CN115239877B - Three-dimensional model matching method of spectrum shape descriptor based on invariant moment - Google Patents

Three-dimensional model matching method of spectrum shape descriptor based on invariant moment Download PDF

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CN115239877B
CN115239877B CN202210793839.XA CN202210793839A CN115239877B CN 115239877 B CN115239877 B CN 115239877B CN 202210793839 A CN202210793839 A CN 202210793839A CN 115239877 B CN115239877 B CN 115239877B
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张丹
武仲科
王醒策
刘娜
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Qinghai Normal University
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Abstract

The invention belongs to the technical field of computer graphics, and particularly relates to a three-dimensional model matching method of a spectrum shape descriptor based on invariant moment, which comprises the following steps: collecting a three-dimensional model; acquiring a ring neighborhood vertex corresponding to each vertex in the three-dimensional model; calculating an LBO operator of the three-dimensional model according to a ring neighborhood vertex of the three-dimensional model; calculating the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model by using the LBO operator of the three-dimensional model; obtaining six geometric moment descriptors of the three-dimensional model according to the characteristic values and the characteristic vectors of the LBO operator of the three-dimensional model; and obtaining the matching degree of the three-dimensional model and other three-dimensional models by using the six geometric moment descriptors of the three-dimensional model. The technical scheme provided by the application not only realizes that the topology and geometric characteristics of various shapes can be well described and represented without depending on the selection of parameters, has universality, but also enhances the recognition capability of a spectrum shape descriptor and reduces the time complexity of shape matching.

Description

Three-dimensional model matching method of spectrum shape descriptor based on invariant moment
Technical neighborhood
The invention belongs to the technical field of computer graphics, and particularly relates to a three-dimensional model matching method of a spectrum shape descriptor based on invariant moment.
Background
Three-dimensional shape matching, which is a research basis for the work of shape recognition, shape retrieval, shape classification, shape segmentation and the like, is widely focused by researchers as a hot research problem of computer vision, pattern recognition, computer graphics and other neighbors. Meanwhile, the non-rigid shape matching also provides a solid theoretical basis for the application fields of shape interpolation, statistical modeling, three-dimensional reconstruction, biological calculation and the like. The three-dimensional shape matching research is a three-dimensional shape similarity measurement problem, which comprises the following specific steps: first, researchers extract a series of meaningful features on a three-dimensional shape for describing the geometric features and topology of the three-dimensional shape; then selecting local features, global features or a combination of the local features and the global features of the three-dimensional shape to replace the three-dimensional shape to be corresponding; and finally, selecting a certain metric function to calculate the similarity of the three-dimensional shape, and carrying out three-dimensional shape analysis based on the similarity result. This can be summarized in two key steps: (1) extracting shape descriptors that are valid in shape; (2) selecting an appropriate similarity measure.
In existing three-dimensional shape analysis tasks based on spectrum shape descriptors, three-dimensional shape matching calculation is generally performed by using empirical values of a single time parameter (e.g., thermonuclear signature, scale invariant thermonuclear signature) and energy parameter (e.g., wave nuclear signature, scale invariant wave nuclear signature) as single parameter point signature descriptors, or selecting a sequence of several time parameters or energy parameters as a sequence of multi-parameter point signature descriptors. However, the two methods have the defects: the first method only can describe the local attribute or the global attribute of the shape independently, and the experience value is only suitable for a certain type of shape or a certain specific shape analysis task, and has no universality; the second parameter selection method expands the single point signature into a point signature vector by introducing a parameter sequence, and compared with the first method, the method expands the description capability of the shape features, but the time complexity of the method is higher, especially when the parameter sequence is too long, so that the time complexity of performing shape matching is exponentially increased.
Disclosure of Invention
In view of the above, the present invention aims to overcome the shortcomings of the prior art, and provide a three-dimensional model matching method based on invariant moment spectrum shape descriptors, so as to solve the problem that the prior art has no universality and the time complexity is high, so that the time complexity for performing shape matching is exponentially increased.
According to a first aspect of embodiments of the present application, there is provided a three-dimensional model matching method based on invariant moment spectrum shape descriptors, the method comprising:
collecting a three-dimensional model;
acquiring a ring neighborhood vertex corresponding to each vertex in the three-dimensional model;
calculating an LBO operator of the three-dimensional model according to a ring neighborhood vertex of the three-dimensional model;
calculating the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model by utilizing the LBO operator of the three-dimensional model;
obtaining six geometric moment descriptors of the three-dimensional model according to the characteristic values and the characteristic vectors of the LBO operator of the three-dimensional model;
and obtaining the matching degree of the three-dimensional model and other three-dimensional models by using the six geometric moment descriptors of the three-dimensional model.
Preferably, the three-dimensional model includes: and each vertex is provided with a serial number corresponding to the vertex.
Preferably, the obtaining a ring neighborhood vertex corresponding to each vertex in the three-dimensional model includes:
in the three-dimensional model, the vertex directly connected with the vertex in the three-dimensional model is a ring neighborhood vertex corresponding to the vertex in the three-dimensional model;
and carrying out ascending sort on the annular neighborhood vertexes corresponding to the vertexes in the three-dimensional model based on the serial numbers corresponding to the annular neighborhood vertexes corresponding to the vertexes in the three-dimensional model.
