A method for non - complete particle shape characterization based on a dynamic graph edge convolution network

Abstract

The present invention provides a method for characterizing the shape of non-intact particles based on a dynamic graph edge convolution network, which relates to the field of characterization and analysis of the shape of sand particles. The shape characterization method uses half of the sand particle point cloud to characterize and classify the roundness and sphericity of the complete sand particles, and takes the non-intact sand particle point cloud obtained by binocular vision technology as the input of the network model; uses a graph generation network to construct the topological relationship of the point cloud; uses a spatial transformation network to align or adjust the point cloud to eliminate the influence of the camera position on the coordinates of the same particle point cloud. Edge convolution is used to integrate the features of the local area of the central point, enhancing the features of the local roundness and sphericity of the non-intact sand particles in the network model; finally, based on the dynamic graph update, after each extraction of the feature map, the k nearest neighbor points of the feature central point will be updated according to the distance to the central point, enabling the non-local diffusion of information in the entire point cloud and enhancing the extraction of the overall features of the non-intact sand particles.

Description

Technical Field

[0001] The present invention relates to the field of characterization and analysis of sand particle shapes, and particularly to a method for characterizing non-complete particle shapes based on a dynamic graph edge convolutional network. Background Art

[0002] The edges and sphericity of particles have a great influence on the macroscopic mechanical properties of soil. Angular particles have sharp protrusions and edges that interlock with each other, forming many contact points, thus strengthening the bearing structure of granular soil. On the other hand, spherical particles are more likely to be arranged neatly and packed tightly when compressed, thereby reducing the voids between soil particles. Experimental and numerical studies have shown that particle angles and roundness have a great influence on the shear strength, compressibility, void structure and deformation behavior of soil.

[0003] In contemporary geotechnical engineering, researchers have adopted a series of advanced three-dimensional imaging methods to capture complex three-dimensional particle geometries. These techniques can be divided into two categories: (1) X-ray computed tomography (X-ray CT) techniques with penetrability and (2) laser scanning, stereophotography and structured light system techniques without penetrability. The former can capture the complete three-dimensional particle surface geometry regardless of the occlusion between particles. However, X-ray CT equipment is expensive, and processing X-ray CT images is computationally demanding and time-consuming. The latter, due to its inability to penetrate sand particles, can only capture the upper half-particle surface exposed in the camera view or semi-particle geometry, called 2.5D (two and a half dimensional) particles. However, compared with X-ray CT, these systems are simple, low-cost, and can easily build test laboratories in ordinary soil. Therefore, non-penetrating scanning techniques are more advantageous in scanning the three-dimensional (3D) particle surface geometry due to their low cost and ease of implementation. Therefore, it is necessary to characterize the edges and sphericity of non-complete particles to study the mechanical properties of soil.

[0004] Traditional characterization methods use 3D computational geometry (CG) methods to calculate the roundness and sphericity of 2.5D and corresponding 3D particles respectively, and try to find the difference law between the two through numerical statistics. However, when the statistical particle data is too large, there is no significant law for the roundness and sphericity of 2.5D and corresponding 3D particles. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides a method for characterizing non-complete particle shapes based on a dynamic graph edge convolutional network, which has the advantages of fast speed and high robustness for characterizing the point cloud of non-complete sand particles.

[0006] To achieve the above objectives, the technical solution of the present invention is realized through the following technical solutions:

[0007] A method for non - complete particle shape characterization based on a dynamic graph edge convolution network, the shape characterization method comprising the following steps:

[0008] S1. Use 3 - D computational geometry methods to calculate the sphericity and roundness values of the complete particle grid of X - ray computed tomography, then obtain 3 - D particle labels, and finally assign the complete particle labels to the non - complete sand particle point clouds reconstructed by the corresponding binocular vision technology;

[0009] S2. Adopt a graph neural network to construct the topological structure of the non - complete sand particle point clouds, propagate separately at the center point of each input non - complete sand particle point cloud, ignore the influence of the input order of nodes on the network model representation, and extract the edges between the center point and neighborhood points to learn the feature dependence information between two nodes;

[0010] S3. The spatial transformation network analyzes the pose of the non - complete sand particle point clouds, generates a 3×3 transformation matrix to perform geometric transformations such as rotation and scaling on the input point clouds, and the spatial transformation network aligns or adjusts the point clouds to eliminate the influence of the camera position on the coordinates of the same sand particle point cloud;

