A method for establishing a Delaunay triangulated surface reconstruction model and its application
Through the deep learning model, the features of three-dimensional point clouds are extracted and the internal and external properties of the Delaunay triangulated tetrahedron are predicted, and the problem that reconstruction accuracy depends on point cloud visibility and high computational cost in the existing technology is solved, achieving efficient surface reconstruction.
Patent Information
- Application Number
- CN202110863404.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-07-29
- Publication Date
- 2025-03-21
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
The existing surface reconstruction method based on Delaunay triangulation depends on the visibility information of point clouds and has tetrahedral classification errors, which affects the reconstruction quality, and the calculation amount is large and the reconstruction efficiency is affected.
Deep learning model is adopted, including feature extraction network, feature aggregation network and label prediction network, and features of points are extracted through the tangent plane convolution module, pooling layer and anti-pooling layer, and the 1×1 convolutional network is used to predict the inner and outer properties of the tetrahedron to construct a Delaunay triangulated surface reconstruction model.
While ensuring reconstruction accuracy, the complexity and calculation amount of the model are reduced, the reconstruction efficiency is improved, and the calculation amount in the surface reconstruction process is reduced.
Smart Images
Figure CN113593037B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of computer vision, and more specifically, relates to a method for establishing a Delaunay triangulated surface reconstruction model and its application. Background Art
[0002] Surface reconstruction is the process of recovering the three-dimensional shape of an object from a 3D point cloud. There are two main types of surface reconstruction methods. One type is the method using implicit functions. Among them, the classic Poisson surface reconstruction discretizes the space through the octree grid, converts the discrete sample points into a continuous and integrable surface function, and then uses the Marching Cubes method to output the reconstructed surface in the octree grid. As the depth of the octree increases, the memory usage of the algorithm also increases, and the efficiency decreases. The other type of method can be called interpolation technology, which often uses Voronoi diagrams and Delaunay triangulation to represent point clouds. One of the more classic processing methods is to subdivide the space into uneven tetrahedrons through Delaunay triangulation. The triangular facets of the object's reconstructed surface can be identified based on the internal and external attributes of the tetrahedron, and the object's surface can be reconstructed by further splicing the triangular facets of the object's reconstructed surface. Compared with the method using implicit functions, Delaunay triangulation can adapt to the sampling density of the point cloud when dividing the space. However, the traditional Delaunay triangulation method based on graph cuts must provide visibility information of the point cloud when completing the reconstruction work; and there are many tetrahedron classification errors, resulting in complex multi-layer surfaces that affect the reconstruction quality.
[0003] In order to solve the problem that the reconstruction accuracy of existing surface reconstruction methods based on Delaunay triangulation depends on the visibility information of point clouds, a surface reconstruction network DeepDT based on learning Delaunay triangulation of point clouds is proposed in "Delaunay: Learning Geometry From Delaunay Triangulation for Surface Reconstruction". DeepDT learns the internal / external labels of Delaunay tetrahedrons in the Delaunay triangulation of point clouds. First, local geometric features are extracted from the input point cloud and aggregated into a standard graph model obtained from the Delaunay triangulation. Then, graph filtering is performed to introduce regularization for the label prediction of tetrahedrons. A multi-label supervision strategy is proposed, which samples multiple points from the tetrahedron and obtains the internal / external labels of the tetrahedron based on the internal / external labels of the points. This solves the problem that the true value label of the tetrahedron cannot be directly generated due to the complex spatial relationship between the tetrahedron and the surface.
[0004] DeepDT can maintain rich geometric details without producing overly complex surfaces. However, in order to achieve this effect, the model structure is relatively complex, especially the graph filtering module, which is still accompanied by a large amount of calculation during the surface reconstruction process, significantly affecting the reconstruction efficiency. In practical applications, in order to quickly complete surface reconstruction, a graphics processing unit (GPU) is often used to complete related calculations. The limited GPU resources can only process a limited number of point clouds at the same time. In practical applications, the number of point clouds is often extremely large. Therefore, when using DeepDT for surface reconstruction, the reconstruction efficiency needs to be further improved. Summary of the invention
[0005] In view of the defects and improvement needs of the prior art, the present invention provides a method for establishing a Delaunay triangulated surface reconstruction model and its application, the purpose of which is to effectively improve the reconstruction efficiency of surface reconstruction while ensuring the accuracy of surface reconstruction.