Preferably, the calculating the LBO operator of the three-dimensional model according to a ring neighborhood vertex of the three-dimensional model includes:
calculating a discrete LBO operator corresponding to an ith vertex in the three-dimensional model according to the following formula:
Figure BDA0003734836560000031
in the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; v i For the ith vertex in the three-dimensional model, f (v i ) For the value of the real value function corresponding to the ith vertex in the three-dimensional model, N j For the jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model, f (N) j ) The value of a real value function corresponding to the jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model; connecting the ith vertex v in the three-dimensional model i A jth one-ring neighborhood vertex N corresponding to the ith vertex in the three-dimensional model j The line segment of (2) is p ij Alpha is then j And beta j Respectively are the sides p ij Opposite angles of two sides;
and discrete LBO operators corresponding to all vertexes in the three-dimensional model form the LBO operator of the three-dimensional model.
Preferably, the obtaining, according to the LBO operator of the three-dimensional model, a feature value and a feature vector of the LBO operator of the three-dimensional model includes:
performing spectrum decomposition on the LBO operator of the three-dimensional model to obtain a characteristic value and a characteristic vector of the LBO operator of the three-dimensional model;
wherein, the eigenvalue and eigenvector of LBO operator of the three-dimensional model are determined according to the following formula:
Figure BDA0003734836560000032
in the above, k is [1, K ]]K is the total number of feature values; ΔM is LBO operator of the three-dimensional model, λ k For the kth eigenvalue of the LBO operator of the three-dimensional model,
Figure BDA0003734836560000033
and the feature vector corresponding to the kth feature value of the LBO operator of the three-dimensional model.
Preferably, the obtaining six geometric moment descriptors of the three-dimensional model according to the eigenvalues and eigenvectors of the LBO operator of the three-dimensional model includes:
step a: calculating a spectrum shape descriptor of each vertex in the three-dimensional model according to the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, and calculating a spectrum shape descriptor of a corresponding ring neighborhood vertex of each vertex in the three-dimensional model;
step b: calculating a first-order time moment mu according to the spectrum shape descriptor of the vertexes in the three-dimensional model and the spectrum shape descriptor of the corresponding ring neighborhood vertexes of each vertex in the three-dimensional model 01 Second order moment mu 02 Third order moment mu 03 First order spatial moment mu 11 Third-order spatial moment mu 12 And third-order spatial moment mu 21 ；
Step c: six geometric moment descriptors gmsps of the three-dimensional model are determined as follows:
GMSDs＝{μ 01 ,μ 02 ,μ 03 ,μ 11 ,μ 12 ,μ 21 }。
preferably, the step a includes:
determining a spectral shape description Fu of an ith vertex in the three-dimensional model as follows i ：
Figure BDA0003734836560000041
Determining a spectral shape description Fu of a jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model by j ：
Figure BDA0003734836560000042
In the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; k is E [1, K]K is the total number of feature values; lambda (lambda) k For the kth eigenvalue of the LBO operator of the three-dimensional model,
Figure BDA0003734836560000043
is the eigenvector corresponding to the kth eigenvalue of the LBO operator of the three-dimensional model, phi (lambda k ) Is a filtering function;
wherein when the spectral shape descriptor is a thermonuclear signature spectral shape descriptor, a filter function
Figure BDA0003734836560000044
t is a time parameter;
when the spectral shape descriptor is a wave kernel signature spectral shape descriptor, a filter function
Figure BDA0003734836560000045
i is an imaginary number i.
Preferably, the step b includes:
the first order moment mu is determined as follows 01 ：
Figure BDA0003734836560000051
Determining the second order moment mu as follows 02 ：
Figure BDA0003734836560000052
Determining the third order moment mu as follows 03 ：
Figure BDA0003734836560000053
The first order spatial moment mu is determined as follows 11 ：
Figure BDA0003734836560000054
Determining the third-order spatial moment mu as follows 12 ：
Figure BDA0003734836560000055
Determining the third-order spatial moment mu as follows 21 ：
Figure BDA0003734836560000056
In the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; phi i For the spectral shape of the ith vertex in the three-dimensional modelA descriptor; phi j And (3) a spectrum shape descriptor of the jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model.
Preferably, the obtaining the matching degree between the three-dimensional model and other three-dimensional models by using the six geometric moment descriptors of the three-dimensional model includes:
the set formed by all the vertexes in the three-dimensional model is set A, and the set formed by all the vertexes in the other three-dimensional models is set B;
determining the matching degree MHD (A, B) of the three-dimensional model and other three-dimensional models according to the following steps:
MHD(A,B)＝max[d(A,B),d(B,A)]
in the above formula, d (A, B) is each vertex v in set A a And each vertex v in set B b Is the average of the distance minima; d (B, A) is each vertex v in set B b With each vertex v in set A a Is the average of the distance minima;
wherein d (A, B) is determined as follows:
Figure BDA0003734836560000061
d (B, A) is determined as follows:
Figure BDA0003734836560000062
in the above formula, a is ∈ [1, N ] A ]，N A Is the total number of vertices in set A; b E [1, N B ]，N B Is the total number of vertices in set B; v a -v b I is the vertex v in set A a To vertex v in set B b Euclidean distance of v b -v a I is the vertex v in set B b To vertex v in set A a Is a euclidean distance of (c).
