A non-rigid three-dimensional shape matching method based on geometric-semantic feature fusion and iterative drift feedback
Patent Information
- Application Number
- CN202610804693.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-05
- Publication Date
- 2026-09-01
AI Technical Summary
[0005]有鉴于此，本发明提供了一种基于几何-语义特征融合与迭代漂移反馈的非刚性三维形状匹配方法，有效克服了现有非刚性三维形状匹配技术在对称结构、弱几何区域、强非等距形变及局部缺失等复杂场景下的匹配失准与不稳定问题
1）本发明针对现有方法在对称结构、弱几何区域及强非等距形变下易失效的缺陷，通过融合内蕴几何特征（DiffusionNet提取）与外蕴语义特征（DINOv2视觉基础模型提取），构建了更具判别力的统一顶点描述子。这一优化显著增强了特征在复杂场景下的鲁棒性，有效缓解了匹配歧义；
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Figure CN122676201A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of three-dimensional shape matching technology, and in particular to a non-rigid three-dimensional shape matching method based on geometric-semantic feature fusion and iterative drift feedback. Background Technology
[0002] Non-rigid 3D shape matching is an important research problem in computer vision and computer graphics, widely applied in 3D reconstruction, texture transfer, statistical shape analysis, and non-rigid target tracking. Existing non-rigid shape matching methods mainly fall into two categories: spatial domain registration methods and spectral domain matching methods. Spectral domain methods are typically represented by the Functional Map framework, which establishes a linear mapping relationship between shapes on the Laplace-Beltrami feature basis to achieve a compact and efficient correspondence representation. In recent years, with the development of deep learning, existing methods have further combined neural networks to learn geometric feature descriptors, achieving good results in non-rigid shape matching tasks between complete shapes.
[0003] In partial shape matching scenarios, especially in partial-to-part non-rigid 3D shape matching tasks, existing technologies typically need to simultaneously achieve two objectives: first, identifying the shared overlapping region between the source and target shapes; and second, establishing dense point correspondences within the overlapping region. Existing methods either employ traditional geometric descriptors or features extracted based on geometric networks for matching, or introduce mechanisms such as overlapping region prediction, cross-attention, or cyclic consistency within a Functional Map framework to improve partial matching performance. Overall, existing non-rigid 3D shape matching techniques primarily rely on geometric features for correspondence estimation. Under conditions of symmetrical structures, weak geometric regions, strong non-equidistant deformation, and local missing features, descriptive ambiguity and unstable matching are prone to occur. Particularly in partial-to-part matching tasks, overlapping region identification and dense correspondence estimation are coupled, making it difficult for existing methods to simultaneously ensure the accuracy of both. Furthermore, most existing technologies employ one-time overlapping prediction or single consistency verification, lacking an iterative feedback correction mechanism for initial errors. This leads to errors propagating further and affecting the final result when noise exists in the initial matching. Furthermore, outliers and discrete noise in non-overlapping regions can contaminate the spectral solution process of function mapping, reducing the robustness of overlap-aware matching. Therefore, existing technologies still suffer from insufficient matching accuracy, poor stability, and limited generalization ability in complex, non-rigid, low-overlap-rate, and highly ambiguous scenarios.
[0004] Therefore, providing a non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback to solve the difficulties of existing technologies is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0005] In view of this, the present invention provides a non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback, which effectively overcomes the matching inaccuracies and instability problems of existing non-rigid 3D shape matching technologies in complex scenarios such as symmetrical structures, weak geometric regions, strong non-equidistant deformations and local missing parts.
[0006] To achieve the above objectives, the present invention adopts the following technical solution: A non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback includes the following steps: Obtain the source 3D shape and the target 3D shape, and generate a training dataset after preprocessing the source 3D shape and the target 3D shape; Add semantic feature enhancement description to the functional mapping framework, and construct an iterative feedback mechanism by combining cyclic consistency constraints to form a non-rigid three-dimensional shape matching model. The training dataset is input into the non-rigid 3D shape matching model, and the trained non-rigid 3D shape matching model is obtained through iterative optimization based on matching-evaluation-feedback. Input the source 3D shape and the target 3D shape to be matched into a trained non-rigid 3D shape matching model, and output the dense correspondence between the source 3D shape and the target 3D shape.