[0006] To achieve the above object, according to one aspect of the present invention, a method for establishing a Delaunay triangulated surface reconstruction model is provided, comprising:
[0007] Delaunay triangulates the 3D point cloud of an object with a known surface to obtain the corresponding tetrahedron mesh, and obtains the tangent plane image corresponding to each point in the 3D point cloud, as well as the internal / external labels of multiple points randomly sampled inside each tetrahedron relative to the surface of the object. The training data set is constructed using the tetrahedron mesh annotated with the internal / external label information of the sampling points inside the tetrahedron and the tangent plane image corresponding to each point;
[0008] A deep learning model is established to predict the inside / outside properties of each tetrahedron in a tetrahedron network located on the surface of an object; the deep learning model includes a feature extraction network, a feature aggregation network and a label prediction network; the feature extraction network includes a cutting plane convolution module, a pooling layer and a de-pooling layer connected in sequence, the cutting plane convolution module is used to perform a convolution operation on the cutting plane image corresponding to each point in the three-dimensional point cloud to obtain the initial features of each point; the pooling layer is used to average the initial features and positions of the points to achieve downsampling of the point cloud; the de-pooling layer is used to assign the features of the downsampled points to the features of the points before downsampling as the final features of each point; the feature aggregation network is used to aggregate the features of each vertex of the tetrahedron into the features of the tetrahedron; the label prediction network is a 1×1 convolution network, which is used to predict the inside / outside properties of each tetrahedron located on the surface of the object based on the features of each tetrahedron in the tetrahedron network;
[0009] The deep learning model is trained using the training data set, so that after the training, a Delaunay triangulated surface reconstruction model is obtained.
[0010] The Delaunay triangulated surface reconstruction model established by the present invention, wherein the feature extraction network completes the feature extraction of the point according to the tangent plane image of the point, and the specific process is: firstly, a convolution operation is performed on the tangent plane image, and then pooling and de-pooling operations are performed. On the one hand, the process only involves simple operations such as 2D convolution, pooling and de-pooling, and the indexes of the points used in these operations are all pre-calculated and do not need to be calculated in real time during training, so the reconstruction efficiency is high, and correspondingly, the structure of the feature extraction network is simple; on the other hand, since the tangent plane image stores the information of neighboring points and encodes the local geometric structure, it can accurately reflect the local geometric information; the Delaunay triangulated surface reconstruction model established by the present invention only uses a 1×1 convolutional network to complete the prediction from tetrahedron features to internal and external attributes of the tetrahedron, which is simple and efficient, and since the feature extraction network can accurately extract the features of the points and ensure the accuracy of the tetrahedron features obtained by aggregation, the internal and external attributes of the tetrahedron can be accurately predicted by using the 1×1 convolutional network, thereby ensuring the accuracy of subsequent surface reconstruction. In general, the present invention utilizes a feature extraction network including a cutting plane convolution module, a pooling layer, and a de-pooling layer to extract the features of a point from the cutting plane image of the point, and utilizes a 1×1 convolutional network to predict the internal and external properties of the tetrahedron based on the features of the tetrahedron. While ensuring the prediction accuracy, the complexity of the model is effectively reduced, the reconstruction efficiency is improved, and the amount of calculation in the surface reconstruction process is effectively reduced.
[0011] Furthermore, the tangent plane image corresponding to each point in the three-dimensional point cloud is obtained, including:
[0012] Each point in the three-dimensional point cloud is taken as a reference point. After obtaining the neighbor points of each reference point through the nearest neighbor search method, the local geometric features represented by each neighbor point are projected to the tangent plane corresponding to the reference point, thereby obtaining the tangent plane image corresponding to each reference point.
[0013] Furthermore, the definition of the tangent plane normal corresponding to the reference point includes:
[0014] Use principal component analysis to calculate the tangent plane normal n corresponding to the reference point p , and calculate the average normal n corresponding to the neighboring points a , if the tangent plane normal n p With the average normal n a If the angle between them is acute, then the normal of the tangent plane is defined as n p Otherwise, n p The negation is defined as the tangent plane normal.
