CN110070096B - Local frequency domain descriptor generation method and device for non-rigid shape matching - Google Patents
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Abstract
The invention belongs to the field of computer vision, and particularly relates to a method and a device for generating a local frequency domain descriptor aiming at non-rigid shape matching, aiming at solving the problem of poor robustness of the local frequency domain descriptor obtained under the influence of different spatial resolutions, sampling and various transformations. The method comprises the following steps: extracting three-dimensional shape local point characteristics in a frequency domain for each vertex in the surface triangular mesh model based on a Laplace-Belltzier operator; and acquiring a vertex frequency domain image corresponding to each vertex of the three-dimensional shape based on the local feature points, and obtaining a local frequency domain descriptor for non-rigid shape matching through a ternary neural network. The local point features extracted by the method have better robustness on the three-dimensional shape under various resolutions, triangulation, scales and rotations, and based on the robustness, the local frequency domain descriptor for non-rigid shape matching can be accurately and robustly obtained through the ternary neural network.
Description
Technical Field
The invention belongs to the field of computer vision, and particularly relates to a method and a device for generating a local frequency domain descriptor for non-rigid shape matching.
Background
Because of the simplicity, effectiveness, and flexibility of three-dimensional shapes (mesh models), they have become a widely used form in the field of computer vision in discrete representations of three-dimensional data. With the development of three-dimensional scanning devices and computer vision reconstruction techniques, it becomes easier to obtain detailed three-dimensional shapes. Thus, the importance of three-dimensional shape analysis (e.g., shape matching, segmentation, correspondence, and retrieval) has increased dramatically. Designing a local descriptor for surface shape is a fundamental problem in computer vision and is the key and foundation for other advanced applications.
Methods for generating local descriptors in the prior art mainly include a spatial domain method, an embedding-based method and a deep learning-based method.
The spatial domain method mainly obtains a statistical histogram to represent the local vertex features by counting the vertex feature information (such as number, angle, direction, etc.) in the local space. For example, a 3DSC (3D shape context) descriptor counts The number of vertices in each histogram block, a SHOT (signal of histogram of orientation features) counts The angle of a neighborhood point normal vector, a Mesh-HOG (Mesh of oriented gradients) describes The direction of a sub-statistical gradient, and a RoPS (rotational projection statistics) describes a plurality of features of a sub-statistical projection two-dimensional plane. Obviously, these conventional methods are based on spatial domain features and are susceptible to various transformations and distortions in resolution and shape.
Most of the embedding-based methods propose built-in descriptors, which aim to solve the problem of equidistant deformation. The method of generating embedded descriptors is generally based on the Laplace-Beltrami operator. Shape-DNA (Shape DNA) uses the eigenvalues of the Laplace-Beltrami operator as features. A GPS (Global Point Signature) combines feature values and feature functions to generate features. HKS (Heat Kernel Signature), scale-invariant Heat Kernel Signature and OSD (optimal spectral descriptors) are proposed based on diffusion geometry. However, these embedding methods are mostly based on global implication characteristics, are not robust enough for local detailed description, and are mostly scale sensitive.
Methods based on deep learning, which mainly include multi-view, voxelization and learning directly on three-dimensional shapes, have been recently used to extract shape descriptors, however, since the information learned by these methods is related to the structure of the shape (such as grid scale, spatial resolution, sampling, etc.), their generalization capability is defective.
Therefore, how to provide a method to solve the above problems (different spatial resolutions, sampling and various transformations) is a problem that those skilled in the art need to solve at present.
Disclosure of Invention
In order to solve the above problems in the prior art, that is, to solve the problem that the robustness of the local frequency domain descriptor obtained under the influence of different spatial resolutions, sampling and various transformations is poor, a first aspect of the present invention provides a method for generating a local frequency domain descriptor for non-rigid shape matching, where the method includes the following steps:
step S10, extracting three-dimensional shape local point characteristics in a frequency domain for each vertex in the surface triangular mesh model based on a Laplace-Belltzim operator;
and step S20, acquiring a vertex frequency domain image corresponding to each vertex of the three-dimensional shape based on the local feature points, and obtaining a local frequency domain descriptor for non-rigid shape matching through a ternary neural network.
In some preferred embodiments, the method for extracting the local point feature of the three-dimensional shape in the frequency domain for each vertex in the surface triangular mesh model based on the laplacian-belonger operator is as follows:
calculating a Laplace-Belladrami matrix L of the surface triangular mesh model based on a surface continuous function f of the three-dimensional shape surface triangular mesh model;
performing characteristic decomposition on the matrix L to obtain a characteristic vector and a characteristic value;
extending the surface continuous function f to a discrete function
And the matrix is expanded under the characteristic vector of the matrix L to obtain a frequency domain expansion coefficient sigmaj；
According to the characteristic decomposition and frequency domain expansion coefficient sigma of the matrix LjCalculating the energy of discrete Dirichlet
Extending a high-dimensional continuous function F based on a surface continuous function F to a high-dimensional discrete function
Calculating discrete Dirichlet energy
And supply the energy
Spreading in a frequency domain to obtain general frequency domain characteristics;
discrete function of high dimension
Setting the three-dimensional coordinate information X of a local patch, and solving discrete energy according to continuous energy E (X)
Taking the discrete energy
Obtaining the local point characteristics by the front Q dimension expanded in the frequency domain; wherein Q is a first set value.