[0011] S4. Adopt edge convolution operations to extract local features, output the features integrating the local area of the center point, and enhance the features of the local roundness and sphericity of the non - complete sand particles in the network model;

[0012] S5. After each extraction of the feature map, use the dynamic graph to update the k nearest neighbor points of the feature center point, update according to the distance to the center point, so that the information diffuses non - locally in the whole point cloud, and enhance the extraction of the overall features of the non - complete sand particles;

[0013] S6. According to the convolution features dynamically updated in the last layer, output the classification result.

[0014] Preferably, in step S1, the non - complete sand particle point clouds are divided into 12 categories, namely: high roundness - high sphericity (WR - HS), high roundness - low sphericity (WR - LS), medium roundness - high sphericity (R - HS), medium roundness - low sphericity (R - LS), sub - roundness - high sphericity (SR - HS), sub - roundness - low sphericity (SR - LS), sub - angularity - high sphericity (SA - HS), sub - angularity - low sphericity (SA - LS), medium angularity - high sphericity (A - HS), medium angularity - low sphericity (A - LS), high angularity - high sphericity (VA - HS), and high angularity - low sphericity (VA - LS).

[0015] Preferably, the specific manner of constructing the topological structure of the non - complete sand particle point clouds in step S2 includes the following steps:

[0016] S2 - 1. In the local directed graph, each point p in the point cloudi are all regarded as a central node once, and the central node p is calculated i and its k nearest neighbor points p j distance

[0017]

[0018] V = {p i | i = 1, 2, …, n};

[0019] S2-2, p i and p j constitute the local topological structure of the non-integral sand particles, e i represents all the edges connected to the point, e ij represents the point p i and p j connected edge:

[0020]

[0021] Preferably, the specific method for the spatial transformation network in step S3 to align or adjust the point cloud to eliminate the influence of the camera position on the point cloud coordinates of the same sand particle includes the following steps:

[0022] S3-1. Use convolution operations to effectively capture the local features of the non-integral sand particle point cloud transformation, and reduce the number of parameters by sharing weights;

[0023] S3-2. Batch normalization normalizes the input distribution of each layer in the deep network, alleviates the problem of gradient disappearance and accelerates the training process;

[0024] S3-3. Adopt the variant Leaky ReLU of the rectified linear unit to introduce non-linearity and prompt the model to learn more advanced abstract features of the non-integral sand particle point cloud:

[0025]

[0026] S3-4. The linear layer of the multi-layer perceptron is used to output the 9-dimensional transformation features in the real number domain and reshape them into a 3×3 transformation matrix.

[0027] Preferably, the specific operation for the edge convolution operation in step S4 to extract local features includes the following steps:

[0028] S4-1. Use MLP to extract the hidden feature vector h(x i , x j - x i ); x i and x j are the inputs of the convolution operation, representing the central point and the k nearest neighbor points x respectivelyj ; x j -x i is the edge e ij , and can also be regarded as x j local coordinates with the center point as the origin:

[0029]

[0030]

[0031] where x ic and x jc are the values of the center point x i and its adjacent point x j in the channel c; the input point x i and the output hidden feature vector h(x i , x j -x i ) have the number of channels C and C' respectively; the value of the hidden feature vector in the channel c' is expressed as The trainable parameters of the MLP are w c'c , w c'(c+C) ;

[0032] S4-2. Apply the symmetric aggregation operation max and the edge feature convolution function h w () to define the edge convolution operation; where the output x' i of the edge convolution at the i-th vertex is given by the following formula; because max is a symmetric function, regardless of the permutation of x j , the output of the layer x' i is always the maximum value:

[0033]

[0034] Preferably, the operation of using the dynamic graph to update the k nearest neighbor points of the feature center point in the step S5 includes the following steps:

[0035] S5-1. After passing through each edge convolution layer, the point at the l-th layer is updated to the k points closest to ; l points;

[0036] S5-2. After passing through each edge convolution layer, the edge at the l-th layer is updated to Finally, the formed network will generate a new graph G (l) =(V (l) , E (l) ).