[0007] Optionally, the source 3D shape and the target 3D shape are preprocessed to construct their Laplace-Beltrami spectral representation, specifically including: Construct the discrete cochet Laplacian matrix and perform eigenvalue decomposition on it to extract the first k eigenfunctions and their corresponding eigenvalue diagonal matrices. The expression is as follows: , , ; in, Let X be the spectral basis matrix composed of the first k Laplacian eigenfunctions of shape X. The spectral basis matrix is composed of the first k Laplacian eigenfunctions of shape Y. Let X be a diagonal matrix consisting of the first k eigenvalues corresponding to shape X. Let be a diagonal matrix consisting of the first k eigenvalues corresponding to shape Y, where x is the source 3D shape or source mesh, and y is the target 3D shape or target mesh. Let m be the number of vertices of the source shape X and n be the number of vertices of the target shape Y.
[0008] Optionally, semantic feature enhancement is used to extract the geometric and semantic features of the preprocessed source and target 3D shapes, specifically including: By extracting vertex-level intrinsic geometric features using a neural network based on the diffusion operator, the geometric features of the source 3D shape and the target 3D shape are obtained, and the corresponding expressions are: , in, Let X be the vertex-level intrinsic geometric feature matrix of the source 3D shape X. Let Y be the vertex-level intrinsic geometric feature matrix of the target 3D shape. Geometric feature dimension; The 3D shape is rendered from multiple perspectives, and the semantic features of the image are extracted using a visual basic model and then mapped back to the 3D vertices to obtain the semantic features of the source 3D shape and the target 3D shape. The corresponding expression is: , in, Let X be the vertex-level intrinsic semantic feature matrix of the source 3D shape X. Let Y be the vertex-level intrinsic semantic feature matrix of the target 3D shape. This is the semantic feature dimension.
[0009] Optional, function mappings include: Geometric and semantic features are fused using a learnable mapping function to obtain fused features, expressed as follows: , in, To represent the vertex-level geometric features after projection transformation, To represent the vertex-level semantic features after projection transformation, For learnable weights, This represents the mapping function of a multilayer perceptron. For feature splicing operations; Based on the fusion features, a bidirectional soft matching relationship is established between the source 3D shape and the target 3D shape to form a functional mapping. The initial soft correspondence expression is obtained as follows: , , in, Let X be the soft matching matrix from the source 3D shape X to the target 3D shape Y. Let X be the soft matching matrix from the target 3D shape Y to the source 3D shape X. This is the feature similarity matrix between the source 3D shape and the target 3D shape.
[0010] Optional, cycle consistency constraints include: Based on the correspondence, a forward-backward mapping is constructed, and the drift residual is calculated in the spectral space. The corresponding expression is:
[0011] in, Let X be the drift residual of the i-th vertex on the source shape X. Let be the drift residual of the i-th vertex on the source shape Y. Let X be the vertex index of the source shape X. Let Y be the vertex index of the target shape Y, and E be the cyclic mapping matrix consisting of the forward soft matching matrix and the backward soft matching matrix. The Laplace spectral basis matrix corresponding to the shape; Determine whether the match is located in the overlapping region based on the drift residual.
[0012] Optional iterative feedback mechanisms include: The drift residuals are converted into vertex-level reliability weights, which are then fed back into the feature and spectrum solving process. After weighted mapping of the features, the function mapping is resolved through regularization optimization, thereby achieving iterative feedback. The corresponding expression is:
[0013] Where C is the functional mapping matrix from the source 3D shape X to the target 3D shape Y; A is the coefficient matrix of the features of the source 3D shape X in the spectral basis space; and B is the coefficient matrix of the features of the target 3D shape Y in the spectral basis space. Let X be the diagonal matrix of Laplacian eigenvalues of the source 3D shape X; Let be the diagonal matrix of Laplacian eigenvalues of the target 3D shape Y; λ is the regularization weight coefficient used to control the influence of the Laplacian commutation constraint term. Denotes the Frobenius norm; This represents the search for the optimal function mapping matrix that minimizes the objective function among all possible C values.
