Loss function calculation method and grid generation method based on grid shape learning

Abstract

The application discloses a loss function calculation method and a grid generation method based on grid shape learning, and the loss function calculation method comprises the following steps: setting the genus of a target network to 0; mapping the target grid to a spherical space to obtain a first grid; calculating the first nearest mapping of a generated grid to the target grid, mapping the generated grid to the spherical space based on the nearest mapping to obtain a second grid; adjusting the discontinuous area of the second grid based on the Laplace smoothing operation of the Laplace-Beltrami operator; calculating the second nearest mapping of the adjusted second grid to the first grid; mapping the generated grid to the target grid based on the second nearest mapping to obtain a final deformation target grid; and calculating the 2-norm average value of each vertex pair between the generated grid and the final deformation target grid as a loss value. The application can realize the loss function calculation based on the grid shape learning to train the generated network, so that the high-quality grid generation is realized.

Description

Technical Field

[0001] This invention relates to the field of mesh shape learning, and in particular to a loss function calculation method and a mesh generation method based on mesh shape learning. Background Technology

[0002] Generating high-quality dental meshes from CBCT images is a crucial step in dental CAGD software. Using deep networks to generate high-quality dental meshes based on acquired 3D oral data is a popular research topic. Currently, mesh deformation-based methods can effectively control the quality of the generated dental meshes; however, in complex multi-root situations, the generated mesh shape at the root area is often poor.

[0003] Mesh deformation-based generative tooth networks struggle with complex multi-root situations, where the mesh shape at the roots is often poor. Experiments reveal that existing loss functions are prone to getting trapped in local optima when dealing with complex tooth roots. Most mesh deformation-based generative tooth networks use chamfer distance as the loss function and have achieved impressive performance. However, surface distance-based metrics fail to accurately assess the similarity between shapes. As... Figure 1 As shown, Figure 1 (a) and Figure 1 (b) The chamfer distance between them is close to the minimum value, and the shape of the mesh is... Figure 1 (c) and Figure 1 (d) is significantly different. This is because the nearest neighbor mapping between the two shapes is discontinuous. The loss function based on chamfer distance does not consider the continuity of the mapping between surfaces, and this problem cannot be penalized by the chamfer distance. Existing surface distance metrics do not take into account the impact of mapping continuity on the generated tooth mesh shape, causing the predicted mesh to converge to an incorrect shape. Summary of the Invention

[0004] The purpose of this invention is to provide a loss function calculation method and a mesh generation method based on mesh shape learning, aiming to solve the problem of poor mesh shape generation.

[0005] This invention discloses a method for calculating a loss function based on mesh shape learning; S1. Set the genus of the target network to 0; S2. Map the target mesh onto the spherical space to obtain the first mesh; S3. Calculate the first nearest mapping from the generated mesh to the target mesh, and map the generated mesh to the spherical space based on the first nearest mapping to obtain the second mesh; S4. Adjust the discontinuous regions of the second grid using the Laplace-Beltramm operator's Laplace smoothing operation; S5. Calculate the second nearest mapping from the adjusted second grid to the first grid; S6. Based on the second nearest mapping, the generated mesh is mapped to the target mesh to obtain the final deformed target mesh; S7. Calculate the average 2-norm of each vertex pair between the generated mesh and the final deformed target mesh as the loss value.

[0006] This invention also provides a loss function calculation system based on mesh shape learning, comprising: The configuration module is used to set the genus of the target network to 0; The first grid module is used to map the target grid onto a spherical space to obtain the first grid; The second mesh module is used to calculate the first nearest mapping from the generated mesh to the target mesh, and to map the generated mesh to the spherical space based on the first nearest mapping to obtain the second mesh. The adjustment module is used to adjust the discontinuous regions of the second grid based on the Laplace smoothing operation of the Laplace-Beltramian operator; The calculation module is used to calculate the adjusted second nearest mapping from the second grid to the first grid; The final deformation module is used to map the generated mesh to the target mesh based on the second nearest mapping to obtain the final deformed target mesh; The loss calculation module is used to calculate the 2-norm average of each vertex pair between the generated mesh and the final deformed target mesh as the loss value.

[0007] This invention also provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor, implements the steps of the above-described method.

[0008] The present invention provides a new method for calculating the loss function, which can result in a well-shaped tooth mesh.

