CN113313831A - Three-dimensional model feature extraction method based on polar coordinate graph convolutional neural network - Google Patents

Three-dimensional model feature extraction method based on polar coordinate graph convolutional neural network Download PDF

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CN113313831A
CN113313831A CN202110565190.1A CN202110565190A CN113313831A CN 113313831 A CN113313831 A CN 113313831A CN 202110565190 A CN202110565190 A CN 202110565190A CN 113313831 A CN113313831 A CN 113313831A
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周燕
徐雪妙
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South China University of Technology SCUT
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Abstract

The invention discloses a three-dimensional model feature extraction method based on a polar coordinate graph convolutional neural network, which comprises the following steps of firstly, uniformly generating and sampling point clouds from three-dimensional grid model data by using an improved point cloud generation method; secondly, the point cloud model is standardized and aligned by using the calculated volume weighted centroid; thirdly, constructing polar coordinate representation and three-dimensional space rectangular coordinate system representation of the point cloud to obtain composite representation; and finally, using a graph convolution neural network to model and compound the representation, capturing local neighborhood and global information, and extracting the characteristics of the three-dimensional model. The method can extract the shape content characteristics of the three-dimensional model with the transformation invariance and high discrimination, and lays a foundation for subsequent tasks such as classification recognition, retrieval and the like.

Description

Three-dimensional model feature extraction method based on polar coordinate graph convolutional neural network
Technical Field
The invention relates to the technical field of three-dimensional model classification identification and retrieval, in particular to a three-dimensional model feature extraction method based on a polar coordinate graph convolutional neural network.
Background
At the present stage, the shape content features of the three-dimensional model with low dimension and high discrimination are effectively extracted, and the classification, the retrieval and the like of the shape content features are facilitated, so that the new method for extracting the three-dimensional model features is an important research content in the current three-dimensional computer vision field. Firstly, the traditional method based on point cloud mostly adopts a single three-dimensional rectangular coordinate system as network input and lacks auxiliary coding information; secondly, the traditional method for generating point cloud from grid sampling mostly uses a segmented interpolation method, lacks a sampling strategy, and easily ignores the actual size condition of a patch, so that the collected point set is not uniform enough; thirdly, the model generally faces the influences of rotation, translation, scale transformation and the like; finally, the traditional multi-layer perceptron MLP is used as a network feature extractor, non-European geometric data similar to point clouds cannot be effectively modeled, effective information of a local field of the model is difficult to capture, and performance improvement is limited.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a three-dimensional model feature extraction method based on a polar coordinate graph convolutional neural network, which can extract the shape content features of a three-dimensional model with transformation invariance and high discrimination and lay the foundation for subsequent tasks such as classification identification and retrieval.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: the three-dimensional model feature extraction method based on the polar coordinate graph convolutional neural network comprises the following steps:
s1, acquiring a plurality of three-dimensional mesh model data, including a vertex set and a patch set;
s2, based on the improved point cloud generating method, for each three-dimensional grid model data, setting and judging according to a threshold value, generating a point cloud, and acquiring a first point cloud corresponding to the point cloud;
s3, acquiring a corresponding volume weighted centroid for each three-dimensional grid model data;
s4, constructing a unit Gaussian sphere with the volume weighted centroid as the sphere center to wrap the first point cloud through translation, proportion and rotation transformation based on the first point cloud and the volume weighted centroid, realizing the operation of converting the first point cloud into a standard unified coordinate space, and acquiring a standardized and aligned second point cloud;
s5, projecting the second point cloud to a polar coordinate system based on the second point cloud, obtaining polar coordinate representation of the second point cloud, and splicing the polar coordinate representation of the second point cloud and three-dimensional rectangular coordinate system representation of the second point cloud to obtain the second point cloud with composite representation;
and S6, acquiring the corresponding deep learning characteristics of each second point cloud with the composite representation based on the polar coordinate graph convolution neural network model.
Further, in step S1, the three-dimensional mesh model data is read, and the vertex set V ═ V of the three-dimensional mesh model is acquiredi I 1,2, n and patch set F j1, 2.·, m }; wherein v isiRepresents the ith vertex element, vi＝(vi 1,vi 2,vi 3) Is the three-dimensional rectangular coordinate system representation of the vertex elements in the vertex set, n is the number of the vertex elements in the vertex set, fjRepresenting the jth patch element, wherein m is the number of patch elements in a patch set, and the patch set stores patch element information by using vertex index information on the patch elements.
