Dynamic graph edge convolutional network-based incomplete particle shape characterization method

Abstract

The invention provides an incomplete particle shape characterization method based on a dynamic graph edge convolutional network, and relates to the field of sand particle shape characterization analysis. The shape characterization method comprises the following steps: characterizing and classifying roundness and sphericity of complete sand particles by using a half sand particle point cloud, and taking an incomplete sand particle point cloud obtained by a binocular vision technology as input of a network model; constructing a point cloud topological relation by using a graph generation network; point clouds are aligned or adjusted by using a spatial transformation network, and the influence of the camera position on the coordinates of the same particle point clouds is eliminated. Integrating the features of the local area of the central point by using edge convolution, and enhancing the features of the network model for the local roundness and sphericity of the incomplete sand particles; and finally, updating k nearest neighbor points of the feature center point according to the distance to the center point after each extraction of the feature map based on dynamic map updating, so that the information is non-locally diffused in the whole point cloud, and the extraction of the whole features of the incomplete sand particles is enhanced.

Description

Technical Field

[0001] The present invention relates to the field of sand particle shape characterization and analysis, and in particular to an incomplete particle shape characterization method based on a dynamic graph edge convolutional network. Background Art

[0002] The angularity and sphericity of particles have a strong influence on the macroscopic mechanical properties of soils. Angular particles have sharp protrusions and corners that intersect each other to form many contact points, thus strengthening the load-bearing structure of granular soils. On the other hand, spherical particles are more likely to align and pack tightly when compressed, thus reducing the voids between soil particles. Both experimental and numerical studies have shown that particle angles and roundness have a strong influence on the shear strength, compressibility, void structure and deformation behavior of soils.

[0003] In contemporary geotechnical engineering, researchers have adopted a range of advanced 3D imaging methods to capture complex 3D particle geometries. These techniques can be divided into two categories: (1) penetrating X-ray computed tomography (X-ray CT) and (2) non-penetrating laser scanning, stereo photography, and structured light systems. The former can capture the complete 3D particle surface geometry regardless of inter-particle occlusion. However, X-ray CT equipment is expensive, and processing X-ray CT images is computationally demanding and time-consuming. The latter cannot penetrate sand particles and can only capture the upper half of the particle surface exposed in the camera view or half-particle geometry, which is called 2.5-dimensional (2.5D) particles. However, compared with X-ray CT, these systems are simple, low-cost, and testing laboratories can be easily constructed in common soils. Therefore, non-penetrating scanning techniques have an advantage in scanning 3D particle surface geometry due to their low cost and ease of implementation. Therefore, characterizing the angularity and sphericity of non-complete particles is essential for studying the mechanical properties of soils.

[0004] The traditional characterization method uses 3D computational geometry (CG) to calculate the roundness and sphericity of 2.5D and corresponding 3D particles respectively, and attempts to find the difference between the two through numerical statistics. However, when there are too many statistical particle data, there is no significant pattern in the roundness and sphericity of 2.5D and corresponding 3D particles. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides an incomplete particle shape characterization method based on a dynamic graph edge convolutional network, which has the advantages of fast and high robustness in the characterization of incomplete sand particle point clouds.

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

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

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

[0009] S2. Use graph neural network to construct the topological structure of incomplete sand particle point cloud, propagate separately on the center point of each input incomplete sand particle point cloud, ignore the influence of the input order of nodes on the representation of the network model, and extract the edges of the center point and the neighborhood point to learn the feature dependency information between the two nodes;

[0010] S3, the spatial transformation network generates a 3×3 transformation matrix by analyzing the posture of the incomplete sand particle point cloud to perform geometric transformations such as rotation and scaling 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;

[0011] S4, using 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;

[0012] S5. After each feature map is extracted, the k nearest neighbor points of the feature center point 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, and the extraction of the overall features of incomplete sand particles is enhanced;

[0013] S6. Output the classification result based on the dynamically updated convolutional features of the last layer.

[0014] Preferably, in the step S1, the incomplete sand particle point cloud is 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), secondary roundness-high sphericity (SR-HS), secondary roundness-low sphericity (SR-LS), secondary edge angle-high sphericity (SA-HS), secondary edge angle-low sphericity (SA-LS), medium edge angle-high sphericity (A-HS), medium edge angle-low sphericity (A-LS), high edge angle-high sphericity (VA-HS) and high edge angle-low sphericity (VA-LS).