By adopting the technical scheme, the invention has the following beneficial effects: acquiring a three-dimensional model, acquiring a ring neighborhood vertex corresponding to each vertex in the three-dimensional model, calculating an LBO operator of the three-dimensional model according to the ring neighborhood vertex of the three-dimensional model, calculating a characteristic value and a characteristic vector of the LBO operator of the three-dimensional model by utilizing the LBO operator of the three-dimensional model, acquiring six geometric moment descriptors of the three-dimensional model according to the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, and acquiring the matching degree of the three-dimensional model and other three-dimensional models by utilizing the six geometric moment descriptors of the three-dimensional model, thereby not only realizing the selection of not depending parameters, but also well describing and representing the topology and geometric characteristics of various shapes, having universality, enhancing the recognition capability of a spectrum shape descriptor and reducing the time complexity of shape matching.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart illustrating a method of three-dimensional model matching based on invariant moment spectrum shape descriptors, in accordance with an exemplary embodiment;
FIG. 2 is a schematic diagram of a three-dimensional model shown in accordance with an exemplary embodiment;
FIG. 3 is a schematic diagram of a three-dimensional model shown in accordance with an exemplary embodiment;
FIG. 4 is a block diagram illustrating a three-dimensional model matching apparatus based on invariant moment spectrum shape descriptors, according to an example embodiment;
in the figure, the 1-acquisition module, the 2-first acquisition module, the 3-first calculation module, the 4-second calculation module, the 5-second acquisition module, the 6-third acquisition module, the 51-first calculation unit, the 52-second calculation unit and the 53-determination unit.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be described in detail below. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by one of ordinary skill in the art without undue burden on the person of ordinary skill in the art based on the examples herein, are within the scope of the invention.
Example 1
FIG. 1 is a flow chart illustrating a method of three-dimensional model matching of invariant moment based spectral shape descriptors, as shown in FIG. 1, which may be used in a terminal, but is not limited to, including the steps of:
step 101: collecting a three-dimensional model;
step 102: acquiring a ring neighborhood vertex corresponding to each vertex in the three-dimensional model;
step 103: calculating an LBO operator of the three-dimensional model according to a ring neighborhood vertex of the three-dimensional model;
step 104: calculating the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model by using the LBO operator of the three-dimensional model;
step 105: according to the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, six geometric moment descriptors of the three-dimensional model are obtained;
step 106: and obtaining the matching degree of the three-dimensional model and other three-dimensional models by using the six geometric moment descriptors of the three-dimensional model.
Specifically, the three-dimensional model includes: and each vertex has a serial number corresponding to the vertex.
It should be noted that, the three-dimensional model acquired in the present application is a three-dimensional model after triangulation. As shown in fig. 2, after triangulation, the three-dimensional model is composed of triangular patches, and the vertex on each triangular patch is the vertex of the three-dimensional model. Each vertex has a unique sequence number corresponding to it, e.g., a three-dimensional model includes 100 vertices, and the sequence numbers of the 100 vertices are 1-100.
According to the three-dimensional model matching method based on the invariant moment spectrum shape descriptor, a ring neighborhood vertex corresponding to each vertex in the three-dimensional model is obtained through collecting the three-dimensional model, the LBO operator of the three-dimensional model is calculated according to the ring neighborhood vertex of the three-dimensional model, the LBO operator of the three-dimensional model is utilized to calculate the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, six geometric moment descriptors of the three-dimensional model are obtained according to the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, and the matching degree of the three-dimensional model and other three-dimensional models is obtained by utilizing the six geometric moment descriptors of the three-dimensional model, so that not only can the choice of parameters be omitted, but also the topology and geometric characteristics of various shapes can be well described and represented, the universality is improved, the recognition capability of the spectrum shape descriptor is improved, and the time complexity of shape matching is reduced.
Further, step 102 includes:
step 1021: in the three-dimensional model, the vertex directly connected with the vertex in the three-dimensional model is a ring neighborhood vertex corresponding to the vertex in the three-dimensional model;
for example, as shown in FIG. 3, v i Is the ith vertex in the three-dimensional model, N j A jth ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model;
step 1022: and performing ascending sort on the adjacent vertices corresponding to the vertices in the three-dimensional model based on the serial numbers corresponding to the adjacent vertices.
It can be understood that by ascending order of the vertices of a ring neighborhood, confusion during subsequent calculation of the LBO operator of the three-dimensional model by using the vertices of the ring neighborhood can be avoided, so that reliability and accuracy of the LBO operator of the three-dimensional model are improved.
Further, step 103 includes:
calculating a discrete LBO operator corresponding to an ith vertex in the three-dimensional model according to the following steps:
Figure BDA0003734836560000091
in the above, i is E [1 ],n]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; v i Is the ith vertex in the three-dimensional model, f (v i ) Is the value of a real value function corresponding to the ith vertex in the three-dimensional model, N j Is the jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model, f (N) j ) The value of a real value function corresponding to the vertex of the jth one-ring neighborhood corresponding to the ith vertex in the three-dimensional model; let the ith vertex v in the connected three-dimensional model i Jth one-ring neighborhood vertex N corresponding to ith vertex in three-dimensional model j The line segment of (2) is p ij Alpha is then j And beta j Respectively are the sides p ij Opposite angles of two sides;
and discrete LBO operators corresponding to all vertexes in the three-dimensional model form the LBO operator of the three-dimensional model.
For example, as shown in FIG. 3, the ith vertex v in the three-dimensional model is connected i Jth one-ring neighborhood vertex N corresponding to ith vertex in three-dimensional model j The line segment of (2) is p ij ，α j And beta j Respectively are the sides p ij Opposite angles of both sides.
