Method for analyzing pore characteristics of steel slag concrete based on CT scanning and image processing

Abstract

The present application provides a steel slag concrete pore feature analysis method based on CT scanning and image processing, relates to the technical field of steel slag concrete pore feature analysis, and realizes accurate capture of the twisted form of crack type pores by quantifying the spatial bending degree of the pore center axis through calculation of the section centroid offset of adjacent two elongated pore connected bodies; the present application sets the cross-sectional area fluctuation threshold and the section centroid offset threshold as the determination criteria, provides clear and quantifiable discrimination basis for the definition of continuous pores, realizes automatic differentiation of harmful connected pores and harmless elongated pores; the present application integrates the continuous pore features and the single pore features through feature splicing after extraction, retains the differentiated influence information of different types of pores on the strength, realizes dimension expansion and information complementation of the feature space, and makes the input data more comprehensively reflect the internal damage state of the test piece.

Description

Technical Field

[0001] This invention relates to the field of pore feature analysis technology for steel slag concrete, specifically a method for pore feature analysis of steel slag concrete based on CT scanning and image processing. Background Technology

[0002] Steel slag is an industrial waste generated during the steelmaking process. Using it as aggregate to replace natural sand and gravel in the preparation of steel slag concrete is an important way to achieve resource recycling and sustainable development. However, the chemical composition (such as free calcium oxide f-CaO) and physical properties (such as porous structure) of steel slag result in poor volume stability and a tendency to form complex pore structures inside. The macroscopic mechanical properties of concrete (especially compressive strength) are closely related to its internal microstructure (such as porosity, pore morphology, and connectivity). Traditional concrete strength testing methods (such as destructive compressive strength tests) can only obtain the final result and cannot reveal the mechanism by which the internal structure affects the performance.

[0003] However, existing technologies mainly classify pores based on pore size (e.g., micropores, mesopores, macropores) or pore morphology (e.g., spherical, elongated), but lack refined analysis of the continuity of different sections within the same interconnected pore body. In watershed segmentation algorithms, while interconnected pores can be divided into multiple independent pores, the continuity of the segmented pores is not evaluated. Although existing studies have established quantitative models relating strength, fractal dimension, and porosity, these models are primarily based on overall pore characteristics and fail to distinguish the differentiated contributions of continuous pores (which may form seepage channels) and isolated pores (whose impact on strength is mainly weakening).

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing, so as to solve the problems mentioned in the background art.

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

[0007] A method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing, specifically including the following steps:

[0008] Step 1: Perform layered CT scanning on the steel slag concrete specimen to be analyzed to obtain a two-dimensional grayscale image sequence, and then use the watershed segmentation algorithm to divide the two-dimensional grayscale image sequence into a two-dimensional pore image sequence and a two-dimensional non-pore image sequence.

[0009] Step 2: Stack the two-dimensional pore image sequence sequentially according to the layer order during scanning to construct the three-dimensional volume data of the pores inside the steel slag concrete specimen to be tested, and mark the connected components of the three-dimensional volume data to obtain several pore connected bodies. Determine the direction of the longest principal axis of the pore connected body and divide the pore connected body into single pore connected bodies and slender pore connected bodies.

[0010] Step 3: Divide each slender pore body into several sub-connected segments along the longest principal axis of the body, extract the difference in cross-sectional area and the centroid offset of the cross-section between two adjacent connected segments, determine whether two adjacent sub-connected segments are continuous, and merge multiple continuous connected segments into a continuous pore.

[0011] Step 4: Extract pore features from continuous pores to obtain a continuous pore feature sequence. Extract pore features from all non-slender pore connected bodies and slender pore connected bodies that are not determined to be continuous sub-connected segments to obtain a single pore feature sequence. Integrate the continuous pore feature sequence and the single pore feature sequence through feature splicing to obtain a pore feature sequence. Determine the pore features of steel slag concrete based on the pore feature sequence.

[0012] Furthermore, the specific steps for dividing the two-dimensional grayscale image sequence into a two-dimensional porous image sequence and a two-dimensional non-porous image sequence are as follows:

[0013] The acquired two-dimensional grayscale image is preprocessed to obtain a preprocessed two-dimensional grayscale image.

[0014] The partial derivatives of the preprocessed two-dimensional grayscale image in two directions are squared and summed to obtain the image sum of squares. The square root of the image sum of squares is then taken to obtain the image gradient magnitude.

[0015] Set a two-dimensional spatial adaptive threshold, compare the preprocessed two-dimensional grayscale image with the two-dimensional spatial adaptive threshold. If the preprocessed two-dimensional grayscale image is less than the two-dimensional spatial adaptive threshold, the output value is 1. If the preprocessed two-dimensional grayscale image is greater than or equal to the two-dimensional spatial adaptive threshold, the output value is 0, thus obtaining a binary foreground label.

[0016] A distance transformation is performed on the binary foreground markers to obtain a distance map. Local maxima regions in the distance map are then identified and used as internal markers for the pore centers. Regions in the preprocessed two-dimensional grayscale image that are higher than twice the two-dimensional spatial adaptive threshold are used as external markers.

[0017] Using the gradient image as the terrain height and the internal and external markers as seed points, the immersion watershed algorithm is applied to obtain the segmentation boundary, dividing the image into porous and non-porous regions.