In some preferred embodiments, the method for calculating the laplacian-belite-larm matrix L of the surface triangular mesh model based on the surface continuous function f of the three-dimensional shape surface triangular mesh model comprises the following steps:
obtaining discrete functions of a continuous function f of a surface
Calculating an element L in a Laplace-Belladrami matrix L of the surface triangular mesh model by the following formulaij：
Wherein alpha isijAnd betaijFor two angles, alpha, opposite to the edges { i, j } in the surface triangular mesh modeliIs a vertex viOf Voronoi polygons, k being adjacent to the verticesAnd (4) the number.
In some preferred embodiments, the "performing feature decomposition on the matrix L to obtain feature vectors and feature values" includes:
the matrix L is decomposed into two symmetric matrices T and a,
TΦi＝λiAΦi,i＝0,1,...,N-1；
wherein the content of the first and second substances,
Aii＝ai
solving by an ARPACK method to obtain the eigenvector phi againiAnd a characteristic value lambdaiAnd N is the number of the surface triangular mesh model vertexes.
In some preferred embodiments, the surface continuous function f is extended to a discrete function
And the matrix is expanded under the characteristic vector of the matrix L to obtain a frequency domain expansion coefficient sigmaj", the method is as follows:
wherein phijIs the jth eigenvector of the matrix L.
In some preferred embodiments, the "frequency domain expansion coefficient σ decomposed according to the characteristics of the matrix LjCalculating the energy of discrete Dirichlet
", the method is as follows:
wherein the content of the first and second substances,
discrete energy form corresponding to Dirichlet energy of continuous real function f, N being number of vertexes, lambdajIs the jth eigenvalue of the matrix L.
In some preferred embodiments, "extending a high-dimensional continuous function F based on a surface continuous function F to a high-dimensional discrete function
Calculating discrete Dirichlet energy
And supply the energy
The method comprises the following steps of developing in a frequency domain to obtain general frequency domain characteristics:
wherein sf is a general frequency domain characteristic, lambdaN-1Is a characteristic value, σiN-1The coefficients are expanded for the high-dimensional frequency domain.
In some preferred embodiments, a "discrete function of high dimension is formed
Setting the three-dimensional coordinate information X of a local patch, and solving discrete energy according to continuous energy E (X)
Taking the discrete energy
The local point feature is obtained from the front Q dimension expanded in the frequency domain, and the method comprises the following steps:
wherein, LPS is the obtained local point characteristics.
In some preferred embodiments, "based on the local feature points, obtaining a vertex frequency domain image corresponding to each vertex of the three-dimensional shape, and obtaining a local frequency domain descriptor for non-rigid shape matching through a ternary neural network", the method includes:
encoding the local point features into Q first sized images;
generating a corresponding vertex frequency domain image for each vertex on the three-dimensional shape surface triangular mesh model to obtain a vertex frequency domain image set;
and obtaining a local frequency domain descriptor for non-rigid shape matching through a preset ternary neural network based on the vertex frequency domain image set.
In some preferred embodiments, the local point features are encoded as Q first sized images by:
taking Q as 16 and setting the first set size as 8 x 8;
local point features are encoded into 16 geometric images of 8 x 8 size using a geometric image method.
In some preferred embodiments, for each vertex on the triangular mesh model of the three-dimensional shape surface, a corresponding vertex frequency domain image is generated by:
initializing a 32 x 32 empty image, filling 16 feature coding images of 8 x 8 local point features into the initialized empty image, and respectively placing a minimum feature value and a maximum feature value at the upper left corner and the lower right corner to generate a 32 x 32 vertex frequency domain image.
In some preferred embodiments, the ternary neural network consists of three identical ConvNet convolutional networks, the training samples of which comprise three-dimensional shapes and corresponding descriptors; when the ternary neural network is trained, the three-dimensional shape in the training sample is input into the ternary neural network by acquiring the corresponding vertex frequency domain image set by the method in the steps S10 and S20.
The invention provides a device for generating a local frequency domain descriptor aiming at non-rigid shape matching, which comprises a local point feature generation module and a local frequency domain descriptor acquisition module;
the local point feature generation module is configured to obtain local point features of each vertex in the three-dimensional shape surface triangular mesh model in a frequency domain based on a Laplace-Belltzian operator;
the local frequency domain descriptor acquisition module is configured to acquire a vertex frequency domain image corresponding to each vertex of the three-dimensional shape based on the local feature points, and obtain a local frequency domain descriptor for non-rigid shape matching through a ternary neural network.
In a third aspect of the present invention, a storage device is provided, in which a plurality of programs are stored, the programs being adapted to be loaded and executed by a processor to implement the above-mentioned local frequency domain descriptor generation method for non-rigid shape matching.
In a fourth aspect of the present invention, a processing apparatus is provided, which includes a processor, a storage device; a processor adapted to execute various programs; a storage device adapted to store a plurality of programs; the program is adapted to be loaded and executed by a processor to implement the above-described method for local frequency domain descriptor generation for non-rigid shape matching.