It should be noted that, since the LBO operator is a semi-positive operator, the LBO operator may analytically calculate some geometric shapes (e.g., rectangular, cylindrical, circular, spherical, etc.). If some shapes, such as animals and plants, change their body pose, e.g. there is only a slight stretch at their joints, this situation is called approximately equidistant change, and the LBO operator is likewise unchanged for approximately equidistant changes. Therefore, the LBO operator has wide applicability, thereby laying a foundation for obtaining the universality of six geometric moment descriptors of the three-dimensional model.
Further, step 104 includes:
performing spectrum decomposition on an LBO operator of the three-dimensional model to obtain a characteristic value and a characteristic vector of the LBO operator of the three-dimensional model;
wherein, the eigenvalue and eigenvector of LBO operator of three-dimensional model are determined according to the following formula:
Figure BDA0003734836560000101
in the above, k is [1, K ]]K is the total number of feature values; ΔM is LBO operator of three-dimensional model, λ k Is the kth eigenvalue of the LBO operator of the three-dimensional model,
Figure BDA0003734836560000102
is the eigenvector corresponding to the kth eigenvalue of the LBO operator of the three-dimensional model.
It should be noted that, the "spectrum decomposition" manner referred to in the embodiments of the present invention is well known to those skilled in the art, and thus, the specific implementation manner thereof is not described too much.
It can be understood that the efficiency of calculating six geometric moment descriptors of the three-dimensional model subsequently is improved by performing spectral decomposition on the LBO operator of the three-dimensional model to obtain the eigenvalues and eigenvectors.
Further, step 105 includes:
step 1051: calculating a spectrum shape descriptor of each vertex in the three-dimensional model according to the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, and calculating a spectrum shape descriptor of a corresponding ring neighborhood vertex of each vertex in the three-dimensional model;
specifically, step 1052 includes:
determining a spectral shape description Fu of an ith vertex in a three-dimensional model as follows i ：
Figure BDA0003734836560000103
Determining a spectral shape description Fu of a jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model as follows j ：
Figure BDA0003734836560000104
In the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; k is E [1, K]K is the total number of feature values; lambda (lambda) k Is the kth eigenvalue of the LBO operator of the three-dimensional model,
Figure BDA0003734836560000105
is the eigenvector corresponding to the kth eigenvalue of the LBO operator of the three-dimensional model, φ (λ k ) Is a filtering function;
wherein, when the spectrum shape descriptor is a thermonuclear signature spectrum shape descriptor, the filter function
Figure BDA0003734836560000106
t is a time parameter;
when the spectral shape descriptor is a wave kernel signature spectral shape descriptor, the filter function
Figure BDA0003734836560000111
i is an imaginary number i;
step 1052: calculating a first-order time moment mu according to the spectrum shape descriptor of the vertexes in the three-dimensional model and the spectrum shape descriptor of the corresponding ring neighborhood vertexes of each vertex in the three-dimensional model 01 Second order moment mu 02 Third order moment mu 03 First order spatial moment mu 11 Third-order spatial moment mu 12 And third-order spatial moment mu 21 ；
Specifically, step 1052 includes:
the first order moment mu is determined as follows 01 ：
Figure BDA0003734836560000112
Determining the second order moment mu as follows 02 ：
Figure BDA0003734836560000113
Determining the third order moment mu as follows 03 ：
Figure BDA0003734836560000114
/>
The first order spatial moment mu is determined as follows 11 ：
Figure BDA0003734836560000115
Determining the third-order spatial moment mu as follows 12 ：
Figure BDA0003734836560000116
Determining the third-order spatial moment mu as follows 21 ：
Figure BDA0003734836560000117
In the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; phi i A spectral shape descriptor for an ith vertex in the three-dimensional model; phi j A spectrum shape descriptor of a jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model;
step 1053: six geometric moment descriptors gmsps of the three-dimensional model are determined as follows:
GMSDs＝{μ 01 ,μ 02 ,μ 03 ,μ 11 ,μ 12 ,μ 21 }。
the moment has different names in different application scenarios, and is called geometric invariant moment, or simply geometric moment when used for describing geometric features of an image or a shape. Shape descriptors based on geometric moments are independent of the choice of parameters, can capture significant features of images or shapes, and can represent objects as an important feature. By utilizing geometric moment descriptors, not only are the topology and geometric features of the shape well described and represented; meanwhile, parameter selection is independent of a specific shape analysis task, so that the method has universality; in other words, the performance of the descriptor is independent of the choice of parameters. A new shape descriptor, called geometric moment spectrum descriptor (Geometric moment spectral descriptors, gmds), is defined by computing the geometric moment of the spectrum shape descriptor in the time domain, while taking into account the conditional moment under the combined action of the spatial and time domains. The GMDs not only inherits the excellent characteristics of the spectrum shape descriptor and overcomes the defect that the spectrum shape descriptor is sensitive to parameter selection, but also has the statistical characteristics of geometric moment theory, and is very suitable for three-dimensional shape analysis.