[0018] Furthermore, the specific steps for constructing the three-dimensional volumetric data of the internal pores of the steel slag concrete specimen to be tested are as follows:

[0019] Obtain a two-dimensional pore image sequence, and define a three-dimensional volumetric data space of the corresponding size based on the size and number of image layers of the two-dimensional pore image sequence;

[0020] The values ​​of all pixels in each layer of the 2D pore image are assigned to the voxels of the corresponding layer in the 3D volume data to obtain the 3D volume data.

[0021] Furthermore, the specific steps for connecting component labeling of 3D volume data are as follows:

[0022] Create a label matrix with the same size as the 3D volume data, initialize all elements to 0, and set the label of the current connected component to 0;

[0023] Scan each voxel sequentially. If the voxel is a pore voxel and is not labeled, start a new connected component with a connected component label value equal to the connected component label value plus 1, and label the current voxel with the connected component label value.

[0024] Using depth-first search, all unlabeled voxels within its 26 neighborhoods that satisfy the condition of being porosity voxels are labeled as connected component labels, and then recursively added to the neighborhood.

[0025] When the queue is empty, the current connected component is marked. Continue scanning the next unmarked pore voxel and repeat the above steps until all pore voxels are marked, and the final marking matrix is ​​obtained.

[0026] Furthermore, the specific steps for determining the longest principal axis direction of each pore interconnection are as follows:

[0027] Obtain the position vector of each voxel inside the pore connected body and the centroid vector of the pore connected body. Subtract the position vector and the centroid vector to obtain the coordinate vector of the voxel. Perform an outer product operation on the single coordinate vector and its transpose to obtain the deviation outer product matrix. Add the deviation outer product matrices of all voxels in each connected body to obtain the deviation outer product sum. Calculate the total number of voxels in each connected body to obtain the number of voxels in a single connected body. Multiply the reciprocal of the number of voxels in a single connected body by the deviation outer product sum to obtain the covariance matrix of all voxels.

[0028] The covariance matrix is ​​decomposed into eigenvalues ​​to obtain eigenvalues ​​and corresponding eigenvectors. The direction pointed to by the eigenvector corresponding to the largest eigenvalue is the principal axis direction of the pore.

[0029] Furthermore, the logic for dividing pore interconnects into single pore interconnects and elongated pore interconnects is as follows:

[0030] Obtain the maximum and minimum eigenvalues. Take the square root of the maximum eigenvalue to obtain the maximum dispersion radius, and take the square root of the minimum eigenvalue to obtain the minimum dispersion radius. Calculate the ratio between the square root of the maximum and minimum eigenvalues ​​to obtain the aspect ratio. Set a threshold for judging slender pores. Compare the slender pore judgment threshold with the aspect ratio. If the aspect ratio is greater than or equal to the slender pore judgment threshold, the pore is judged to be a slender pore; otherwise, the pore is a non-slender pore.

[0031] Furthermore, the specific steps for extracting the cross-sectional area difference are as follows:

[0032] Obtain the number of voxels contained in each connected segment, the side length of a single voxel in the X direction, the side length of a single voxel in the Y direction, and the side length of a single voxel in the Z direction. Multiply the number of voxels contained in each connected segment, the side length of a single voxel in the X direction, the side length of a single voxel in the Y direction, and the side length of a single voxel in the Z direction to obtain the total volume of each connected segment. Compare the total volume of each connected segment with the length of each segment to obtain the cross-sectional area of ​​each connected segment.

[0033] Calculate the difference in cross-sectional area between each connected segment and its adjacent connected segments based on the cross-sectional area of ​​each connected segment.

[0034] Furthermore, the specific steps to obtain the number of voxels contained in each connected segment are as follows:

[0035] For each voxel coordinate in each connected segment, determine whether its projection value in the principal axis direction belongs to the projection interval of the corresponding connected segment in the principal axis direction; if it does, count it as 1, otherwise ignore it; finally, sum the count values ​​of all voxels to obtain the number of voxels contained in each connected segment.

[0036] Furthermore, the specific steps for extracting the centroid offset of the cross-section of two adjacent slender pore connected bodies are as follows:

[0037] The three-dimensional spatial coordinates of each voxel in each connected segment are converted into column vectors. The column vectors of all voxels in each connected segment are added together to obtain the sum of the coordinate vectors. The number of voxels contained in each connected segment is inverted. The sum of the coordinate vectors is multiplied by the inverted value of each connected segment to obtain the centroid coordinate vector of each connected segment.

[0038] The three-dimensional Euclidean distance between the centroid coordinate vector of each connected segment and the centroid coordinate vector of its adjacent connected segments is calculated to obtain the cross-sectional centroid offset of two adjacent sub-connected segments.

[0039] Furthermore, the specific logic for determining whether two adjacent sub-connected segments are continuous is as follows:

[0040] Set a cross-sectional area fluctuation threshold and a cross-sectional centroid offset threshold. If the cross-sectional area difference is less than or equal to the cross-sectional area fluctuation threshold and the cross-sectional centroid offset is less than or equal to the cross-sectional centroid offset threshold, then mark the two sub-connected segments as continuous adjacent segments, and count the number of consecutive adjacent segments. The ratio of the number of consecutive adjacent segments to the total number of segments minus 1 is used as the continuity index of the slender pores.

[0041] Compared with the prior art, the beneficial effects of the present invention are:

[0042] This invention divides the slender pore interconnected body into N equal segments along the longest principal axis and extracts the cross-sectional area, which can capture the details of the diameter change of the pore along the extension direction, realize the quantitative description of the pore uniformity, and effectively identify local narrowing or expansion defects caused by the expansion of steel slag.