The invention has the beneficial effects that:
the local point characteristics extracted by the method have better robustness on the three-dimensional shape under various resolutions, triangulation (sampling), scales and rotations, and based on the robustness, the local frequency domain descriptor for non-rigid shape matching can be accurately and robustly obtained by the ternary neural network.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
FIG. 1 is a schematic flow chart of a method for generating a local frequency domain descriptor for non-rigid shape matching according to an embodiment of the present invention;
FIG. 2 is an exemplary diagram of matching results for different resolutions, samples, scales, and rotations using descriptors obtained by the present invention;
FIG. 3 is an exemplary diagram of angles and Voronoi areas in a discrete Laplace-Beltrami operator in accordance with an embodiment of the present invention;
FIG. 4 is an exemplary diagram of differently shaped structural models generated in one embodiment of the present invention;
FIG. 5 is an exemplary diagram of VSIs of frequency domain images of vertices at different locations in an embodiment in accordance with the invention;
FIG. 6 is a graph of the results of LPS characterization on different resolution and triangularization models in one embodiment of the present invention;
FIG. 7 is a graph of the results of a descriptor on different resolution and triangularization models in one embodiment of the present invention;
FIG. 8 is a graph comparing the results of the descriptor and LPS features at 6890 and 8K resolution and other methods in one embodiment of the present invention;
FIG. 9 is a graph comparing the results of the descriptor and LPS features at 6890 and 12K resolution and other methods in one embodiment of the present invention;
FIG. 10 is a graph comparing the results of descriptor and LPS characterization on a set of rotational models and other methods in one embodiment of the present invention;
FIG. 11 is a graph comparing the results of descriptors and LPS features on different scale model sets and other methods in one embodiment of the invention;
FIG. 12 is a graph comparing results of corresponding frames and other corresponding frames in one embodiment of the invention;
fig. 13 is a schematic diagram of a frame of a local frequency domain descriptor generation apparatus for non-rigid shape matching according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
The invention relates to a local frequency domain descriptor generation method aiming at non-rigid shape matching, which comprises the following steps:
step S10, extracting three-dimensional shape local point characteristics in a frequency domain for each vertex in the surface triangular mesh model based on a Laplacian-Belladrami (Laplace-Beltrami) operator;
and step S20, acquiring a vertex frequency domain image corresponding to each vertex of the three-dimensional shape based on the local feature points, and obtaining a local frequency domain descriptor for non-rigid shape matching through a ternary neural network.
Fig. 1 is a schematic flow chart of a method for generating a local frequency domain descriptor for non-rigid shape matching according to an embodiment of the present invention, where the descriptor obtained in the schematic flow chart is 256-dimensional. Fig. 2 is a schematic diagram of matching results of descriptors with different resolutions, sampling, scales and rotations obtained by the present invention, where the leftmost model is a reference model, the number of points is 6890 points, and then the model, the scale scaling model and the rotation model with high resolution and different sampling of 12K are sequentially used.
In order to more clearly explain the present invention, the steps of the present invention will be described in detail below with reference to the accompanying drawings.
The local frequency domain descriptor generation method for non-rigid shape matching of one embodiment of the invention comprises steps S10 and S20.
And step S10, extracting the local point characteristics of the three-dimensional shape in the frequency domain for each vertex in the surface triangular mesh model based on the Laplace-Belltzim operator. The local point features obtained by the method of the step keep robustness on all resolutions, triangulation (sampling), scales and rotations of the three-dimensional shape. This step may be further subdivided into steps S101-S106.
Step S101, calculating a Laplace-Belladrami matrix L of the surface triangular mesh model based on a surface continuous function f of the three-dimensional shape surface triangular mesh model.
Knowing the surface continuum real function f on the surface of the three-dimensional shape:
in the function
For a continuous surface, R is a real number domain, the Dirichlet (Dirichlet) energy of the function can be found, as shown in equation (1):
wherein the content of the first and second substances,
for gradient, f (v) is the feature on the vertex v, v is the point on the continuous surface.
As shown in fig. 3, in a discrete grid
If there is a continuous real function f of the surface shape:
in discrete form
V → R, then Δ f at vertex ViIs as shown in formula (2):
where V is a discrete vertex, aiIs the vertex viVoronoi polygon area of (c), N (v)i) Representing a vertex viA circle of neighborhood points, αijAnd betaijRepresenting two corners opposite the edges i, j; v in FIG. 3i、VjTwo discrete vertices.
Therefore, a discrete Laplace-Bellamy matrix L can approximate the Laplace-Beltrami operator Δ, as shown in equation (3):
where k is the number of adjacent vertices.
