A comprehensive index construction method for the distribution law of three-dimensional pore structure characteristics of soil

Abstract

A comprehensive index construction method for the distribution law of three-dimensional pore structure characteristics in soil. It relates to the cross-technology field of soil science and computer technology, and specifically relates to the technical field of analyzing the distribution law of three-dimensional pore structure characteristics by constructing a comprehensive index. The present invention constructs an index for the distribution law of three-dimensional pore structure characteristics based on the estimated value of three-dimensional Minkowski functionals, which can comprehensively and intuitively reflect key parameters such as soil porosity, specific surface area, and connectivity. The method includes the following steps: obtaining a binary image and performing preprocessing; cutting the pixel matrix data set to obtain a representative basic volume data set of the soil pore structure; calculating the estimated value of the Minkowski functional in three-dimensional space; analyzing the estimated value of the Minkowski functional based on the characteristics of skewness and kurtosis in statistics; constructing an index for the distribution law of three-dimensional pore structure characteristics based on the pore structure distribution characteristic parameters of different soil types.

Description

Technical Field

[0001] The present invention relates to the cross - technical field of soil science and computer technology, and particularly to a technical field of analyzing the distribution law of soil three - dimensional pore structure characteristics by constructing a comprehensive index. Background Art

[0002] The three - dimensional pore structure of soil plays a crucial role in regulating soil functions such as water movement, nutrient exchange, and microbial activities. Studying the characteristics and distribution law of the soil three - dimensional pore structure helps to reveal the internal relationship between soil physical, chemical, and biological properties, and is of great significance for soil improvement, farmland production management, and ecosystem research. Traditional research methods for soil pore structure mainly focus on two - dimensional slice observations, which are difficult to comprehensively and truly reflect the morphology and distribution of three - dimensional pores.

[0003] In recent years, with the development of computer tomography (CT), three - dimensional reconstruction, and image - processing technologies, new technical means have been provided for the study of soil three - dimensional pore structure. However, existing research mainly focuses on single soil or simple geometric models, and it is difficult to comprehensively reveal the morphology, distribution, and connectivity characteristics of multi - scale soil pores. In addition, when characterizing pore characteristics, existing methods often only focus on macroscopic indicators such as porosity, and cannot deeply explore pore shape, surface characteristics, connectivity, and the spatial distribution law of various pores.

[0004] At the same time, the influence of different soil types, tillage methods, and environmental conditions on soil pore structure has not been fully clarified. Especially during long - term tillage or ecological restoration, the evolution law and driving mechanism of soil pore structure still lack systematic research. This research limitation restricts the wide application of soil pore characteristics in precision agriculture, environmental protection, and soil health assessment.

[0005] Therefore, researchers in this field are committed to adopting new methods based on advanced technologies, which can efficiently and accurately integrate a large amount of soil pore structure data, generate accurate soil health and performance prediction models, and provide strong technical support for future soil management and sustainable agriculture. Summary of the Invention

[0006] In view of the above problems, the object of the present invention is to propose a method for constructing a comprehensive index of the distribution law of soil three - dimensional pore structure characteristics. By constructing an index of the distribution law of three - dimensional pore structure characteristics based on the estimated value of three - dimensional Minkowski functionals, it can comprehensively and intuitively reflect key parameters such as soil porosity, specific surface area, and connectivity.

[0007] The method includes the following steps:

[0008] S1. Obtain binary images and pre - process them to obtain a pixel matrix data set;

[0009] S2. Cut the pixel matrix dataset to obtain a representative basic volume dataset of the soil pore structure , , where represents the pore sub-structure pixel matrix, represents the set of real numbers, N represents the number of soil types, and M represents the number of samples contained in each soil type, represents the number of overlapping sub-matrices obtained by cutting the pixel matrix dataset;

[0010] S3. Calculate the estimated value of the Minkowski functional of in three-dimensional space: , where represents the pore sub-structure pixel matrix of porosity, represents the pore surface area of the pore sub-structure pixel matrix , represents the pore connectivity of the pore sub-structure pixel matrix ;

[0011] S4. Analyze the estimated value of the Minkowski functional based on the characteristics of skewness and kurtosis in statistics to obtain the pore structure distribution characteristic parameters of different soil types;

[0012] S5. Construct a three-dimensional pore structure characteristic distribution law index based on the pore structure distribution characteristic parameters of different soil types.

