction and visualization of the pore 3D reconstruction model.

8. A 3D pore reconstruction system based on rock images, characterized in that: The system has a program module corresponding to the steps of any one of claims 1 to 7, and executes the steps of the above-mentioned rock image-based pore three-dimensional reconstruction method when running.

Images