Step S102, performing characteristic decomposition on the matrix L to obtain a characteristic value lambdaiAnd the eigenvector phii。
If a continuous surface is present
Last set of consecutive orthogonal basis functions [ phi ]iI | 0, 1., N-1} minimizes Dirichlet (Dirichlet) energy, then the solution to the problem (the set of orthogonal basis functions) is the first N feature functions of Laplace-Beltrami operator Δ (N is the number of surface triangular mesh model vertices), and equation (4) is satisfied:
Δφi＝λiφi,i＝0,1,...,N-1 (4)
in the formula (4), Delta is a Laplace-Beltrami operator, phiiFor the ith characteristic function, { λiI ═ 0, 1., N-1} is the first N eigenvalues in increasing order, corresponding to the discrete case as shown in equation (5):
LΦi＝λiΦi,i＝0,1,...,N-1 (5)
wherein phiiBeing discrete orthogonal bases (i.e. eigenvectors), λiThe characteristic value after decomposition.
The Laplace-Beltrami matrix L is decomposed into two symmetric matrices T and A, thus obtaining the formula (6) from the formula (5),
TΦi＝λiAΦi,i＝0,1,...,N-1 (6)
wherein A isii＝ai，TijAs shown in formula (7)
Solving is adopted to obtain a characteristic vector phiiAnd a characteristic value lambdai。
Method for calculating eigenvector phi by using ARPACK method for solving generalized eigenvalue of matrixiAnd a characteristic value lambdaiTime, feature vector phiiIs orthogonal to A, and is embodied as<Φi,Φj>A＝Φi TAΦjWherein phi isi、ΦjRespectively two different feature vectors.
Step S103, expanding the surface continuous function f to a discrete function
And the matrix is expanded under the characteristic vector of the matrix L to obtain a frequency domain expansion coefficient sigmaj。
Similar to the fourier expansion, the continuous function f can be expanded by a basis function, as shown in equation (8):
wherein σjIs the frequency domain expansion coefficient, phijIs the jth characteristic function. Expansion to discrete case yields expansion coefficient σjAs shown in formula (9).
Step S104, according to the characteristic decomposition of the matrix L and the frequency domain expansion coefficient sigmajCalculating the energy of discrete Dirichlet
According to a continuous Dirichlet energy formula, obtaining a discrete energy form of a continuous real function f
From the eigen decomposition and frequency domain expansion coefficient sigma of the matrix LjDetermining the energy of the discrete Dirichlet (Dirichlet)
Is represented by the formula (10).
Wherein N is the number of vertexes, lambdajIs the jth eigenvalue.
Step S105, extending a high-dimensional continuous function F based on a surface continuous function F to a high-dimensional discrete function
Calculating discrete Dirichlet energy
And supply the energy
And spreading in the frequency domain to obtain universal frequency domain characteristics.
For high dimensional continuous functions F ═ F1,f2,...,fd):S→RdThe Dirichlet energy formula is shown in formula (11):
wherein f is1,f2,...,fdRespectively d low-dimensional continuous functions, and d continuous functions,
is the gradient of the function in the higher dimension,
is the gradient of a low-dimensional function.
Extension to high dimensional functions
Its discrete Dirichlet energy
As shown in equation (12):
wherein σijIs the j frequency domain expansion coefficient in the i dimension, lambdajIs the jth eigenvalue.
The specific formula for obtaining the general frequency domain characteristics by expanding in the frequency domain is shown as the formula (13):
wherein sf is a general frequency domain characteristic, lambdaN-1Is the Nth characteristic value, σiN-1And the coefficient is the Nth frequency domain expansion coefficient under the ith dimension.
Step S106, high-dimensional discrete function
Setting the three-dimensional coordinate information X of a local patch, and solving discrete energy according to continuous energy E (X)
Taking the discrete energy
Obtaining the local point characteristics by the front Q dimension expanded in the frequency domain; wherein Q is a first set value.
The local patch is obtained by the local geodesic radius of the vertex, the local three-dimensional coordinate information is shown as a formula (14),
X＝(x1,x2,x3):V→R3 (14)
wherein x is1,x2,x3Are three-dimensional coordinates.
For the case where the function X is continuous, the continuous energy E (X) is as shown in equation (15),
wherein the content of the first and second substances,
is the gradient of the function of X,
is the gradient of the function x, and P is the local patch.
Extending it to discrete cases, as shown in equation (16),
and (3) taking a front Q dimension of the discrete energy expanded in the frequency domain to obtain the LPS characteristic, wherein the value of Q is 16 as shown in a formula (17).
The existing frequency domain characteristic methods of GPS, HKS and the like avoid using extrinsic characteristics to obtain a global intrinsic characteristic, and the local description is not strong. Although the intrinsic features are invariant to the equal distances, the non-equal distance deformation cannot be effectively solved. It has been found experimentally that many methods achieve better results using non-intrinsic descriptors such as SHOT as input. In the invention, vertex coordinate information is effectively introduced, and a new frequency domain characteristic is designed through a Dirichlet framework, so that the invention combines the information of intrinsic and extrinsic information to obtain a local frequency domain descriptor with more discriminability. In addition, some methods of extrinsic implications (e.g., SHOT) or intrinsic implications (e.g., HKS) are extremely sensitive to scaling, and the descriptors of the present invention remain invariant over scaling.
In this embodiment, in order to check the effectiveness of the method, models of locally different shapes of structures are generated, as shown in fig. 4, the three individual models on the left are models of different resolutions (6890, 8K, 15K) and triangularization, and the model on the right is shown as a model of different dimensions and different rotation directions.