[0015] Since the direction of the tangent plane is ambiguous, the directions obtained by different calculation methods may be completely opposite; the normal of the tangent plane directly affects the positive and negative signed distance of the projection, and the signed distance is a key feature in surface reconstruction. Therefore, surface reconstruction is closely related to the surface normal, and the ambiguity of the tangent plane direction has a great impact on network performance; when defining the tangent plane normal of a reference point, the present invention not only calculates the corresponding tangent plane normal based on the reference point, but also calculates the average normal corresponding to the neighboring points, and finally defines the tangent plane normal of the reference point based on the angle between the two normals, thereby accurately defining the tangent plane normal with the help of the information of the neighboring points, so that the normals calculated for the same data are consistent, so that the features of the points calculated based on the tangent plane image can better reflect the local features of the consistent surface, ensuring that the correct features are input into the network and are consistent.
[0016] Furthermore, the nearest neighbor search method is a spherical radius search, thereby ensuring that the relevant operations of the cutting plane convolution module are performed within a fixed area.
[0017] Furthermore, the local geometric features represented by the neighbor points include normal and signed projected distance.
[0018] Furthermore, the pooling layer and the de-pooling layer are implemented using grid hashing, thereby ensuring that the related operations of the pooling layer and the de-pooling layer are performed within a fixed area.
[0019] Furthermore, the tangent plane image includes the signed projection distance and normal direction of each neighbor point therein.
[0020] Furthermore, when the deep learning model is trained using the training data set, the loss function used is:
[0021] L=λ m L m +λ n L n ;
[0022] Where, L is the total loss; L m represents the multi-label loss calculated based on the labels of random sampling points inside the tetrahedron, which is used to measure the error between the labels of multiple sampling points inside the tetrahedron and the predicted results; L n represents the cross entropy loss calculated based on the prediction results of the tetrahedron, which is used to measure the attribute difference between the tetrahedron and its surrounding neighboring tetrahedrons; λ m and λ n Respectively represent the loss L m and L n The weight coefficient of .
[0023] When calculating the loss of model training, the present invention not only considers the error between the prediction result output by the network and the label information, but also considers the attribute difference between the tetrahedron and its surrounding adjacent tetrahedrons, thereby providing more constraints on the model training effect and further improving the model training effect.
[0024] According to another aspect of the present invention, a Delaunay triangulated surface reconstruction method is provided, comprising:
[0025] Delaunay triangulates the three-dimensional point cloud of the object to be reconstructed to obtain the corresponding tetrahedron network, and obtains the tangent plane image corresponding to each point in the three-dimensional point cloud of the object to be reconstructed;
[0026] Inputting the three-dimensional point cloud of the object to be reconstructed together with the corresponding tetrahedron mesh and the tangent plane image corresponding to each point in the three-dimensional point cloud into the Delaunay triangulated surface reconstruction model obtained by the method for establishing the Delaunay triangulated surface reconstruction model provided by the present invention, so as to obtain the inside / outside properties of each tetrahedron in the tetrahedron mesh located on the surface of the object;
[0027] The common triangular facet of two adjacent tetrahedrons with opposite attributes is identified as one of the triangular facets of the reconstructed surface of the object to be reconstructed, and the surface of the object to be reconstructed is reconstructed using all the identified triangular facets of the reconstructed surface of the object to be reconstructed.
[0028] According to another aspect of the present invention, a computer-readable storage medium is provided, comprising a stored computer program. When the computer program is executed by a processor, the device where the computer-readable storage medium is located is controlled to execute the method for establishing the Delaunay triangulated surface reconstruction model provided by the present invention, and / or the Delaunay triangulated surface reconstruction method provided by the present invention.