Further, the step S2 includes the steps of:
s201, based on a patch set F ═ Fj1, 2., m }, m is the number of patch elements in the patch set, and the area of each patch element in the patch set is obtained through formula calculation, wherein the formula is as follows:
Figure BDA0003080454670000021
wherein
Figure BDA0003080454670000022
aj＝||(vj1-vj2)||2，bj＝||(vj1-vj3)||2，cj＝||(vj2-vj3)||2
In the formula, S (f)j) Representing the jth patch element f in a patch setjArea of (v)j1、vj2、vj3As elements f of a patchjThree ofVertex, ajRepresenting the vertex vj1And vertex vj2Two norms of the constructed vector, bjRepresenting the vertex vj1And vertex vj3Two norms of the constructed vector, cjRepresenting the vertex vj2And vertex vj3Two norms, p, of the constructed vectorjIs represented by aj、bj、cjCalculating the obtained intermediate process variable;
s202, area S (f) based on each patch element in patch setj) Calculating the average value of the whole patch element area in the patch set by a formula
Figure BDA0003080454670000031
Then, taking the average value as a threshold value, the formula is as follows:
Figure BDA0003080454670000032
s203, an original point cloud generating method is to directly perform point cloud generating operation without considering the distribution condition of the area size of each patch element in the three-dimensional grid model; the improved point cloud generating method adds condition judgment, selectively performs point cloud generating operation on the patch elements through threshold setting judgment, performs linear interpolation based on information of the patch elements in the patch set, and calculates to obtain a new vertex set, specifically as follows:
based on the set of patches F ═ FjAnd if j is 1,2, the other words, m, performing point cloud generation operation on the patch elements with the area larger than the threshold value S according to a formula, and not performing point cloud generation operation on the patch elements with the area smaller than the threshold value S, so as to obtain the point cloud generated by the corresponding three-dimensional mesh model, wherein the formula is as follows:
Figure BDA0003080454670000033
Figure BDA0003080454670000034
in the above formula, Set (f)j) For the jth patch element f in the patch setjSet of vertices of, vj' representation set
Figure BDA0003080454670000035
J-th vertex set in (1), q1、q2Represents [0,1 ]]Number of divisions, ω1、ω2O, p are intermediate process variables,
Figure BDA0003080454670000036
point clouds generated for the corresponding three-dimensional mesh models;
s204, point cloud generated based on corresponding three-dimensional grid model
Figure BDA0003080454670000037
According to a farthest point sampling algorithm or a random sampling method, point clouds with fixed vertex numbers are collected, a first point cloud corresponding to a three-dimensional grid model is obtained, and the formula is as follows:
Figure BDA0003080454670000041
wherein, Sample _ Function is a farthest point sampling algorithm Function or a random sampling algorithm Function, V ' is a first point cloud corresponding to the three-dimensional grid model, n ' represents the number of vertex elements in the first point cloud to be sampled, V 'kIs the kth element in the first point cloud.
Further, the step S3 includes the steps of:
s301, for each three-dimensional mesh model, based on the vertex set V ═ Vi1, 2., n }, and calculating a corresponding centroid through a formula, wherein the formula is as follows:
Figure BDA0003080454670000042
in the formula，
Figure BDA0003080454670000043
Representing the centroid, v, of a three-dimensional mesh modeliIs the ith vertex element in the vertex set, and n is the number of vertex elements in the vertex set.
S302, F ═ { F } based on the patch setj1,2, the., m is the number of patch elements in the patch set, and the centroid v and the patch element f in the patch set are obtained through formula calculationjThe volume of the formed tetrahedron is obtained, and meanwhile, the gravity center of the element of the patch set is obtained according to the formula, wherein the formula is respectively as follows:
Figure BDA0003080454670000044
Figure BDA0003080454670000045
in the formula, VoljRepresenting centroid v and patch element f in jth patch setjVolume of tetrahedron formed, vj1、vj2、vj3As elements f of a patchjThree vertices of upper, gjRepresenting patch element f in jth patch setjThe center of gravity of;
s303 tetrahedron-based volume VoljAnd the center of gravity g of patch elements in the patch setjAnd calculating to obtain the volume weighted centroid corresponding to the three-dimensional grid model through a formula, wherein the formula is as follows:
Figure BDA0003080454670000051
in the formula (I), the compound is shown in the specification,
Figure BDA0003080454670000052
representing the corresponding volumetric weighted centroid of the three-dimensional mesh model.
Further, the step S4 includes the steps of:
s401, based on the first point cloud V ═ { V ═ Vk'| k ═ 1,2,. ·, n' } and the volume weighted centroid
Figure BDA0003080454670000053
v′kFor the kth element in the first point cloud, n' represents the number of vertex elements in the first point cloud, the first point cloud is translated to the volume weighted centroid according to a formula, and the first point cloud after translation transformation is obtained, wherein the formula is as follows:
Figure BDA0003080454670000054
V″＝{v″k|k＝1,2,...n′}
in the formula, v ″)kThe k element of the first point cloud after the translation transformation is shown, and V' is the first point cloud after the translation transformation;
s402, based on the first point cloud V ″ ═ { V ″) after translation transformation k1, 2.. n', calculating a scale conversion factor according to a formula, further calculating a converted model, and obtaining a first point cloud after translation conversion and scale conversion, wherein the formula is as follows:
Figure BDA0003080454670000055
v″′k＝s·v″k,v″k∈V″
V″′＝{v″′k|k＝1,2,...n′}
wherein s is a scaling factor, v'kThe kth element of the first point cloud V' after the translation transformation and the scale transformation;
s403, based on the first point cloud V ' "{ V '" after the translation transformation and the scaling transformation 'k1,2,. n' }, calculating a rotation matrix R according to a formula; wherein the step of obtaining the rotation matrix comprises:
s4031, and first point cloud V' based on translation transformation and scale transformationCovariance matrix (V')T；
S4032, covariance matrix (V')TCarrying out feature decomposition to obtain the feature Vector corresponding to the first three maximum feature values3×3；
S4033, constructing a rotation matrix R according to a formula, wherein the formula is as follows:
R＝Vector3×3·I
in the formula, I is a unit matrix with the size of 3 multiplied by 3;
s404, based on the first point cloud V ' { V ' after translation transformation and scaling transformation 'kN 'and a rotation matrix R, further performing rotation transformation on V' ″ to obtain a second point cloud after translation transformation, scaling transformation and rotation transformation, as follows:
Figure BDA0003080454670000061
Figure BDA0003080454670000062
in the formula (I), the compound is shown in the specification,
Figure BDA0003080454670000063
the k-th element of the second point cloud after the translation transformation, the scaling transformation and the rotation transformation,
Figure BDA0003080454670000064
the second point cloud is the second point cloud after translation transformation, scaling transformation and rotation transformation.