[0015] Preferably, the specific method of constructing the incomplete sand particle point cloud topological structure 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 central nodes, 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 The local topological structure of the incomplete sand particles, e i represents all edges connected to the point, e ij Represents point p i and p j Connected edges:

[0020]

[0021] Preferably, the specific method of aligning or adjusting the point cloud by the space transformation network in step S3 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 operation to effectively capture the local features of the incomplete sand particle point cloud transformation and reduce the number of parameters by sharing weights.

[0023] S3-2, batch normalization standardizes the input distribution of each layer in the deep network, alleviates the gradient vanishing problem and accelerates the training process;

[0024] S3-3. Leaky ReLU, a variant of the rectified linear unit, is used to introduce nonlinearity, which enables the model to learn more advanced abstract features of the incomplete sand particle point cloud:

[0025]

[0026] 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.

[0027] Preferably, the specific operation of extracting local features by edge convolution operation in step S4 includes the following steps:

[0028] S4-1. Using MLP to extract hidden feature vector h(x i ,x j -x i ); x i and x j is the input of the convolution operation, representing the center point and k nearest neighbor points xj ;x j -x i For edge e ij , which can also be seen as x j Local coordinates with the center point as the origin:

[0029]

[0030]

[0031] where x ic and x jc is the center point x i and its adjacent points x j The value in channel c; input point x i And output hidden feature vector h(x i ,x j -x i ) have C and C' channels respectively; the value of the hidden feature vector in channel c' is expressed as The trainable parameters of 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 edge convolution output x' at the i-th vertex i Given by the following formula; because max is a symmetric function, no matter x j How is the arrangement of layer x' i The output of is always the maximum value:

[0033]

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

[0035] S5-1 passes through each edge convolution layer, at the lth layer The point is updated to be closest K l points;

[0036] S5-2 passes through each edge convolution layer, and the edge at layer l is updated as Finally, the 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 convolutional features in step S6 specifically includes the following steps:

[0038] S6-1 max-pools the convolutional features into a 1024-dimensional feature vector F 1024 :

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

[0040] Among them G (l) It is the graph feature of the last layer;

[0041] S6-2 uses softmax() to transform the 1024-dimensional feature vector F 1024 , reduced 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:

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

[0043] The present invention provides a non-complete particle shape characterization method based on a dynamic graph edge convolutional network, which has the following advantages over the prior art:

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

[0045] Figure 1 A network structure diagram for implementing the incomplete geotechnical point cloud classification of the present invention;

[0046] Figure 2 3D and 2.5D model diagrams of 12 types of rock and soil particles in Example 1 of the present invention;

[0047] Figure 3 This is a schematic diagram of a 2.5D sand particle acquisition system in Example 1 of the present invention;

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

[0049] Figure 5 This is a schematic diagram of 3D sand grain acquisition and segmentation in Example 1 of the present invention;

[0050] Figure 6 Schematic diagram of 12 types of 2.5D and 3D sand particle point clouds in Example 1 of the present invention;

[0051] Figure 7 This is a schematic diagram of the process of making 2.5D particle roundness and sphericity labels in Example 1 of the present invention;

[0052] Figure 8 Schematic diagram of the process of generating a point cloud image of sand and gravel particles in Example 2 of the present invention;

[0053] Fig. 9 This is a diagram of the spatial transformation network structure in Embodiment 2 of the present invention;

[0054] Fig.10 Schematic diagram of the point cloud edge convolution process in Example 2 of the present invention;

[0055] Fig.11 This is a schematic diagram showing the visualization of the classification results of the dynamic edge convolutional neural network on the 2.5D particle point cloud on the test set in Example 2 of the present invention. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention is clearly and completely described below in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] Embodiment 1:

[0058] (1) 12 types of complete sand particles and corresponding incomplete particle 3D models Figure 2 As shown;

[0059] The widely used non-penetrating binocular vision technology is used to obtain 2.5D sand particles. This technology has the advantages of being simple, effective and inexpensive, and can obtain accurate upper surface information of particles. The binocular vision device that collects 2.5D geometric information of particles is as follows: Figure 3(a) shows the soil particles placed naturally on a flat surface in the xy plane so that the maximum projection of the particles faces upward. By moving one camera at two locations, it acts as two cameras to reduce hardware costs. A triangle is formed between the two shooting locations and the soil particles, similar to the principle of human eye perception of depth. The image analysis algorithm fuses the two images and creates the depth of the scene. The calculated 2.5D particle result is shown in Figure 3 (b) as shown.