[0029] In general, the above technical scheme conceived by the present invention can achieve the following beneficial effects: first calculate the tangent plane image corresponding to each point in the three-dimensional point cloud, and use a feature extraction network including a tangent plane convolution module, a pooling layer, and a de-pooling layer to accurately extract the local geometric features of each point according to the tangent plane image, aggregate the features of each point in the tetrahedron, and use simple operations such as 1×1 convolution to predict whether the tetrahedron is located inside or outside the object. In this process, only simple operations such as simple 2D convolution, pooling, de-pooling, feature aggregation, and 1×1 convolution are involved. The model is simple, the amount of calculation is small, and the reconstruction efficiency is high. Based on the accurately extracted geometric features of each point, the model's prediction accuracy for the internal and external attributes of the tetrahedron is guaranteed. In general, while ensuring the prediction accuracy, the complexity of the model is effectively reduced, the reconstruction efficiency is improved, and the amount of calculation in the surface reconstruction process is effectively reduced. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Figure 1A flow chart of a method for establishing a Delaunay triangulated surface reconstruction model provided by an embodiment of the present invention;
[0031] Figure 2 A schematic diagram of a Delaunay triangulated surface reconstruction model provided by an embodiment of the present invention;
[0032] Figure 3 A schematic diagram of triangle recognition on the surface of an object to be reconstructed provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0033] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
[0034] In the present invention, the terms "first", "second", etc. (if any) in the present invention and the accompanying drawings are used to distinguish similar objects but not necessarily to describe a specific order or sequence.
[0035] In order to solve the technical problem that the existing DeepDT, in surface reconstruction, brings a large amount of calculation in order to maintain rich geometric details to ensure the quality of the reconstructed surface, affects the reconstruction efficiency, and limits the number of point clouds that can be processed by DeepDT in a GPU with limited resources, the present invention provides a method for establishing a Delaunay triangulated surface reconstruction model and its application, the overall idea of which is to use 1×1 convolution to predict whether the tetrahedron is located inside or outside the object according to the characteristics of the tetrahedron, so as to effectively reduce the model complexity and calculation amount, and use a feature extraction network including a cutting plane convolution module, a pooling layer and a depooling layer to extract the geometric features of each point according to the cutting plane image, so as to improve the feature quality of the points in the point cloud, thereby ensuring that the overall model has a high prediction accuracy.
[0036] The following are examples.
[0037] Embodiment 1:
[0038] A method for establishing a Delaunay triangulated surface reconstruction model, such as Figure 1 As shown, including:
[0039] Delaunay triangulates the 3D point cloud of an object with a known surface to obtain the corresponding tetrahedron mesh, and obtains the tangent plane image corresponding to each point in the 3D point cloud, as well as the internal / external labels of multiple points randomly sampled inside each tetrahedron relative to the surface of the object. The training data set is constructed using the tetrahedron mesh annotated with the internal / external label information of the sampling points inside the tetrahedron and the tangent plane image corresponding to each point;
[0040] A deep learning model is established to predict the internal / external properties of each tetrahedron in the tetrahedron network located on the surface of the object; Figure 2 As shown, the deep learning model includes a feature extraction network, a feature aggregation network and a label prediction network; the feature extraction network includes a cutting plane convolution module, a pooling layer and a de-pooling layer connected in sequence, the cutting plane convolution module is used to perform a convolution operation on the cutting plane image corresponding to each point in the three-dimensional point cloud to obtain the initial features of each point; the pooling layer is used to average the initial features and positions of the points to achieve downsampling of the point cloud; the de-pooling layer is used to assign the features of the downsampled points to the features of the points before downsampling as the final features of each point; the feature aggregation network is used to aggregate the features of each vertex of the tetrahedron into the features of the tetrahedron; the label prediction network is a 1×1 convolution network, which is used to predict the inside / outside properties of each tetrahedron on the surface of the object according to the features of each tetrahedron in the tetrahedron network;
[0041] The deep learning model is trained using the training data set, so that after the training, a Delaunay triangulated surface reconstruction model is obtained.