[0009] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0010] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0011] Figure 1 It is a tooth mesh shape diagram in the prior art; Figure 2 This is a flowchart of a loss function calculation method based on mesh shape learning according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the network design for the loss function calculation method based on mesh shape learning according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the loss function design for the loss function calculation method based on mesh shape learning according to an embodiment of the present invention; Figure 5 This is a flowchart illustrating the loss function calculation method based on mesh shape learning according to an embodiment of the present invention. Figure 6 This is a schematic diagram of a loss function calculation system based on grid shape learning according to an embodiment of the present invention. Detailed Implementation

[0012] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0013] Method Implementation Examples According to an embodiment of the present invention, a method for calculating a loss function based on mesh shape learning is provided. Figure 2 This is a flowchart of the loss function calculation method based on mesh shape learning according to an embodiment of the present invention, as shown below. Figure 2 As shown, it specifically includes: S1. Set the genus of the target network to 0; S2. Map the target mesh onto the spherical space to obtain the first mesh; S3. Calculate the first nearest mapping from the generated mesh to the target mesh, and map the generated mesh to the spherical space based on the first nearest mapping to obtain the second mesh; S4. Adjust the discontinuous regions of the second grid using the Laplace-Beltramm operator's Laplace smoothing operation; S5. Calculate the second nearest mapping from the adjusted second grid to the first grid; S6. Based on the second nearest mapping, the generated mesh is mapped to the target mesh to obtain the final deformed target mesh; S7. Calculate the average 2-norm of each vertex pair between the generated mesh and the final deformed target mesh as the loss value.

[0014] S2 specifically includes: based on the conformal spherical mapping algorithm, mapping the target mesh to a spherical space to obtain the first mesh.

[0015] S4 specifically includes the following formula for the discrete Laplace operation based on the vertex function: Formula 1; L is the Laplace matrix. For Laplace weights, This is a simplified form of performing the Laplace operation at point i, for the vertex. Sum all adjacent points j, where j is the index of the point adjacent to i. It is a vertex on the second grid. any discrete function The value of is set when applying vertex space coordinate functions. Let i = 1, 2, 3...n, where n is the total number of vertices in the second grid. The following equation is used iteratively to achieve vertex smoothing: Formula 2; constant Used to control the convergence rate. = ; To constrain the vertices on the second mesh to the unit sphere, the vertices on the second mesh are projected onto the unit sphere after each smoothing step. This projection operation is denoted as... The formula is as follows: Formula 3; Vertex It is any vertex on the second grid. It is the vertex on the first grid corresponding to the first nearest mapping. It is the vertex , The normal direction of the vertex is such that the following expression is satisfied: : Formula 4; in It was set to 0.5. It is the set of vertices on the overlapping region.

[0016] S7 specifically includes: calculating the average 2-norm of the vertex pairs between the generated mesh and the final deformed target mesh as the loss value, using the following formula: Formula 5; in, For the k-th point on the final deformable target mesh, To generate the k-th point on the grid, n is the number of vertices in the target grid.

[0017] The specific implementation method is as follows: The tooth mesh deformation generation method uses CBCT (cone-beam computed tomography) images as input and a tooth mesh model as output, typically employing a 3D Unet network structure. We use 3D Unet prediction to attempt to predict the deformation flow field from a standard sphere to a specific tooth. Iteratively, the motion direction in the flow field is sampled at each vertex location to drive mesh deformation. Our method effectively captures the complex changes in shape from a standard sphere to a specific tooth, and adjusts the mesh at each vertex location according to the flow field direction to achieve accurate shape deformation. Figure 3 This is a schematic diagram of the network design for the loss function calculation method based on mesh shape learning according to an embodiment of the present invention.

[0018] The main improvement of this invention is the design of the loss function, and the method for calculating the loss function is as follows: Figure 4 This is a schematic diagram of the loss function design for the loss function calculation method based on mesh shape learning according to an embodiment of the present invention; Generate tooth mesh and target tooth mesh All are 0 in deficiency. and yes and The vertices. From the predicted grid. To the target tooth mesh There exists a nearest neighbor mapping In order to make Continuous, there exists a movement distance .when When the chamfer distance is low, we can obtain a generated tooth mesh with high similarity to the target tooth mesh. This is calculated in Euclidean space. It is very difficult; however, this invention provides a method for optimization based on spherical parameterization. .