[0013] Further, the preprocessing is specifically: select consecutive and identically sized regions of interest with a size of pixels from binary images, and convert the regions of interest into a pixel matrix dataset.

[0014] Further, the cutting of the pixel matrix dataset is specifically: cut the pixel matrix dataset in combination with the representative basic volume size and a sliding window; the size of the sliding window is set to , and the step size is L pixels.

[0015] Further, the is calculated by the formula: , where represents the volume of the pore part in the three-dimensional matrix , represents the total volume of the three-dimensional matrix ; the is calculated by the formula: , where represents the three-dimensional matrix total area; the is calculated by the formula: where represents the number of connected components of pores in the three-dimensional matrix and represents the number of holes in the three-dimensional matrix .

[0016] Furthermore, the characteristic parameters of the pore structure distribution of different soil types are specifically: and , where represents the kurtosis of the estimated value, represents the skewness of the estimated value, where , represents the porosity of the , represents the pore surface area of the , represents the pore connectivity of the .

[0017] Furthermore, the is calculated by the formula: where represents the number of elements in the set ; the is calculated by the formula: .

[0018] Furthermore, the characteristic distribution law index of the three-dimensional pore structure is specifically: , where , when represents the kurtosis function, when represents the skewness function, represents the soil porosity of the th characteristic sample of the th soil type, represents the soil pore surface area of the th characteristic sample of the th soil type, represents the soil pore connectivity of the th characteristic sample of the th soil type, , and respectively represent the fitting weight parameters of soil porosity, soil pore surface area, and soil pore connectivity.

[0019] Further, the size of the pixel matrix data set is: .

[0020] The beneficial effects of the method of the present invention are as follows:

[0021] (1) The method for analyzing the distribution law of the three-dimensional pore structure characteristics of soil provided by the present invention can accurately and efficiently characterize the microscopic characteristics of the soil pore structure, providing a scientific and reliable solution for studying the soil structure characteristics and their functional relationships.

[0022] (2) By using the representative elementary volume (REV) cutting theory, the present invention significantly expands the sample size, improves the representativeness and diversity of the overall data distribution, and provides strong data support for studying the statistical characteristics and parameter variation laws of the soil pore structure.

[0023] (3) The present invention proposes a method for calculating characteristic parameters based on three-dimensional Minkowski functionals, which can comprehensively and intuitively reflect key parameters such as soil porosity, specific surface area, and connectivity, and analyze their distribution laws in combination with statistical methods, providing an important reference for studying soil water storage, air permeability, and nutrient transport characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0025] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention fall within the protection scope of the present invention.

[0026] This embodiment provides a method for constructing a comprehensive index for the distribution law of the three-dimensional pore structure characteristics of soil. The flowchart of the method is as Figure 1 shown, and the method includes the following steps:

[0027] S1. Obtain binary images and perform preprocessing to obtain a pixel matrix data set.

[0028] The relevant operations of step S1 will be introduced with specific examples:

[0029] As shown in Table 1, soil sample data of four different soil types, namely black soil , chernozem , meadow soil , and aeolian sandy soil , are collected in the corn planting area of Jilin Province.

[0030] Table 1

[0031]

[0032] As shown in Tables 2, 3 and 4, based on the soil sample data, the soil sample data was scanned, parameter-adjusted, reconstructed, de-ringed and hard beam reduced by using an X-ray micro-CT system. For each processing action, 3 samples were randomly selected for CT scanning, and Image J software was used for image reconstruction. Finally, 36 data samples were obtained.

[0033] Table 2

[0034]

[0035] Table 3

[0036]

[0037] Table 4

[0038]

[0039] For each data sample, 1000 binary two-dimensional slice images were generated. During the binarization process, the white area was represented by the value 1 for pores, and the black area was represented by the value 0 for the soil matrix. 300 consecutive regions of interest (ROIs) with a size of pixels were selected and converted into a pixel matrix to obtain the pixel matrix dataset of the original soil pore structure. In this embodiment, has a value of 300, should take a positive integer value.