[0037] Preferably, the operation of outputting the classification result according to the dynamically updated convolution features in step S6 specifically includes the following steps:

[0038] S6-1 Max-pool the convolution features into a 1024-dimensional feature vector F 1024 :

[0039] F 1024 = maxpool(G (l) )

[0040] where G (l) is the graph feature of the last layer;

[0041] S6-2 Use softmax() to reduce the dimensionality of the 1024-dimensional feature vector F 1024 , to C dimensions, where C is the number of classification categories, and the value of each dimension represents the probability of the corresponding category. The dimension with the largest value is the predicted category:

[0042] F C = softmax(F 1024 ).

[0043] The present invention provides a method for characterizing the shape of non-integral particles based on a dynamic graph edge convolution network. Compared with the prior art, the advantages are as follows:

[0044] The present invention uses a dynamic graph edge convolution neural network model to characterize the roundness and sphericity of corresponding integral particles based on the non-integral geotechnical particle point cloud. While maintaining the invariance of the 2.5D soil particle point cloud arrangement, this model constructs a multi-scale local feature map, enabling the same neighborhood with different arrangements to generate a consistent feature map. Through dynamic graph update, larger-scale local features are obtained to identify roundness, sphericity, and noise in large regions. Edge convolution generates features by analyzing the connection relationship between a point and its neighboring points, rather than relying solely on the features of a single point. The convolution pooling operation obtains the angle and sphericity features with less parameter overhead, improving the speed and accuracy of characterizing the roundness and sphericity of corresponding integral particles based on the non-integral geotechnical particle point cloud. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is the structural diagram of the non-integral geotechnical point cloud classification network of the present invention;

[0046] Figure 2 is the 3D and 2.5D model diagrams of 12 types of geotechnical particles in Embodiment 1 of the present invention;

[0047] Figure 3 is the schematic diagram of the 2.5D sand grain acquisition system in Embodiment 1 of the present invention;

[0048] Figure 4 is the schematic diagram of 2.5D sand grain acquisition and segmentation in Embodiment 1 of the present invention;

[0049] Figure 5 Schematic diagram of 3D sand grain acquisition and segmentation in Embodiment 1 of the present invention;

[0050] Figure 6 Schematic diagram of point clouds of 12 categories of 2.5D and 3D sand and soil particles in Embodiment 1 of the present invention;

[0051] Figure 7 Schematic diagram of the production process of 2.5D particle roundness and sphericity labels in Embodiment 1 of the present invention;

[0052] Figure 8 Schematic diagram of the generation process of sand and gravel particle point cloud map in Embodiment 2 of the present invention;

[0053] Figure 9 Spatial transformation network structure diagram in Embodiment 2 of the present invention;

[0054] Figure 10 Schematic diagram of the edge convolution process of the point cloud map in Embodiment 2 of the present invention;

[0055] Figure 11 Schematic diagram of the visualization of the classification results of the dynamic edge convolution neural network on the 2.5D particle point cloud in the test set in Embodiment 2 of the present invention. Detailed implementation manners

[0056] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts fall within the protection scope of the present invention.

[0057] Embodiment 1:

[0058] (1) 3D models of 12 categories of complete sand and soil particles and corresponding incomplete particles are as Figure 2 shown;

[0059] Binocular vision using the widely used non-penetrating technology is used to obtain 2.5D sand and soil particles. This technology has the advantages of being simple, effective and inexpensive, and can obtain the accurate upper surface of the particles. The binocular vision device for collecting the 2.5D geometric information of the particles is as Figure 3(a). The soil particles are naturally placed on a flat surface in the x-y plane with the maximum projection of the particles facing upwards. The movement of a camera at two positions is used to act as two cameras to reduce hardware costs. A triangle is formed between the two shooting positions and the soil particles, similar to the principle of human eye depth perception. The image analysis algorithm fuses the two images and creates the depth of the scene. The calculated 2.5D particle results are as Figure 3 (b).

