Non-rigid three-dimensional shape corresponding method, training method, device and electronic equipment

Abstract

The invention provides a non-rigid three-dimensional shape corresponding method, training method, device and electronic equipment, and the method comprises the steps: firstly processing shape data to obtain a generalized feature matrix and shape feature sub-matrixes, carrying out the calculation to obtain a point-by-point corresponding matrix based on the similarity of the shape feature sub-matrixes, and then obtaining a non-rigid three-dimensional shape through the point-by-point corresponding matrix and the generalized feature matrix. According to the method, a corresponding functional mapping matrix is obtained through calculation, so that the functional mapping matrix is calculated only by using a spatial domain single branch without depending on spectral branch calculation, and time redundancy and algorithm instability caused by the calculation are avoided; any post-processing functional mapping matrix method is not used, so that the training overhead is greatly reduced, the network structure is simplified, the calculation timeliness is high, and the generalization ability is strong; the unsupervised deep learning only utilizes shape pair feature similarity to obtain a corresponding result with high accuracy, and compared with a refined iterative optimization algorithm, the calculation is more efficient.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to a corresponding method, training method, device and electronic equipment for non-rigid three-dimensional shapes. Background Art

[0002] 3D shape correspondence is an important basic task in computer graphics and computer vision. It aims to mine the consistent structure and semantic relationship between 3D models through intelligent algorithms, so as to establish meaningful correspondence between points on multiple 3D shapes. 3D shape correspondence is the basis of shape recognition, shape retrieval, shape registration and shape segmentation. It also provides solid support for application fields such as 3D visualization, biocomputing, face recognition and medical image processing. As the core technology of many applications such as medical imaging, computer animation or simulation, the accuracy of 3D shape correspondence directly affects the effect of subsequent applications.

[0003] The current 3D shape correspondence task faces huge challenges, mainly because: the rapid development of data scanning equipment and the changes in application requirements have greatly increased the complexity of 3D shapes. The specific challenges are reflected in the following aspects: (1) Shape deformation has gradually expanded from simple rigid deformations such as translation and rotation to more complex non-rigid deformations; (2) The requirements are not limited to homogeneous models with isometric deformation, but also extend to non-isometric models with non-isometric deformation; (3) The shape data actually acquired by the equipment usually has inconsistent resolution and topological connection, and may lead to low-quality models due to the limitations of equipment technology; (4) In modern intelligent application scenarios, the requirements for the accuracy of shape representation are getting higher and higher, resulting in a large amount of shape data, which puts higher requirements on the computational efficiency of the algorithm; (5) Some data are expensive to acquire and label.

[0004] With the rapid development of deep learning technology, the organic combination of deep technology and axiomatic correspondence methods has greatly improved the performance of correspondence technology to an unprecedented level. However, existing deep correspondence technology still has many limitations when processing challenging shape data such as non-rigid three-dimensional shape data. The main limitations are: it cannot effectively process low-quality data models, and the network structure design of some technologies is relatively complex, and the computational stability and generalization are poor. For example, the existing mainstream deep functional mapping methods usually use spectral branches and spatial branches to calculate the functional mapping matrix at the same time, resulting in very large network overhead, time-consuming training, and unsatisfactory generalization; using spectral branch calculations will bring time redundancy, resulting in algorithm instability. Summary of the invention

[0005] The present application proposes a non-rigid three-dimensional shape correspondence method, training method, device and electronic device, which can solve the problems of complex network structure, time consumption, poor computational stability and generalization in existing networks.

