CN-121982091-A - Depth non-rigid three-dimensional shape corresponding method, system, equipment and medium

CN121982091ACN 121982091 ACN121982091 ACN 121982091ACN-121982091-A

Abstract

The application discloses a depth non-rigid three-dimensional shape corresponding method, a system, equipment and a medium, wherein the method determines a first eigenvector matrix and a second eigenvector matrix; in the micro-iteration process, a symbolized soft mapping operator based on a kernel function and used for describing the corresponding relation between vertexes is constructed based on a current spectrum domain mapping matrix, a first eigenvector matrix and a second eigenvector matrix, the symbolized soft mapping operator is reprojected into a spectrum space to obtain intermediate state spectrum mapping estimation, multi-channel filtering processing is carried out on the intermediate state spectrum mapping estimation to obtain a refined coupling mapping matrix, the refined coupling mapping matrix is used as the current spectrum domain mapping matrix of the next iteration until the preset iteration times are reached to obtain a target coupling mapping matrix, and the target coupling mapping matrix is converted into a point-by-point mapping matrix to realize point-by-point correspondence between a source shape and a target shape. The application can improve the accuracy of the depth non-rigid three-dimensional shape correspondence.

Inventors

LI QINSONG
CHENG NAN
SHI MEI
LONG JUN
KUI XIAOYAN

Assignees

中南大学

Dates

Publication Date: 20260505
Application Date: 20260408

Claims (10)