The FAUST model library is a widely used standard data set in the field of shape matching, and the data set has rich details and more accurate corresponding relation. The present embodiment generates models of different shaped structures (resolution, triangularization (sampling), scale, and rotation) based on the dataset.
Since all the FAUST model libraries have the same triangularization and 6890-point resolution, and in addition, a large number of models need to be generated by an automatic method, the embodiment generates a multi-resolution model library with different triangularization by referring to the existing re-gridding method, and ensures that each shape contains the number of vertices specified by the user. The regridding method can be seen in: 1. marion Dunyach, David Vanderhaeghe,
Barthe,and Mario Botsch.Adaptive remeshing for real-time mesh deformation.Eurographics.2013；2、Yiqun Wang,Dong-Ming Yan,Xiaohan Liu,Chengcheng Tang,Jianwei Guo,Xiaopeng Zhang,and Peter Wonka.Isotropic surface remeshing without large and small angles.IEEE Trans.on Vis.and Comp.Graphics,2018.
in order to accurately maintain the corresponding relationship, each original vertex is marked as "locked" in the present embodiment, which means that the original vertex cannot be moved or deleted. Vertices are then added or subtracted in iterations through edge splitting and edge folding operations. In the iteration, the embodiment applies a random edge flipping operation to obtain an irregular triangulated model. Followed by several smoothing operations to avoid most cases where the triangle shape is too poor. At the same time, these operations will keep the local details from being destroyed. For the generation of low resolution models, the method uses the 5K model provided in documents Jing Ren, Adrien Poulenard, Peter Wonka, and Maks Ovsjankov. continuous and orientation-predicting corrispondence of the visa functional maps. ACM tracks. on Graphics,37(6):248:1-248:16, dec.2018, which model is generated independently by a CVT (Central Voronoi Tesselllation, based on centre of gravity Voronoi diagram) method. Finally, six different resolution models (5K,6890,8K,10K,12K and 15K) were obtained. The CVT method adopted in this embodiment can be referred to as: Dong-Ming Yan, Guinbo Bao, Xiaoopeng Zhang, and Peter Wonka. Low-resolution remeasured using the localized restrained voronoi diagrami. IEEE Trans. on Vis. and Comp. graphics,20(10):1418, 1427, 2014.
For different scale models, the present embodiment randomly selects one of five scaling factors (0.2,0.5,1.0,2.0, and 4.0) for scaling. In addition, the present embodiment also randomly rotates the model to generate a model library with different rotation directions, and the effect is shown in fig. 4.
And step S20, acquiring a vertex frequency domain image corresponding to each vertex of the three-dimensional shape based on the local feature points, and obtaining a local frequency domain descriptor for non-rigid shape matching through a ternary neural network. The step specifically includes steps S201 to S203.
Based on the acquired characteristic LPS, the invention designs a novel and compact geometric image (VSI), which can effectively code the LPS and is used for training a neural network, based on the acquired characteristic LPS, the VSI can effectively utilize the VSI to learn a local descriptor for non-rigid matching, and the stage from the LPS characteristic to a 256-dimensional descriptor is shown in FIG. 2.
Step S201, the local point features are encoded into Q images of a first set size.
Taking Q as 16 and setting the first set size as 8 x 8;
the local point features are encoded into 16 geometric images of 8 x 8 size using a geometric image (geometry image) method. Unlike previous methods, which typically encode low-level information (curvature, normal, etc.) that is sensitive to different shape structures, and low-level features require large size (32 x 32) to obtain sufficient local information, LPS features are high-level features that can represent local detail, thereby reducing the amount of data without reducing the amount of information.
Step S202, generating a corresponding vertex frequency domain image for each vertex on the three-dimensional shape surface triangular mesh model to obtain a vertex frequency domain image set.
Initializing a 32 x 32 empty image, filling 16 feature coding images of 8 x 8 local point features into the initialized empty image, and respectively placing a minimum feature value and a maximum feature value at the upper left corner and the lower right corner to generate a 32 x 32 vertex frequency domain image.
As in the example of fig. 5, the vertex frequency domain images of three different parts (fingers, navel, knee) are shown. Each VSI consists of 16 small geometric images. The method can fully utilize the convolution characteristic in the training process of the convolution neural network, and useful information can be learned from 16 different frequency bands. Furthermore, this method can only be applied to features that are independent of coordinates (e.g. LPS in the present invention), and if features are related to coordinates, then problems with order can arise during the encoding process. The present embodiment uses multiscale VSI as input, while the present embodiment generates 12 VSIs of different rotational directions as training data to learn the rotational invariance of the geometric image.
And step S203, obtaining a local frequency domain descriptor for non-rigid shape matching through a preset ternary neural network based on the vertex frequency domain image set.
In the implementation, the ternary neural network consists of three identical ConvNet convolutional networks, and each ConvNet convolutional network consists of a network structure of CONV128-3x3-/2+ CONV256-3x3-/2+ CONV512-3x3-/2+ FC512+ FC256, wherein CONVx represents that the convolutional layer has an output of an x-dimensional feature map, 3x3 represents the size of a convolutional kernel,/2 represents the step of the pooling operation, and FCx represents a fully-connected layer with the output of an x-dimensional vector.