Further, the step S5 includes the steps of:
s501, based on second point cloud
Figure BDA0003080454670000065
Figure BDA0003080454670000066
Is subjected to translation transformation and scaling transformationTransforming and rotating the k-th element of the transformed second point cloud,
Figure BDA0003080454670000067
representing by a rectangular coordinate system of a three-dimensional space of second point cloud, wherein n' represents the number of vertex elements in the second point cloud, projecting the second point cloud to a polar coordinate system according to a formula, and obtaining the polar coordinate representation of the second point cloud, wherein the formula is as follows:
Figure BDA0003080454670000068
wherein (theta)k,φk,rk) As a polar coordinate representation of the second point cloud, fsphAn operator is projected for the polar coordinate system,
Figure BDA0003080454670000069
s502, expressing the polar coordinates (theta) of the second point cloud according to a formulak,φk,rk) Three-dimensional rectangular coordinate system with second point cloud
Figure BDA0003080454670000071
The representations are spliced to obtain a composite representation
Figure BDA0003080454670000072
The second point cloud of (1).
Further, the step S6 includes the steps of:
s601, representing based on having composite
Figure BDA0003080454670000073
The second point cloud and the polar coordinate graph convolution neural network model obtain corresponding deep learning characteristics; the step of obtaining the polar coordinate graph convolution neural network model comprises the following steps:
s6011, designing a network structure of a polar coordinate graph convolution neural network model based on a graph convolution network mode; wherein the input of the polar plot convolutional neural network model is based onWith a composite representation
Figure BDA0003080454670000074
The output of the second point cloud is the corresponding deep learning characteristic; the structure of the polar coordinate graph convolution neural network model comprises a graph building module, a residual dynamic graph convolution block, a fusion module and a prediction module; the mapping module is based on a second point cloud having a composite representation
Figure BDA0003080454670000075
Constructing a hole k neighbor graph representation of the corresponding 3 branches by using a hole k neighbor algorithm to serve as input; the residual dynamic graph convolution block comprises an EdgeConv edge convolution layer connected based on the dynamic graph convolution layer and a residual graph, and an SE attention mechanism block is embedded; the fusion module comprises a 1 × 1 convolution kernel layer and two pooling layers, wherein the 1 × 1 convolution kernel layer is followed by a Batch Normalization function of Batch by Batch and an LeakyReLU activation function, and the two pooling layers respectively use maximum pooling and average pooling; the prediction module comprises two fully-connected layers, wherein one fully-connected layer is followed by a Batch Normalization function of Batch, a LeakyReLU activation function and Dropout random inactivation;
s6012, representing based on having a composite
Figure BDA0003080454670000076
The second point cloud of (2) building a database of network training, and dividing 80% of the database into a training set and 20% of the database into a verification set, wherein the intersection of the training set and the verification set is empty, and the second point cloud is used for corresponding to the labeled real class label; on the training set, will have a composite representation
Figure BDA0003080454670000077
Inputting the second point cloud into the polar coordinate graph convolutional neural network model to obtain an output characteristic vector and a classification probability, calculating the difference between the classification probability and a real class label, and reversely adjusting the parameter value of the polar coordinate graph convolutional neural network model; on the verification set, there will be a composite representation
Figure BDA0003080454670000081
Inputting the second point cloud into a polar coordinate graph convolutional neural network model to obtain an output characteristic vector and a classification probability, calculating the difference between the classification probability and a class label, and evaluating the performance of the polar coordinate graph convolutional neural network model; until the training is finished, using the output feature vector as the feature of the representation three-dimensional model;
s602, a second point cloud with a composite representation is to be based on
Figure BDA0003080454670000082
And inputting the data into a polar coordinate graph convolution neural network model, and extracting corresponding deep learning characteristics.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention samples and generates the three-dimensional grid model into a uniformly distributed point cloud set by an improved point cloud generation method. By calculating volume weighted centroid coordinates in the original three-dimensional mesh model, the model can be made to take into account volume set information when performing normalization and alignment operations. By constructing the graph of the k neighbor graph representation of the 3 branch cavities, the subsequent graph convolution neural network can obtain a larger receptive field. By combining an attention mechanism, the polar coordinate graph convolutional neural network model better considers information on the dimension of the characteristic channel, and can better model the local and global characteristic information of the model. The technical process of the invention can reduce the calculated amount in the sampling process and avoid the influence on feature extraction caused by translation, proportion, rotation and other transformations, thereby laying a foundation for the subsequent graph convolution neural network modeling.
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FIG. 1 is a schematic flow diagram of the process of the present invention.
Fig. 2 is a schematic diagram of a polar plot convolutional neural network model acquisition process.