[0006] In order to achieve the above purpose, this application adopts the following technical solutions:

[0007] In a first aspect, a method for training a non-rigid three-dimensional shape correspondence model is provided, the method comprising:

[0008] obtaining training data; and

[0009] training the non-rigid three-dimensional shape correspondence model using the training data,

[0010] Wherein, obtaining the training data specifically includes:

[0011] Obtaining a shape pair data set, wherein the shape pair data set includes a plurality of paired shape data;

[0012] Processing the shape data to obtain a corresponding generalized feature matrix and a shape feature submatrix;

[0013] Based on the similarity of the two shape feature sub-matrices corresponding to each shape pair, a point-by-point correspondence matrix corresponding to each shape pair is calculated; and

[0014] The corresponding functional mapping matrix is ​​calculated from the point-by-point correspondence matrix and the generalized characteristic matrix.

[0015] The non-rigid three-dimensional shape correspondence model adopts unsupervised deep learning, and during training, the characteristics of the point-by-point correspondence matrix and the functional mapping matrix are penalized.

[0016] Based on the above technical solution, the shape data is first processed to obtain a generalized feature matrix and a shape feature submatrix. Based on the similarity of the shape feature submatrix, the point-by-point correspondence matrix is ​​calculated. Then, the corresponding functional mapping matrix is ​​calculated from the point-by-point correspondence matrix and the generalized feature matrix. In this way, only a single branch in the spatial domain is used to calculate the functional mapping matrix without relying on spectral branch calculations, thereby avoiding the resulting time redundancy and algorithm instability. The method of not using any post-processing of the functional mapping matrix greatly reduces the training overhead, simplifies the network structure, has high computational timeliness, and has strong generalization ability. Unsupervised deep learning can obtain highly accurate correspondence results by only using the similarity of shape pairs of features, which is more efficient than relying on refined iterative optimization algorithms.

[0017] In a possible design manner of the first aspect, processing the shape data to obtain a corresponding generalized feature matrix specifically includes:

[0018] Calculating the Laplacian matrix on each of the shape data;

[0019] Performing generalized eigenvalue decomposition on the Laplace matrix to obtain corresponding first K eigenvectors and eigenvalues; and

[0020] The first K eigenvectors and the eigenvalues ​​are expressed as the corresponding generalized eigenmatrix.

[0021] In a possible design manner of the first aspect, processing the shape data to obtain a corresponding shape feature submatrix specifically includes:

[0022] Using an axiomatic method, calculating an initial feature descriptor at each point on the shape data;

[0023] Inputting the initial feature descriptor into DiffusionNet for optimization calculation to obtain a secondary feature descriptor; and

[0024] The secondary feature descriptor is represented as the shape feature sub-matrix.

[0025] In a possible design manner of the first aspect, based on the similarity of the shape feature submatrices corresponding to each shape pair, a point-by-point correspondence matrix corresponding to each shape pair is calculated, specifically:

[0026] Using the Softmax algorithm, the shape feature sub-matrix corresponding to each shape pair is used and The similarity of each shape pair is calculated to obtain the point-by-point correspondence matrix.

[0027]

[0028] Among them, τ is the adjustment corresponding matrix and The scale parameter of the degree of softness or hardness, T represents transposition.

[0029] In a possible design manner of the first aspect, the relationship between the point-by-point correspondence matrix and the generalized characteristic matrix is ​​specifically:

[0030]

[0031] Among them, Φ M , is a matrix with the first K eigenvectors of the corresponding shape as columns.

[0032] In a possible design manner of the first aspect, the loss function of the unsupervised deep learning is defined as:

[0033] L final =L fmap +λ constrast L constrast +λ diriL diri

[0034] in,

[0035] L fmap =λ bij L bij +λ diri L orth

[0036]

[0037] For shape The Laplace matrix of For shape Vertex coordinate function, ||·|| F Represents the Frobenius Norm norm of the matrix, the matrix norm The matrix I is the identity matrix, λ bij , orth , constrast and diri is the weight parameter,

[0038] Penalizing the characteristics of the point-by-point correspondence matrix and the functional mapping matrix, specifically including:

[0039] Penalizing the smoothness of the point-wise correspondence matrix; and,

[0040] Penalizing the bidirectional bijectivity, bidirectional orthogonality and contrast of the functional mapping matrix,

[0041] The non-rigid three-dimensional shape correspondence model is approximately solved using a nearest neighbor search algorithm.

