A method and device for characterizing concave particle morphology based on convex decomposition

Abstract

The present application relates to the technical field of particle morphology characterization, and discloses a concave particle morphology characterization method and device based on convex decomposition, which comprises the following steps: S1, concave particle contour extraction, high-definition photographing of the concave particle, obtaining the concave particle contour through digital image processing, and performing a standardization processing procedure to obtain the simplest concave particle morphology; S2, morphology pre-decomposition, Delaunay triangulation is performed to serve as the morphology pre-decomposition line of the concave particle; S3, morphology optimization decomposition, the weight value of the morphology concave point is calculated, an optimal decomposition matrix is established, and morphology optimization convex decomposition is performed with the maximum total weight value of the decomposition points as the target; and S4, morphology quantitative characterization, the area distribution of the convex decomposition particle is taken as the basis to define the convex decomposition coefficient of the concave particle and characterize the morphology characteristics of the concave particle. The present application improves the calculation efficiency of the morphology parameters, realizes the morphology characterization of the concave particle at different levels, and provides a reference for the research on the macro-micro mechanical characteristics of the concave particle.

Description

A method and apparatus for characterizing concave particle morphology based on convex decomposition Technical Field

[0001] This invention relates to the field of particle morphology characterization technology, and discloses a method and apparatus for characterizing concave particle morphology based on convex decomposition. Background Technology

[0002] Under geological processes, a large amount of natural rock and soil materials can form concave particles with complex morphologies. Concave particles are widely distributed in nature; typical examples include broken rock particles, calcareous sand particles (coral sand), and coal dust particles. Concave particles are widely used in foundation engineering, and their morphological characteristics are an important factor affecting their physical and mechanical properties. The morphological characteristics of particles are closely related to their compressibility, filling capacity, and other mechanical properties. Concave particles are characterized by high angularity and irregular shapes. Therefore, it is necessary to characterize their geometric morphology to provide a reference for the study of the macroscopic and microscopic mechanical properties of concave particles.

[0003] In the field of particle morphology characterization, sphericity is typically used to characterize the basic outline of a particle, roundness to characterize the edges and corners around the particle, and roughness to characterize the surface texture of the particle. Sphericity measures the degree of similarity between a particle and a sphere. Commonly used types of sphericity include area sphericity, perimeter sphericity, diameter sphericity, and the ratio of inscribed circle to circumscribed circle sphericity, but perimeter sphericity (the ratio of the circumference of a circle with the same area as the particle to the actual circumference of the particle) is the most widely used. Roundness is used to characterize the sharpness of the edges and corners of the particle surface. Calculating roundness requires solving for all the protruding feature points on the outline and the radius of the tangent circle corresponding to the protruding part of the particle. The roundness calculation process is complex and not conducive to engineering practice. Therefore, roundness is usually described qualitatively, following the particle classification criteria proposed by Lussel et al. (1937) based on roundness values: angular, subangular, sub-rounded, round, and extremely rounded. Roughness is used to characterize the surface texture of a particle and is the particle morphology parameter with the smallest dimensionality. The roughness of a particle is characterized by the deviation between the particle outline curve and the average curve. The fitting accuracy of the average curve is difficult to control, often resulting in overfitting or underfitting, which in turn affects the characterization of the morphology. Although the above-mentioned morphological parameters play a prominent role in basic research, the complexity of their solution process and the limited scope of morphological characterization seem to hinder their routine application in the characterization of geotechnical materials.

[0004] In representing the complex morphology of concave particles, the presence of concave points on the contour increases the difficulty of morphological processing and the computational load of morphological parameters. Therefore, an algorithm capable of decomposing contour concave points is urgently needed to effectively simplify the complex morphology of particles. In computational geometry, polygon convex decomposition algorithms can decompose concave points, thereby simplifying the morphology. Many scholars both domestically and internationally have researched polygon convex decomposition algorithms. Chazelle et al. achieved the convex decomposition ADDIN with the fewest possible objectives by constructing Xk-patterned concave point strings. Keil used the idea of ​​merging base convex polygons for convex decomposition. Liu et al. performed bi-space decomposition of concave polygons using linear programming. Xiao Zhonghui et al., in their literature, coded and classified concave points according to their positional relationship with their preceding and following adjacent points, and then selected a partitioning strategy based on the coding of the concave point pairs.