FIG. 3 is a schematic diagram of an application process of a polar coordinate graph convolutional neural network model in three-dimensional model feature extraction.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Referring to fig. 1, the method for extracting three-dimensional model features based on a polar coordinate graph convolutional neural network provided in this embodiment includes the following steps:
s1, obtaining a plurality of three-dimensional mesh model data, including a vertex set and a patch set, as follows:
reading three-dimensional mesh model data, and acquiring vertex set V ═ V of the three-dimensional mesh modeliI 1,2, n and patch set F j1, 2.·, m }; wherein v isiRepresents the ith vertex element, vi＝(vi 1,vi 2,vi 3) Is the three-dimensional rectangular coordinate system representation of the vertex elements in the vertex set, n is the number of the vertex elements in the vertex set, fjRepresenting the jth patch element, wherein m is the number of patch elements in a patch set, and the patch set stores patch element information by using vertex index information on the patch elements.
S2, based on the improved point cloud generating method, for each three-dimensional grid model data, according to threshold setting judgment, point cloud generation is carried out, and a first point cloud corresponding to the point cloud generation is obtained, wherein the specific process is as follows:
s201, based on a patch set F ═ Fj1, 2., m }, m is the number of patch elements in the patch set, and the area of each patch element in the patch set is obtained through formula calculation, wherein the formula is as follows:
Figure BDA0003080454670000091
wherein
Figure BDA0003080454670000092
aj＝||(vj1-vj2)||2，bj＝||(vj1-vj3)||2，cj＝||(vj2-vj3)||2
In the formula, S (f)j) Representing the jth face in a patch setFlake element fjArea of (v)j1、vj2、vj3As elements f of a patchjThree vertices of (a)jRepresenting the vertex vj1And vertex vj2Two norms of the constructed vector, bjRepresenting the vertex vj1And vertex vj3Two norms of the constructed vector, cjRepresenting the vertex vj2And vertex vj3Two norms, p, of the constructed vectorjIs represented by aj、bj、cjCalculating the obtained intermediate process variable;
s202, area S (f) based on each patch element in patch setj) Calculating the average value of the whole patch element area in the patch set by a formula
Figure BDA0003080454670000093
Then, taking the average value as a threshold value, the formula is as follows:
Figure BDA0003080454670000094
s203, the original point cloud generating method is to directly perform point cloud generating operation, and the distribution condition of the area size of each patch element in the three-dimensional grid model is not considered. The improved point cloud generating method adds condition judgment, and selectively performs point cloud generating operation on the patch elements through threshold setting judgment, wherein the point cloud generating operation is to perform linear interpolation based on information of the patch elements in the patch set, and calculate to obtain a new vertex set, and specifically, the method comprises the following steps:
based on the set of patches F ═ FjAnd if j is 1,2, the other words, m, performing point cloud generation operation on the patch elements with the area larger than the threshold value S according to a formula, and not performing point cloud generation operation on the patch elements with the area smaller than the threshold value S, so as to obtain the point cloud generated by the corresponding three-dimensional mesh model, wherein the formula is as follows:
Figure BDA0003080454670000101
Figure BDA0003080454670000102
in the above formula, Set (f)j) For the jth patch element f in the patch setjSet of vertices of, vj' representation set
Figure BDA0003080454670000103
J-th vertex set in (1), q1、q2Represents [0,1 ]]Number of divisions, ω1、ω2O, p are intermediate process variables,
Figure BDA0003080454670000104
point clouds generated for the corresponding three-dimensional mesh models;
s204, point cloud generated based on corresponding three-dimensional grid model
Figure BDA0003080454670000105
According to a farthest point sampling algorithm or a random sampling method, point clouds with fixed vertex numbers are collected, a first point cloud corresponding to a three-dimensional grid model is obtained, and the formula is as follows:
Figure BDA0003080454670000106
wherein, Sample _ Function is a farthest point sampling algorithm Function or a random sampling algorithm Function, V ' is a first point cloud corresponding to the three-dimensional grid model, n ' represents the number of vertex elements in the first point cloud to be sampled, V 'kIs the kth element in the first point cloud.
S3, for each three-dimensional grid model data, obtaining the corresponding volume weighted centroid, and the specific process is as follows:
s301, for each three-dimensional mesh model, based on the vertex set V ═ Vi1, 2., n }, and calculating a corresponding centroid through a formula, wherein the formula is as follows:
Figure BDA0003080454670000111
in the formula (I), the compound is shown in the specification,
Figure BDA0003080454670000112
representing the centroid, v, of a three-dimensional mesh modeliIs the ith vertex element in the vertex set, and n is the number of vertex elements in the vertex set.
S302, F ═ { F } based on the patch setj1,2, the., m is the number of patch elements in the patch set, and the centroid v and the patch element f in the patch set are obtained through formula calculationjThe volume of the formed tetrahedron is obtained, and meanwhile, the gravity center of the element of the patch set is obtained according to the formula, wherein the formula is respectively as follows:
Figure BDA0003080454670000113
Figure BDA0003080454670000114
in the formula, VoljRepresenting centroid v and patch element f in jth patch setjVolume of tetrahedron formed, vj1、vj2、vj3As elements f of a patchjThree vertices of upper, gjRepresenting patch element f in jth patch setjThe center of gravity of;
s303 tetrahedron-based volume VoljAnd the center of gravity g of patch elements in the patch setjAnd calculating to obtain the volume weighted centroid corresponding to the three-dimensional grid model through a formula, wherein the formula is as follows:
Figure BDA0003080454670000115
in the formula (I), the compound is shown in the specification,
Figure BDA0003080454670000121
representing the corresponding volumetric weighted centroid of the three-dimensional mesh model.