[0014] Optionally, weighted mapping of features includes: The drift residual is mapped using a Gaussian function, and the corresponding expression is: , in, Let be the reliability weight of the i-th vertex, and ri be the drift residual of the i-th vertex. This is the bandwidth parameter of the Gaussian function; The features are weighted, and the expression is: , in, The vertex-level reliability weights for the source and target shapes are given. For element-wise weighted operations, These are the original vertex features of the source and target shapes. The weighted vertex features; Projecting the weighted features onto the spectral space, the corresponding expression is: , in, , respectively, are the pseudo-inverses of the spectral basis matrices of the source shape and the target shape, and A and B are the spectral domain coefficient matrices of the weighted features of the source shape and the target shape, respectively.
[0015] As can be seen from the above technical solution, compared with the prior art, the present invention provides a non-rigid three-dimensional shape matching method based on geometric-semantic feature fusion and iterative drift feedback, which has the following beneficial effects: 1) This invention addresses the shortcomings of existing methods that are prone to failure under symmetrical structures, weak geometric regions, and strong non-equidistant deformations. By fusing intrinsic geometric features (extracted by DiffusionNet) and extrinsic semantic features (extracted by the DINOv2 visual base model), a more discriminative unified vertex descriptor is constructed. This optimization significantly enhances the robustness of features in complex scenes and effectively alleviates matching ambiguity; 2) To address the shortcomings of existing methods, such as the lack of iterative correction of initial errors leading to noise contamination of the spectrum solution in non-overlapping regions, this invention designs an iterative drift feedback mechanism. This mechanism utilizes cyclic consistency constraints to compute cyclic drift in the computation space and transforms it into vertex-level reliability weights. These weights serve as attention masks, dynamically weighting the input features and resolving the function mapping in the spectral domain. This closed-loop optimization process of "matching—evaluation—feedback—rematching" can proactively suppress interference in non-overlapping regions, gradually correct initial errors, and avoid error accumulation and propagation. 3) This invention achieves a dual improvement in matching accuracy and robustness: the two core optimizations mentioned above work synergistically, enabling this invention to achieve outstanding results in the most challenging part-to-part matching tasks. Experimental data shows that on the BeCoS dataset, the corresponding quality of match (AUC) of this invention reaches 60.5, and the inter-overlap region prediction quality (IoU) is as high as 65.2%, both significantly better than the current state-of-the-art methods. Ablation experiments demonstrate that geometric-semantic fusion and iterative feedback mechanisms each contribute key performance gains, and their combination produces a synergistic effect. Furthermore, this invention also exhibits strong generalization ability in cross-domain non-equidistant matching tasks. For example, in the cross-domain test from SMAL to DT4D-H, the mean geodesic error (MGE) is as low as 16.5, far superior to the baseline method. Attached Figure Description
[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0017] Figure 1 This is a schematic diagram of the non-rigid 3D shape matching principle based on geometric-semantic feature fusion and iterative drift feedback disclosed in this invention; Figure 2 This is a qualitative comparison of the present invention with the current best method, Echo Match, on the BeCoS dataset. Figure 3a This is a comparison chart of the correct matching ratio and ground error threshold of CP2P24 disclosed in this invention on three benchmarks; Figure 3b This is a comparison chart of the correct matching ratio and ground error threshold of the PSMAL disclosed in this invention on three benchmarks. Figure 3c This is a comparison chart of the correct matching ratio and ground error threshold of BeCoS disclosed in this invention on three benchmarks. Detailed Implementation
[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.
[0019] Reference Figure 1 As shown, this invention discloses a non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback, comprising the following steps: Obtain the source 3D shape and the target 3D shape, and generate a training dataset after preprocessing the source 3D shape and the target 3D shape; Add semantic feature enhancement description to the functional mapping framework, and construct an iterative feedback mechanism by combining cyclic consistency constraints to form a non-rigid three-dimensional shape matching model. The training dataset is input into the non-rigid 3D shape matching model, and the trained non-rigid 3D shape matching model is obtained through iterative optimization based on matching-evaluation-feedback. Input the source 3D shape and the target 3D shape to be matched into a trained non-rigid 3D shape matching model, and output the dense correspondence between the source 3D shape and the target 3D shape.