[0042] Since the cutting plane image is formed by projecting the neighbor point information onto the cutting plane, the features of the points extracted based on the cutting plane image can accurately reflect the local geometric information; as an optional implementation, in this embodiment, the cutting plane image corresponding to each point in the three-dimensional point cloud is obtained, including:
[0043] Taking each point in the three-dimensional point cloud as a reference point, after obtaining the neighbor points of each reference point through the nearest neighbor search method, the local geometric features represented by each neighbor point are projected to the tangent plane corresponding to the reference point, so as to obtain the tangent plane image corresponding to each reference point; optionally, in this embodiment, the local geometric features represented by the neighbor points include normal and signed projection distance, thereby effectively improving the reconstruction efficiency while ensuring the calculation accuracy.
[0044] Since the direction of the tangent plane is ambiguous, the directions obtained by different calculation methods may be completely opposite; the normal of the tangent plane directly affects the positive or negative of the projected signed distance, and the signed distance is a key feature in surface reconstruction. Therefore, surface reconstruction is closely related to the surface normal, and the ambiguity of the tangent plane direction has a great impact on network performance; in order to accurately define the tangent plane normal when acquiring the tangent plane image corresponding to the point, so as to avoid affecting the quality of the extracted features due to the ambiguity of the input of the feature extraction network, in this embodiment, the definition method of the tangent plane normal corresponding to the reference point includes:
[0045] Use principal component analysis to calculate the tangent plane normal n corresponding to the reference point p , and calculate the average normal n corresponding to the neighboring points a , if the tangent plane normal np With the average normal n a If the angle between them is acute, then the normal of the tangent plane is defined as n p Otherwise, n p The negation is defined as the tangent plane normal.
[0046] This embodiment defines the tangent plane normal in the above manner. In addition to calculating the corresponding tangent plane normal based on the reference point, it also calculates the average normal corresponding to the neighboring points, and finally defines the tangent plane normal of the reference point based on the angle between the two normals. In this way, the tangent plane normal can be accurately defined with the help of the information of the neighboring points, so that the normals calculated for the same data are consistent, so that the features of the points calculated based on the tangent plane image can better reflect the local features of the consistent surface, ensuring that the correct features are input into the network and are consistent.
[0047] In order to ensure that the related operations of the cutting plane convolution module, the pooling layer and the de-pooling layer in the feature extraction network are all performed within a fixed area, in this embodiment, the nearest neighbor search method is a ball radius search, and the pooling layer and the de-pooling layer are implemented using grid hashing;
[0048] The nearest neighbor search method used by the tangent plane convolution is a spherical radius search, which will find all points within a fixed radius of the reference point; grid hash sampling averages the features and positions of points in the same grid to obtain a sparser point cloud.
[0049] In this embodiment, the tangent plane image includes the signed projection distance and normal direction of each neighbor point therein.
[0050] In order to further ensure the training effect of the model, as an optional implementation, in this embodiment, when the deep learning model is trained using the training data set, the loss function used is:
[0051] L=λ m L m +λ n L n ;
[0052] Where, L is the total loss; L m It represents the multi-label loss calculated based on the labels of random sampling points inside the tetrahedron. It is used to measure the error between the labels of multiple sampling points inside the tetrahedron and the predicted results. The loss L can be calculated by calculating the difference between the predicted results of the tetrahedron and the labels of each sampling point inside it. m ; L n Represents the cross entropy loss calculated based on the tetrahedron label, which is used to measure the attribute difference between the tetrahedron and its surrounding adjacent tetrahedrons. The loss L can be calculated by calculating the difference between the prediction result of the tetrahedron and the prediction result of each adjacent tetrahedron.n ; m and λ n Respectively represent the loss L m and L n The weight coefficient, optionally, in this embodiment, λ m =0.9,λ n =0.1.
[0053] When calculating the loss of model training, this embodiment not only considers the error between the prediction result output by the network and the label information, but also considers the attribute difference between the tetrahedron and its surrounding adjacent tetrahedrons, thereby providing more constraints on the model training effect and further improving the model training effect.