[0005] Existing convex decomposition algorithms suffer from two significant drawbacks when applied to concave particle decomposition, limiting their practical application in engineering. The first drawback is that existing algorithms fail to consider the salience of concavity points. In real-world applications, the varying degrees of concavity at different points within a concave particle can drastically affect the decomposition results. The second drawback is that existing convex decomposition algorithms struggle to balance decomposition speed with the quality of the decomposed morphology. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a method and apparatus for morphological characterization of concave particles based on convex decomposition, which improves the efficiency of morphological parameter calculation and realizes morphological characterization of concave particles at different levels.

[0007] In a first aspect, the present invention provides a method for characterizing concave particle morphology based on convex decomposition.

[0008] A method for characterizing concave particle morphology based on convex decomposition, comprising:

[0009] S1: Concave particle contour extraction;

[0010] S2: Morphological pre-decomposition;

[0011] S3: Morphological optimization decomposition;

[0012] S4: Quantitative morphological characterization;

[0013] Furthermore, step S1 is as follows:

[0014] First, high-resolution images of the concave particles are taken, and their outlines are obtained through digital image processing. Second, a standardized processing procedure is performed to obtain the simplest concave particle morphology.

[0015] Furthermore, step S2 is as follows:

[0016] ① Delaunay triangulation: The concave grain morphology is subjected to constrained Delaunay triangulation, with the concave grain contour as the constraint.

[0017] ② Obtain the pre-section lines; obtain the morphological pre-section lines based on the constrained Delaunay triangulation results.

[0018] Furthermore, step S3 is as follows:

[0019] ① Calculate the weights of the concave points; based on the weight function, calculate the weights of the concave points; the weight function is as follows:

[0020]

[0021]

[0022]

[0023]

[0024] Wherein K(p i () is the concavity function; all vertices of the concave particle profile are numbered in either counterclockwise or clockwise order, namely p1, p2, ..., p i-1 p i p i+1 ..., where i is an integer, i≥2; then p i-1 p is the (i-1)th vertex of the concave particle profile. i p is the i-th vertex of the concave particle profile. i+1 p is the (i+1)th vertex of the concave particle profile. i+k Let be the (i+k)th vertex of the concave particle profile, where k is a positive integer. For vertex p i With the adjacent previous vertex p i-1 The vector formed For vertex p i With the adjacent next vertex p i+1 The vector formed, K(p) i ) is the vertex p i The concavity, K(p) i+k ) is the vertex p i+k The concavity is given by α, where α is the angle between the pre-subdivision line and the first adjacent line, and β is the angle between the pre-subdivision line and the second adjacent line. The first adjacent line is the line connecting the concave point to one of its adjacent vertices, and the second adjacent line is the line connecting the concave point to another of its adjacent vertices. For weights.

[0025] ② Establish the optimal partitioning matrix; based on the weights of the concave points, establish the optimal partitioning matrix, aiming to maximize the total weight of the partitioning points, and perform optimized convex decomposition of the concave particle morphology. The process is as follows:

[0026] Q = [x1, x2, ..., x n ]

[0027] maximize

[0028] Satisfy x i ∈K i ;

[0029] Where Q is the optimal partitioning matrix, and the concave points are sorted from largest to smallest according to their concavity, namely c1, c2, ..., c n-1 c n ..., where n is the number of concave points; K i For the concave point c i The set formed by the pre-section lines; x i It is set K i The elements are the pre-section lines.

[0030] Furthermore, step S4 is as follows:

[0031] ① Convex particle area distribution; Calculate the convex particle area distribution after optimized decomposition using the following formula:

[0032]

[0033] Among them, A i S represents the area ratio of the i-th convex decomposition particle; i Let S represent the area of ​​the i-th convex decomposition particle; S represents the total area of ​​the concave particles.