Further, step 106 includes:
the set formed by all the vertexes in the three-dimensional model is set A, and the set formed by all the vertexes in other three-dimensional models is set B;
the degree of matching MHD (a, B) of the three-dimensional model with other three-dimensional models is determined as follows:
MHD(A,B)＝max[d(A,B),d(B,A)]
in the above formula, d (A, B) is each vertex v in set A a And each vertex v in set B b Is the average of the distance minima; d (B, A) is each vertex v in set B b With each vertex v in set A a Is the average of the distance minima;
wherein d (A, B) is determined as follows:
Figure BDA0003734836560000131
d (B, A) is determined as follows:
Figure BDA0003734836560000132
in the above formula, a is ∈ [1, N ] A ]，N A Is the total number of vertices in set A; b E [1, N B ]，N B Is the total number of vertices in set B; v a -v b I is the vertex v in set A a To top in set BPoint v b Euclidean distance of v b -v a I is the vertex v in set B b To vertex v in set A a Is a euclidean distance of (c).
It should be noted that, the matching degree between the three-dimensional model and other three-dimensional models provided by the embodiment of the invention is calculated by adopting a calculation method for correcting the Hausdorff distance. The similarity of the three-dimensional model is defined by a modified Hausdorff distance between gmscs based on a pair of three-dimensional models, with sufficient robustness and stability.
In order to further illustrate the technical effects of the three-dimensional model matching method based on invariant moment spectrum shape descriptors provided by the embodiment of the invention, experiments are performed by using a TOSCA high-resolution database and an SHREC2010query database, and a large number of three-dimensional shapes are provided for non-rigid three-dimensional shape analysis. The invention compares the robustness and the high efficiency of different GMSPDs descriptors through several experiments. The SHREC2010query database is selected, and the equidistant invariance, the topological robustness, the scaling invariance, the hole-adding robustness and the noise robustness of the GMSDs are compared. The present invention has been discussed separately for HKS and WKS, in which the geometric moment spectrum descriptor for HKS is denoted gmsps (HKS), and 6 geometric moments are denoted: mu 01 (HKS), mu 02 (HKS), mu 03 (HKS), mu 11 (HKS), mu 12 (HKS), mu 21 (HKS); the geometric moment spectrum descriptor for WKS is denoted gmsps (WKS), and 6 geometric moments are denoted: mu 01 (WKS), mu 02 (WKS), mu 03 (WKS), mu 11 (WKS), mu 12 (WKS), mu 21 (WKS).
Tables 1 to 5 show the invariance and robustness values of gmscs (HKS) between the original and deformed shapes of gmscs (HKS), including equidistant, topological, cavitated, noisy and resampled, respectively. Tables 6 to 9 show the invariance and robustness values of gmscs (WKS) between the original shape and the deformable shape of gmscs (WKS), including equidistant, topological, cavitated, noisy, and resampled. Among the above results, the same results were found for GMSTDs (HKS) and GMSTDs (WKS): under different transformations, 6 geometric moments have better robustness, the error value of mu 03 is the smallest, and the robustness of mu 03 is better than that of other five geometric moments, because mu 03 describes the asymmetry degree of different spectrum shape descriptors under a parameter sequence, and the multi-scale characteristics of HKS and WKS are linearly transformed, so that the deviation degree of the spectrum shape descriptors relative to the expected spectrum shape descriptors is lower; whereas μ12 has a larger error, indicating that μ12 is less robust than the other five geometric moments, because μ12 is a conditional moment describing the conditional expectation of a ring of neighborhood vertices of any vertex on the surface, where the condition is represented by the variance of the spectral shape descriptor of the neighborhood vertex, describing the degree of dispersion of the spectral shape descriptor from the expected under different parameters, which value varies relatively much. Overall, the robustness error values of gmds (WKS) after different transformations are smaller than gmds (HKS).
TABLE 1 equidistant invariance of GMSDs (HKS) for different classes of shapes based on SHREC2010query database
Figure BDA0003734836560000141
TABLE 2 GMSPS (HKS) topology robustness of different classes of shapes based on SHREC2010query database
Figure BDA0003734836560000142
TABLE 3 GMSPS (HKS) hole robustness for different classes of shapes based on SHREC2010query database
Figure BDA0003734836560000151
Table 4 gmds (HKS) resampling robustness for different classes of shapes based on the SHREC2010query database
Figure BDA0003734836560000152
TABLE 5 GMSPS (HKS) noise robustness for different class shapes based on SHREC2010query database
Figure BDA0003734836560000153
TABLE 6 GMSDs (WKS) equidistant invariance of different class shapes based on SHREC2010query database
Figure BDA0003734836560000161
TABLE 7 GMSPS (WKS) topology robustness of different class shapes based on SHREC2010query database
Figure BDA0003734836560000162
TABLE 8 GMDs (WKS) hole robustness for different classes of shapes based on SHREC2010query database
Figure BDA0003734836560000163
TABLE 9 GMSDs (WKS) noise robustness for different class shapes based on SHREC2010query database
Figure BDA0003734836560000171
According to the three-dimensional model matching method of the spectrum shape descriptor based on invariant moment, based on geometric invariant moment and conditional moment theory, six geometric moments of HKS and WKS are respectively obtained, geometric moment spectrum descriptors GMSDs are defined, the GMSDs not only inherit good characteristics of the spectrum shape descriptor, the defect that the spectrum shape descriptor is sensitive to parameter selection is overcome, but also statistical characteristics of the invariant moment theory are provided, and the method is very suitable for three-dimensional shape analysis. In addition, the method provided by the embodiment of the invention achieves the most advanced performance on the shape analysis standard of the SHREC2010query and the TOSCA. Meanwhile, the method provided by the embodiment of the invention has universality and can be also expanded into shape descriptors of other multi-parameter sequences, including SIHKS and the like.