[0042] Based on the above technical scheme, the loss function used has more sufficient geometric constraints on the point-by-point correspondence matrix and the functional mapping properties, and comprehensively considers the geometric properties of the point-by-point correspondence matrix and the functional mapping matrix. Compared with the traditional method that generally only focuses on constraining the properties of the functional mapping matrix, more accurate and smooth shape features can be learned; the design of the above network structure, especially the optimal selection of the loss function, makes: the correspondence accuracy obtained on general shape data sets and on challenging shapes (such as models with large non-isometric deformations) better than the existing correspondence technology, and at the same time, it has stronger generalization on different types of databases.

[0043] In a second aspect, a non-rigid three-dimensional shape correspondence method is provided, wherein the correspondence method is based on the non-rigid three-dimensional shape correspondence model trained as described above.

[0044] In a third aspect, a training device for a non-rigid three-dimensional shape correspondence model is provided, the training device comprising:

[0045] an acquisition unit, configured to acquire training data; and

[0046] a training unit, configured to train the non-rigid three-dimensional shape correspondence model using the training data,

[0047] Wherein, the acquisition unit specifically includes:

[0048] An obtaining subunit, used for obtaining a shape pair data set, wherein the shape pair data set includes a plurality of paired shape data;

[0049] A processing subunit, used for processing the shape data to obtain a corresponding generalized feature matrix and a shape feature submatrix;

[0050] A first calculation subunit is used to calculate the point-by-point correspondence matrix corresponding to each shape pair based on the similarity of the shape feature submatrices corresponding to each shape pair; and

[0051] The second calculation subunit is used to calculate the corresponding functional mapping matrix from the point-by-point correspondence matrix and the generalized characteristic matrix.

[0052] The non-rigid three-dimensional shape correspondence model adopts unsupervised deep learning, and during training, the characteristics of the point-by-point correspondence matrix and the functional mapping matrix are penalized.

[0053] In a fourth aspect, a non-rigid three-dimensional shape corresponding device is provided, wherein the corresponding device is based on the non-rigid three-dimensional shape corresponding model trained as above.

[0054] In a fifth aspect, an electronic device is provided, comprising: a processor, and a memory coupled to the processor, the memory being used to store a computer program; the processor being used to execute the computer program stored in the memory, so that the electronic device executes the method for measuring the core quality index as any possible implementation method in the first aspect. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or related technical descriptions will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0056] Figure 1 It is a schematic diagram of the network structure provided by the embodiment of the present application;

[0057] Figure 2is a comparison of the color and texture mapping results of each method provided in the embodiments of the present application on the shape pairs from SHREC'19;

[0058] Figure 3 1 is a comparison of the color and texture mapping results of each method provided in the embodiments of the present application on the SMAL shape pair (the distorted area is marked with a circle);

[0059] Figure 4 This is the corresponding visualization result of the solution provided in the embodiment of the present application on the shape with no structural loss. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application 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 application and are not used to limit the present application.

[0061] It should be noted that, although the functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first", "second", etc. in the specification, claims and the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0062] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0063] An embodiment of the present application, such as Figure 1 As shown, a network structure of a non-rigid three-dimensional shape depth correspondence model is provided, and the training method and testing method of the network structure are as follows:

[0064] Step 1: Obtain training data and test data, usually represented as mesh shape data or point cloud shape data, to generate a shape dataset.

[0065] Step 2: Preprocess the given shape dataset as follows. First, given the shape pairs represented as triangular meshes, and They have m and n vertices respectively.

[0066] (1) Calculate the Laplacian matrix L = A on each input shape -1 B; The calculation of this matrix uses the Meyer algorithm, and the specific process is:

[0067] Let ai Denotes the Voronoi cell area of ​​vertex i, and let the weight

[0068] where α ij With β ij are the two angles opposite to the side (i, j), cot represents the cotangent,

[0069] Then the matrix A=diag(a i ), weight matrix B=(m ij ),in

[0070]

[0071] Perform generalized eigenvalue decomposition on the matrix L, that is, solve the system of equations Βφ k =λAφ k .