[0034] ② Define the convex decomposition coefficient; based on the area distribution of convex particles, generate the convex decomposition coefficient to achieve quantitative characterization of concave particle morphology. The formula is as follows:

[0035]

[0036] Among them, S i Let Si represent the area ratio of the convex decomposition particles in the i-th concave particle. The area ratio of the convex decomposition particles is obtained based on the area distribution of each concave particle. The area ratios of the convex decomposition particles are sorted in descending order as S1, S2, ..., Si. i ...; k is the convex decomposition area threshold, R is the convex decomposition coefficient, and i and R are both positive integers.

[0037] Secondly, the present invention also provides a concave particle morphology characterization device based on convex decomposition.

[0038] A concave particle morphology characterization device based on convex decomposition, comprising:

[0039] The concave particle contour extraction module is configured to first perform digital image processing on the high-definition imaging of concave particles to obtain the concave particle contour, and then perform a standardization process to obtain the simplest concave particle morphology.

[0040] The morphological pre-decomposition module is configured to perform constrained Delaunay triangulation, which serves as the morphological pre-decomposition line for concave particles.

[0041] The morphological optimization decomposition module is configured to calculate the weights of concave points, establish the optimal partitioning matrix, and perform morphological optimization convex decomposition with the goal of maximizing the total weight of partitioning points.

[0042] The morphological quantitative characterization module is configured to define the convex decomposition coefficient of concave particles based on the area distribution of convex decomposition particles, and characterize the morphological features of concave particles.

[0043] Thirdly, the present invention also provides another concave particle morphology characterization device based on convex decomposition.

[0044] An apparatus for concave particle morphology characterization based on convex decomposition includes a processor and a memory storing program instructions, the processor being configured to execute, when running the program instructions, a method for concave particle morphology characterization based on convex decomposition as described above.

[0045] As can be seen from the above technical solution, the beneficial technical effects of the present invention are as follows:

[0046] 1. By weighting the concave points in the morphology, an optimal partitioning matrix is ​​established. This matrix is ​​then used to optimize the convex decomposition of concave particles, and the convex decomposition coefficient is calculated using the area distribution of the decomposed particles. This approach fully considers the saliency of the concave points in the particle outline, improving the morphological quality and decomposition efficiency of the decomposed particles. Simultaneously, the complex morphology of concave particles is decomposed into multiple simpler and more stable forms. The convex decomposition coefficient characterizes the morphological features of the concave particles; a larger coefficient indicates smaller sphericity, larger particle size, and greater convexity. This achieves morphological characterization of concave particles at different levels, providing a reference for the study of the macroscopic and microscopic mechanical properties of concave particles.

[0047] 2. Based on the weights of the concave points, an optimal partitioning matrix is ​​established using linear programming. With the goal of maximizing the total weight of the partitioning points, the concave particle morphology is optimized by convex decomposition. This effectively reduces computation time and improves the quality of the convex decomposed particle morphology, thereby simplifying the complex morphology of concave particles and thus helping to characterize the complex morphology of concave particles. Attached Figure Description

[0048] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0049] Figure 1 is a schematic diagram of a concave particle morphology characterization method based on convex decomposition provided in this embodiment;

[0050] Figure 2 is a comparison of the efficiency of different convex decomposition algorithms provided in this embodiment;

[0051] Figure 3 is an exploded view of this embodiment without considering the concavity of the concave points;

[0052] Figure 4 is a decomposition diagram considering the concavity of the concave point provided in this embodiment;

[0053] Figure 5 shows the results of the decomposition of concave particles provided in this embodiment;

[0054] Figure 6 is a statistical chart of the convex decomposition coefficients of the concave particles provided in this embodiment;

[0055] Figure 7 is a simplified concave particle morphology diagram after standardization provided in this embodiment; Detailed Implementation

[0056] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0057] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning understood by those skilled in the art. The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for implementation of the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. Unless otherwise stated, the term "a plurality of" means two or more. In this disclosure, the character " / " indicates an "or" relationship between the preceding and following objects. For example, A / B means: A or B. The term "and / or" describes an association relationship between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or, A and B. The term "corresponding" can refer to an association or binding relationship; A corresponding to B means that there is an association or binding relationship between A and B.