1. A depth non-rigid three-dimensional shape correspondence method, the method comprising: representing a source shape and a target shape in a target scene as triangular grids with a plurality of vertexes, and obtaining triangular grids of the source shape and triangular grids of the target shape, wherein the source shape and the target shape are non-rigid three-dimensional shapes; extracting feature vectors in the source shape and the target shape to obtain a first original geometric feature vector of the source shape and a second original geometric feature vector of the target shape; According to the first original geometric feature vector and the second original geometric feature vector, calculating an initial functional mapping matrix, and taking the initial functional mapping matrix as a current spectrum domain mapping matrix capable of being subjected to initial micro-iteration; Calculating respective Laplace matrixes of the triangular mesh of the source shape and the triangular mesh of the target shape to obtain a first Laplace matrix of the source shape and a second Laplace matrix of the target shape; Performing generalized eigenvalue decomposition on the first Laplace matrix, determining a first eigenvector matrix, and performing generalized eigenvalue decomposition on the second Laplace matrix, determining a second eigenvector matrix; In a micro-iteration process, constructing a kernel function-based symbolized soft mapping operator for describing the corresponding relation between vertexes based on the current spectrum domain mapping matrix, the first eigenvector matrix and the second eigenvector matrix, re-projecting the kernel function-based symbolized soft mapping operator back to a spectrum space to obtain intermediate state spectrum mapping estimation, performing multi-channel filtering processing on the intermediate state spectrum mapping estimation to obtain a refined coupling mapping matrix, and taking the refined coupling mapping matrix as the current spectrum domain mapping matrix of the next iteration until reaching preset iteration times to obtain a target coupling mapping matrix; and converting the target coupling mapping matrix into a point-by-point mapping matrix, and realizing point-by-point correspondence between the source shape and the target shape through the point-by-point mapping matrix.
2. The depth non-rigid three-dimensional shape correspondence method of claim 1, wherein constructing a kernel-based symbolized soft mapping operator for describing a correspondence between vertices based on the current spectral domain mapping matrix, the first eigenvector matrix, and the second eigenvector matrix comprises: calculating the similarity of the first eigenvector matrix and the second eigenvector matrix under the current spectrum domain mapping matrix; Calculating the ratio of the similarity to the parameter for adjusting the mapping sharpness to obtain a ratio calculation result; And processing the ratio calculation result through a Softmax function, and constructing a kernel function-based symbolized soft mapping operator for describing the corresponding relation between the vertexes.
3. The depth non-rigid three-dimensional shape corresponding method according to claim 1, wherein the reprojecting the kernel-based symbolized soft mapping operator back into a spectral space to obtain an intermediate state spectral mapping estimate, comprising: multiplying the signed soft mapping operator based on the kernel function with the first eigenvector matrix through a combination law to obtain a multiplication result; Performing pseudo-inverse operation on the second eigenvector matrix to obtain a pseudo-inverse operation result; And multiplying the multiplication result and the pseudo-inverse operation result to obtain intermediate state spectrum mapping estimation.
4. The method according to claim 1, wherein the performing a multi-channel filtering process on the intermediate state spectrum mapping estimate to obtain a refined coupling mapping matrix comprises: Constructing a filter function through KAN grids, and constructing a multi-channel filter module based on the filter function; and carrying out multi-channel filtering processing on the intermediate state spectrum mapping estimation by adopting the multi-channel filtering module to obtain a refined coupling mapping matrix.
5. The depth non-rigid three-dimensional shape corresponding method of claim 4, wherein the constructing a filter function through a KAN grid comprises: ; Wherein, the Representing the filtering function and, Representing the accumulation index, Representing the number of laplace-belleville operator eigenvalues, Representation of The spline function under the index is used for the purpose of, Representation of Index lower th Spline functions corresponding to the laplace-bellte-lami operators, Represent the first And (3) the characteristic values of the Laplace-Bellamide operators.
6. The method of claim 4, wherein the performing the multi-channel filtering on the intermediate state spectrum mapping estimate by using the multi-channel filtering module to obtain a refined coupling mapping matrix comprises: performing generalized eigenvalue decomposition on the first Laplace matrix, determining a first diagonal eigenvalue matrix, and performing generalized eigenvalue decomposition on the second Laplace matrix, determining a second diagonal eigenvalue matrix; inputting the first diagonal eigenvalue matrix to the multi-channel filtering module to obtain a first module result; inputting the second diagonal eigenvalue matrix to the multi-channel filtering module to obtain a second module result; Multiplying the first module result, the second module result and the intermediate state spectrum mapping estimation to obtain a refined coupling mapping matrix.
7. The depth non-rigid three-dimensional shape corresponding method of claim 1, wherein the converting the target coupling mapping matrix into a point-by-point mapping matrix comprises: performing rotation alignment on the first eigenvector matrix through the target coupling mapping matrix to obtain an alignment result; And carrying out nearest neighbor search in a spectrum space based on the alignment result to obtain a point-by-point mapping matrix, wherein the point-by-point mapping matrix comprises semantic indexes from the vertexes of the source shape to the vertexes of the target shape.
8. A depth non-rigid three-dimensional shape correspondence system, the system comprising: A triangular mesh representation unit for representing a source shape and a target shape in a target scene as triangular meshes with a plurality of vertexes, and obtaining triangular meshes of the source shape and triangular meshes of the target shape, wherein the source shape and the target shape are non-rigid three-dimensional shapes; a feature vector extraction unit, configured to extract feature vectors in the source shape and the target shape, to obtain a first original geometric feature vector of the source shape and a second original geometric feature vector of the target shape; The first data calculation unit is used for calculating an initial functional mapping matrix according to the first original geometric feature vector and the second original geometric feature vector, and taking the initial functional mapping matrix as a current spectrum domain mapping matrix which can be subjected to initial micro iteration; a second data calculation unit, configured to calculate respective laplace matrices of the triangular mesh of the source shape and the triangular mesh of the target shape, to obtain a first laplace matrix of the source shape and a second laplace matrix of the target shape; The characteristic value decomposition unit is used for performing generalized characteristic value decomposition on the first Laplace matrix, determining a first characteristic vector matrix, and performing generalized characteristic value decomposition on the second Laplace matrix, and determining a second characteristic vector matrix; The micro-iteration unit is used for constructing a kernel function-based symbolized soft mapping operator for describing the corresponding relation between vertexes based on the current spectrum domain mapping matrix, the first eigenvector matrix and the second eigenvector matrix in a micro-iteration process, re-projecting the kernel function-based symbolized soft mapping operator back to a spectrum space to obtain intermediate state spectrum mapping estimation, performing multi-channel filtering processing on the intermediate state spectrum mapping estimation to obtain a refined coupling mapping matrix, and taking the refined coupling mapping matrix as the current spectrum domain mapping matrix of the next iteration until the preset iteration times are reached to obtain a target coupling mapping matrix; And the shape point-to-point correspondence unit is used for converting the target coupling mapping matrix into a point-to-point mapping matrix, and realizing point-to-point correspondence between the source shape and the target shape through the point-to-point mapping matrix.
9. An electronic device comprising at least one control processor and a memory communicatively coupled to the at least one control processor, the memory storing instructions executable by the at least one control processor to enable the at least one control processor to perform the deep non-rigid three-dimensional shape correspondence method of any one of claims 1 to 7.
10. A computer-readable storage medium storing computer-executable instructions for causing a computer to perform the deep non-rigid three-dimensional shape correspondence method according to any one of claims 1 to 7.