[0060] Based on the 2.5D particle point cloud, the roundness and sphericity of the complete particles are inferred through a neural network model. In the training stage, the network model needs to learn the mapping relationship between the shape of the 2.5D particle point cloud and the roundness and sphericity of the corresponding complete particles. Therefore, it is necessary to first obtain the 2.5D particles as the input point cloud and the corresponding complete 3D particles to make the roundness and sphericity labels. As Figure 4 shown, the sand grains are placed flat on the tabletop, and the 2.5D geometry of the particles is obtained using the above binocular vision. As Figure 5 shown, the sand grains are loaded into a cylindrical tube, and the 3D geometry of the complete sand grains is obtained using X-ray CT. Then, an improved watershed algorithm is used to segment individual sand grains that are in contact with each other and can effectively solve over-segmentation. As Figure 4 (b) shown, after segmentation, each particle generated by X-ray CT scanning and structured light is assigned a color.

[0061] (2) The geotechnical particle point cloud of the grid converted into the network input is as Figure 5 shown. The specific conversion process is as follows:

[0062] The deep learning network model only needs to input the point cloud of the 2.5D sand grains to infer the roundness and sphericity of the 3D sand grains: To form the 2.5D point cloud, only the vertices of the 2.5D sand grains in the STL file need to be retained while deleting the triangular faces. Figure 6 Twelve types of point clouds of 2.5D and corresponding 3D sand grains are shown. The upper point clouds of the 2.5D and corresponding 3D particles are basically the same and belong to the effective information in point cloud analysis. However, due to imaging occlusion, the lower point cloud of the 2.5D particles is the extension of the maximum projection of the upper point cloud and belongs to invalid noise. The deep learning network model can simultaneously extract the features of the upper real particle point cloud and the lower extended noise point cloud and establish a mapping relationship with the roundness and sphericity of the 3D particles.

[0063] (3) The steps for creating the 2.5D particle labels are as Figure 7 shown. Specifically, they are as follows:

[0064] First, use the 3D CG method to calculate the sphericity and angular values of the 3D particle grid. Then, obtain the 3D particle labels according to the roundness and sphericity value intervals in the Power's chart. Finally, assign the labels to the corresponding 2.5D particle point clouds.

[0065] The neural network model needs to learn the mapping relationship between the geometry of 2.5D particles and the corresponding 3D particle labels. In supervised deep learning, the three-dimensional particles in the dataset need to be pre-labeled for model training and testing. The present invention calculates the definition of roundness as shown in formula (1). The definition formula of sphericity is the average value of all 3D sphericities of formulas (2)-(6), as shown in formula (7).

[0066]

[0067] S = (S I,3 + S V,3 + S D,3 + S C,3 + S A,3 ) / 5 (7)

[0068] Where r 3,i is the radius of the sphere fitted to the i-th corner point, r ins,3 is the radius of the largest inscribed sphere of the 3D particle, N is the number of corner points, S I,3 is the radial sphericity, d1, d2, and d3 are the length, width, and height of the particle respectively, V is the volume of the particle, V cir is the volume of the circumscribed sphere of the particle, D e,3 is the diameter of a sphere with the same volume, D c,3 is the diameter of the smallest circumscribed sphere, D i,3 is the diameter of the smallest inscribed sphere.

[0069] Example 2:

[0070] Based on the training dataset obtained from the above Example 1, by analyzing the 2.5D particle point cloud to infer the sphericity and roundness of the complete particle, it is necessary to focus on the local features at multiple scales of the point cloud to identify the upper effective geometric point cloud and the lower noise point cloud. The convolution object of the dynamic edge network is the graph formed by each point in the point cloud and its neighborhood points. Convolution operations are applied on the edges of the neighborhood graph to capture the local geometric structures at multiple scales. In a convolutional neural network, the convolutional graph being invariant throughout the network will result in insufficient information processing by the model at different scales. However, the dynamic edge convolutional network updates the graph after each layer of edge convolution. That is, after each extracted feature map, the k nearest neighbor points of the transformed feature center point are updated according to the distance to the center point. Therefore, different proximity metrics enable the non-local diffusion of information throughout the point cloud. The features of a certain point spread to points far away from it in the feature space, rather than being limited to its neighboring points in the input space. The range of information propagation may no longer be restricted by physical proximity, which is beneficial to enhancing the receptive field of the model.