According to the three-dimensional model matching method based on the invariant moment spectrum shape descriptor, a ring neighborhood vertex corresponding to each vertex in the three-dimensional model is obtained through collecting the three-dimensional model, the LBO operator of the three-dimensional model is calculated according to the ring neighborhood vertex of the three-dimensional model, the LBO operator of the three-dimensional model is utilized to calculate the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, six geometric moment descriptors of the three-dimensional model are obtained according to the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, and the matching degree of the three-dimensional model and other three-dimensional models is obtained by utilizing the six geometric moment descriptors of the three-dimensional model, so that not only can the choice of parameters be omitted, but also the topology and geometric characteristics of various shapes can be well described and represented, the universality is improved, the recognition capability of the spectrum shape descriptor is improved, and the time complexity of shape matching is reduced.
Example two
In order to cooperate with implementing the three-dimensional model matching method of the spectrum shape descriptor based on invariant moment provided by the above embodiment, the embodiment of the present invention provides a three-dimensional model matching device of the spectrum shape descriptor based on invariant moment, referring to fig. 4, the device includes:
the acquisition module 1 is used for acquiring a three-dimensional model;
the first acquisition module 2 is used for acquiring a ring neighborhood vertex corresponding to each vertex in the three-dimensional model;
the first calculation module 3 is used for calculating an LBO operator of the three-dimensional model according to a ring neighborhood vertex of the three-dimensional model;
a second calculation module 4, configured to calculate a feature value and a feature vector of the LBO operator of the three-dimensional model by using the LBO operator of the three-dimensional model;
the second obtaining module 5 is configured to obtain six geometric moment descriptors of the three-dimensional model according to the eigenvalues and eigenvectors of the LBO operator of the three-dimensional model;
and the third acquisition module 6 is used for acquiring the matching degree of the three-dimensional model and other three-dimensional models by using the six geometric moment descriptors of the three-dimensional model.
Further, the three-dimensional model includes: and each vertex has a serial number corresponding to the vertex.
Further, the first obtaining module 2 is specifically configured to:
in the three-dimensional model, the vertex directly connected with the vertex in the three-dimensional model is a ring neighborhood vertex corresponding to the vertex in the three-dimensional model;
and performing ascending sort on the adjacent vertices corresponding to the vertices in the three-dimensional model based on the serial numbers corresponding to the adjacent vertices.
Further, the first computing module 3 is specifically configured to:
calculating a discrete LBO operator corresponding to an ith vertex in the three-dimensional model according to the following steps:
Figure BDA0003734836560000181
in the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; v i Is the ith vertex in the three-dimensional model, f (v i ) Is the value of a real value function corresponding to the ith vertex in the three-dimensional model, N j Is the jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model, f (N) j ) The value of a real value function corresponding to the vertex of the jth one-ring neighborhood corresponding to the ith vertex in the three-dimensional model; let the ith vertex v in the connected three-dimensional model i Jth one-ring neighborhood vertex N corresponding to ith vertex in three-dimensional model j The line segment of (2) is p ij Alpha is then j And beta j Respectively are the sides p ij Opposite angles of two sides;
and discrete LBO operators corresponding to all vertexes in the three-dimensional model form the LBO operator of the three-dimensional model.
Further, the second computing module 4 is specifically configured to:
performing spectrum decomposition on an LBO operator of the three-dimensional model to obtain a characteristic value and a characteristic vector of the LBO operator of the three-dimensional model;
wherein, the eigenvalue and eigenvector of LBO operator of three-dimensional model are determined according to the following formula:
Figure BDA0003734836560000191
in the above, k is [1, K ]]K is the total number of feature values; ΔM is LBO operator of three-dimensional model, λ k Is the kth eigenvalue of the LBO operator of the three-dimensional model,
Figure BDA0003734836560000192
is the eigenvector corresponding to the kth eigenvalue of the LBO operator of the three-dimensional model.
Further, the second acquisition module 5 includes:
a first calculation unit 51, configured to calculate, according to the eigenvalues and eigenvectors of the LBO operator of the three-dimensional model, a spectral shape descriptor of a vertex in the three-dimensional model, and calculate a spectral shape descriptor of a corresponding one-ring neighborhood vertex of each vertex in the three-dimensional model;
a second calculation unit 52 for calculating a first-order moment mu based on the spectral shape descriptors of the vertices in the three-dimensional model and the spectral shape descriptors of the corresponding one-ring neighborhood vertices of each vertex in the three-dimensional model 01 Second order moment mu 02 Third order moment mu 03 First order spatial moment mu 11 Third-order spatial moment mu 12 And third-order spatial moment mu 21 ；
A determining unit 53 for determining six geometrical moment descriptors gmsps of the three-dimensional model according to:
GMSDs＝{μ 01 ,μ 02 ,μ 03 ,μ 11 ,μ 12 ,μ 21 }。
further, the first calculating unit 51 is specifically configured to:
determining a spectral shape description Fu of an ith vertex in a three-dimensional model as follows i ：
Figure BDA0003734836560000193
Pressing down typeDetermining Fu of spectral shape of a jth one-ring neighborhood vertex corresponding to an ith vertex in a three-dimensional model j ：
Figure BDA0003734836560000201
In the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; k is E [1, K]K is the total number of feature values; lambda (lambda) k Is the kth eigenvalue of the LBO operator of the three-dimensional model,
Figure BDA0003734836560000202
is the eigenvector corresponding to the kth eigenvalue of the LBO operator of the three-dimensional model, φ (λ k ) Is a filtering function;
wherein, when the spectrum shape descriptor is a thermonuclear signature spectrum shape descriptor, the filter function
Figure BDA0003734836560000203
t is a time parameter;
when the spectral shape descriptor is a wave kernel signature spectral shape descriptor, the filter function
Figure BDA0003734836560000204
i is an imaginary number i.