[0054] In general, the Delaunay triangulated surface reconstruction model established in this embodiment, wherein the feature extraction network completes the feature extraction of the point according to the tangent plane image of the point, that is, the image formed by the projection of its neighboring points in its corresponding tangent plane. The specific process is: firstly, a convolution operation is performed on the tangent plane image, and then pooling and de-pooling operations are performed. On the one hand, the process only involves simple operations such as 2D convolution, pooling and de-pooling, and the indexes of the points used in these operations are all pre-calculated and do not need to be calculated in real time during training. Therefore, the reconstruction efficiency is high, and accordingly, the feature extraction network structure Simple; on the other hand, since the cutting plane image is composed of neighboring points projected onto the cutting plane, the features of the points extracted based on the cutting plane image can accurately reflect the local geometric information of the points; the Delaunay triangulated surface reconstruction model established in this embodiment only uses a 1×1 convolutional network to complete the prediction from tetrahedron features to the internal and external attributes of the tetrahedron, which is simple and efficient, and since the feature extraction network can accurately extract the features of the points and ensure the accuracy of the aggregated tetrahedron features, the 1×1 convolutional network can accurately predict the internal and external attributes of the tetrahedron, thereby ensuring the accuracy of subsequent surface reconstruction. In general, this embodiment uses a feature network including a cutting plane convolution module, a pooling layer, and a depooling layer to extract the features of the points from the cutting plane image of the points, and uses a 1×1 convolutional network to predict the internal and external attributes of the tetrahedron based on the features of the tetrahedron. While ensuring the prediction accuracy, the complexity of the model is effectively reduced, thereby effectively reducing the amount of calculation in the surface reconstruction process and improving the reconstruction efficiency. Comparative experiments show that the prediction accuracy of the internal and external attributes of the tetrahedron in this embodiment is comparable to that of DeepDT, but in actual applications, the reconstruction efficiency can be improved by about 10%.
[0055] Embodiment 2:
[0056] A Delaunay triangulated surface reconstruction method, comprising:
[0057] Delaunay triangulates the three-dimensional point cloud of the object to be reconstructed to obtain the corresponding tetrahedron network, and obtains the tangent plane image corresponding to each point in the three-dimensional point cloud of the object to be reconstructed;
[0058] Inputting the three-dimensional point cloud of the object to be reconstructed together with the corresponding tetrahedron mesh and the tangent plane image corresponding to each point in the three-dimensional point cloud into the Delaunay triangulated surface reconstruction model obtained by the method for establishing the Delaunay triangulated surface reconstruction model provided in the above-mentioned embodiment 1, so as to obtain the inside / outside property of each tetrahedron in the tetrahedron mesh located on the surface of the object;
[0059] The common triangular facets of two adjacent tetrahedrons with opposite attributes are identified as one of the triangular facets of the reconstructed surface of the object to be reconstructed, such as Figure 3 As shown; the surface of the object to be reconstructed is reconstructed using all the triangular facets of the identified surface of the object to be reconstructed.
[0060] Since the Delaunay triangulated surface reconstruction model provided in Example 1 of the present invention can accurately and efficiently predict the internal and external properties of a tetrahedron, this embodiment can quickly and effectively complete the surface reconstruction of an object with high reconstruction quality based on the model.
[0061] Embodiment 3:
[0062] A computer-readable storage medium includes a stored computer program. When the computer program is executed by a processor, the device where the computer-readable storage medium is located is controlled to execute the method for establishing the Delaunay triangulated surface reconstruction model provided in the above-mentioned embodiment 1, and / or the Delaunay triangulated surface reconstruction method provided in the above-mentioned embodiment 2.
[0063] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.
Claims
1. A method for establishing a Delaunay triangulated surface reconstruction model, characterized in that: include: Delaunay triangulates the 3D point cloud of an object with a known surface to obtain the corresponding tetrahedron mesh, and obtains the tangent plane image corresponding to each point in the 3D point cloud, as well as the internal / external labels of multiple points randomly sampled inside each tetrahedron relative to the surface of the object. The training data set is constructed using the tetrahedron mesh annotated with the internal / external label information of the sampling points inside the tetrahedron and the tangent plane image corresponding to each point; A deep learning model is established to predict the internal / external properties of each tetrahedron in a tetrahedron network located on the surface of an object; the deep learning model includes a feature extraction network, a feature aggregation network and a label prediction network; the feature extraction network is composed of a cutting plane convolution module, a pooling layer and a de-pooling layer connected in sequence, the cutting plane convolution module is used to perform a convolution operation on the cutting plane image corresponding to each point in the three-dimensional point cloud to obtain the initial features of each point; the pooling layer is used to average the initial features and positions of the points to achieve downsampling of the point cloud; the de-pooling layer is used to assign the features of the points after downsampling to the features of the points before downsampling as the final features of each point; The feature aggregation network is used to aggregate the features of each vertex of the tetrahedron into the features of the tetrahedron; the label prediction network is a 1×1 convolutional network, which is used to predict the internal / external properties of each tetrahedron located on the surface of the object according to the features of each tetrahedron in the tetrahedron network; The deep learning model is trained using the training data set, so that after the training is completed, the Delaunay triangulated surface reconstruction model is obtained.