[0043] This invention sets a cross-sectional area fluctuation threshold and a cross-sectional centroid offset threshold as judgment criteria, providing a clear and quantifiable basis for the definition of continuous pores, realizing the automatic distinction between harmful connected pores and harmless slender pores, and avoiding subjective misjudgment;

[0044] This invention extracts continuous pore features and individual pore features separately and integrates them through feature splicing. This preserves the information on the differentiated influence of different types of pores on strength, realizes the dimensional expansion and information complementarity of the feature space, and enables the input data to more comprehensively reflect the internal damage state of the specimen. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0046] Figure 2 The fitted curve is a graph showing the relationship between the number of voxels and the cross-sectional area.

[0047] Figure 3 A fitted curve plot of the relationship between the number of consecutive segments and the continuous exponent;

[0048] Figure 4 Example image of a two-dimensional tomographic grayscale image of steel slag concrete obtained by CT scan;

[0049] Figure 5 A schematic diagram of the microscopic finite element model of steel slag fine aggregate concrete reconstructed in data integration and computing software;

[0050] Figure 6 This is a schematic diagram of the three-dimensional distribution model of steel slag fine aggregate identified after image segmentation.

[0051] Figure 7 A schematic diagram of the finite element model of steel slag fine aggregate reconstructed in finite element software;

[0052] Figure 8This is a schematic diagram of a microscopic finite element model of steel slag fine aggregate concrete reconstructed in finite element software. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0054] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0055] Example:

[0056] Please see Figures 1-8 The present invention provides a technical solution:

[0057] A method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing, specifically including the following steps:

[0058] Step 1: Based on CT scanning of the steel slag concrete specimen to be tested, a two-dimensional grayscale image sequence is obtained, and the two-dimensional grayscale image sequence is divided into a two-dimensional pore image sequence and a two-dimensional non-pore image sequence by watershed segmentation algorithm.

[0059] In this embodiment, the specific steps for dividing the two-dimensional grayscale image sequence into a two-dimensional aperture image sequence and a two-dimensional non-aperture image sequence are as follows:

[0060] The acquired two-dimensional grayscale image sequence is preprocessed to obtain a preprocessed two-dimensional grayscale image sequence.

[0061] The partial derivatives in both directions of the preprocessed two-dimensional grayscale image sequence are squared and summed to obtain the image sum of squares. The square root of the image sum of squares is then taken to obtain the image gradient magnitude. The mathematical expression for calculating the gradient magnitude is as follows:

[0062]

[0063] in,

[0064]

[0065]

[0066] In the formula, This indicates the pixel coordinates of the preprocessed 2D grayscale image. Gradient magnitude at; Represents the gradient in the horizontal direction; Represents the gradient in the vertical direction; Indicates to The first one obtained after median filtering and denoising Layered images;

[0067] A two-dimensional spatial adaptive threshold is set. The preprocessed two-dimensional grayscale image is compared with the two-dimensional spatial adaptive threshold. If the preprocessed two-dimensional grayscale image is smaller than the two-dimensional spatial adaptive threshold, the output value is 1; if the preprocessed two-dimensional grayscale image is greater than or equal to the two-dimensional spatial adaptive threshold, the output value is 0. This yields the binary foreground label, and the mathematical expression for the binary foreground label is:

[0068]

[0069] In the formula, This represents a two-dimensional image sequence, where 0 represents non-pores and 1 represents pores; This represents a two-dimensional adaptive threshold used to roughly distinguish dark pores. To ensure that the marker falls on the center of the pore, a distance transformation is usually performed on this binary image, and then local maxima in the distance image are found as internal markers.

[0070] Regions in the preprocessed 2D grayscale image that exceed twice the 2D spatial adaptive threshold are used as external markers.

[0071] The original gradient map is modified using internal and external markers. By forcing a minimum value at the marker locations, the original gradient map has the lowest "elevation" at these locations, thus guiding the subsequent "flood" process to begin from these marker points.

[0072]

[0073] In the formula, This represents the modified gradient magnitude map, forcing the marker points to be the minimum values ​​to avoid over- or under-segmentation of the watershed. It is a morphological operation that ensures that these locations are unique local minima in the gradient map by performing an erosion operation at specified locations. Indicates an internal marker, a marker point at the center of the pore (guiding the watershed to "submerge" from the center of the pore); Indicates external markers, marker points in solid background areas (defining the boundary range of the watershed division);

[0074] Applying a watershed transform to the modified gradient map, starting from all labeled minimum values, gradually submerges the entire terrain upwards (towards higher gradient values). When water from different basins is about to converge, a "watershed" dam is constructed, thus segmenting the image into different regions. The mathematical expression for applying the watershed transform to the gradient map is:

[0075]

[0076] In the formula, Indicates the first The watershed segmentation results of the layer image.

[0077] In this embodiment, the partial derivatives in the two directions are squared and summed, and then the square root is taken. The purpose is to integrate the gray-level change rate in the two-dimensional direction into a scalar value, which represents the overall gray-level change intensity (i.e., the slope of the terrain) of the point. Watershed segmentation is usually performed on the gradient magnitude map of the image. The gradient map can highlight the areas where the pixel values ​​change drastically. These areas usually correspond to the boundaries between different materials (such as pores and solids).

[0078] In this embodiment, the pixel values ​​of the segmented pore regions are set to 1, and the non-pore regions are set to 0 to obtain a two-dimensional pore image; at the same time, the non-pore regions are output separately as a two-dimensional non-pore image sequence.