[0060] The roundness and sphericity of the complete particle are inferred based on the 2.5D particle point cloud through the neural network model. During the training phase, the network model needs to learn the mapping relationship between the 2.5D particle point cloud shape and the corresponding roundness and sphericity of the complete particle. Therefore, it is necessary to first obtain the 2.5D particle as the input point cloud and the corresponding complete 3D particle to produce the roundness and sphericity labels. Figure 4 As shown in FIG. 1 , the sand particles are placed flat on the table, and the 2.5D geometric shape of the particles is obtained using the above binocular vision. Figure 5 As shown in the figure, the sand grains are placed in a cylindrical tube and the 3D geometry of the complete sand grains is obtained using X-ray CT. Then the improved watershed algorithm is used to segment the individual sand grains that are in contact with each other and can effectively solve the problem of over-segmentation. Figure 4 As shown in (b), after segmentation, each particle generated by X-ray CT scan and structured light is assigned a color.

[0061] (2) The grid is converted into a point cloud of rock and soil particles as input to the network. Figure 5 As shown in the figure, the conversion process is as follows:

[0062] The deep learning network model can infer the roundness and sphericity of 3D sand grains by simply inputting the point cloud of 2.5D sand grains: in order to form a 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 The 12 types of point clouds of 2.5D and corresponding 3D sand particles are displayed. The upper point clouds of 2.5D and corresponding 3D particles are basically the same, which is valid information in point cloud analysis. However, due to imaging occlusion, the lower point cloud of 2.5D particles is an extension of the maximum projection of the upper point cloud and is 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 3D particles.

[0063] (3) The steps for creating 2.5D particle labels are as follows: Figure 7 As shown, specifically:

[0064] First, the sphericity and angle values ​​of the 3D particle mesh are calculated using the 3D CG method. Then, the 3D particle labels are obtained according to the roundness and sphericity value intervals in the Power's chart. Finally, the labels are assigned to the corresponding 2.5D particle point clouds.

[0065] The neural network model needs to learn the mapping relationship between the geometric shape of 2.5D particles and the corresponding 3D particle labels. In supervised deep learning, the three-dimensional particles in the data set 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 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 fitting sphere of the i-th corner point, r ins,3 is the maximum inscribed sphere radius of the 3D particle, N is the number of corner points, S I,3 is the sphericity, d 1 d 2 and d 3 are the length, width and height of the particle, V is the volume of the particle, and V cir is the volume of the sphere surrounding the particle, D e,3 is the diameter of a sphere of equal volume, D c,3 is the diameter of the smallest circumscribed sphere, D i,3 is the diameter of the smallest inscribed sphere.

[0069] Embodiment 2:

[0070] Based on the training data set obtained in Example 1 above, 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 of the point cloud at multiple scales to identify the upper valid geometric point cloud and the lower noise point cloud. The convolution object of the dynamic edge network is the graph composed of each point in the point cloud and its neighborhood points. The convolution operation is applied on the edge of the neighborhood graph to capture the local geometric structure of multiple scales. In the convolutional neural network, the convolution graph is invariant throughout the network, which will lead to insufficient information processing of the model at different scales. However, the dynamic edge convolutional network updates the graph after each layer of edge convolution. That is, after each feature map is extracted, the k nearest neighbors of the transformed feature center point are updated according to the distance to the center point. Therefore, different proximity metrics can enable non-local diffusion of information throughout the point cloud. The features of a point propagate to points far away from it in the feature space, rather than just being limited to its neighboring points in the input space. The range of information propagation may no longer be limited 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] Graph neural network is a point cloud processing method suitable for constructing point cloud topological relationships. It is a pre-step before point cloud convolution. This method propagates separately on each center point and can ignore the influence of the input order of the nodes on the representation of the network model. It can also extract the edges between the center point and the neighborhood point to learn the feature dependency information between the 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 the three-dimensional coordinates v i =(x i ,y i ,z i ).