2. The method for establishing a Delaunay triangulated surface reconstruction model according to claim 1, characterized in that: Obtain the tangent plane image corresponding to each point in the 3D point cloud, including: Each point in the three-dimensional point cloud is taken as a reference point. After obtaining the neighbor points of each reference point through the nearest neighbor search method, the local geometric features represented by each neighbor point are projected to the tangent plane corresponding to the reference point, thereby obtaining the tangent plane image corresponding to each reference point.
3. The method for establishing a Delaunay triangulated surface reconstruction model according to claim 2, characterized in that: The definition of the tangent plane normal corresponding to the reference point includes: Use principal component analysis to calculate the tangent plane normal n corresponding to the reference point p , and calculate the average normal n corresponding to the neighboring points a , if the tangent plane normal n p With the average normal n a If the angle between them is acute, then the normal of the tangent plane is defined as n p Otherwise, n p The negation is defined as the tangent plane normal.
4. The method for establishing a Delaunay triangulated surface reconstruction model according to claim 2, characterized in that: The nearest neighbor search method is spherical radius search.
5. The method for establishing a Delaunay triangulated surface reconstruction model according to claim 2, characterized in that: The local geometric features represented by the neighbor points include the normal and the signed projected distance.
6. The method for establishing a Delaunay triangulated surface reconstruction model according to any one of claims 1 to 5, characterized in that: The pooling layer and the unpooling layer are implemented using grid hashing.
7. The method for establishing a Delaunay triangulated surface reconstruction model according to claim 1, characterized in that: When the deep learning model is trained using the training data set, the loss function used is: L=λ m L m +λ n L n ; Where, L is the total loss; L m represents the multi-label loss calculated based on the labels of random sampling points inside the tetrahedron, which is used to measure the error between the labels of multiple sampling points inside the tetrahedron and the predicted results; L n represents the cross entropy loss calculated based on the prediction results of the tetrahedron, which is used to measure the attribute difference between the tetrahedron and its surrounding neighboring tetrahedrons; λ m and λ n Respectively represent the loss L m and L n The weight coefficient of .
8. A Delaunay triangulated surface reconstruction method, characterized in that: include: Performing Delaunay triangulation on the three-dimensional point cloud of the object to be reconstructed to obtain a corresponding tetrahedron mesh, and obtaining a tangent plane image corresponding to each point in the three-dimensional point cloud of the object to be reconstructed; Inputting the three-dimensional point cloud of the object to be reconstructed together with the corresponding tetrahedron mesh and the tangent plane image corresponding to each point in the three-dimensional point cloud into the Delaunay triangulated surface reconstruction model obtained by the method for establishing the Delaunay triangulated surface reconstruction model according to any one of claims 1 to 7, so as to obtain the inside / outside properties of each tetrahedron in the tetrahedron mesh located on the surface of the object; A common triangular facet of two adjacent tetrahedrons with opposite attributes is identified as one of the triangular facets of the reconstructed surface of the object to be reconstructed, and the surface of the object to be reconstructed is reconstructed using all the identified triangular facets of the reconstructed surface of the object to be reconstructed.
9. A computer-readable storage medium, characterized in that: It includes a stored computer program, which, when executed by a processor, controls the device where the computer-readable storage medium is located to execute the method for establishing a Delaunay triangulated surface reconstruction model as described in any one of claims 1 to 7, and / or the Delaunay triangulated surface reconstruction method as described in claim 8.