Further, the second calculating unit 52 is specifically configured to:
the first order moment mu is determined as follows 01 ：
Figure BDA0003734836560000205
Determining the second order moment mu as follows 02 ：
Figure BDA0003734836560000206
Determining third order moment of time by pressingμ 03 ：
Figure BDA0003734836560000207
The first order spatial moment mu is determined as follows 11 ：
Figure BDA0003734836560000208
Determining the third-order spatial moment mu as follows 12 ：
Figure BDA0003734836560000211
Determining the third-order spatial moment mu as follows 21 ：
Figure BDA0003734836560000212
In the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; phi i A spectral shape descriptor for an ith vertex in the three-dimensional model; phi j And the spectrum shape descriptor is a spectrum shape descriptor of the vertex of the jth one-ring neighborhood corresponding to the ith vertex in the three-dimensional model.
Further, the third obtaining module 6 is specifically configured to:
the set formed by all the vertexes in the three-dimensional model is set A, and the set formed by all the vertexes in other three-dimensional models is set B;
the degree of matching MHD (a, B) of the three-dimensional model with other three-dimensional models is determined as follows:
MHD(A,B)＝max[d(A,B),d(B,A)]
in the above formula, d (A, B) is each vertex v in set A a And each vertex v in set B b Is the average of the distance minima; d (B, A) is each vertex v in set B b And each top in set APoint v a Is the average of the distance minima;
wherein d (A, B) is determined as follows:
Figure BDA0003734836560000213
d (B, A) is determined as follows:
Figure BDA0003734836560000214
in the above formula, a is ∈ [1, N ] A ]，N A Is the total number of vertices in set A; b E [1, N B ]，N B Is the total number of vertices in set B; v a -v b I is the vertex v in set A a To vertex v in set B b Euclidean distance, v b -v a I is the vertex v in set B b To vertex v in set A a Is a euclidean distance of (c).
According to the three-dimensional model matching device based on the invariant moment spectrum shape descriptor, the three-dimensional model is acquired through the acquisition module 1, the first acquisition module 2 acquires one ring neighborhood vertex corresponding to each vertex in the three-dimensional model, the first calculation module 3 calculates the LBO operator of the three-dimensional model according to the ring neighborhood vertex of the three-dimensional model, the second calculation module 4 calculates the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model by utilizing the LBO operator of the three-dimensional model, the second acquisition module 5 acquires six geometric moment descriptors of the three-dimensional model according to the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, and the third acquisition module 6 acquires the matching degree of the three-dimensional model and other three-dimensional models by utilizing the six geometric moment descriptors of the three-dimensional model, so that the topology and geometric characteristics of various shapes can be well described and represented without depending on parameter selection, the device has universality, the recognition capability of the spectrum shape descriptor is enhanced, and the time complexity of shape matching is reduced.
It can be understood that the above-provided device embodiments correspond to the above-described method embodiments, and corresponding specific details may be referred to each other, which is not described herein again.
It is to be understood that the same or similar parts in the above embodiments may be referred to each other, and that in some embodiments, the same or similar parts in other embodiments may be referred to.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, magnetic disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any person skilled in the art will readily recognize that changes and substitutions are within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A method for matching a three-dimensional model of a invariant moment based spectral shape descriptor, the method comprising:
collecting a three-dimensional model;
acquiring a ring neighborhood vertex corresponding to each vertex in the three-dimensional model;
calculating an LBO operator of the three-dimensional model according to a ring neighborhood vertex of the three-dimensional model;
calculating the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model by utilizing the LBO operator of the three-dimensional model;
obtaining six geometric moment descriptors of the three-dimensional model according to the characteristic values and the characteristic vectors of the LBO operator of the three-dimensional model; comprising the following steps:
step a: calculating a spectrum shape descriptor of each vertex in the three-dimensional model according to the characteristic value and the characteristic vector of the LBO operator of the three-dimensional model, and calculating a spectrum shape descriptor of a corresponding ring neighborhood vertex of each vertex in the three-dimensional model;
obtaining the matching degree of the three-dimensional model and other three-dimensional models by using six geometric moment descriptors of the three-dimensional model;
wherein, the step a comprises the following steps:
determining a spectral shape description Fu of an ith vertex in the three-dimensional model as follows i ：
Figure FDA0004150514400000011
Determining a spectral shape description Fu of a jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model by j ：
Figure FDA0004150514400000012
In the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; k is E [1, K]K is the total number of feature values; lambda (lambda) k For the kth eigenvalue of the LBO operator of the three-dimensional model,
Figure FDA0004150514400000013
is the eigenvector corresponding to the kth eigenvalue of the LBO operator of the three-dimensional model, phi (lambda k ) Is a filtering function;
wherein when the spectral shape descriptor is a thermonuclear signature or a scale invariant thermonuclear signature spectral shape descriptor, the filter function
Figure FDA0004150514400000021
t is a time parameter;
when the spectral shape descriptor is a wave kernel signature or a scale invariant thermal kernel signature spectral shape descriptor, a filter function
Figure FDA0004150514400000022
i is an imaginary number i.