[0079] In this embodiment, the specific steps for preprocessing the scanned two-dimensional grayscale image sequence to obtain a preprocessed two-dimensional grayscale image sequence are as follows:

[0080] First, the steel slag concrete specimen under test was scanned using X-ray microcomputed tomography (CT). X-rays attenuate as they penetrate a material; the degree of attenuation is determined by the material's density and atomic number. The solid phases (aggregates and paste) in concrete have high density and attenuate X-rays strongly, appearing as brighter areas in the projection image. Conversely, the pores (air) have low density and attenuate weakly, appearing as darker areas. The CT scanning process follows Beer-Lambert's law; when a beam of intensity... Monochromatic X-rays pass through a length of After the object, the emission intensity It is determined by the following integrals:

[0081]

[0082] In the formula, This represents the intensity received by the detector after passing through the steel slag concrete under test, and is a function of the X-ray energy E; It represents the intensity of the ray at the time of its emission, i.e., a function of its energy E; This represents the density of the steel slag concrete to be tested, where... The small amount indicates that the radiation is hardly weakened. The large indicates that the radiation has been greatly reduced; This represents the line integral along the X-ray path L, which sums up all the attenuation along the entire X-ray path. It is a tiny unit of length on the path;

[0083] By acquiring a large amount of projection data from different angles and using mathematical algorithms such as filtered backprojection or iterative reconstruction for three-dimensional reconstruction, a series of two-dimensional tomographic images are finally obtained. ,in The number of scan layers; for any image layer It is a size of The matrix, each voxel in the matrix The gray value represents the voxel, and the magnitude of the gray value is positively correlated with the average atomic number and density of the material;

[0084] To eliminate salt-and-pepper noise or Gaussian noise while preserving the sharpness of the aperture edges, median filtering is typically used. The mathematical expression for this is:

[0085]

[0086] In the formula, This represents the defined neighborhood window; This represents the grayscale value after filtering.

[0087] In this embodiment, the specific steps for constructing the three-dimensional volumetric data of the internal pores of the steel slag concrete specimen to be tested by sequentially superimposing the two-dimensional pore image sequence according to the layer order during scanning are as follows:

[0088] Obtain a two-dimensional pore image sequence, and define a three-dimensional volumetric data space of the corresponding size based on the size and number of image layers of the two-dimensional pore image sequence;

[0089] The values ​​of all pixels in each layer of the 2D pore image are assigned to the voxels of the corresponding layer in the 3D volume data to obtain the 3D volume data, i.e., for any pixel coordinate... ,make ,in For the first Layer images in Given the binary pixel values ​​at a given location, the mathematical expression for constructing the three-dimensional volumetric data of the internal pores of the steel slag concrete specimen to be tested is:

[0090]

[0091] In the formula, Represents three-dimensional volume data, where Indicates that it is located at Voxels belong to pores. This indicates that it belongs to the non-porous category; Indicates the image layer number; It represents the pixel position in a two-dimensional image.

[0092] In this embodiment, all two-dimensional pore image sequences are extracted (binary images, where a pixel value of 0 represents a non-pore and 1 represents a pore); assuming a total of Layered images, each layer having a size of [size missing]. (Width Pixels, High (pixels), numbered sequentially according to the layer order during scanning (from bottom to top or top to bottom). .

[0093] In this embodiment, a three-dimensional array is established. Its dimensions are ,in:

[0094] The axis corresponds to the width direction of the image (column index), and its value range is... ; The axis corresponds to the image height direction (row index), and its value range is... ; The axis corresponds to the slice direction (scan depth), and its value range is... .

[0095] Step 2: Stack the two-dimensional pore image sequence sequentially according to the layer order during scanning to construct the three-dimensional volume data of the pores inside the steel slag concrete specimen to be tested, and mark the connected components of the three-dimensional volume data to obtain several pore connected bodies. Determine the direction of the longest principal axis of the pore connected body, and divide the pore connected body into single pore connected bodies and slender pore connected bodies.

[0096] In this embodiment, the specific steps for connecting component labeling of 3D volume data are as follows:

[0097] Create a label matrix with the same size as the 3D volume data, initialize all elements to 0, and set the label of the current connected component to 0;

[0098] In order (e.g.) , , Scan each voxel If the voxel is (Porosity voxel) and If (not marked), a new connected component is started, whose connected component label value is equal to the connected component label value plus 1, and the current voxel is marked with the connected component label value;

[0099] Using depth-first search, all unlabeled voxels within its 26 neighborhoods that satisfy the condition of being porosity voxels are labeled as connected component labels, and then recursively added to the neighborhood.

[0100] When the queue is empty, the current connected component is marked. Continue scanning the next unmarked pore voxel, repeating the above steps until all pore voxels are marked, obtaining the final marking matrix. The mathematical expression for obtaining the final marking matrix is:

[0101]

[0102] In the formula, Let the final label matrix be... Indicates non-porous voxels. This indicates that the voxel belongs to the first... A series of interconnected pores, in which This represents the total number of connected components.

[0103] In this embodiment, a three-dimensional 26-neighborhood connectivity criterion (i.e., each voxel is adjacent to 26 surrounding voxels, including face adjacency, edge adjacency, and corner adjacency) is used to accurately label the connectivity of pores. Let the voxel coordinates be... Its 26-neighborhood set is:

[0104]

[0105] In the formula, Represents the 26-neighborhood set; This represents the coordinates of neighboring points after the center point has been offset. This represents the offset in the x, y, and z directions.