[0072] Get the corresponding first K eigenvalues and the eigenvector And expressed in order as a matrix and That is, Φ=(φ 1 ,φ 2 ,…,φ K ).

[0073] (2) Using the axiomatic method, the 128-dimensional WKS feature descriptor at each point on the input shape is calculated, and the WKS at point x on the shape is calculated according to the following formula, that is;

[0074]

[0075] Take the first K of the Laplacian matrix wks = 300 eigenvalues, let the first 300 eigenvalues ​​with the largest absolute value be ||λ|| max , the smallest one is ||λ|| min , then calculate, v = 7 (||λ|| max -||λ|| min ) / 128, E is a 128-dimensional vector, each of whose components is in ||λ|| min The amount of successive increase is δ=(||λ|| max -||λ|| min ) / 128, C E It is a 128-dimensional vector generated by broadcasting based on E, and log represents logarithmic operation.

[0076] Step 3: Input the WKS descriptor obtained above into the DiffusionNet network for optimization calculation, thereby obtaining a data-driven descriptor that more accurately describes the shape features.

[0077] The network structure of DiffusionNet is as follows: the first layer contains a fully connected layer; the second layer contains three matrix multiplication operations, one exponential operation, two numerical multiplication operations, five fully connected layers, one activation function layer, and one dropout layer; the third layer contains three matrix multiplication operations, one exponential operation, two numerical multiplication operations, five fully connected layers, one activation function layer, and one dropout layer; the fourth layer contains three matrix multiplication operations, one exponential operation, two numerical multiplication operations, five fully connected layers, one activation function layer, and one dropout layer; the fifth layer contains three matrix multiplication operations, one exponential operation, two numerical multiplication operations, five fully connected layers, one activation function layer, and one dropout layer; the sixth layer contains a fully connected layer.

[0078] Step 4: Represent the shape feature descriptor optimized by the DiffusionNet network as a matrix and That is, the 128-dimensional descriptor at each point of the shape is used as the row vector of the matrix in turn as the input of the connected calculation functional mapping matrix module:

[0079] (1) Using the Softmax algorithm, based on the obtained shape feature matrix and Similarity of row vectors, calculate point-by-point correspondence matrix

[0080]

[0081] Where τ is the adjustment corresponding matrix or The scale parameters of softness and hardness are all set to 0.07, and T represents transposition.

[0082] (2) The functional mapping matrix is ​​calculated using the relationship between the point-by-point correspondence matrix and the functional mapping matrix, that is, let the functional mapping matrix in, is a matrix consisting of the first K eigenvectors of the corresponding shape in order as columns.

[0083] Note that, unlike general methods of the same type, this solution does not use any post-processing module to optimize the obtained functional mapping matrix.

[0084] Step 5: Carefully design the loss function of the unsupervised deep learning network, and learn the network by penalizing the corresponding geometric properties of the functional mapping matrix or the point-by-point correspondence matrix. In this way, the network can learn highly accurate shape feature descriptors, and based on their similarities, efficient shape correspondences can be calculated. Follow the steps below:

[0085] (1) Calculate the loss function that penalizes the bidirectional bijectivity of the functional mapping matrix,

[0086]

[0087] Among them, matrix I is the identity matrix; ||·|| F Represents the FrobeniusNorm norm of the matrix.

[0088] (2) Calculate the loss function that penalizes the bidirectional orthogonality of the functional mapping matrix,

[0089]

[0090] Let the loss function L fmap is the weighted sum of the above two penalty terms, i.e. L fmap =λ bij L bij +λ diri L orth .