[0071] (1) The specific construction of the topological relationship of the incomplete sand particle point cloud is as follows:

[0072] The graph neural network is a point cloud processing method suitable for constructing the topological relationship of point clouds, which is a pre-step before point cloud convolution. This method propagates separately at each central point, can ignore the influence of the input order of nodes on the network model representation, and can extract the edges between the central point and the neighboring points to learn the feature dependence information between two nodes. Therefore, the first step of the graph neural network is to convert the point cloud into a directed graph. The graph G consists of vertices V and edges E:

[0073]

[0074] where F is the dimension of each point. When F = 3, each point contains three-dimensional coordinates v i =(x i , y i , z i ).

[0075] Connecting any two points in the point cloud is impractical because this operation will greatly increase the time complexity and space complexity, resulting in the failure of the network model. The K-NN algorithm can efficiently construct a local directed graph, as shown in Figure 8 . In the local directed graph, each point p i in the point cloud is regarded as a central node once, and the distance d i between the central node p j and its k nearest neighbor points p ij is calculated. p i and p j form the local topological structure of the 2.5D particle, and e i represents all the edges connected to the points. e ij represents the edge connecting the point p i and pj. The specific formula is as follows:

[0076]

[0077] (2) The point cloud aligned or adjusted by the spatial transformation network can eliminate the influence of the camera position on the point cloud coordinates of the same particle. The specific method is as follows:

[0078] In point cloud processing, the spatial transformation network is a network structure for learning the transformation features of point clouds. By analyzing the pose of the 2.5D sand and gravel particle point cloud, the spatial transformation network generates a 3×3 transformation matrix to perform geometric transformations such as rotation and scaling on the input point cloud. The point cloud aligned or adjusted can eliminate the influence of the camera position on the point cloud coordinates of the same particle. The network structure is as shown in Figure 9 .

[0079] The spatial transformation network first uses k-nn to generate the graph structure of each point in 2.5D, and then passes through the feature extraction layer multiple times to extract the corresponding transformation features. The feature extraction layer includes a convolutional layer, a batch normalization layer, and LeakyReLU. The convolutional operation can effectively capture the local features of the point cloud transformation and reduce the number of parameters by sharing weights. Batch normalization is used to normalize the input distribution of each layer in the deep network, which helps to alleviate the vanishing gradient problem and accelerate the training process. LeakyReLU is a variant of the rectified linear unit, which helps to introduce non-linearity and prompts the model to learn more advanced abstract features of 2.5D particles. Compared with ReLU, Leaky ReLU solves the problem that the activation function fails when the input value is negative by introducing a small negative slope, as shown in Equation (10). After the feature extraction layer, the max pooling layer is used to reduce the dimension of the point cloud data, extract the most significant features, which helps to reduce the computational complexity and reduce overfitting. The MLP layer reduces the 1024-dimensional features output by the second max pooling layer to 256 dimensions through two fully connected layers with LeakyReLU. Finally, the Linear layer of the MLP is used to output the 9-dimensional transformation features in the real number domain and reshape them into a 3×3 transformation matrix.

[0080]

[0081] (3) The specific calculation steps for extracting local features by edge convolution operation include:

[0082] When extracting features, the convolutional operation can fully consider the influence of the element neighborhood and has a strong ability to extract local features. The output integrates the features of the local area of the central point, which can enhance the feature extraction of the local roundness and sphericity of the half-particle by the network model. As Figure 10 shown, use MLP to extract the hidden feature vector h(x i ,x j -x i ). x i and xj are the inputs of the convolutional operation, representing the central point and the k-nearest neighbor point xj respectively. x j -x i is the edge eij, which can also be regarded as the local coordinate of xj with the central point as the origin. Converting the global coordinates to local coordinates ensures the translational invariance of the network model to the point cloud. Mlp can learn the complex non-linear relationship between adjacent points through the hidden layer. This enables it to express more complex and abstract roundness and sphericity features.

[0083] h(x i ,x j -x i) is the edge convolution function, which can extract the local circularity and sphericity features formed by the central point and neighboring points, as shown in formulas (11) and (12). The essence of convolution is to set a set of learnable weight parameters w, perform element-wise multiplication with adjacent elements at the corresponding positions, and finally sum all the products to obtain the output.

[0084]

[0085] where x ic and x jc are the values of the central point x i and its adjacent point x j in channel c. The input point x i and the output hidden feature vector h(x i ,x j -x i ) have the number of channels C and C' respectively. The value of the hidden feature vector in channel c' is denoted as The trainable parameters of the MLP are w c'c , w' c(c+C) .