[0106] In this embodiment, the specific steps for determining the longest principal axis direction of each pore connection are as follows:

[0107] Obtain the position vector of each voxel within the pore connected volume and the centroid vector of the pore connected volume. Subtract the position vector from the centroid vector to obtain the coordinate vector of that voxel. Perform an outer product operation on the individual coordinate vector and its transpose to obtain the deviation outer product matrix. Add the deviation outer product matrices of all voxels in each connected volume to obtain the deviation outer product sum. Calculate the total number of voxels in each connected volume to obtain the number of voxels in a single connected volume. Multiply the reciprocal of the number of voxels in a single connected volume by the deviation outer product sum to obtain the covariance matrix of all voxels. The mathematical expression for calculating the covariance matrix of all voxels is:

[0108]

[0109] In the formula, Let represent the covariance matrix of all voxels, describing the dispersion and correlation of all voxel coordinates in various directions within the pore connectivity. Its mathematical form is: ; The coordinate vector representing a voxel; Indicates the coordinates of the centroid of a connected volume; Indicates the first The total number of voxels in the body connected by each pore;

[0110] Eigenvalue decomposition of the covariance matrix yields eigenvalues ​​and their corresponding eigenvectors. The direction pointed to by the eigenvector corresponding to the largest eigenvalue is the principal axis direction of the pores. Therefore, the mathematical expression for eigenvalue decomposition of the covariance matrix is:

[0111]

[0112] In the formula, Indicates the first 1 eigenvector These are indices of eigenvalues ​​and eigenvectors, representing the direction of pore distribution. Indicates the direction of maximum (major axis direction). Indicates the second largest direction (second principal axis). The direction representing the smallest point (the third principal axis) is represented as follows: ; Indicates the first There are eigenvalues, representing the magnitude of the variance along the corresponding eigenvector direction, where , This represents the variance (maximum) along the principal axis direction. This indicates the variance (maximum) in the direction of the second principal axis. This represents the variance (minimum) in the direction of the third principal axis.

[0113] The mathematical expression for the principal axis direction is:

[0114]

[0115] In the formula, This represents the direction vector of the principal axis.

[0116] In this embodiment, the specific steps for calculating the total number of voxels within a connected body are as follows:

[0117] For all elements in the label matrix belonging to the first... The voxel coordinates of each connected component are iterated and summed. A voxel is counted as 1 if its connected component label value equals its connected component number, and as 0 otherwise. The sum of all counts yields the total number of voxels in each connected component. For each connected component... The statistical marker value is The mathematical expression for the number of voxels is:

[0118]

[0119] in It is an indicator function.

[0120]

[0121] In the formula, Indicates the first The total number of voxels in the body is connected by each pore.

[0122] In this embodiment, the logic for dividing the pore interconnection into a single pore interconnection and an elongated pore interconnection is as follows:

[0123] Obtain the maximum and minimum eigenvalues. Take the square root of the maximum eigenvalue to obtain the maximum scatter radius, and take the square root of the minimum eigenvalue to obtain the minimum scatter radius. Calculate the ratio between the square root of the maximum and minimum eigenvalues ​​to obtain the aspect ratio. Set a threshold for classifying slender pores. Compare the slender pore classification threshold with the aspect ratio. If the aspect ratio is greater than or equal to the slender pore classification threshold, the pore is determined to be a slender pore; otherwise, the pore is not a slender pore. The mathematical expression for calculating the aspect ratio is:

[0124]

[0125] In the formula, Indicates the aspect ratio.

[0126] In this embodiment, focusing on crack-like pores, the threshold for judging elongated pores is typically... ,like ,Right now Then the pores are nearly spherical; if ,Right now Then the pores are disc-shaped; if ,Right now Then the pores are rod-shaped.

[0127] Step 3: Divide each slender pore body into several sub-connected segments along the longest principal axis of the body, extract the difference in cross-sectional area and the centroid offset of the cross-section between two adjacent connected segments, determine whether two adjacent sub-connected segments are continuous, and merge multiple continuous sub-connected segments into a continuous pore.

[0128] In this embodiment, the specific steps for extracting the cross-sectional area difference are as follows:

[0129] Obtain the number of voxels, the side length of a single voxel in the X direction, the side length of a single voxel in the Y direction, and the side length of a single voxel in the Z direction for each connected segment. Multiply these values ​​together to obtain the total volume of each connected segment. Compare the total volume of each connected segment with the length of each segment to obtain the cross-sectional area of ​​each connected segment. The mathematical expression for calculating the cross-sectional area of ​​each connected segment is:

[0130]

[0131] In the formula, Indicates the first The cross-sectional area of ​​the connected segments, where This indicates the segment number, showing which segment the current segment is; Indicates the first The number of voxels contained in the segment; This represents the side length of a single voxel in the X direction; This represents the side length of a single voxel in the Y direction; This represents the side length of a single voxel in the Z direction; Indicates the length of each segment;

[0132] Based on the cross-sectional area of ​​each connected segment, the difference in cross-sectional area between each connected segment and its adjacent connected segments is calculated. The mathematical expression for calculating the difference in cross-sectional area is as follows:

[0133]

[0134] In the formula, Indicates the first The cross-sectional area of ​​a connected segment; This represents the difference in cross-sectional area.