[0058] Extensive research by the applicant revealed that this method is universally applicable and widely suitable for concave particles. Concave particles include broken rock particles, calcareous sand particles (coral sand), coal dust particles, etc. Coral sand is a typical example of a concave particle, which is a type of marine sediment with high angularity, high porosity, and irregular shape.

[0059] Referring to Figure 1, this embodiment provides a method for characterizing concave particle morphology based on convex decomposition, including:

[0060] S1: Concave particle contour extraction;

[0061] S2: Morphological pre-decomposition;

[0062] S3: Morphological optimization decomposition;

[0063] S4: Quantitative morphological characterization.

[0064] Optionally, concave particle contour extraction includes:

[0065] First, high-resolution images of the concave particles are taken, and their outlines are obtained through digital image processing. Second, a standardized processing procedure is performed to obtain the simplest concave particle morphology.

[0066] In some embodiments, a high-definition camera is used to photograph the concave particles, and the contours of the concave particles are obtained through digital image processing. A standardization process is then applied to obtain the simplified concave particle morphology. As shown in Figure 7, the thicker lines at the top represent the initial contour of the concave particles, while the thinner lines at the bottom represent the simplified concave particle morphology obtained after the standardization process. As can be seen from the figure, the standardization process significantly reduces the number of contour points while preserving the contour features, thus simplifying the concave particle contour.

[0067] Optionally, morphological pre-decomposition includes:

[0068] ① Delaunay triangulation: The concave grain morphology is subjected to constrained Delaunay triangulation, with the concave grain contour as the constraint.

[0069] ② Obtain the pre-section lines; obtain the morphological pre-section lines based on the constrained Delaunay triangulation results.

[0070] In some embodiments, after selecting any concave point of the concave particle polygonal profile as the concave point to be sectioned, the other vertices outside the concave point to be sectioned are determined as sectioning junction points. A constrained Delaunay triangulation is performed on the concave particle morphology, using the concave particle profile as the constraint. Based on the constrained Delaunay triangulation results, multiple morphological pre-sectioning lines are obtained, formed by connecting the concave point to be sectioned with the sectioning junction points.

[0071] Optionally, the decomposition is optimized, including:

[0072] ① Calculate the weights of the concave points; based on the weight function, calculate the weights of the concave points; the weight function is as follows:

[0073]

[0074]

[0075]

[0076]

[0077] Wherein K(p i () is the concavity function; all vertices of the concave particle profile are numbered in either counterclockwise or clockwise order, namely p1, p2, ..., p i-1 p i p i+1 ..., where i is an integer, i≥2; then p i-1 p is the (i-1)th vertex of the concave particle profile. i p is the i-th vertex of the concave particle profile. i+1 p is the (i+1)th vertex of the concave particle profile. i+k Let be the (i+k)th vertex of the concave particle profile, where k is a positive integer. For vertex p i With the adjacent previous vertex p i-1 The vector formed For vertex p i With the adjacent next vertex p i+1 The vector formed, K(p) i ) is the vertex p i The concavity, K(p) i+k ) is the vertex p i+k The concavity is given by α, where α is the angle between the pre-subdivision line and the first adjacent line, and β is the angle between the pre-subdivision line and the second adjacent line. The first adjacent line is the line connecting the concave point to one of its adjacent vertices, and the second adjacent line is the line connecting the concave point to another of its adjacent vertices. For weights.

[0078] ② Establish the optimal partitioning matrix; based on the weights of the concave points, establish the optimal partitioning matrix, aiming to maximize the total weight of the partitioning points, and perform optimized convex decomposition of the concave particle morphology. The process is as follows:

[0079] Q = [x1, x2, ..., x n ]

[0080] maximize

[0081] Satisfy x i ∈K i ;

[0082] Where Q is the optimal partitioning matrix, and the concave points are sorted from largest to smallest according to their concavity, namely c1, c2, ..., c n-1 c n ..., where n is the number of concave points; K i For the concave point c i The set formed by the pre-section lines; x i It is set K i The elements are the pre-section lines.