[0040] S2. Cut the pixel matrix dataset to obtain the representative elementary volume dataset of the soil pore structure , , where represents the pixel matrix of the pore sub-structure, represents the set of real numbers, N represents the number of soil types, M represents the number of samples contained in each soil type, represents the number of overlapping sub-matrices obtained by cutting the pixel matrix dataset. In this embodiment, the values of N, M and K are 4, 9 and 100 respectively.

[0041] The relevant operations of step S2 are introduced with specific examples:

[0042] Based on the representative elementary volume (REV) cutting theory, the pixel matrix dataset was cut by determining the representative elementary volume size and combining the sliding window method to expand the sample size by cutting. The sliding window size was set to , with a step size of 25 pixels to ensure partial overlap between samples and improve the representativeness of the overall distribution. During the cutting process, for each pixel image matrix, 100 overlapping sub-matrices are generated to further increase sample diversity. In this embodiment, the value of is 50, and

[0043] S3. Calculate the Minkowski functional estimate value in three-dimensional space: , where represents the porosity of the pore sub-structure pixel matrix , represents the pore surface area of the pore sub-structure pixel matrix , represents the pore connectivity of the pore sub-structure pixel matrix .

[0044] The relevant operations of step S3 are introduced with a specific example:

[0045] The zero-order Minkowski functional characterizes the soil porosity , and the represents the ability of soil aggregates to store fluids. The is calculated by the formula: , where represents the volume of the pore part in the three-dimensional matrix , , respectively represent the first dimension, the second dimension, and the third dimension of the three-dimensional matrix , represents the total volume of the three-dimensional matrix . In this embodiment, ;

[0046] The first-order Minkowski functional characterizes the pore specific surface area , and the represents the adsorption and dissolution process of soil aggregates; traverse each element of the three-dimensional matrix and check the values of its surrounding elements to find all pore elements (value is 1). For each pore element, check the element values in the six directions of up, down, left, right, front, and back. If the adjacent element is a soil element (value is 0), then the pore element has a boundary in that direction. Calculate the number of boundaries of each pore element in each direction and accumulate them to obtain the total surface area contribution of the pore element. Accumulate the surface area contributions of all pore elements to obtain the surface area of the entire three-dimensional binary image matrix ; The definition formula of is: , where Indicates the first-order surface area of a three-dimensional matrix through integration ; the is calculated by the formula: where, represents the total area of the three-dimensional matrix ;

[0047] The third-order Minkowski functional characterizes the pore connectivity , and the represents the connectivity between pores in the soil; using the connectivity analysis method, calculate the number of connected components of the pores in the three-dimensional matrix specifically: starting from a pore element in , gradually search for the surrounding pore elements and mark them as the same connected component; by traversing all pore elements, the number of connected components can be calculated ; using the hole filling method, calculate the number of holes in the three-dimensional matrix : starting from the soil element in , gradually search for the surrounding soil elements and mark them as the same hole; by traversing all soil elements, the number of holes can be calculated The definition formula of is: and the is calculated by the formula:

[0048] S4. Based on the characteristics of skewness and kurtosis in statistics, analyze the estimated values of the Minkowski functional to obtain the pore structure distribution characteristic parameters of different soil types.

[0049] Introduce the relevant operations of step S4 with a specific example:

[0050] For the th soil type, calculate the estimated values of the three Minkowski functionals for all soil samples belonging to this type of soil to obtain three sets:

[0051]

[0052]

[0053]

[0054] Calculate the distribution characteristic parameters of these three sets to obtain the pore structure distribution characteristic parameters of different soil types: and , where represents the kurtosis of the th estimated value, and represents the skewness of the th estimated value, , represents the porosity of the th one, represents the pore surface area of the th one, represents the pore connectivity of the th one.

[0055] The is calculated by the formula: wherein, represents the number of elements in the set , represents a sharp peak, represents a flat peak, represents being consistent with the normal distribution; the is calculated by the formula: wherein, represents right skewness, represents left skewness, represents complete symmetry.

[0056] S5. Based on the pore structure distribution characteristic parameters of different soil types, construct a three-dimensional pore structure characteristic distribution law index.