[0135] In this embodiment, 50 sets of cross-sectional area data for connected segments were obtained, among which , , and For fixed values, It is 1mm. The partial data is shown below:

[0136] Table 1: Cross-sectional area data of connected segments

[0137]

[0138] According to Table 1 and Figure 2 It can be seen that the number of pore voxels The cross-sectional area increased from 213 to 817. As the number of pore voxels increases from 0.21 mm² to 0.9 mm², the corresponding pore cross-sectional area increases significantly with the increase in the number of pore voxels.

[0139] In this embodiment, the specific steps for obtaining the number of voxels contained in each connected segment are as follows:

[0140] For each voxel coordinate within each connected segment, determine whether its projection value along the principal axis belongs to the projection interval of the corresponding connected segment along the principal axis; if it does, count it as 1; otherwise, ignore it. Finally, sum the counts of all voxels to obtain the number of voxels contained in each connected segment. The mathematical expression for obtaining the number of voxels contained in each connected segment is:

[0141]

[0142] in,

[0143]

[0144]

[0145] In the formula, Indicates the first The number of voxels contained in the segment; This represents the projection value of a single voxel onto the principal axis.

[0146] In this embodiment, the elongated pore-connected body is divided into N equal segments along the longest principal axis of the body. The specific steps for determining the length of each segment are as follows:

[0147] Calculate the projected length of the slender, interconnected pore volume along the principal axis:

[0148]

[0149] In the formula, The projected length represents the total length of a slender, interconnected pore along its longest principal axis, which is the length obtained by "flattening" a three-dimensional pore along the principal axis. Indicates the first A connected entity; The position vector of a voxel is the coordinate of a voxel in three-dimensional space within a connected volume; Represents the unit vector along the principal axis, which is the longest extension direction of the slender pore;

[0150] Divide the slender pores into equal parts along the principal axis. Segments, each segment has a length of:

[0151]

[0152] In the formula, Indicates the length of each segment; Represents the number of equal segments;

[0153] Then the first The projection interval of the segment is:

[0154]

[0155]

[0156]

[0157] In the formula, Indicates the first The projection interval of the segment; The minimum projection value represents the minimum projection of all voxels in the connected volume along the principal axis, i.e., the starting position of the pore. The maximum projection value represents the maximum value of the projections of all voxels in the connected volume along the principal axis, which is the end point of the pore.

[0158] No. The voxel set of the segment is:

[0159]

[0160] In the formula, Indicates the first A set of voxels for a segment.

[0161] In this embodiment, the specific steps for extracting the centroid offset of the cross-section of two adjacent slender pore connected bodies are as follows:

[0162] Convert the 3D spatial coordinates of each voxel in each connected segment into column vectors. Sum the column vectors of all voxels in each connected segment to obtain the sum of the coordinate vectors. Take the inverse of the number of voxels contained in each connected segment, and multiply the sum of the coordinate vectors by the inverted value of each connected segment to obtain the centroid coordinate vector of each connected segment. The mathematical expression for calculating the centroid coordinate vector of each connected segment is:

[0163]

[0164] In the formula, Indicates the first The centroid coordinate vectors of each connected segment, i.e. ,in Indicates the first The X-coordinate of the centroid of a connected segment. Indicates the first The Y-coordinate of the centroid of each connected segment. Indicates the first Z-coordinates of the centroids of each connected segment; A column vector representing the position of a single voxel (transpose means converting a row vector to a column vector).

[0165] The three-dimensional Euclidean distance between the centroid coordinate vector of each connected segment and the centroid coordinate vector of its adjacent connected segments is calculated to obtain the centroid offset of the cross-section of two adjacent sub-connected segments. The mathematical expression for calculating the three-dimensional Euclidean distance is:

[0166]

[0167] In the formula, This represents the centroid offset of the cross section between two adjacent connected segments; Indicates the first The centroid coordinate vectors of each connected segment; Indicates the first The X coordinates of the centroids of each connected segment; Indicates the first The Y-coordinate of the centroid of each connected segment. Indicates the first The Z-coordinate of the centroid of a connected segment.

[0168] In this embodiment, the specific logic for determining whether two adjacent sub-connected segments are continuous is as follows:

[0169] Set a cross-sectional area fluctuation threshold and a cross-sectional centroid offset threshold. If the difference in cross-sectional area is less than or equal to the cross-sectional area fluctuation threshold, and the cross-sectional centroid offset is less than or equal to the cross-sectional centroid offset threshold, then mark the two sub-connected segments as consecutive adjacent segments. Count the number of consecutive adjacent segments. The ratio of the number of consecutive adjacent segments to the total number of segments minus 1 is used as the continuity index of the slender pores. The mathematical expression for calculating the continuity index of the slender pores is:

[0170]

[0171] In the formula, The continuity index indicates the number of slender pores; It represents the number of consecutive adjacent segments.

[0172] In this embodiment, continuous index data for 50 sets of slender pores were statistically analyzed, and some of the data are as follows:

[0173] Table 2: Continuity index data for slender pores

[0174]

[0175] According to Table 2 and Figure 3It can be seen that the continuity index generally increases with the number of continuous segments. In the early stage (0-10 continuous segments), the continuity index is very low, in the range of 0-0.23. In the middle stage (10-30), it rises slowly, in the range of 0.23-0.5. In the later stage (30-50), it rises rapidly and approaches 1. The continuity index of the 48th segment is 0.96, and the continuity index of the 49th segment is 0.99. This shows that the longer the number of continuous segments, the higher the continuity index, and the closer it is to the state of complete continuity. When the number of continuous segments reaches 49, it almost reaches the state of complete continuity / complete connection / complete penetration.