[0086] Finally, the symmetric aggregation operation max and the edge feature convolution function h w () are applied to define the edge convolution operation. Among them, the output x' i of the edge convolution at the i-th vertex is given by equation (13). Since max is a symmetric function, regardless of the permutation of x j , the output of layer x' i is always the maximum value. This property ensures permutation invariance.

[0087]

[0088] (4) Use the dynamic graph to update the k nearest neighbor points of the feature center point, specifically:

[0089] Experiments show that in the circularity and sphericity feature space generated by each edge convolution layer, it is beneficial to recalculate the k nearest neighbor points to form new graph features. Dynamically updating the feature map is the key difference between the graph CNN that convolves on a fixed input graph. The upper part of the 2.5D sand particle point cloud contains useful information, and the lower part contains noise information. After dynamically updating the feature map, the receptive field of the neural network is enhanced, making it possible for the upper and lower points that were originally far apart to form a graph. Moreover, the edge convolution layer can simultaneously convolve the upper and lower points to automatically identify the upper valid points and the bottom noise points, enhancing the model's ability to infer the circularity and sphericity of complete particles using the 2.5D sand point cloud.

[0090] After each edge convolution layer, the network will generate a different graph G (l) =(V(l) , E (l) ). Among them, at the l-th layer is the k points closest to l , and the form of the edge is When l = 0, G (0) =(V (0) , E (0) ) is a graph composed of the 2.5D sand particle point cloud in the three-dimensional physical space. If G (0) is used as a fixed graph for convolution in the edge convolution of each layer, due to the long distance, it is difficult for the effective points in the upper part and the noise points in the lower part to be learned together, resulting in the inability to distinguish these two types of points. When l≠0, G (l) =(V (l) , E (l) ) is composed of the feature points after convolution in the l-th layer. At this time, and are close in the feature space, but may be far apart in the three-dimensional physical space. This characteristic enables two points that originally could not form an edge to indirectly form an edge of the graph in the feature space, thereby enabling the network model to learn the difference between effective points and noise points. And it has the ability to strongly rely on the upper points and ignore the lower points when characterizing roundness and sphericity.

[0091] (5) According to the dynamically updated convolution features, output the classification result, specifically:

[0092] Max-pool the convolution features into a 1024-dimensional feature vector F 1024 :

[0093] F 1024 = maxpool(G (l) (14)

[0094] where G (l) is the graph feature of the last layer.

[0095] Use softmax() to reduce the 1024-dimensional feature vector F 1024 to C dimensions, where C is the number of classification categories, and the value of each dimension represents the probability of the corresponding category. The largest dimension number is the predicted category:

[0096] F C = softmax(F 1024 ) (15)

[0097] According to the classification methods of Embodiment 1 and 2 above, further verify the performance of non-complete sand particles in characterizing the roundness and sphericity of complete sand particles, and use the trained dynamic edge convolution neural network to classify the soil particles in the test set; Figure 11Twelve categories are shown. Different colors of the 2.5D particles represent different angle-sphericity prediction categories. The boxes outside the particles indicate that the particles are misclassified, and the colors of the boxes represent the categories of the true particles. The correspondence between colors and categories is shown in the legend on the right. As shown by the example particle in the figure, the corresponding 3D particle of this particle is misclassified as SA-LS, but the true category is SR-LS.

[0098] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A non-complete particle shape characterization method based on dynamic graph edge convolutional network, characterized in that: The shape characterization method comprises the following steps: S1. Calculate the sphericity and roundness values of the complete particle grid from X-ray computed tomography using 3D computational geometry methods, then obtain 3D particle labels. Finally, assign the complete particle labels to the corresponding incomplete sand particle point cloud reconstructed using binocular vision technology. S2. Use a graph neural network to construct the topological structure of an incomplete sand particle point cloud. Propagate separately at the center point of each input incomplete sand particle point cloud, ignoring the effect of the input order of nodes on the network model representation. Extract the edges between the center point and the neighboring points to learn the feature dependency information between the two nodes. S3, the spatial transformation network generates a 3×3 transformation matrix by analyzing the posture of the incomplete sand particle point cloud and performs rotation and scaling geometric transformations on the input point cloud. The spatial transformation network aligns or adjusts the point cloud to eliminate the influence of the camera position on the coordinates of the same sand particle point cloud; S4. Use edge convolution operation to extract local features, output the features of the local area of the integrated center point, and enhance the network model's local roundness and sphericity features of incomplete sand particles; S5. After each feature map extraction, the k nearest neighbor points of the feature center are updated using a dynamic map according to the distance to the center point, so that the information is non-locally diffused in the entire point cloud, thereby enhancing the extraction of the overall features of incomplete sand particles. S6. Output the classification results based on the dynamically updated convolutional features of the last layer.