[0091] (3) Penalize the contrast of the functional mapping matrix to improve the resolution of the shape features learned by the network, that is, calculate the loss function

[0092] (4) Penalize the smoothness of the point-by-point correspondence matrix, that is, calculate the loss function in For shape Vertex coordinate function, matrix norm in For shape The Laplace matrix of .

[0093] (5) The final loss function of the network is defined as

[0094] L final =L fmap +λ constrast L constrast +λ diri L diri

[0095] The weight parameters are set to λ bij =1,λ orth =1,λ constrast =1,λ diri =0.5

[0096] Step 6: In the testing phase, the shape correspondence is established using the similarity of the learned shape features, that is, solving the optimization problem:

[0097]

[0098] This optimization problem can be approximately solved using the nearest neighbor search algorithm, that is,

[0099]

[0100] Similarly, we can calculate the matrix

[0101] Experimental configuration: The experimental environment of this scheme is 128GB DDR5 RAM, Intel Core i7 12700K, NVIDIA4090, and the software environment includes CUDA 11.7, Python 3.9 and PyTorch 2.0.1. In the experiment, this scheme uses 128-dimensional WKS as input and sets the initial learning rate of the Adam optimizer to 0.001. For each shape, the first 256 eigenvalues ​​and eigenvectors of the Laplace Beltermi operator (LBO) are pre-calculated.

[0102] Corresponding performance:

[0103] The corresponding accuracy achieved by this project is significantly higher than that of existing similar technologies, as shown in the following aspects:

[0104] (1) Evaluation on approximately isometric benchmark shape datasets. The training and testing datasets include the standard and remeshed benchmark test sets FAUST (F_r) and SCAPE (S_r), as well as the SHREC'19 dataset. FAUST consists of 100 human shapes, which are 10 people with 10 different poses. It is divided into 80 / 20 for training and testing respectively. SCAPE contains 71 human shapes, which are the same person with different poses, and is divided into 51 / 20 for training and testing respectively. SHREC'19 is a more challenging dataset, containing a total of 430 pairs of shapes, of which 44 pairs are human shapes, and the mesh connectivity and appearance geometry of the shapes contained are significantly different. This database is only used as a test dataset to evaluate the robustness of the method to different discretization methods of the shape.

[0105] Table 1. Corresponding accuracies for training and testing on the refreted versions of the benchmark datasets FAUST, SCAPE, and SHREC’19. The numbers in the table are the average geodesic error (%), and the best result is highlighted in each column.

[0106]

[0107] The above results show that the method of this scheme is superior to previous axiomatic methods, unsupervised methods and even supervised methods, including the latest complex two-branch methods ULRSSM, DiffZO, etc., and demonstrates stronger cross-dataset generalization capabilities.

[0108] (2) Evaluation on non-isometric benchmark test shape datasets. Non-isometric deformation test datasets are usually highly deformed and extremely challenging. For this reason, two such datasets, SMAL_r and DT4D-H, were selected for evaluation. The SMAL_r dataset contains 49 shapes, including eight species of quadrupeds, five of which are used for training and three for testing, with a 29 / 20 split. DT4D-H contains 9 types of human shapes, divided into 198 and 95 instances for training and testing, respectively. In this classification method, since the training shapes do not appear in any test set, the generalization and robustness of the method are required to be relatively high.

[0109] Table 2 Corresponding results on the non-equidistant datasets SMAL_r and DT4D-H. The highest performance results in each column are highlighted, and the numbers in the table are the corresponding average geodesic errors (%).

[0110]

[0111] The above results show that the corresponding accuracy achieved by the method of this scheme on the non-isometric deformation database is still higher than all existing advanced methods, which fully confirms the effectiveness of this scheme.

[0112] Figure 2 The results of different techniques for establishing corresponding visualizations on SHREC'19 shape pairs are shown. This experiment uses the corresponding color and texture of the shape to migrate. The results show that the color and texture of the migrated color based on our scheme (ours) are least distorted, which fully demonstrates that the accuracy and generalization of our scheme are significantly better than existing similar technologies.