[0083] In some embodiments, a concave point to be partitioned may have multiple morphological pre-partitioning lines. The above formula is used to perform linear programming with the objective of maximizing the total weight of the partitioning points to find the optimal partitioning matrix. Finally, the optimal partitioning matrix is ​​used to optimize the convex decomposition of the concave particles. By decomposing the concave particles using the optimal partitioning matrix, at least one concave point will be reduced after each partitioning process, and the entire process requires at most m partitioning operations. If all the connecting vertices of the formed partitioning lines are concave points, then two concave points will be reduced each time, thus reducing the number of partitioning operations. This scheme introduces weights to guide the partitioning; the larger the weight, the greater the probability that the partitioning point connected by the pre-partitioning line is a concave point, and the greater the probability that the pre-partitioning line will eliminate two concave points. Establishing the optimal partitioning matrix increases the probability of eliminating two concave points in each partitioning, which helps to reduce the number of partitioning operations, thereby effectively reducing the computation time and improving the partitioning efficiency.

[0084] Optionally, quantitative morphological characterization includes:

[0085] ① Convex particle area distribution; Calculate the convex particle area distribution after optimized decomposition using the following formula:

[0086]

[0087] Among them, A i S represents the area ratio of the i-th convex decomposition particle; i Let S represent the area of ​​the i-th convex decomposition particle; S represents the total area of ​​the concave particles.

[0088] ② Generation of convex decomposition coefficients: Based on the area distribution of convex particles, convex decomposition coefficients are generated to achieve quantitative characterization of concave particle morphology. The formula is as follows:

[0089]

[0090] Among them, S iLet Si represent the area ratio of the convex decomposition particles in the i-th concave particle. The area ratio of the convex decomposition particles is obtained based on the area distribution of each concave particle. The area ratios of the convex decomposition particles are sorted in descending order as S1, S2, ..., Si. i ...; k is the convex decomposition area threshold, R is the convex decomposition coefficient, and i and R are both positive integers.

[0091] Optionally, the convex decomposition area threshold is a preset value. In some embodiments, k = 0.9.

[0092] In some embodiments, the convex decomposition coefficients R satisfy the inequality The smallest integer.

[0093] This scheme characterizes the morphological features of concave particles by using convex decomposition coefficients. Compared with existing methods that directly characterize the morphology of concave particles, the morphological characterization method based on convex decomposition proposed in this scheme improves the efficiency of morphological parameter calculation and realizes the morphological characterization of concave particles at different levels, thus providing a reference for the study of the macro- and micro-mechanical properties of concave particles.

[0094] In some embodiments, concave particles are decomposed using Rogers algorithm, global partitioning algorithm and the algorithm provided in this scheme respectively. The efficiency of each algorithm is shown in Figure 2. As can be seen from Figure 2, the more concave points there are and the more complex the shape, the longer the decomposition time is required. The method provided in this invention takes the least time and has the highest decomposition efficiency.

[0095] In some embodiments, the convex decomposition of concave particles includes two cases: considering concavity and not considering concavity. Experiments are conducted to verify these two cases, decomposing the same concave particles separately. The first case is a convex decomposition without considering concavity, as shown in Figure 3. The second case is a convex decomposition considering concavity, as shown in Figure 4. It is evident that considering concavity results in better morphological quality after decomposition. Therefore, this scheme considers concavity during decomposition, thereby improving the morphological quality after decomposition.