Description

Depth non-rigid three-dimensional shape corresponding method, system, equipment and medium Technical Field The application relates to the technical field of computer vision, in particular to a depth non-rigid three-dimensional shape corresponding method, a system, equipment and a medium. Background Establishing correspondence between non-rigid shapes is an important and fundamental problem in the fields of computer graphics, geometric processing and computer vision, and the core goal is to establish point-to-point semantic mapping relationships between different geometric entities. The research of the problem not only has a deep theoretical root, but also shows important research value and application prospect in digital twinning, role animation, augmented reality and medical image analysis. Because the deformation of the three-dimensional shape in the real world is mostly approximately equidistant, finding the point-by-point approximately equidistant correspondence between models becomes a core problem in the research field of shape correspondence. After entering the deep learning era, three-dimensional shape correspondence still faces serious challenges in complex practical applications. Although feature characterization capabilities are improved, existing deep learning frameworks exhibit severe static limitations on spectral domain filtering mechanisms. The mainstream method mostly adopts a predefined fixed filtering strategy or a simple feedforward learning mode when constructing a function mapping matrix, ignores the distribution specificity of different geometric features in a spectrum domain, and leads to the fact that the model cannot adaptively and dynamically adjust the frequency response according to a specific deformation type. The more central technical bottleneck is the optimized fault between the feature learning link and the geometric refinement process. In order to obtain a high precision match, spectral domain upsampling must typically be performed by means of classical refinement algorithms. For example, the widely used ZoomOut module (an existing algorithm for optimizing correspondence between three-dimensional shapes), while capable of significantly improving alignment accuracy, contains discrete operations that are not mathematically trivial in nature. This results in a severe gradient barrier during the training phase, so that the feature learning module and refinement link are forced to be disjointed, resulting in that the filter parameters cannot be dynamically optimized along with the refinement trajectory. Even if the use of symbolic operations is currently occurringHowever, these attempts have focused on the microminiaturization of the flow, failing to achieve deep coupling of feature characterization and iterative refinement trajectories. Due to the lack of real-time feedback of the downstream geometric convergence target, the current shape corresponding method cannot identify what frequency modulation is most beneficial to the convergence of the subsequent refinement target, and the accuracy and the consistency of the whole flow are still greatly insufficient when complex non-equidistant deformation is processed. Disclosure of Invention The application aims to provide a method, a system, equipment and a medium for corresponding a depth non-rigid three-dimensional shape, which can improve the accuracy of the corresponding depth non-rigid three-dimensional shape and ensure the consistency of the whole process. In a first aspect, embodiments of the present application provide a depth non-rigid three-dimensional shape correspondence method, the method comprising: representing a source shape and a target shape in a target scene as triangular grids with a plurality of vertexes, and obtaining triangular grids of the source shape and triangular grids of the target shape, wherein the source shape and the target shape are non-rigid three-dimensional shapes; extracting feature vectors in the source shape and the target shape to obtain a first original geometric feature vector of the source shape and a second original geometric feature vector of the target shape; According to the first original geometric feature vector and the second original geometric feature vector, calculating an initial functional mapping matrix, and taking the initial functional mapping matrix as a current spectrum domain mapping matrix capable of being subjected to initial micro-iteration; Calculating respective Laplace matrixes of the triangular mesh of the source shape and the triangular mesh of the target shape to obtain a first Laplace matrix of the source shape and a second Laplace matrix of the target shape; Performing generalized eigenvalue decomposition on the first Laplace matrix, determining a first eigenvector matrix, and performing generalized eigenvalue decomposition on the second Laplace matrix, determining a second eigenvector matrix; In a micro-iteration process, constructing a kernel function-based s