[0019] Figure 5 This is a flowchart illustrating the loss function calculation method based on mesh shape learning according to an embodiment of the present invention. In our method, invertible mapping based on conformal spherical transport is used. Target tooth mesh Mapped to a spherical mesh Generate a tooth mesh. With target tooth mesh Nearest neighbor mapping in Euclidean space Used as a feature, it will generate a tooth mesh. Mapping to the same spherical space, then obtaining the mesh. However, in There are likely to be overlapping regions, which represent discontinuous mappings and require adjustment. The Laplace smoothing operation based on the Laplace-Beltrami operator is used to adjust these overlapping regions. A discrete Laplace operation based on a vertex function is as follows: (1) For vertices Sum all adjacent points j. It is the vertex For any discrete function The value of . When applying the vertex space coordinate function, we set Where n is the total number of vertices. Smooth vertices are achieved by iteratively calculating the following equation: (2) constant Used to control the convergence rate. When the value is a very small positive value, smoothing is robust but inefficient. To constrain vertices to the unit sphere, vertices are projected onto the unit sphere after each smoothing step; this projection operation is denoted as... The complete formula is as follows: (3) If we are By performing multiple iterative operations on the above equation, all [elements] can be removed. Overlapping region. However, such If the changes are too large from the initial conditions, the network will have difficulty learning such variations. To limit... The changes concentrate the changes on the vertex set in the overlapping region. Above, these vertices are mapped to their nearest neighbors. The above performance was poor, so we only changed the iteration operation by changing only the... .

[0020] We provide a The method for determining the vertex: yes Any vertex on, yes According to The corresponding vertex, It is the vertex , The normal direction of the vertex is such that the following expression is satisfied: : (4) in It was set to 0.5.

[0021] The physical interpretation of the above calculation is as follows: It is a mass-spring system, where the vertices represent point masses, the edges are contracting springs, and some vertex positions are fixed. In this case, equation (2) is a gradient descent equation used to minimize the quadratic spring energy.

[0022] Such a mass spring system cannot guarantee the elimination of overlapping areas every time, but It tends to converge to a unit sphere with no overlapping regions, and the adjustment operation does not cause... It got worse. After multiple iterative calculations, we obtained... . The inverse mapping can Tooth mesh mapped back to Euclidean space dental mesh and The nearest neighbor mapping between them will not be greater than Poor. Therefore, the dental mesh... yes The target of vertex-by-vertex deformation. , yes , For any vertex, the new loss function is as follows: (5) Under the supervision of this loss function, the accuracy of the neural network in generating tooth meshes can be effectively improved, avoiding reconstruction errors at adjacent root points.

[0023] Our method can effectively improve the accuracy of tooth meshes output by tooth generation networks. Shape generative neural networks based on mesh generation are one of the development directions of automated 3D modeling, and our method can be used as its loss function to improve modeling accuracy.

[0024] System Implementation Example 1 According to embodiments of the present invention, a loss function calculation system based on mesh shape learning is provided. Figure 6 This is a schematic diagram of a loss function calculation system based on mesh shape learning according to an embodiment of the present invention, as shown below. Figure 6 As shown, it specifically includes: The configuration module is used to set the genus of the target network to 0; The first grid module is used to map the target grid onto a spherical space to obtain the first grid; The second mesh module is used to calculate the first nearest mapping from the generated mesh to the target mesh, and to map the generated mesh to the spherical space based on the first nearest mapping to obtain the second mesh. The adjustment module is used to adjust the discontinuous regions of the second grid based on the Laplace smoothing operation of the Laplace-Beltramian operator; The calculation module is used to calculate the adjusted second nearest mapping from the second grid to the first grid; The final deformation module is used to map the generated mesh to the target mesh based on the second nearest mapping to obtain the final deformed target mesh; The loss calculation module is used to calculate the 2-norm average of each vertex pair between the generated mesh and the final deformed target mesh as the loss value.

[0025] The embodiments of the present invention are system embodiments corresponding to the above method embodiments. The specific operation of each module can be understood by referring to the description of the method embodiments, and will not be repeated here.

[0026] This invention provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor, implements the steps described in the method embodiments above.

[0027] 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; and these modifications or substitutions to the technical solutions of the embodiments of the present invention do not cause the essence of the corresponding technical solutions to deviate from the scope of the present solution.

Claims

1. A loss function calculation method based on mesh shape learning, characterized in that, include: S1. Set the genus of the target network to 0; S2. Map the target mesh onto the spherical space to obtain the first mesh; S3. Calculate the first nearest mapping from the generated mesh to the target mesh, and map the generated mesh to the spherical space based on the first nearest mapping to obtain the second mesh; S4. Adjust the discontinuous regions of the second grid using the Laplace-Beltramm operator's Laplace smoothing operation; S5. Calculate the second nearest mapping from the adjusted second grid to the first grid; S6. Based on the second nearest mapping, the generated mesh is mapped to the target mesh to obtain the final deformed target mesh; S7. Calculate the average 2-norm of each vertex pair between the generated mesh and the final deformed target mesh as the loss value; The tooth network generated by mesh deformation uses CBCT as input and a tooth mesh model as output.