[0096] In some embodiments, the method provided in this scheme is experimentally verified as follows: ① High-resolution photography of concave particles is performed, and the contour of the concave particles is obtained through digital image processing. A standardization process is then applied to obtain the simplest concave particle morphology. ② Morphological pre-decomposition is performed, and the concave particle morphology is subjected to constrained Delaunay triangulation, using the concave particle contour as a constraint. The morphological pre-decomposition lines are obtained based on the constrained Delaunay triangulation results. ③ Morphological optimization decomposition is performed, calculating the weights of the concave points and establishing an optimal decomposition matrix. With the goal of maximizing the total weight of the decomposition points, morphological optimization convex decomposition is performed to obtain convex decomposed particles, as shown in Figure 5. ④ Quantitative morphological characterization is performed, defining the convex decomposition coefficient of the concave particles based on the area distribution of the convex decomposed particles. The obtained convex decomposition coefficient R is shown in Figure 6. As shown in Figure 6, through convex decomposition morphological characterization experiments on a large number of concave particles, the experimental results show that the convex decomposition coefficient of most concave particles is between 7 and 13, and the convex decomposition coefficient exhibits a negatively skewed distribution. The statistical regularity of the convex decomposition coefficient reflects, to some extent, the mechanical properties of concave particles, such as their complex morphology, uneven surface contours, and fragility. This can provide a reference for the study of the macro- and micro-mechanical properties of concave particles.

[0097] In some embodiments, a concave particle morphology characterization device based on convex decomposition includes: a concave particle contour extraction module, configured to first perform digital image processing on high-definition images of concave particles to obtain the concave particle contour, and then perform a standardization process to obtain the simplified concave particle morphology; a morphology pre-decomposition module, configured to perform constrained Delaunay triangulation, using it as the morphology pre-division line of the concave particles; a morphology optimization decomposition module, configured to calculate the weights of the concave points, establish an optimal subdivision matrix, and perform morphology optimization convex decomposition with the objective of maximizing the total weight of the subdivision points; and a morphology quantitative characterization module, configured to define the convex decomposition coefficient of the concave particles based on the area distribution of the convexly decomposed particles, and characterize the morphological features of the concave particles.

[0098] In some embodiments, the present invention provides another concave particle morphology characterization apparatus based on convex decomposition, including a processor and a memory storing program instructions, the processor being configured to execute a method for concave particle morphology characterization based on convex decomposition as described above when running the program instructions.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for characterizing concave particle morphology based on convex decomposition, characterized in that, include: S1: Concave particle contour extraction; S2: Morphological pre-decomposition; S3: Morphological optimization decomposition; S4: Quantitative morphological characterization; ① Calculate the weights of the concave points; based on the weight function, calculate the weights of the concave points; the weight function is as follows: in, The concavity function is used; all vertices of the concave particle profile are numbered in either counter-clockwise or clockwise order, respectively. 、 、 、 、 、 、 ， It is an integer. ;but The first concave particle profile One vertex, The first concave particle profile One vertex, The first concave particle profile One vertex, The first concave particle profile One vertex, It is a positive integer. As vertex With the adjacent previous vertex The vector formed As vertex With the adjacent next vertex The vector formed As vertex concavity, As vertex concavity, The angle between the pre-divided line and the first adjacent line. The angle between the pre-dividing line and the second adjacent line is defined as follows: the first adjacent line is the line connecting the concave point to one of its adjacent vertices, and the second adjacent line is the line connecting the concave point to another of its adjacent vertices. ① Assign weights; ② Establish the optimal partitioning matrix; Based on the weights of the concave points, establish the optimal partitioning matrix, and with the goal of maximizing the total weight of the partitioning points, perform optimized convex decomposition of the concave particle morphology; The process is as follows: maximize satisfy in, To obtain the optimal partitioning matrix, the concave points are sorted in descending order of their four-degree size, as follows: 、 、 、 、 、 ， The number of concave points; For the concave point The set of pre-sectioned lines; It is a set The elements, i.e., pre-partition lines; ① Convex particle area distribution: Calculate the convex particle area distribution after optimized decomposition; the formula is as follows: in, Indicates the first The area ratio of blocky decomposition particles; Indicates the first The area of ​​the blocky decomposition particles; ① Represents the total area of ​​concave particles; ② Defines the convex decomposition coefficient: Based on the area distribution of convex particles, the convex decomposition coefficient is defined to achieve a quantitative characterization of the morphology of concave particles; the formula is as follows: in, Indicates the first The area ratio of concave particles to convex decomposition particles is obtained based on the area distribution of each concave particle to convex decomposition particle. The area ratios of the convex decomposition particles are sorted in descending order, as follows: 、 、 、 、 ； The threshold for convex decomposition area. The coefficients are convex decomposition coefficients. and All are positive integers.