In this embodiment, the training sample of the ternary neural network includes a three-dimensional shape and a corresponding descriptor; during the training of the ternary neural network, the three-dimensional shapes in the training samples are input into the ternary neural network by acquiring the corresponding vertex frequency domain image sets by adopting the methods in the steps S10 and S20.
After the trained ternary neural network is obtained, the generated VSI image data set is sent to the ternary neural network, and then the 256-dimensional descriptor can be obtained.
The existing method can only learn through key point data, and in the embodiment, all vertexes can be used as a training set through a compact geometric image representation mode of VSI, so that a descriptor with more discriminability can be learned.
In practical application, the robustness of the descriptor provided by the invention can be evaluated through experiments, the experimental platform of the embodiment is a central processing unit of Intel i 7-77004.20 GH, a computer of 16GB RAM and a 64-bit windows 10 operating system, and open source software is used for designing a non-rigid shape matching local frequency domain descriptor generation system on the platform. The offline training is run on a NVIDIA GeForce GTX 1080Ti (11GB memory) GPU.
In practical applications, standard evaluation frameworks, namely CMC (cumulative matching feature) and PP (Princeton protocol preston protocol) may be used. The CMC evaluates the probability of finding a correct match in the k-nearest neighbors. PP measures the quality of the match by plotting the percentage of nearest neighbor matches within r geodetic distance.
In describing the invariance of resolution and triangulation, four types of shapes were chosen for this embodiment, namely thin men, thick women, thick men, and thin girls, in order to demonstrate the invariance of the frequency domain features proposed by the present invention to resolution and triangulation. Each shape has five different resolution and differently triangulated models. The LPS frequency domain features of 16 dimensions were calculated for each model, and then reduced using the classical PCA (principal component analysis) method. The dimension reduction result is shown as the principal component analysis result shown on the left of fig. 6, and the results of five different resolutions and the same category are gathered together, which shows that the method of the invention is insensitive to the spatial resolution and the triangulation. Fig. 6 shows the result of shape matching on the right, and in the two-dimensional graph of geodesic radius and accuracy, OUR-LPS Ori-8000, OUR-LPS Ori-10000, OUR-LPS Ori-12000, or OUR-LPS Ori-15000 are the result of LPS feature matching of the original vertex, the result of LPS feature matching of the original vertex with the 8000 resolution vertex, the result of LPS feature matching of the original vertex with the 10000 resolution vertex, the result of LPS feature matching of the original vertex with the 12000 resolution vertex, and the result of LPS feature matching of the original vertex with the 15000 resolution vertex, respectively.
To illustrate the discriminability and resolution and triangularization robustness of the learned descriptors, the performance of the descriptors learned only at the original 6890 resolution tested at low and high resolutions is demonstrated by the matching times and hit rate two-dimensional graph, geodesic radius and correct correspondence two-dimensional graph, respectively, as shown in fig. 7. In the figure, "our" represents the matching of shapes between original shapes, "our Ori-8K" represents the matching result between an original shape and a high-resolution 8K shape, and so on. The present embodiment applies to two extreme tests, namely the matching of the 10K model and the 100K model and the matching between the 5K CVT model and the 10K model. For the CVT model, the present embodiment selects the closest geodesic distance as the true matching corresponding point. In addition, comparison was made with the latest geometry method LDGI. The performance of the original FAUST resolution test is shown in FIG. 7 to be higher than that of the LDGI method, and furthermore, the performance of the present invention is not degraded much for low resolution and other high resolution tests, thus demonstrating the robustness of the learned descriptors. The geometry method LDGI can be referred to as: hanyu Wang, Jianwei Guo, Dong-Ming Yan, Weize Quan, and Xiaoope Zhang. learning 3d keypoint descriptors for non-rectangular shape matching. in European Conference on Computer Vision (ECCV), pages 3-20.Springer, 2018.
Further comparisons were made with a number of most advanced methods, including three deep learning descriptors (OSD, CGF32 and LDGI), and four manual descriptors (SI, SHOT, RoPS and HKS). Fig. 8 and 9 show the matching results between the original 6890 model and the 8K and 12K models, respectively. All trainable methods are trained on the original data set and applied to high resolution models. Experimental results show that many methods cannot handle the conditions on different resolutions, and on the contrary, the method disclosed by the invention has good performance.
In order to illustrate the discriminability and the scale and rotation robustness of the learned descriptor, the test can be directly carried out under different models of rotation, translation and different scales. Fig. 10 and 11 show that the present invention exhibits performance in terms of Rotation (Rotation) and Scale (Scale), respectively, that exceeds the best current approach.
Shape correspondence and matching are two different tasks, and many methods (such as GCNN, mont, etc.) convert the correspondence problem into a learning label problem. Furthermore, the OURS-CORR configuration represents that the present invention converts learned triplet losses to cross-entropy losses for comparison with the remaining methods to learn the tag problem. Figure 12 shows the results of a comparison of the shape correspondences performed on the FAUST dataset showing that both configurations are comparable to the performance of the current state-of-the-art method.