[0176] Step 4: Extract pore features from continuous pores to obtain a continuous pore feature sequence. Extract pore features from all non-slender pore connected bodies and slender pore connected bodies that are not determined to be continuous sub-connected segments to obtain a single pore feature sequence. Integrate the continuous pore feature sequence and the single pore feature sequence through feature splicing to obtain a pore feature sequence. Determine the pore features of steel slag concrete based on the pore feature sequence.

[0177] In this embodiment, a single pore includes the original non-elongated pore connected body (length-to-diameter ratio < threshold) and the sub-connected segments (isolated segments) in the elongated pore connected body that are not determined to be continuous.

[0178] In this embodiment, the specific steps for extracting the feature sequence of a single pore are as follows:

[0179] Obtain the volume of each pore, compare 3 times the pore volume with 4 times π to obtain the first divisor, multiply the cube root of the first divisor by 2 to obtain the equivalent diameter of each pore. The mathematical expression for calculating the equivalent diameter of each pore is:

[0180]

[0181] in,

[0182]

[0183]

[0184] middle, Indicates the first The equivalent diameter of each pore; Indicates the first The volume of each pore; Indicates the first The spatial domain of a pore; Represents the volume of a single voxel;

[0185] To obtain the total volume and total number of pores in the steel slag concrete to be tested, the sum of the volumes of all pores is calculated to obtain the pore volume sum. The ratio between the pore volume sum and the total volume of the steel slag concrete to be tested is then calculated to obtain the pore volume fraction. The mathematical expression for calculating the pore volume fraction is as follows:

[0186]

[0187] In the formula, Indicates the pore volume fraction; Indicates the total number of pores; This represents the total volume of the steel slag concrete to be measured;

[0188] To obtain the surface area of ​​each pore, multiply the square of 6 times the volume of each pore by the cube root of π to get the equivalent spherical surface area of ​​each pore. Compare the equivalent spherical surface area of ​​each pore with the surface area of ​​each pore to obtain the sphericity of each pore. The mathematical expression for calculating the sphericity of each pore is as follows:

[0189]

[0190] in,

[0191]

[0192] In the formula, Indicates the first The sphericity of each pore (value range (0,1], the closer to 1, the closer the pore is to a sphere); Indicates the first Surface area of ​​each pore;

[0193] Using cubes of varying side lengths to cover the porous space, as the side lengths approach 0, the fractal dimension is obtained by calculating the negative of the ratio of the natural logarithm of the number of cubes required to cover the porous structure to the natural logarithm of the side length. The mathematical expression for calculating the fractal dimension is:

[0194]

[0195] In the formula, It represents the fractal dimension (characterizing the complexity, irregularity, and degree of fragmentation of pore morphology); Indicates the side length of the cube box; This represents the side length required to cover all pores. The total number of cube boxes.

[0196] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0197] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0198] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0199] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing, characterized in that, The specific steps include: Step 1: Perform layered CT scanning on the steel slag concrete specimen to be analyzed to obtain a two-dimensional grayscale image sequence, and then use the watershed segmentation algorithm to divide the two-dimensional grayscale image sequence into a two-dimensional pore image sequence and a two-dimensional non-pore image sequence. Step 2: Stack the two-dimensional pore image sequence sequentially according to the layer order during scanning to construct the three-dimensional volume data of the pores inside the steel slag concrete specimen to be tested, and mark the connected components of the three-dimensional volume data to obtain several pore connected bodies. Determine the direction of the longest principal axis of the pore connected body and divide the pore connected body into single pore connected bodies and slender pore connected bodies. Step 3: Divide each slender pore body into several sub-connected segments along the longest principal axis of the body, extract the difference in cross-sectional area and the centroid offset of the cross-section between two adjacent connected segments, determine whether two adjacent sub-connected segments are continuous, and merge multiple continuous connected segments into a continuous pore. Step 4: Extract the pore features of continuous pores to obtain a continuous pore feature sequence. Extract the pore features of all non-slender pore connected bodies and slender pore connected bodies that are not determined to be continuous sub-connected segments to obtain a single pore feature sequence. Integrate the continuous pore feature sequence and the single pore feature sequence through feature splicing to obtain a pore feature sequence. Determine the pore features of steel slag concrete based on the pore feature sequence. The specific logic for determining whether two adjacent sub-connected segments are continuous is as follows: Set a cross-sectional area fluctuation threshold and a cross-sectional centroid offset threshold. If the cross-sectional area difference is less than or equal to the cross-sectional area fluctuation threshold and the cross-sectional centroid offset is less than or equal to the cross-sectional centroid offset threshold, then mark the two sub-connected segments as continuous adjacent segments, and count the number of consecutive adjacent segments. The ratio of the number of consecutive adjacent segments to the total number of segments minus 1 is used as the continuity index of the slender pores.