S4, based on the first point cloud and the volume weighted centroid, through translation, proportion and rotation transformation, constructing a unit Gaussian sphere with the volume weighted centroid as a sphere center to wrap the first point cloud, realizing the operation of converting the first point cloud into a standard unified coordinate space, and acquiring a standardized and aligned second point cloud, wherein the specific process is as follows:
s401, based on the first point cloud V ═ { V ═ Vk'| k ═ 1,2,. ·, n' } and the volume weighted centroid
Figure BDA0003080454670000122
v′kFor the kth element in the first point cloud, n' represents the number of vertex elements in the first point cloud, the first point cloud is translated to the volume weighted centroid according to a formula, and the first point cloud after translation transformation is obtained, wherein the formula is as follows:
Figure BDA0003080454670000124
V″＝{v″k|k＝1,2,...n′}
in the formula, v ″)kThe k element of the first point cloud after the translation transformation is shown, and V' is the first point cloud after the translation transformation;
s402, based on the first point cloud V ″ ═ { V ″) after translation transformation k1, 2.. n', calculating a scale conversion factor according to a formula, further calculating a converted model, and obtaining a first point cloud after translation conversion and scale conversion, wherein the formula is as follows:
Figure BDA0003080454670000123
v″′k＝s·v″k,v″k∈V″
V″′＝{v″′k|k＝1,2,...n′}
in the formula (I), the compound is shown in the specification,s is a scaling factor, v'kThe kth element of the first point cloud V' after the translation transformation and the scale transformation;
s403, based on the first point cloud V '"after the translation transformation and the scaling transformation, { V'" ]k1,2,. n' }, calculating a rotation matrix R according to a formula; wherein the step of obtaining the rotation matrix comprises:
s4031, based on the translation transformation and the first point cloud V ', constructing a covariance matrix (V')T；
S4032, covariance matrix (V')TCarrying out feature decomposition to obtain the feature Vector corresponding to the first three maximum feature values3×3；
S4033, constructing a rotation matrix R according to a formula, wherein the formula is as follows:
R＝Vector3×3·I
in the formula, I is a unit matrix with the size of 3 multiplied by 3;
s404, based on the first point cloud V ' { V ' after translation transformation and scaling transformation 'kN 'and a rotation matrix R, further performing rotation transformation on V' ″ to obtain a second point cloud after translation transformation, scaling transformation and rotation transformation, as follows:
Figure BDA0003080454670000131
Figure BDA0003080454670000132
in the formula (I), the compound is shown in the specification,
Figure BDA0003080454670000133
the k-th element of the second point cloud after the translation transformation, the scaling transformation and the rotation transformation,
Figure BDA0003080454670000134
after translation transformation, scaling transformation and rotation transformationAnd (5) second point cloud.
S5, projecting the second point cloud to a polar coordinate system based on the second point cloud, obtaining polar coordinate representation of the second point cloud, splicing the polar coordinate representation of the second point cloud and three-dimensional space rectangular coordinate representation of the second point cloud, and obtaining the second point cloud with composite representation, wherein the specific process is as follows:
s501, based on second point cloud
Figure BDA0003080454670000135
Figure BDA0003080454670000136
The k-th element of the second point cloud after the translation transformation, the scaling transformation and the rotation transformation,
Figure BDA0003080454670000137
representing by a rectangular coordinate system of a three-dimensional space of second point cloud, wherein n' represents the number of vertex elements in the second point cloud, projecting the second point cloud to a polar coordinate system according to a formula, and obtaining the polar coordinate representation of the second point cloud, wherein the formula is as follows:
Figure BDA0003080454670000138
wherein (theta)k,φk,rk) As a polar coordinate representation of the second point cloud, fsphAn operator is projected for the polar coordinate system,
Figure BDA0003080454670000141
s502, expressing the polar coordinates (theta) of the second point cloud according to a formulak,φk,rk) Three-dimensional rectangular coordinate system with second point cloud
Figure BDA0003080454670000142
The representations are spliced to obtain a composite representation
Figure BDA0003080454670000143
The second point cloud of (1).