As shown in fig. 13, a local frequency domain descriptor generating apparatus 100 for non-rigid shape matching according to a second embodiment of the present invention includes a local point feature generating module 101, a local frequency domain descriptor obtaining module 102;
the local point feature generation module 101 is configured to obtain, based on a laplacian-belt-larm operator, a local point feature of each vertex in the three-dimensional shape surface triangular mesh model in a frequency domain;
the local frequency domain descriptor obtaining module 102 is configured to obtain a vertex frequency domain image corresponding to each vertex of the three-dimensional shape based on the local feature point, and obtain a local frequency domain descriptor for non-rigid shape matching through a ternary neural network.
It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working process and related descriptions of the above-described apparatus may refer to the corresponding process in the foregoing method embodiments, and are not described herein again.
It should be noted that, the apparatus for generating a local frequency domain descriptor for non-rigid shape matching provided in the foregoing embodiment is only illustrated by the division of the foregoing functional modules, and in practical applications, the above functions may be allocated to different functional modules according to needs, that is, the modules or steps in the embodiment of the present invention are further decomposed or combined, for example, the modules in the foregoing embodiment may be combined into one module, or may be further split into multiple sub-modules, so as to complete all or part of the functions described above. The names of the modules and steps involved in the embodiments of the present invention are only for distinguishing the modules or steps, and are not to be construed as unduly limiting the present invention.
A storage apparatus of a third embodiment of the present invention stores a plurality of programs adapted to be loaded and executed by a processor to implement the above-described local frequency domain descriptor generation method for non-rigid shape matching.
A processing apparatus according to a fourth embodiment of the present invention includes a processor, a storage device; a processor adapted to execute various programs; a storage device adapted to store a plurality of programs; the program is adapted to be loaded and executed by a processor to implement the above-described method for local frequency domain descriptor generation for non-rigid shape matching.
It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working processes and related descriptions of the storage device and the processing device described above may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
Those of skill in the art would appreciate that the various illustrative modules, method steps, and modules described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that programs corresponding to the software modules, method steps may be located in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. To clearly illustrate this interchangeability of electronic hardware and software, various illustrative components and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as electronic hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The terms "first," "second," and the like are used for distinguishing between similar elements and not necessarily for describing or implying a particular order or sequence.
The terms "comprises," "comprising," or any other similar term are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present invention is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can fall into the protection scope of the invention.
Claims (14)
1. A method for generating a local frequency domain descriptor for non-rigid shape matching, the method comprising the steps of:
step S10, calculating a Laplace-Belladrami matrix L of the surface triangular mesh model based on the surface continuous function f of the three-dimensional shape surface triangular mesh model;
performing characteristic decomposition on the matrix L to obtain a characteristic vector and a characteristic value;
extending the surface continuous function f to a discrete function
And the matrix is expanded under the characteristic vector of the matrix L to obtain a frequency domain expansion coefficient sigmaj；
According to the characteristic decomposition and frequency domain expansion coefficient sigma of the matrix LjCalculating the energy of discrete Dirichlet
Extending a high-dimensional continuous function F based on a surface continuous function F to a high-dimensional discrete function
Calculating discrete Dirichlet energy
And supply the energy
Spreading in a frequency domain to obtain general frequency domain characteristics;
discrete function of high dimension
Setting the three-dimensional coordinate information X of a local patch, and solving discrete energy according to continuous energy E (X)
Taking the discrete energy
Obtaining local point characteristics by using a front Q dimension expanded in a frequency domain; wherein Q is a first set value;
and step S20, acquiring a vertex frequency domain image corresponding to each vertex of the three-dimensional shape based on the local point characteristics, and obtaining a local frequency domain descriptor for non-rigid shape matching through a ternary neural network.
2. The method of generating local frequency-domain descriptors for non-rigid shape matching according to claim 1, wherein the laplacian-belite matrix L "of the surface triangular mesh model is calculated based on the surface continuous function f of the three-dimensional shape surface triangular mesh model by:
obtaining discrete functions of a continuous function f of a surface
Calculating an element L in a Laplace-Belladrami matrix L of the surface triangular mesh model by the following formulaij：
Wherein the content of the first and second substances,αijand betaijFor two angles, alpha, opposite to the edges { i, j } in the surface triangular mesh modeliIs a vertex viK is the number of adjacent vertices.
3. The method according to claim 2, wherein the method for generating the local frequency domain descriptor for non-rigid shape matching comprises the steps of performing eigen decomposition on the matrix L to obtain eigenvectors and eigenvalues:
the matrix L is decomposed into two symmetric matrices T and a,
TΦi＝λiAΦi,i＝0,1,...,N-1；
wherein A isii＝ai
Solving by adopting an ARPACK method to obtain a characteristic vector phiiAnd a characteristic value lambdaiAnd N is the number of the surface triangular mesh model vertexes.
4. The method of claim 3, wherein the surface continuous function f is extended to a discrete function
And the matrix is expanded under the characteristic vector of the matrix L to obtain a frequency domain expansion coefficient sigmaj", the method is as follows:
wherein phijIs the jth feature vector.