2. The method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing according to claim 1, characterized in that, The specific steps to divide a two-dimensional grayscale image sequence into a two-dimensional porous image sequence and a two-dimensional non-porous image sequence are as follows: The acquired two-dimensional grayscale image is preprocessed to obtain a preprocessed two-dimensional grayscale image. The partial derivatives of the preprocessed two-dimensional grayscale image in two directions are squared and summed to obtain the image sum of squares. The square root of the image sum of squares is then taken to obtain the image gradient magnitude. Set a two-dimensional spatial adaptive threshold, compare the preprocessed two-dimensional grayscale image with the two-dimensional spatial adaptive threshold. If the preprocessed two-dimensional grayscale image is less than the two-dimensional spatial adaptive threshold, the output value is 1. If the preprocessed two-dimensional grayscale image is greater than or equal to the two-dimensional spatial adaptive threshold, the output value is 0, thus obtaining a binary foreground label. A distance transformation is performed on the binary foreground markers to obtain a distance map. Local maxima regions in the distance map are then identified and used as internal markers for the pore centers. Regions in the preprocessed two-dimensional grayscale image that are higher than twice the two-dimensional spatial adaptive threshold are used as external markers. Using the gradient image as the terrain height and the internal and external markers as seed points, the immersion watershed algorithm is applied to obtain the segmentation boundary, dividing the image into porous and non-porous regions.

3. The method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing according to claim 1, characterized in that, The specific steps for constructing the three-dimensional volumetric data of the internal pores of the steel slag concrete specimen to be tested are as follows: Obtain a two-dimensional pore image sequence, and define a three-dimensional volumetric data space of the corresponding size based on the size and number of image layers of the two-dimensional pore image sequence; The values ​​of all pixels in each layer of the 2D pore image are assigned to the voxels of the corresponding layer in the 3D volume data to obtain the 3D volume data.

4. The method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing according to claim 1, characterized in that, The specific steps for connecting component labeling of 3D volume data are as follows: Create a label matrix with the same size as the 3D volume data, initialize all elements to 0, and set the label of the current connected component to 0; Scan each voxel sequentially. If the voxel is a pore voxel and is not labeled, start a new connected component with a connected component label value equal to the connected component label value plus 1, and label the current voxel with the connected component label value. Using depth-first search, all unlabeled voxels within its 26 neighborhoods that satisfy the condition of being porosity voxels are labeled as connected component labels, and then recursively added to the neighborhood. When the queue is empty, the current connected component is marked. Continue scanning the next unmarked pore voxel and repeat the above steps until all pore voxels are marked, and the final marking matrix is ​​obtained.

5. The method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing according to claim 1, characterized in that, The specific steps for determining the longest principal axis direction of each pore-connected body are as follows: Obtain the position vector of each voxel inside the pore connected body and the centroid vector of the pore connected body. Subtract the position vector and the centroid vector to obtain the coordinate vector of the voxel. Perform an outer product operation on the single coordinate vector and its transpose to obtain the deviation outer product matrix. Add the deviation outer product matrices of all voxels in each connected body to obtain the deviation outer product sum. Calculate the total number of voxels in each connected body to obtain the number of voxels in a single connected body. Multiply the reciprocal of the number of voxels in a single connected body by the deviation outer product sum to obtain the covariance matrix of all voxels. The covariance matrix is ​​decomposed into eigenvalues ​​to obtain eigenvalues ​​and corresponding eigenvectors. The direction pointed to by the eigenvector corresponding to the largest eigenvalue is the principal axis direction of the pore.

6. The method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing according to claim 5, characterized in that, The logic for dividing pore interconnects into single pore interconnects and elongated pore interconnects is as follows: Obtain the maximum and minimum eigenvalues. Take the square root of the maximum eigenvalue to obtain the maximum dispersion radius, and take the square root of the minimum eigenvalue to obtain the minimum dispersion radius. Calculate the ratio between the square root of the maximum and minimum eigenvalues ​​to obtain the aspect ratio. Set a threshold for judging slender pores. Compare the slender pore judgment threshold with the aspect ratio. If the aspect ratio is greater than or equal to the slender pore judgment threshold, the pore is judged to be a slender pore; otherwise, the pore is a non-slender pore.

7. The method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing according to claim 1, characterized in that, The specific steps for extracting the cross-sectional area difference are as follows: Obtain the number of voxels contained in each connected segment, the side length of a single voxel in the X direction, the side length of a single voxel in the Y direction, and the side length of a single voxel in the Z direction. Multiply the number of voxels contained in each connected segment, the side length of a single voxel in the X direction, the side length of a single voxel in the Y direction, and the side length of a single voxel in the Z direction to obtain the total volume of each connected segment. Compare the total volume of each connected segment with the length of each segment to obtain the cross-sectional area of ​​each connected segment. Calculate the difference in cross-sectional area between each connected segment and its adjacent connected segments based on the cross-sectional area of ​​each connected segment.

8. The method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing according to claim 7, characterized in that, The specific steps to obtain the number of voxels contained in each connected segment are as follows: For each voxel coordinate in each connected segment, determine whether its projection value along the principal axis belongs to the projection interval of the corresponding connected segment along the principal axis. If it belongs to the category, the count is 1; otherwise, it is ignored. Finally, the counts of all voxels are summed to obtain the number of voxels contained in each connected segment.

9. The method for analyzing the pore characteristics of steel slag concrete based on CT scanning and image processing according to claim 1, characterized in that, The specific steps for extracting the centroid offset of the cross section of two adjacent slender pore connected bodies are as follows: The three-dimensional spatial coordinates of each voxel in each connected segment are converted into column vectors. The column vectors of all voxels in each connected segment are added together to obtain the sum of the coordinate vectors. The number of voxels contained in each connected segment is inverted. The sum of the coordinate vectors is multiplied by the inverted value of each connected segment to obtain the centroid coordinate vector of each connected segment. The three-dimensional Euclidean distance between the centroid coordinate vector of each connected segment and the centroid coordinate vector of its adjacent connected segments is calculated to obtain the cross-sectional centroid offset of two adjacent sub-connected segments.

Images