[0075] It is impractical to connect any two points in the point cloud, because this operation will greatly increase the time complexity and space complexity and cause the network model to fail. The K-NN algorithm can efficiently construct a local directed graph, such as Figure 8 As shown. In the local directed graph, each point p in the point cloud i are all regarded as central nodes, and the central node p is calculated i and its k nearest neighbor points p j The distance d ij . p i and p j The local topological structure of the 2.5D particle is composed of i Represents all edges connected to the point. ij Represents point p i The edge connected to 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 coordinates of the same particle point cloud. The specific method is as follows:

[0078] In point cloud processing, the spatial transformation network is a network structure used to learn point cloud transformation features. By analyzing the posture of the 2.5D sandstone 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 aligned or adjusted point cloud can eliminate the influence of the camera position on the coordinates of the same particle point cloud. The network structure is as follows: Fig. 9 shown.

[0079] The spatial transformer network first uses k-nn to generate a 2.5D graph structure for each point, and then passes through the feature extraction layer multiple times to extract the corresponding transformation features. The feature extraction layer includes convolution layer, batch normalization layer and LeakyReLU. The convolution 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 standardize the input distribution of each layer in the deep network, which helps to alleviate the gradient vanishing problem and thus accelerate the training process. LeakyReLU is a variant of the rectified linear unit that helps introduce nonlinearity and prompts the model to learn more advanced abstract features of 2.5D particles. Compared with ReLU, Leaky ReLU solves the problem of activation function failure when the input value is negative by introducing a small negative slope, as shown in formula (10). After the feature extraction layer, the maximum pooling layer is used to reduce the dimension of the point cloud data and extract the most significant features, which helps to reduce computational complexity and reduce overfitting. The MLP layer reduces the 1024-dimensional features output by the second maximum pooling layer to 256 dimensions after two Leaky ReLU full connections. Finally, the Linear layer of the MLP is used to output the 9-dimensional transformation features in the real domain and reshape them into a 3×3 transformation matrix.

[0080]

[0081] (3) The specific calculation steps of edge convolution operation to extract local features include:

[0082] The convolution operation can fully consider the influence of the element neighborhood when extracting features, and has a strong ability to extract local features. This output integrates the features of the local area of ​​the center point, which can enhance the network model's feature extraction of the local roundness and sphericity of the halfparticle. Fig.10 As shown, MLP is used to extract the hidden feature vector h(x i ,x j -x i ). i and xj are the inputs of the convolution operation, representing the center point and the k nearest neighbor points xj respectively. j -x i is the edge eij, which can also be regarded as the local coordinates of xj with the center point as the origin. The conversion of global coordinates to local coordinates ensures the translation invariance of the network model to the point cloud. Mlp can learn the complex nonlinear relationship between adjacent points through hidden layers. 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 roundness and sphericity features formed by the center point and the neighborhood 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 add all the products to get the output.

[0084]

[0085]

[0086] where x ic and x jc is the center point x i and its adjacent points x j The value in channel c. Input point x i And output hidden feature vector h(x i ,x j -x i ) have C and C' channels respectively. The value of the hidden feature vector in channel c' is expressed as The trainable parameters of MLP are w c'c 、w' c(c+C) .

[0087] Finally, the symmetric aggregation operation max and the edge feature convolution function h are applied. w () to define the edge convolution operation. Among them, the edge convolution output x' at the i-th vertex i Given by equation (13). Since max is a symmetric function, no matter x j How is the arrangement of layer x' i The output of is always the maximum value. This property ensures permutation invariance.

[0088]

[0089] (4) Use the dynamic graph to update the k nearest neighbor points of the feature center point, specifically:

[0090] Experiments show that it is beneficial to recalculate the k nearest neighbors to form new graph features in the roundness and sphericity feature space generated by each edge convolution layer. Dynamically updating the feature map is the key difference from graph CNNs that convolve on a fixed input map. The upper part of the 2.5D sand particle point cloud contains useful information, while 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. In addition, 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 use the 2.5D sand point cloud to infer the roundness and sphericity of the complete particle.

[0091] After each edge convolution layer, the network will produce a different graph G (l) =(V (l) ,E (l) ). Among them, at layer l is closest K l points, and the edge is of the form When l = 0, G (0) =(V (0) ,E (0) ) is a graph composed of 2.5D sand particle point clouds in three-dimensional physical space. (0) As a fixed graph, it is convolved in each layer of edge convolution. Due to the large distance, the valid points on the upper part and the noise points on the lower part are difficult to be learned together, resulting in the inability to distinguish between the two types of points. When l≠0, G (l) =(V (l) ,E (l) ) is composed of the feature points after the lth convolution. and The distance between them is very close in the feature space, but they may be far apart in the three-dimensional physical space. This feature allows two points that originally could not form an edge to indirectly form an edge in the feature space, thereby allowing the network model to learn the difference between valid points and noise points. In addition, it has the ability to strongly rely on the upper points and ignore the lower points when characterizing roundness and sphericity.