2. The method according to claim 1, characterized in that, Concave particle contour extraction includes: first, taking high-resolution photos of the concave particles and obtaining their contours through digital image processing; second, performing a standardization process on the concave particle contours to obtain the simplest concave particle morphology.

3. The method according to claim 2, characterized in that, Morphological pre-decomposition includes: ① Delaunay triangulation; constrained Delaunay triangulation of concave particle morphology, using the concave particle contour as constraint; ② Obtaining pre-section lines; obtaining morphological pre-section lines based on the constrained Delaunay triangulation results.

4. A device for characterizing concave particle morphology based on convex decomposition, characterized in that, include: The concave particle contour extraction module is configured to first perform digital image processing on the high-definition imaging of concave particles to obtain the concave particle contour, and then perform a standardization process on the concave particle contour to obtain the simplest concave particle morphology. The morphology pre-decomposition module is configured to perform constrained Delaunay triangulation, which serves as the morphology pre-decomposition line for concave particles. The morphological optimization decomposition module is configured to calculate the weights of morphological concave points, establish the optimal partitioning matrix, and perform morphological optimization convex decomposition with the objective of maximizing the total weight of partitioning points; ① Calculate the weights of morphological concave points; Based on the weight function, calculate the weights of morphological concave points; The weight function is as follows: in, The concavity function is used; all vertices of the concave particle profile are numbered in either counter-clockwise or clockwise order, respectively. 、 、 、 、 、 、 ， It is an integer. ;but The first concave particle profile One vertex, The first concave particle profile One vertex, The first concave particle profile One vertex, The first concave particle profile One vertex, It is a positive integer. As vertex With the adjacent previous vertex The vector formed As vertex With the adjacent next vertex The vector formed As vertex concavity, As vertex concavity, The angle between the pre-divided line and the first adjacent line. The angle between the pre-dividing line and the second adjacent line is defined as follows: the first adjacent line is the line connecting the concave point to one of its adjacent vertices, and the second adjacent line is the line connecting the concave point to another of its adjacent vertices. ① Assign weights; ② Establish the optimal partitioning matrix; Based on the weights of the concave points, establish the optimal partitioning matrix, and with the goal of maximizing the total weight of the partitioning points, perform optimized convex decomposition of the concave particle morphology; The process is as follows: maximize satisfy in, To obtain the optimal partitioning matrix, the concave points are sorted in descending order of their four-degree size, as follows: 、 、 、 、 、 ， The number of concave points; For the concave point The set of pre-sectioned lines; It is a set The elements, i.e., pre-section lines; the morphological quantitative characterization module, is configured to define the convex decomposition coefficient of concave particles based on the area distribution of convex decomposed particles, characterizing the morphological features of concave particles; ① Convex particle area distribution: calculate the area distribution of convex particles after optimized decomposition; the formula is as follows: in, Indicates the first The area ratio of blocky decomposition particles; Indicates the first The area of ​​the blocky decomposition particles; ① Represents the total area of ​​concave particles; ② Defines the convex decomposition coefficient: Based on the area distribution of convex particles, the convex decomposition coefficient is defined to achieve a quantitative characterization of the morphology of concave particles; the formula is as follows: in, Indicates the first The area ratio of concave particles to convex decomposition particles is obtained based on the area distribution of each concave particle to convex decomposition particle. The area ratios of the convex decomposition particles are sorted in descending order, as follows: 、 、 、 、 ； The threshold for convex decomposition area. The coefficients are convex decomposition coefficients. and All are positive integers.

5. An apparatus for characterizing concave particle morphology based on convex decomposition, comprising a processor and a memory storing program instructions, characterized in that, The processor is configured to, when executing the program instructions, perform a method for characterizing concave particle morphology based on convex decomposition as described in any one of claims 1 to 3.

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