[0020] Furthermore, the source and target 3D shapes are preprocessed to construct their Laplace-Beltrami spectral representations, specifically including: Construct the discrete cochet Laplace matrix and perform eigenvalue decomposition on the discrete cochet Laplace moments to extract the first k eigenfunctions and their corresponding eigenvalue diagonal matrices. The expression is as follows: , , ; in, Let X be the spectral basis matrix composed of the first k Laplacian eigenfunctions of shape X. The spectral basis matrix is composed of the first k Laplacian eigenfunctions of shape Y. Let X be a diagonal matrix consisting of the first k eigenvalues corresponding to shape X. Let be a diagonal matrix consisting of the first k eigenvalues corresponding to shape Y, where x is the source 3D shape or source mesh, and y is the target 3D shape or target mesh. Let m be the number of vertices of the source shape X and n be the number of vertices of the target shape Y.
[0021] Furthermore, semantic feature enhancement is used to extract the geometric and semantic features of the preprocessed source and target 3D shapes, such as... Figure 1 As shown in the DiffusionNet and DINOv2 modules, these modules are used to alleviate matching ambiguities caused by symmetrical structures and weak geometric regions, specifically including: By extracting vertex-level intrinsic geometric features using a neural network based on the diffusion operator, the geometric features of the source 3D shape and the target 3D shape are obtained, and the corresponding expressions are: , in, Let X be the vertex-level intrinsic geometric feature matrix of the source 3D shape X. Let Y be the vertex-level intrinsic geometric feature matrix of the target 3D shape. Geometric feature dimension; The 3D shape is rendered from multiple perspectives, and the semantic features of the image are extracted using a visual basic model and then mapped back to the 3D vertices to obtain the semantic features of the source 3D shape and the target 3D shape. The corresponding expression is: , in, Let X be the vertex-level intrinsic semantic feature matrix of the source 3D shape X. Let Y be the vertex-level intrinsic semantic feature matrix of the target 3D shape. This is the semantic feature dimension.
[0022] Furthermore, the function mapping includes: Geometric and semantic features are fused using a learnable mapping function to obtain fused features, expressed as follows: , in, To represent the vertex-level geometric features after projection transformation, To represent the vertex-level semantic features after projection transformation, For learnable weights, This represents the mapping function of a multilayer perceptron. For feature splicing operations; Based on the fusion features, a bidirectional soft matching relationship is established between the source 3D shape and the target 3D shape to form a functional mapping. The initial soft correspondence expression is obtained as follows: , , in, Let X be the soft matching matrix from the source 3D shape X to the target 3D shape Y. Let X be the soft matching matrix from the target 3D shape Y to the source 3D shape X. This is the feature similarity matrix between the source 3D shape and the target 3D shape.
[0023] Furthermore, cycle consistency constraints include: Based on the correspondence, a forward-backward mapping is constructed, and the drift residual is calculated in the spectral space. The corresponding expression is:
[0024] in, Let X be the drift residual of the i-th vertex on the source shape X. Let be the drift residual of the i-th vertex on the source shape Y. Let X be the vertex index of the source shape X. Let Y be the vertex index of the target shape Y, and E be the cyclic mapping matrix consisting of the forward soft matching matrix and the backward soft matching matrix. The Laplace spectral basis matrix corresponding to the shape; The drift amount reflects the degree of offset of the point during the round-trip mapping process. The drift residual is used to determine whether the match is located in the overlapping area.
[0025] Furthermore, the iterative feedback mechanism includes: The drift residuals are converted into vertex-level reliability weights, which are then fed back into the feature and spectrum solving process. After weighted mapping of the features, the function mapping is resolved through regularization optimization, thereby achieving iterative feedback. The corresponding expression is:
[0026] Where C is the functional mapping matrix from the source 3D shape X to the target 3D shape Y; A is the coefficient matrix of the features of the source 3D shape X in the spectral basis space; and B is the coefficient matrix of the features of the target 3D shape Y in the spectral basis space. Let X be the diagonal matrix of Laplacian eigenvalues of the source 3D shape X; Let be the diagonal matrix of Laplacian eigenvalues of the target 3D shape Y; λ is the regularization weight coefficient used to control the influence of the Laplacian commutation constraint term. Denotes the Frobenius norm; This represents the search for the optimal function mapping matrix that minimizes the objective function among all possible C values.