5. The method of claim 4 for non-rigid shape matchingThe method for generating a local frequency domain descriptor according to (1), wherein the "frequency domain expansion coefficient σ is decomposed according to the characteristics of the matrix LjCalculating the energy of discrete Dirichlet
", the method is as follows:
wherein the content of the first and second substances,
is a discrete energy form corresponding to Dirichlet energy of a continuous real function f, N is the number of vertexes, and lambdajIs the jth eigenvalue.
6. The method of claim 5, wherein "extending a high-dimensional continuous function F based on a surface continuous function F to a high-dimensional discrete function
Calculating discrete Dirichlet energy
And supply the energy
The method comprises the following steps of developing in a frequency domain to obtain general frequency domain characteristics:
wherein sf is a general frequency domain characteristic, lambdaN-1Is the Nth characteristic value, σiN-1For the Nth frequency domain expansion coefficient under the ith dimension。
7. The method of claim 6, wherein 'high-dimensional discrete function' is generated
Setting the three-dimensional coordinate information X of a local patch, and solving discrete energy according to continuous energy E (X)
Taking the discrete energy
The local point feature is obtained from the front Q dimension expanded in the frequency domain, and the method comprises the following steps:
wherein, LPS is the obtained local point characteristics.
8. The method according to claim 1, wherein the method for generating the local frequency domain descriptor for non-rigid shape matching is characterized in that, based on the local point features, a vertex frequency domain image corresponding to each vertex of the three-dimensional shape is obtained, and the local frequency domain descriptor for non-rigid shape matching is obtained through a ternary neural network, and the method comprises:
encoding the local point features into Q first sized images;
generating a corresponding vertex frequency domain image for each vertex on the three-dimensional shape surface triangular mesh model to obtain a vertex frequency domain image set;
and obtaining a local frequency domain descriptor for non-rigid shape matching through a preset ternary neural network based on the vertex frequency domain image set.
9. The method of claim 8, wherein the local point features are encoded as Q first sized images by:
taking Q as 16 and setting the first set size as 8 x 8;
local point features are encoded into 16 geometric images of 8 x 8 size using a geometric image method.
10. The method of claim 9, wherein the method of generating the local frequency domain descriptor for non-rigid shape matching comprises, for each vertex on the triangular mesh model of the three-dimensional surface, generating a corresponding vertex frequency domain image:
initializing a 32 x 32 empty image, filling 16 feature coding images of 8 x 8 local point features into the initialized empty image, and respectively placing a minimum feature value and a maximum feature value at the upper left corner and the lower right corner to generate a 32 x 32 vertex frequency domain image.
11. The method for generating local frequency domain descriptors for non-rigid shape matching according to any one of claims 1-10, wherein the ternary neural network is composed of three identical ConvNet convolutional networks, and the training samples thereof include three-dimensional shapes and corresponding descriptors; when the ternary neural network is trained, the three-dimensional shape in the training sample is input into the ternary neural network by acquiring the corresponding vertex frequency domain image set by the method in the steps S10 and S20.
12. A local frequency domain descriptor generation device aiming at non-rigid shape matching is characterized by comprising a local point feature generation module and a local frequency domain descriptor acquisition module;
the local point feature generation module is configured to obtain local point features of each vertex in the three-dimensional shape surface triangular mesh model in a frequency domain based on a Laplace-Belltzian operator;
the local frequency domain descriptor acquisition module is configured to acquire a vertex frequency domain image corresponding to each vertex of the three-dimensional shape based on the local point characteristics, and obtain a local frequency domain descriptor for non-rigid shape matching through a ternary neural network;
based on the Laplace-Bell-Delaum operator, for each vertex in the surface triangular mesh model, extracting the local point characteristics of the three-dimensional shape in a frequency domain, wherein the method comprises the following steps:
calculating a Laplace-Belladrami matrix L of the surface triangular mesh model based on a surface continuous function f of the three-dimensional shape surface triangular mesh model;
performing characteristic decomposition on the matrix L to obtain a characteristic vector and a characteristic value;
extending the surface continuous function f to a discrete function
And the matrix is expanded under the characteristic vector of the matrix L to obtain a frequency domain expansion coefficient sigmaj；
According to the characteristic decomposition and frequency domain expansion coefficient sigma of the matrix LjCalculating the energy of discrete Dirichlet
Extending a high-dimensional continuous function F based on a surface continuous function F to a high-dimensional discrete function
Calculating discrete Dirichlet energy
And supply the energy
Spreading in a frequency domain to obtain general frequency domain characteristics;
discrete function of high dimension
Setting the three-dimensional coordinate information X of a local patch, and solving discrete energy according to continuous energy E (X)
Taking the discrete energy
Obtaining local point characteristics by using a front Q dimension expanded in a frequency domain; wherein Q is a first set value.
13. A storage device having stored thereon a plurality of programs, wherein the programs are adapted to be loaded and executed by a processor to implement the method for local frequency domain descriptor generation for non-rigid shape matching according to any of claims 1-11.
14. A processing device comprising a processor, a storage device; a processor adapted to execute various programs; a storage device adapted to store a plurality of programs; characterized in that the program is adapted to be loaded and executed by a processor to implement the method for local frequency domain descriptor generation for non-rigid shape matching of any of claims 1-11.
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