[0113] Figure 3 The corresponding visualization results of different technologies on the non-isometric deformation database SMAL are shown. The experimental results on this database also confirm that the method proposed in this scheme still outperforms similar technologies when dealing with challenging data such as non-isometric deformation.

[0114] Figure 4 The visualization results of establishing correspondence on shapes with local missing parts are shown. The missing parts are divided into two categories: cuts and holes. The results show that the proposed method still has very accurate correspondence accuracy on such shapes, confirming the effectiveness and practicality of the proposed method and its ability to handle challenging data.

[0115] This solution can provide underlying technology for applications such as medical imaging, computer animation or simulation that is simpler than existing method frameworks, has higher corresponding accuracy, better generalization, and better ability to handle challenging data.

[0116] This embodiment of the solution also provides a training device for a non-rigid three-dimensional shape corresponding model, the training device comprising:

[0117] an acquisition unit, configured to acquire training data; and

[0118] a training unit, configured to train the non-rigid three-dimensional shape correspondence model using the training data,

[0119] Wherein, the acquisition unit specifically includes:

[0120] An obtaining subunit, used for obtaining a shape pair data set, wherein the shape pair data set includes a plurality of paired shape data;

[0121] A processing subunit, used for processing the shape data to obtain a corresponding generalized feature matrix and a shape feature submatrix;

[0122] A first calculation subunit is used to calculate the point-by-point correspondence matrix corresponding to each shape pair based on the similarity of the shape feature submatrices corresponding to each shape pair; and

[0123] The second calculation subunit is used to calculate the corresponding functional mapping matrix from the point-by-point correspondence matrix and the generalized characteristic matrix.

[0124] The non-rigid three-dimensional shape correspondence model adopts unsupervised deep learning, and during training, the characteristics of the point-by-point correspondence matrix and the functional mapping matrix are penalized.

[0125] This embodiment of the solution also provides a non-rigid three-dimensional shape corresponding device, which is based on the non-rigid three-dimensional shape corresponding model trained as above.

[0126] An embodiment of the present solution also provides an electronic device, comprising: a processor, and a memory coupled to the processor, wherein the memory is used to store a computer program; the processor is used to execute the computer program stored in the memory, so that the electronic device executes a method as described in any one of the above embodiments.

[0127] The electronic device may be a computing device such as a desktop computer, a notebook, a palmtop computer, a cloud server, etc. The electronic device may include, but is not limited to, a processor and a memory.

[0128] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the electronic device, and various interfaces and lines are used to connect various parts of the entire device.

[0129] The memory may be used to store the computer program, and the processor implements various functions of the electronic device by running or executing the computer program stored in the memory and calling the data stored in the memory.

[0130] The memory may mainly include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function, etc.; the data storage area may store data created according to the use of the mobile phone, etc. In addition, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (SmartMedia Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0131] The above is a preferred implementation of the present scheme. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present scheme. These improvements and modifications are also considered to be within the scope of protection of the present scheme.

Claims

1. A method for training a non-rigid three-dimensional shape correspondence model, characterized in that: The method comprises: obtaining training data; and training the non-rigid three-dimensional shape correspondence model using the training data, Wherein, obtaining the training data specifically includes: Obtaining a shape pair data set, wherein the shape pair data set includes a plurality of paired shape data; Processing the shape data to obtain a corresponding generalized feature matrix and a shape feature submatrix; Based on the similarity of the two shape feature sub-matrices corresponding to each shape pair, a point-by-point correspondence matrix corresponding to each shape pair is calculated; and The corresponding functional mapping matrix is ​​calculated from the point-by-point correspondence matrix and the generalized characteristic matrix. The non-rigid three-dimensional shape correspondence model adopts unsupervised deep learning, and during training, the characteristics of the point-by-point correspondence matrix and the functional mapping matrix are penalized.