2. The method for characterizing incomplete particle shape based on a dynamic graph edge convolutional network according to claim 1, characterized in that: In step S1, the incomplete sand particle point cloud is divided into 12 categories, namely: high roundness-high sphericity, high roundness-low sphericity, medium roundness-high sphericity, medium roundness-low sphericity, secondary roundness-high sphericity, secondary roundness-low sphericity, secondary prism angle-high sphericity, secondary prism angle-low sphericity, medium prism angle-high sphericity, medium prism angle-low sphericity, high prism angle-high sphericity and high prism angle-low sphericity.

3. The method for characterizing incomplete particle shape based on dynamic graph edge convolutional network according to claim 1, characterized in that: The specific method of constructing the incomplete sand particle point cloud topological structure in step S2 includes the following steps: S2-1. In the local directed graph, each point in the point cloud are all considered as central nodes, and the central nodes are calculated and its k nearest neighbors distance : ； S2-2, and It constitutes the local topological structure of incomplete sand particles. represents all edges connected to the point, Indicates a point and Connected edges: 。 4. The method for characterizing incomplete particle shape based on dynamic graph edge convolutional network according to claim 1, characterized in that: The specific method of aligning or adjusting the point cloud by the spatial transformation network in step S3 to eliminate the influence of the camera position on the coordinates of the same sand particle point cloud includes the following steps: S3-1. Use convolution operation to effectively capture the local features of incomplete sand particle point cloud transformation and reduce the number of parameters by sharing weights. S3-2, Batch Normalization normalizes the input distribution of each layer in the deep network, alleviating the gradient vanishing problem and accelerating the training process; S3-3. Leaky ReLU, a variant of the rectified linear unit, is used to introduce nonlinearity, enabling the model to learn more advanced abstract features of the incomplete sand particle point cloud: ； S3-4. The linear layer of the multilayer perceptron is used to output the 9-dimensional transformation features in the real domain and reshape them into a 3×3 transformation matrix.

5. The method for characterizing incomplete particle shape based on dynamic graph edge convolutional network according to claim 1, characterized in that: The specific operation of extracting local features by edge convolution operation in step S4 includes the following steps: S4-1. Extracting hidden feature vectors using MLP ; and is the input of the convolution operation, representing the center point and Neighboring points; For the edge , or as Local coordinates with the center point as the origin: ； in and is the center point and its adjacent points In the channel The value in; input point and output hidden feature vector The number of channels are and ;aisle The value of the hidden feature vector in is expressed as ; The trainable parameters of MLP are 、 ; S4-2. Apply symmetric aggregation operation max and edge feature convolution function To define the edge convolution operation; where the edge convolution is i Output of vertices Given by the following formula; because max is a symmetric function, no matter How is the arrangement of layers The output of is always the maximum value: 。 6. The method for characterizing incomplete particle shape based on dynamic graph edge convolutional network according to claim 1, characterized in that: In step S5, the dynamic graph is used to update the feature center point The nearest neighbor operation includes the following steps: S5-1 After each edge convolution layer, layer The point is updated to the closest of points; S5-2 After each edge convolution layer, The edges of the layer are updated to , , , and finally the network will produce a new graph .

7. The method for characterizing incomplete particle shape based on dynamic graph edge convolutional network according to claim 1, characterized in that: The operation of outputting the classification result according to the dynamically updated convolutional features in step S6 specifically includes the following steps: S6-1 max-pools the convolutional features into a 1024-dimensional feature vector : ； in It is the graph feature of the last layer; S6-2 uses softmax() to transform the 1024-dimensional feature vector , dimensionality reduction to C dimensions, where C is the number of categories, each dimension value represents the probability of the corresponding category, and the largest one-dimensional number is the predicted category: 。

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