[0027] Furthermore, weighted mapping of features includes: The drift residual is mapped using a Gaussian function, and the corresponding expression is: , in, Let r be the reliability weight of the i-th vertex. i Let i be the drift residual of the i-th vertex. This is the bandwidth parameter of the Gaussian function; The features are weighted, and the expression is: , in, The vertex-level reliability weights for the source and target shapes are given. For element-wise weighted operations, These are the original vertex features of the source and target shapes. The weighted vertex features; Projecting the weighted features onto the spectral space, the corresponding expression is: , in, , respectively, are the pseudo-inverses of the spectral basis matrices of the source shape and the target shape, and A and B are the spectral domain coefficient matrices of the weighted features of the source shape and the target shape, respectively.
[0028] Furthermore, the matching, drift estimation, and feedback processes can be iteratively updated, such as... Figure 1 Mid-time step (t=0) As shown in the feedback process of t=1), by continuously updating the matching relationship and reliability weight, the non-overlapping region is gradually suppressed and the matching accuracy is continuously improved, and the dense correspondence between the source shape and the target shape is output. This application can maintain a stable and consistent matching effect under partial overlap and complex non-rigid deformation conditions.
[0029] In one specific embodiment, the method used in this application is compared with the current best method, EchoMatch, on the BeCoS dataset, and the results are as follows: Figure 2 As shown, in easily confused areas such as the horse's forehooves (top row red circles) and head (bottom row red circles), EchoMatch exhibits significant cross-anatomical mismatches (e.g., incorrectly mapping the blue area of the source model to the orange area of the target model), while the present invention successfully maintains a consistent structural correspondence (continuous color transition without jumps). This fully demonstrates that the present invention can effectively suppress matching drift caused by geometric ambiguity or local missing data.
[0030] In one specific embodiment, this application matches the results with other existing methods on three benchmarks: CP2P24, PSMAL, and BeCoS. The obtained correct matching ratio vs. geodetic error threshold is as follows: Figures 3a-3c As shown, this invention (blue solid line) significantly outperforms baseline methods across all datasets and error thresholds. Particularly in the high-precision range (error < 0.1), this method achieves a 59% matching rate on the most challenging BeCoS dataset, significantly higher than EchoMatch's 55%; moreover, the curve slope is steeper, indicating its sensitivity to minute shape changes—a result of the self-correcting capability provided by the iterative feedback mechanism.
[0031] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback, characterized in that, Includes the following steps: Obtain the source 3D shape and the target 3D shape, and generate a training dataset after preprocessing the source 3D shape and the target 3D shape; Add semantic feature enhancement description to the functional mapping framework, and construct an iterative feedback mechanism by combining cyclic consistency constraints to form a non-rigid three-dimensional shape matching model. The training dataset is input into the non-rigid 3D shape matching model, and the trained non-rigid 3D shape matching model is obtained through iterative optimization based on matching-evaluation-feedback. Input the source 3D shape and the target 3D shape to be matched into a trained non-rigid 3D shape matching model, and output the dense correspondence between the source 3D shape and the target 3D shape.
2. The non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback according to claim 1, characterized in that... The source and target 3D shapes are preprocessed to construct their Laplace-Beltrami spectral representations, specifically including: Construct the discrete cochet Laplace matrix and perform eigenvalue decomposition on the discrete cochet Laplace moments to extract the first k eigenfunctions and their corresponding eigenvalue diagonal matrices. The expression is as follows: ， ， ； in, Let X be the spectral basis matrix composed of the first k Laplacian eigenfunctions of shape X. The spectral basis matrix is composed of the first k Laplacian eigenfunctions of shape Y. Let X be a diagonal matrix consisting of the first k eigenvalues corresponding to shape X. Let be a diagonal matrix consisting of the first k eigenvalues corresponding to shape Y, where x is the source 3D shape or source mesh, and y is the target 3D shape or target mesh. Let m be the number of vertices of the source shape X and n be the number of vertices of the target shape Y.