[0092] (5) Based on the dynamically updated convolutional features, the classification results are output, specifically:

[0093] The convolutional features are max-pooled into a 1024-dimensional feature vector F 1024 :

[0094] F 1024 =maxpool(G (l) (14)

[0095] Among them G (l) It is the graph feature of the last layer.

[0096] Use softmax() to transform the 1024-dimensional feature vector F 1024 , reduced 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:

[0097] F C =softmax(F 1024 ) (15)

[0098] According to the classification methods of Examples 1 and 2 above, the performance of incomplete sand particles in characterizing the roundness and sphericity of complete sand particles was further verified, and the soil particles of the test set were classified using the trained dynamic edge convolutional neural network; Fig.11 There are 12 categories shown in the figure. Different colors of 2.5D particles represent different angle-sphericity prediction categories. The box outside the particle means that the particle is misclassified, and the color of the box represents the category of the real particle. The correspondence between color and category is shown in the legend on the right. As shown in the example particle in the figure, the 3D particle corresponding to the particle is misclassified as SA-LS, but the real category is SR-LS.

[0099] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for characterizing incomplete particle shapes based on a dynamic graph edge convolutional network, characterized in that: The shape characterization method comprises the following steps: S1. Use 3D computational geometry methods to calculate the sphericity and roundness values ​​of the complete particle grid of X-ray computed tomography, then obtain 3D particle labels, and finally assign the complete particle labels to the corresponding incomplete sand particle point cloud reconstructed by binocular vision technology; S2. Use graph neural network to construct the topological structure of incomplete sand particle point cloud, propagate separately on the center point of each input incomplete sand particle point cloud, ignore the influence of the input order of nodes on the representation of the network model, and extract the edges of the center point and the neighborhood point 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 to perform geometric transformations such as rotation and scaling 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, using 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 is extracted, the k nearest neighbor points of the feature center point 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, and the extraction of the overall features of incomplete sand particles is enhanced; S6. Output the classification result 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 the 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 edge angle-high sphericity, secondary edge angle-low sphericity, medium edge angle-high sphericity, medium edge angle-low sphericity, high edge angle-high sphericity and high edge 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 p in the point cloud i are all regarded as central nodes, and the central node p is calculated i and its k nearest neighbor points p j Distance V={p i ∣i=1,2,…,n}; S2-2, p i and p j The local topological structure of the incomplete sand particles, e i represents all edges connected to the point, e ij Represents point p i and p j 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 the incomplete sand particle point cloud transformation and reduce the number of parameters by sharing weights. S3-2, batch normalization standardizes the input distribution of each layer in the deep network, alleviates the gradient vanishing problem and accelerates the training process; S3-3. Leaky ReLU, a variant of the rectified linear unit, is used to introduce nonlinearity, which enables 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. Using MLP to extract hidden feature vector h(x i ,x j -x i ); x i and x j is the input of the convolution operation, representing the center point and k nearest neighbor points x j ;x j -x i For edge e ij , which can also be seen as x j Local coordinates with the center point as the origin: where x ic and x jc is the center point x i and its adjacent points x j The value in channel c; input point x i And output hidden feature vector h(x i ,x j -x i ) have C and C' channels respectively; the value of the hidden feature vector in channel c' is expressed as The trainable parameters of MLP are w c'c 、w c'(c+C) ; S4-2. Apply the symmetric aggregation operation max and the edge feature convolution function h w () to define the edge convolution operation; where the edge convolution output x' at the i-th vertex i Given by the following formula; because max is a symmetric function, no matter x j How is the arrangement of layer x' i 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: The operation of using the dynamic graph to update the k nearest neighbor points of the feature center point in step S5 includes the following steps: S5-1 passes through each edge convolution layer, at the lth layer The point is updated to be closest K l points; S5-2 passes through each edge convolution layer, and the edge at layer l is updated as Finally, the network will generate a new graph G (l) =(V (l) ,E (l) ).

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 F 1024 : F 1024 =maxpool(G (l) ) Among them G (l) It is the graph feature of the last layer; S6-2 uses softmax() to transform the 1024-dimensional feature vector F 1024 , reduced 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: F C =softmax(F 1024 )。

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