2. The method of claim 1, wherein the three-dimensional model comprises: and each vertex is provided with a serial number corresponding to the vertex.
3. The method of claim 1, wherein the obtaining a ring neighborhood vertex corresponding to each vertex in the three-dimensional model comprises:
in the three-dimensional model, the vertex directly connected with the vertex in the three-dimensional model is a ring neighborhood vertex corresponding to the vertex in the three-dimensional model;
and carrying out ascending sort on the annular neighborhood vertexes corresponding to the vertexes in the three-dimensional model based on the serial numbers corresponding to the annular neighborhood vertexes corresponding to the vertexes in the three-dimensional model.
4. The method of claim 1, wherein said computing LBO operators of said three-dimensional model from a ring neighborhood vertex of said three-dimensional model comprises:
calculating a discrete LBO operator corresponding to an ith vertex in the three-dimensional model according to the following formula:
Figure FDA0004150514400000023
in the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; v i For the ith vertex in the three-dimensional model, f (v i ) For the value of the real value function corresponding to the ith vertex in the three-dimensional model, N j For the jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model, f (N) j ) The value of a real value function corresponding to the jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model; connecting the ith vertex v in the three-dimensional model i A jth one-ring neighborhood vertex N corresponding to the ith vertex in the three-dimensional model j The line segment of (2) is p ij Alpha is then j And beta j Respectively are the sides p ij Opposite angles of two sides;
and discrete LBO operators corresponding to all vertexes in the three-dimensional model form the LBO operator of the three-dimensional model.
5. The method according to claim 1, wherein the obtaining eigenvalues and eigenvectors of the LBO operator of the three-dimensional model from the LBO operator of the three-dimensional model comprises:
performing spectrum decomposition on the LBO operator of the three-dimensional model to obtain a characteristic value and a characteristic vector of the LBO operator of the three-dimensional model;
wherein, the eigenvalue and eigenvector of LBO operator of the three-dimensional model are determined according to the following formula:
Figure FDA0004150514400000031
in the above, k is [1, K ]]K is the total number of feature values; ΔM is LBO operator of the three-dimensional model, λ k For the kth eigenvalue of the LBO operator of the three-dimensional model,
Figure FDA0004150514400000032
and the feature vector corresponding to the kth feature value of the LBO operator of the three-dimensional model.
6. The method of claim 1, wherein the obtaining six geometric moment descriptors of the three-dimensional model from eigenvalues and eigenvectors of LBO operators of the three-dimensional model further comprises:
step b: calculating six geometric moment descriptors of the three-dimensional model according to the spectrum shape descriptors of the vertexes in the three-dimensional model and the spectrum shape descriptors of the vertexes of a corresponding ring neighborhood of each vertex in the three-dimensional model; wherein the six geometric moment descriptors of the three-dimensional model include: first order moment of time mu 01 Second order moment mu 02 Third order moment mu 03 First order spatial moment mu 11 Third-order spatial moment mu 12 And third-order spatial moment mu 21 ；
Step c: six geometric moment descriptors gmsps of the three-dimensional model are determined as follows:
GMSDs＝{μ 01 ,μ 02 ,μ 03 ,μ 11 ,μ 12 ,μ 21 }。
7. the method according to claim 6, wherein step b comprises:
the first order moment mu is determined as follows 01 ：
Figure FDA0004150514400000033
Determining the second order moment mu as follows 02 ：
Figure FDA0004150514400000041
Determining the third order moment mu as follows 03 ：
Figure FDA0004150514400000042
The first order spatial moment mu is determined as follows 11 ：
Figure FDA0004150514400000043
Determining the third-order spatial moment mu as follows 12 ：
Figure FDA0004150514400000044
Determining the third-order spatial moment mu as follows 21 ：
Figure FDA0004150514400000045
In the above formula, i is [1, n ]]N is the total number of vertices in the three-dimensional model; j E [1, m]M is the total number of the vertices of a ring neighborhood corresponding to the ith vertex in the three-dimensional model; phi i A spectral shape descriptor for an ith vertex in the three-dimensional model; phi j And (3) a spectrum shape descriptor of the jth one-ring neighborhood vertex corresponding to the ith vertex in the three-dimensional model.
8. The method according to claim 1, wherein the obtaining the matching degree of the three-dimensional model and other three-dimensional models by using six geometric moment descriptors of the three-dimensional model includes:
the set formed by all the vertexes in the three-dimensional model is set A, and the set formed by all the vertexes in the other three-dimensional models is set B;
determining the matching degree MHD (A, B) of the three-dimensional model and other three-dimensional models according to the following steps:
MHD(A,B)＝max[d(A,B),d(B,A)]
in the above formula, d (A, B) is each vertex v in set A a And each vertex v in set B b Is the average of the distance minima; d (B, A) is each vertex v in set B b With each vertex v in set A a Is the average of the distance minima;
wherein d (A, B) is determined as follows:
Figure FDA0004150514400000051
d (B, A) is determined as follows:
Figure FDA0004150514400000052
in the above formula, a is ∈ [1, N ] A ]，N A Is the total number of vertices in set A; b E [1, N B ]，N B Is the total number of vertices in set B; v a -v b I is the vertex v in set A a To vertex v in set B b Euclidean distance of v b -v a I is the vertex v in set B b To vertex v in set A a Is a euclidean distance of (c).
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