3. The non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback as described in claim 1, Its features are, Semantic feature enhancement is used to extract the geometric and semantic features of the preprocessed source and target 3D shapes, specifically including: By extracting vertex-level intrinsic geometric features using a neural network based on the diffusion operator, the geometric features of the source 3D shape and the target 3D shape are obtained, and the corresponding expressions are: ， ， in, Let X be the vertex-level intrinsic geometric feature matrix of the source 3D shape X. Let Y be the vertex-level intrinsic geometric feature matrix of the target 3D shape. Geometric feature dimension; The 3D shape is rendered from multiple perspectives, and semantic features of the image are extracted using a visual basic model and then mapped back to 3D vertices to obtain the semantic features of the source 3D shape and the target 3D shape. The corresponding expression is: ， ， in, Let X be the vertex-level intrinsic semantic feature matrix of the source 3D shape X. Let Y be the vertex-level intrinsic semantic feature matrix of the target 3D shape. This refers to the semantic feature dimension.
4. The non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback according to claim 1, characterized in that, Function mapping includes: Geometric and semantic features are fused using a learnable mapping function to obtain fused features, expressed as follows: ， in, To represent the vertex-level geometric features after projection transformation, To represent the vertex-level semantic features after projection transformation, For learnable weights, This represents the mapping function of a multilayer perceptron. For feature splicing operations; Based on the fusion features, a bidirectional soft matching relationship is established between the source 3D shape and the target 3D shape to form a functional mapping. The initial soft correspondence expression is obtained as follows: ， ， in, Let X be the soft matching matrix from the source 3D shape X to the target 3D shape Y. Let X be the soft matching matrix from the target 3D shape Y to the source 3D shape X. This is the feature similarity matrix between the source 3D shape and the target 3D shape.
5. The non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback according to claim 4, characterized in that, Cyclic consistency constraints include: Based on the correspondence, a forward-backward mapping is constructed, and the drift residual is calculated in the spectral space. The corresponding expression is: ， ， in, Let X be the drift residual of the i-th vertex on the source shape X. Let be the drift residual of the i-th vertex on the source shape Y. Let X be the vertex index of the source shape X. Let Y be the vertex index of the target shape Y, and E be the cyclic mapping matrix consisting of the forward soft matching matrix and the backward soft matching matrix. The Laplace spectral basis matrix corresponding to the shape; Determine whether the match is located in the overlapping region based on the drift residual.
6. The non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback according to claim 5, characterized in that, Iterative feedback mechanisms include: The drift residuals are converted into vertex-level reliability weights, which are then fed back into the feature and spectrum solving process. After weighted mapping of the features, the function mapping is resolved through regularization optimization, thereby achieving iterative feedback. The corresponding expression is: ， Where C is the functional mapping matrix from the source 3D shape X to the target 3D shape Y; A is the coefficient matrix of the features of the source 3D shape X in the spectral basis space; and B is the coefficient matrix of the features of the target 3D shape Y in the spectral basis space. Let X be the diagonal matrix of Laplacian eigenvalues of the source 3D shape X; Let be the diagonal matrix of Laplacian eigenvalues of the target 3D shape Y; λ is the regularization weight coefficient used to control the influence of the Laplacian commutation constraint term. Denotes the Frobenius norm; This represents the search for the optimal function mapping matrix that minimizes the objective function among all possible C values.
7. A non-rigid 3D shape matching method based on geometric-semantic feature fusion and iterative drift feedback as described in claim 6. Its features are, Weighted mapping of features includes: The drift residual is mapped using a Gaussian function, and the corresponding expression is: ， in, Let be the reliability weight of the i-th vertex, and ri be the drift residual of the i-th vertex. This is the bandwidth parameter of the Gaussian function; The features are weighted, and the expression is: ， in, The vertex-level reliability weights for the source and target shapes are given. For element-wise weighted operations, These are the original vertex features of the source and target shapes. The weighted vertex features; Projecting the weighted features onto the spectral space, the corresponding expression is: ， in, , respectively, are the pseudo-inverses of the spectral basis matrices of the source shape and the target shape, and A and B are the spectral domain coefficient matrices of the weighted features of the source shape and the target shape, respectively.