S6, referring to fig. 2, based on the polar-coordinate graph convolutional neural network model, for each second point cloud having a composite representation, obtaining a corresponding deep learning feature, where the specific process is as follows:
s601, representing based on having composite
Figure BDA0003080454670000144
The second point cloud and the polar coordinate graph convolution neural network model obtain corresponding deep learning characteristics; the method comprises the following steps of obtaining a polar coordinate graph convolution neural network model, wherein the steps comprise:
s6011, designing a network structure of a polar coordinate graph convolution neural network model based on a graph convolution network mode; wherein the input of the polar plot convolutional neural network model is based on having a composite representation
Figure BDA0003080454670000145
The output of the second point cloud is the corresponding deep learning characteristic; the structure of the polar coordinate graph convolution neural network model comprises a graph building module, a residual dynamic graph convolution block, a fusion module and a prediction module; the mapping module is based on a second point cloud having a composite representation
Figure BDA0003080454670000146
Constructing a hole k neighbor graph representation of the corresponding 3 branches by using a hole k neighbor algorithm to serve as input; the residual dynamic graph convolution block comprises an EdgeConv edge convolution layer connected based on the dynamic graph convolution layer and a residual graph, and an SE attention mechanism block is embedded; the fusion module comprises a 1 × 1 convolution kernel layer and two pooling layers, wherein the 1 × 1 convolution kernel layer is followed by a Batch Normalization function of Batch by Batch and an LeakyReLU activation function, and the two pooling layers respectively use maximum pooling and average pooling; the prediction module comprises two fully-connected layers, wherein one fully-connected layer is followed by a Batch Normalization function of Batch, a LeakyReLU activation function and Dropout random inactivation;
s6012, representing based on having a composite
Figure BDA0003080454670000147
The second point cloud of (2) building a database of network training, and dividing 80% of the database into a training set and 20% of the database into a verification set, wherein the intersection of the training set and the verification set is empty, and the second point cloud is used for corresponding to the labeled real class label; on the training set, will have a composite representation
Figure BDA0003080454670000151
Inputting the second point cloud into the polar coordinate graph convolutional neural network model to obtain an output characteristic vector and a classification probability, calculating the difference between the classification probability and a real class label, and reversely adjusting the parameter value of the polar coordinate graph convolutional neural network model; on the verification set, there will be a composite representation
Figure BDA0003080454670000152
Inputting the second point cloud into a polar coordinate graph convolutional neural network model to obtain an output characteristic vector and a classification probability, calculating the difference between the classification probability and a class label, and evaluating the performance of the polar coordinate graph convolutional neural network model; until the training is finished, using the output feature vector as the feature of the representation three-dimensional model;
s602, a second point cloud with a composite representation is to be based on
Figure BDA0003080454670000153
And inputting the data into a polar coordinate graph convolution neural network model, and extracting corresponding deep learning characteristics.
Referring to fig. 3, an application process of the above-mentioned polar-coordinate-diagram convolutional neural network model in three-dimensional model feature extraction in this embodiment includes:
step 1: reading three-dimensional mesh model data, and acquiring a vertex set and a patch set of the three-dimensional mesh model; the patch set stores patch element information by using the vertex index information on patch elements;
step 2: based on an improved point cloud generation method, for each three-dimensional grid model, point cloud generation is carried out according to threshold setting judgment, and a first point cloud corresponding to the point cloud generation is obtained; wherein, the threshold value is the average value of the element areas of the whole patches in the patch set;
and step 3: for each three-dimensional grid model, acquiring a corresponding weighted volume centroid;
and 4, step 4: constructing a unit Gaussian sphere wrapped point cloud with the volume weighted centroid as a sphere center through translation, proportion and rotation transformation based on the first point cloud and the volume weighted centroid, realizing the operation of converting the first point cloud into a standard unified coordinate space, and acquiring an aligned second point cloud;
and 5: based on the second point cloud, projecting the second point cloud to a polar coordinate system to obtain polar coordinate representation of the second point cloud, and splicing the polar coordinate representation of the second point cloud and three-dimensional rectangular coordinate system representation of the second point cloud to obtain the second point cloud with composite representation;
step 6: acquiring a corresponding deep learning characteristic based on a second point cloud with composite representation and a polar coordinate graph convolution neural network model; the polar coordinate graph convolution neural network model is constructed by a graph building module, a residual dynamic graph convolution block, a fusion module and a prediction module.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (7)

1. The three-dimensional model feature extraction method based on the polar coordinate graph convolutional neural network is characterized by comprising the following steps of:
s1, acquiring a plurality of three-dimensional mesh model data, including a vertex set and a patch set;
s2, based on the improved point cloud generating method, for each three-dimensional grid model data, setting and judging according to a threshold value, generating a point cloud, and acquiring a first point cloud corresponding to the point cloud;
s3, acquiring a corresponding volume weighted centroid for each three-dimensional grid model data;
s4, constructing a unit Gaussian sphere with the volume weighted centroid as the sphere center to wrap the first point cloud through translation, proportion and rotation transformation based on the first point cloud and the volume weighted centroid, realizing the operation of converting the first point cloud into a standard unified coordinate space, and acquiring a standardized and aligned second point cloud;
s5, projecting the second point cloud to a polar coordinate system based on the second point cloud, obtaining polar coordinate representation of the second point cloud, and splicing the polar coordinate representation of the second point cloud and three-dimensional rectangular coordinate system representation of the second point cloud to obtain the second point cloud with composite representation;
and S6, acquiring the corresponding deep learning characteristics of each second point cloud with the composite representation based on the polar coordinate graph convolution neural network model.
2. The method of claim 1, wherein in step S1, the three-dimensional mesh model data is read to obtain a vertex set V ═ V { V } of the three-dimensional mesh modeliI 1,2, n and patch set Fj1, 2.·, m }; wherein v isiRepresents the ith vertex element, vi＝(vi 1,vi 2,vi 3) Is the three-dimensional rectangular coordinate system representation of the vertex elements in the vertex set, n is the number of the vertex elements in the vertex set, fjRepresenting the jth patch element, wherein m is the number of patch elements in a patch set, and the patch set stores patch element information by using vertex index information on the patch elements.