[0057] The following is an introduction to the relevant operations in step S5 with specific examples:

[0058] The three-dimensional pore structure characteristic distribution law index is specifically: where , when represents the kurtosis function, when represents the skewness function, represents the soil porosity of the th characteristic sample of the th soil type, represents the pore surface area of the soil of the th characteristic sample of the th soil type, represents the pore connectivity of the soil of the th characteristic sample of the th soil type, , and respectively represent the fitting weight parameters of soil porosity, soil pore surface area and soil pore connectivity. , and The calculation formulas of

[0059]

[0060]

[0061]

[0062] Among them, represents the variance function, represents the variance of the soil porosity of the -th soil type, and represents the variance of the soil pore connectivity of the

[0063] Finally, the three-dimensional pore structure characteristic distribution law indexes of chernozem, chernozem, meadow soil, and aeolian sandy soil are obtained, that is, , , , .

Claims

1. A method for constructing a comprehensive index of soil three-dimensional pore structure characteristic distribution law, characterized in that: The method comprises the following steps: S1. Acquisition Binarize the image and preprocess it to get a pixel matrix data set; S2. Cut the pixel matrix dataset to obtain a representative basic volume dataset of soil pore structure , ,in, represents the pore substructure pixel matrix, represents a set of real numbers, N represents the number of soil types, M represents the number of samples contained in each soil type, Indicates the number of overlapping sub-matrices obtained by cutting the pixel matrix data set; S3. Calculation Minkowski functional estimate in three dimensions: ,in, Represents the pixel matrix of the pore substructure The porosity, Represents the pixel matrix of the pore substructure The pore surface area, Represents the pixel matrix of the pore substructure The pore connectivity of S4. Based on the characteristics of skewness and kurtosis in statistics, the Minkowski functional estimation value is analyzed to obtain the characteristic parameters of pore structure distribution of different soil types; S5. Based on the pore structure distribution characteristic parameters of different soil types, a three-dimensional pore structure characteristic distribution law index is constructed.

2. The method for constructing a comprehensive index of soil three-dimensional pore structure characteristic distribution law according to claim 1, characterized in that: The pre-processing is specifically as follows: Select from the binary image Continuous and of the same size A region of interest of pixels is converted into a pixel matrix dataset.

3. The method for constructing a comprehensive index of soil three-dimensional pore structure characteristic distribution law according to claim 1, characterized in that: The pixel matrix data set is specifically cut as follows: the pixel matrix data set is cut in combination with the representative basic volume size and the sliding window; the size of the sliding window is set to , with a step size of L pixels.

4. The method for constructing a comprehensive index of soil three-dimensional pore structure characteristic distribution law according to claim 1, characterized in that: Said By formula: Calculate, where Represents a three-dimensional matrix The volume of the mesoporous part, Represents a three-dimensional matrix The total volume of By formula: Calculate, where Represents a three-dimensional matrix the total area of By formula: Calculate, where Represents a three-dimensional matrix The number of connected components of the mesopores, Represents a three-dimensional matrix The number of holes in .

5. The method for constructing a comprehensive index of soil three-dimensional pore structure characteristic distribution law according to claim 1, characterized in that: The pore structure distribution characteristic parameters of different soil types are specifically: and ,in, Indicates The kurtosis of the estimate, Indicates The skewness of the estimate, where , Indicates The porosity, Indicates The pore surface area, Indicates pore connectivity.

6. A method for constructing a comprehensive index of soil three-dimensional pore structure characteristic distribution law according to claim 5, characterized in that: Said By formula: Calculate, where Representing a collection The number of elements in By formula: calculate.

7. A method for constructing a comprehensive index of soil three-dimensional pore structure characteristic distribution law according to claim 6, characterized in that: The three-dimensional pore structure characteristic distribution law index is specifically: ,in , hour, represents the kurtosis function, hour, represents the skewness function, Indicates Soil type Soil porosity of characteristic samples, Indicates Soil type The soil pore surface area of ​​the characteristic sample, Indicates Soil type Soil pore connectivity of characteristic samples, , and represent the fitting weight parameters of soil porosity, soil pore surface area and soil pore connectivity, respectively.

8. According to the method for constructing a comprehensive index of soil three-dimensional pore structure characteristic distribution law according to claim 2, the size of the pixel matrix data set is: .

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