2. The method according to claim 1, characterized in that, S2 specifically includes: mapping the target mesh to a spherical space based on a conformal spherical mapping algorithm to obtain the first mesh.

3. The method according to claim 2, characterized in that, Specifically, S4 includes the following formula for the discrete Laplace operation based on the vertex function: Official 1; L is the Laplace matrix. For Laplace weights, This is a simplified form of performing the Laplace operation at point i, for the vertex. Sum all adjacent points j, where j is the index of the point adjacent to i. It is a vertex on the second grid. any discrete function The value of is set when applying vertex space coordinate functions. Let i = 1, 2, 3...n, where n is the total number of vertices in the second grid. The following equation is used iteratively to achieve vertex smoothing: Formula 2; constant Used to control the convergence rate. = ; To constrain the vertices on the second mesh to the unit sphere, the vertices on the second mesh are projected onto the unit sphere after each smoothing step. This projection operation is denoted as... The formula is as follows: Formula 3; Vertex It is any vertex on the second grid. It is the vertex on the first grid corresponding to the first nearest mapping. It is the vertex , The normal direction of the vertex is such that the following expression is satisfied: : Official 4; in It was set to 0.

5. It is the set of vertices on the overlapping region.

4. The method according to claim 3, characterized in that, S7 specifically includes: calculating the average 2-norm of the vertex pairs between the generated mesh and the final deformed target mesh as the loss value, and the calculation formula is as follows: Official 5; in, For the k-th point on the final deformable target mesh, To generate the k-th point on the grid, n is the number of vertices in the target grid.

5. A loss function calculation system based on mesh shape learning, characterized in that, include: The configuration module is used to set the genus of the target network to 0; The first grid module is used to map the target grid onto a spherical space to obtain the first grid; The second mesh module is used to calculate the first nearest mapping from the generated mesh to the target mesh, and to map the generated mesh to the spherical space based on the first nearest mapping to obtain the second mesh. The adjustment module is used to adjust the discontinuous regions of the second grid based on the Laplace smoothing operation of the Laplace-Beltramian operator; The calculation module is used to calculate the adjusted second nearest mapping from the second grid to the first grid; The final deformation module is used to map the generated mesh to the target mesh based on the second nearest mapping to obtain the final deformed target mesh; The loss value calculation module is used to calculate the 2-norm average of each vertex pair between the generated mesh and the final deformed target mesh as the loss value; The tooth network generated by mesh deformation uses CBCT as input and a tooth mesh model as output.

6. The system according to claim 5, characterized in that, The first mesh module is specifically used to: map the target mesh to a spherical space to obtain the first mesh based on a conformal spherical mapping algorithm.

7. The system according to claim 6, characterized in that, The adjustment module is specifically used for: the discrete Laplace operation formula based on the vertex function is as follows: Official 1; L is the Laplace matrix. For Laplace weights, This is a simplified form of performing the Laplace operation at point i, for the vertex. Sum all adjacent points j, where j is the index of the point adjacent to i. It is a vertex on the second grid. any discrete function The value of is set when applying vertex space coordinate functions. Let i = 1, 2, 3...n, where n is the total number of vertices in the second grid. The following equation is used iteratively to achieve vertex smoothing: Formula 2; constant Used to control the convergence rate. = ; To constrain the vertices on the second mesh to the unit sphere, the vertices on the second mesh are projected onto the unit sphere after each smoothing step. This projection operation is denoted as... The formula is as follows: Formula 3; Vertex It is any vertex on the second grid. It is the vertex on the first grid corresponding to the first nearest mapping. It is the vertex , The normal direction of the vertex is such that the following expression is satisfied: : Official 4; in It was set to 0.

5. It is the set of vertices on the overlapping region.

8. The system according to claim 7, characterized in that, The loss calculation module is specifically used to calculate the average L2 norm of the vertex pairs between the generated mesh and the final deformed target mesh as the loss value. The calculation formula is as follows: Official 5; in, For the k-th point on the final deformable target mesh, To generate the k-th point on the grid, n is the number of vertices in the target grid.

9. A mesh generation method, characterized in that, The generator network is trained using the method described in any one of claims 1 to 4 as the loss function to obtain the trained generator network. The cone beam imaging computer reconstructed tomographic image is then input into the generator network to obtain a mesh.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an implementation program for information transmission, which, when executed by a processor, implements the steps of the mesh generation method as described in any one of claims 9.

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