3. The method for extracting features from a three-dimensional model based on a polar graph convolutional neural network as claimed in claim 1, wherein the step S2 comprises the steps of:
s201, based on a patch set F ═ Fj1,2,., m }, m is the number of patch elements in the patch set, and the area of each patch element in the patch set is obtained through formula calculation, wherein the formula is as followsShown below:
Figure FDA0003080454660000021
wherein
Figure FDA0003080454660000022
aj＝||(vj1-vj2)||2，bj＝||(vj1-vj3)||2，cj＝||(vj2-vj3)||2
In the formula, S (f)j) Representing the jth patch element f in a patch setjArea of (v)j1、vj2、vj3As elements f of a patchjThree vertices of (a)jRepresenting the vertex vj1And vertex vj2Two norms of the constructed vector, bjRepresenting the vertex vj1And vertex vj3Two norms of the constructed vector, cjRepresenting the vertex vj2And vertex vj3Two norms, p, of the constructed vectorjIs represented by aj、bj、cjCalculating the obtained intermediate process variable;
s202, area S (f) based on each patch element in patch setj) Calculating the average value of the whole patch element area in the patch set by a formula
Figure FDA0003080454660000023
Then, taking the average value as a threshold value, the formula is as follows:
Figure FDA0003080454660000024
s203, an original point cloud generating method is to directly perform point cloud generating operation without considering the distribution condition of the area size of each patch element in the three-dimensional grid model; the improved point cloud generating method adds condition judgment, selectively performs point cloud generating operation on the patch elements through threshold setting judgment, performs linear interpolation based on information of the patch elements in the patch set, and calculates to obtain a new vertex set, specifically as follows:
based on the set of patches F ═ Fj1, 2., m }, according to a formula, the area is larger than a threshold value
Figure FDA0003080454660000025
Performing a point cloud generation operation on the patch elements to obtain a patch element having an area less than a threshold
Figure FDA0003080454660000026
The patch elements do not carry out point cloud generation operation, so that point clouds generated by corresponding three-dimensional grid models are obtained, and the formula is as follows:
Figure FDA0003080454660000031
Figure FDA0003080454660000032
in the above formula, Set (f)j) For the jth patch element f in the patch setjSet of vertices of, vj' representation set
Figure FDA0003080454660000033
J-th vertex set in (1), q1、q2Represents [0,1 ]]Number of divisions, ω1、ω2O, p are intermediate process variables,
Figure FDA0003080454660000034
point clouds generated for the corresponding three-dimensional mesh models;
s204, point cloud generated based on corresponding three-dimensional grid model
Figure FDA0003080454660000035
According toAccording to the farthest point sampling algorithm or the random sampling method, point clouds with fixed vertex numbers are collected, a first point cloud corresponding to a three-dimensional grid model is obtained, and the formula is as follows:
Figure FDA0003080454660000036
wherein, Sample _ Function is a farthest point sampling algorithm Function or a random sampling algorithm Function, V ' is a first point cloud corresponding to the three-dimensional grid model, n ' represents the number of vertex elements in the first point cloud to be sampled, V 'kIs the kth element in the first point cloud.
4. The method for extracting features from a three-dimensional model based on a polar graph convolutional neural network as claimed in claim 1, wherein the step S3 comprises the steps of:
s301, for each three-dimensional mesh model, based on the vertex set V ═ Vi1, 2., n }, and calculating a corresponding centroid through a formula, wherein the formula is as follows:
Figure FDA0003080454660000037
in the formula (I), the compound is shown in the specification,
Figure FDA0003080454660000038
representing the centroid, v, of a three-dimensional mesh modeliIs the ith vertex element in the vertex set, and n is the number of vertex elements in the vertex set.
S302, F ═ { F } based on the patch setj1,2, the sum of m, m is the number of patch elements in the patch set, and the centroid is obtained through formula calculation
Figure FDA0003080454660000041
And patch element f in the patch setjThe volume of the formed tetrahedron, and the gravity center and the male degree of the surface patch assembly elements are obtained according to a formulaThe formulae are respectively as follows:
Figure FDA0003080454660000042
Figure FDA0003080454660000043
in the formula, VoljRepresenting the center of mass
Figure FDA0003080454660000048
With patch element f in jth patch setjVolume of tetrahedron formed, vj1、vj2、vj3As elements f of a patchjThree vertices of upper, gjRepresenting patch element f in jth patch setjThe center of gravity of;
s303 tetrahedron-based volume VoljAnd the center of gravity g of patch elements in the patch setjAnd calculating to obtain the volume weighted centroid corresponding to the three-dimensional grid model through a formula, wherein the formula is as follows:
Figure FDA0003080454660000044
in the formula (I), the compound is shown in the specification,
Figure FDA0003080454660000045
representing the corresponding volumetric weighted centroid of the three-dimensional mesh model.