2. The training method according to claim 1, characterized in that: Processing the shape data to obtain a corresponding generalized feature matrix specifically includes: Calculating the Laplacian matrix on each of the shape data; Performing generalized eigenvalue decomposition on the Laplace matrix to obtain corresponding first K eigenvectors and eigenvalues; and The first K eigenvectors and the eigenvalues ​​are expressed as the corresponding generalized eigenmatrix.

3. The training method according to claim 1, characterized in that: Processing the shape data to obtain a corresponding shape feature sub-matrix specifically includes: Using an axiomatic method, calculating an initial feature descriptor at each point on the shape data; Inputting the initial feature descriptor into DiffusionNet for optimization calculation to obtain a secondary feature descriptor; and The secondary feature descriptor is represented as the shape feature sub-matrix.

4. The training method according to claim 1, characterized in that: Based on the similarity of the two shape feature sub-matrices corresponding to each shape pair, the point-by-point correspondence matrix corresponding to each shape pair is calculated, specifically: Using the Softmax algorithm, the shape feature sub-matrix corresponding to each shape pair is used and The similarity of each shape pair is calculated to obtain the point-by-point correspondence matrix. Among them, τ is the adjustment corresponding matrix The scale parameter of the degree of softness or hardness, T represents transposition.

5. The training method according to claim 4, characterized in that: The relationship between the point-by-point correspondence matrix and the generalized characteristic matrix is ​​specifically: Among them, Φ M , is a matrix with the first K eigenvectors of the corresponding shape as columns.

6. The training method according to claim 5, characterized in that: The loss function of the unsupervised deep learning is defined as: L final =L fmap +λ constrast L constrast +λ diri L diri in, L fmap =λ bij L bij +λ diri L orth For shape The Laplace matrix of For shape Vertex coordinate function, ||·|| F Represents the Frobenius Norm norm of the matrix, the matrix norm The matrix I is the identity matrix, λ bij , orth , constrast and diri is the weight parameter, Penalizing the characteristics of the point-by-point correspondence matrix and the functional mapping matrix, specifically including: Penalizing the smoothness of the point-wise correspondence matrix; and, Penalizing the bidirectional bijectivity, bidirectional orthogonality and contrast of the functional mapping matrix, The non-rigid three-dimensional shape correspondence model is approximately solved using a nearest neighbor search algorithm.

7. A method for corresponding a non-rigid three-dimensional shape, characterized in that: The correspondence method is based on the non-rigid three-dimensional shape correspondence model trained as claimed in any one of claims 1 to 6.

8. A training device for a non-rigid three-dimensional shape correspondence model, characterized in that: The training device comprises: an acquisition unit, configured to acquire training data; and a training unit, configured to train the non-rigid three-dimensional shape correspondence model using the training data, Wherein, the acquisition unit specifically includes: An obtaining subunit, used for obtaining a shape pair data set, wherein the shape pair data set includes a plurality of paired shape data; A processing subunit, used for processing the shape data to obtain a corresponding generalized feature matrix and a shape feature submatrix; A first calculation subunit is used to calculate the point-by-point correspondence matrix corresponding to each shape pair based on the similarity of the shape feature submatrices corresponding to each shape pair; and The second calculation subunit is used to calculate the corresponding functional mapping matrix from the point-by-point correspondence matrix and the generalized characteristic matrix. The non-rigid three-dimensional shape correspondence model adopts unsupervised deep learning, and during training, the characteristics of the point-by-point correspondence matrix and the functional mapping matrix are penalized.

9. A non-rigid three-dimensional shape corresponding device, characterized in that The corresponding means is based on the non-rigid three-dimensional shape correspondence model trained as claimed in any one of claims 1 to 6.

10. An electronic device, characterized in that: The electronic device comprises: a processor, and a memory coupled to the processor, The memory is used to store computer programs; The processor is used to execute the computer program stored in the memory, so that the electronic device performs the training method as described in any one of claims 1 to 6, or performs the corresponding method as described in claim 7.

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