5. The method for extracting features from a three-dimensional model based on a polar graph convolutional neural network as claimed in claim 1, wherein the step S4 comprises the steps of:
s401, based on the first point cloud V ═ { V ═ Vk'| k ═ 1,2,. ·, n' } and the volume weighted centroid
Figure FDA0003080454660000046
v′kFor the kth element in the first point cloud, n' represents the number of vertex elements in the first point cloud, the first point cloud is translated to the volume weighted centroid according to a formula, and the first point cloud after translation transformation is obtained, wherein the formula is as follows:
Figure FDA0003080454660000047
V″＝{v″k|k＝1,2,...n′}
in the formula, v ″)kThe k element of the first point cloud after the translation transformation is shown, and V' is the first point cloud after the translation transformation;
s402, based on the first point cloud V ″ ═ { V ″) after translation transformationk1, 2.. n', calculating a scale conversion factor according to a formula, further calculating a converted model, and obtaining a first point cloud after translation conversion and scale conversion, wherein the formula is as follows:
Figure FDA0003080454660000051
v″′k＝s·v″k,v″k∈V″
V″′＝{v″′k|k＝1,2,...n′}
wherein s is a scaling factor, v'kThe kth element of the first point cloud V' after the translation transformation and the scale transformation;
s403, based on the first point cloud V ' "{ V '" after the translation transformation and the scaling transformation 'k1,2,. n' }, calculating a rotation matrix R according to a formula; wherein the step of obtaining the rotation matrix comprises:
s4031, based on the translation transformation and the first point cloud V ', constructing a covariance matrix (V')T；
S4032, covariance matrix (V')TPerforming characteristic decomposition to obtain the first three maximumsEigenvector Vector corresponding to eigenvalue3×3；
S4033, constructing a rotation matrix R according to a formula, wherein the formula is as follows:
R＝Vector3×3·I
in the formula, I is a unit matrix with the size of 3 multiplied by 3;
s404, based on the first point cloud V ' { V ' after translation transformation and scaling transformation 'kN 'and a rotation matrix R, further performing rotation transformation on V' ″ to obtain a second point cloud after translation transformation, scaling transformation and rotation transformation, as follows:
Figure FDA0003080454660000052
Figure FDA0003080454660000061
in the formula (I), the compound is shown in the specification,
Figure FDA0003080454660000062
the k-th element of the second point cloud after the translation transformation, the scaling transformation and the rotation transformation,
Figure FDA0003080454660000063
the second point cloud is the second point cloud after translation transformation, scaling transformation and rotation transformation.
6. The method for extracting features from a three-dimensional model based on a polar graph convolutional neural network as claimed in claim 1, wherein the step S5 comprises the steps of:
s501, based on second point cloud
Figure FDA0003080454660000064
Figure FDA0003080454660000065
The k-th element of the second point cloud after the translation transformation, the scaling transformation and the rotation transformation,
Figure FDA0003080454660000066
representing by a rectangular coordinate system of a three-dimensional space of second point cloud, wherein n' represents the number of vertex elements in the second point cloud, projecting the second point cloud to a polar coordinate system according to a formula, and obtaining the polar coordinate representation of the second point cloud, wherein the formula is as follows:
Figure FDA0003080454660000067
wherein (theta)k,φk,rk) As a polar coordinate representation of the second point cloud, fsphAn operator is projected for the polar coordinate system,
Figure FDA0003080454660000068
s502, expressing the polar coordinates (theta) of the second point cloud according to a formulak,φk,rk) Three-dimensional rectangular coordinate system with second point cloud
Figure FDA0003080454660000069
The representations are spliced to obtain a composite representation
Figure FDA00030804546600000610
The second point cloud of (1).
7. The method for extracting features from a three-dimensional model based on a polar graph convolutional neural network as claimed in claim 1, wherein the step S6 comprises the steps of:
s601, representing based on having composite
Figure FDA00030804546600000611
The second point cloud and the polar coordinate graph convolution neural network model are obtained, and the corresponding depth science is obtainedLearning characteristics; the step of obtaining the polar coordinate graph convolution neural network model comprises the following steps:
s6011, designing a network structure of a polar coordinate graph convolution neural network model based on a graph convolution network mode; wherein the input of the polar plot convolutional neural network model is based on having a composite representation
Figure FDA0003080454660000071
The output of the second point cloud is the corresponding deep learning characteristic; the structure of the polar coordinate graph convolution neural network model comprises a graph building module, a residual dynamic graph convolution block, a fusion module and a prediction module; the mapping module is based on a second point cloud having a composite representation
Figure FDA0003080454660000072
Constructing a hole k neighbor graph representation of the corresponding 3 branches by using a hole k neighbor algorithm to serve as input; the residual dynamic graph convolution block comprises an EdgeConv edge convolution layer connected based on the dynamic graph convolution layer and a residual graph, and an SE attention mechanism block is embedded; the fusion module comprises a 1 × 1 convolution kernel layer and two pooling layers, wherein the 1 × 1 convolution kernel layer is followed by a Batch Normalization function of Batch by Batch and an LeakyReLU activation function, and the two pooling layers respectively use maximum pooling and average pooling; the prediction module comprises two fully-connected layers, wherein one fully-connected layer is followed by a Batch Normalization function of Batch, a LeakyReLU activation function and Dropout random inactivation;
s6012, representing based on having a composite
Figure FDA0003080454660000073
The second point cloud of (2) building a database of network training, and dividing 80% of the database into a training set and 20% of the database into a verification set, wherein the intersection of the training set and the verification set is empty, and the second point cloud is used for corresponding to the labeled real class label; on the training set, will have a composite representation
Figure FDA0003080454660000074
Inputting the second point cloud into the polar coordinate graph convolutional neural network model to obtain an output characteristic vector and a classification probability, calculating the difference between the classification probability and a real class label, and reversely adjusting the parameter value of the polar coordinate graph convolutional neural network model; on the verification set, there will be a composite representation
Figure FDA0003080454660000075
Inputting the second point cloud into a polar coordinate graph convolutional neural network model to obtain an output characteristic vector and a classification probability, calculating the difference between the classification probability and a real class label, and evaluating the performance of the polar coordinate graph convolutional neural network model; until the training is finished, using the output feature vector as the feature of the representation three-dimensional model;
s602, a second point cloud with a composite representation is to be based on
Figure FDA0003080454660000076
And inputting the data into a polar coordinate graph convolution neural network model, and extracting corresponding deep learning characteristics.
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