CN111291793A - Element classification method and device for mesh curved surface and storage medium - Google Patents

Element classification method and device for mesh curved surface and storage medium Download PDF

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CN111291793A
CN111291793A CN202010068285.8A CN202010068285A CN111291793A CN 111291793 A CN111291793 A CN 111291793A CN 202010068285 A CN202010068285 A CN 202010068285A CN 111291793 A CN111291793 A CN 111291793A
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陈虎
李虹
王勇
孙玉春
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Peking University School of Stomatology
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Abstract

The application relates to the technical field of three-dimensional modeling, and provides a method and a device for classifying elements of a mesh curved surface and a storage medium. The element classification method of the mesh surface comprises the following steps: acquiring an attribute value of each element of the mesh curved surface, wherein the element is a vertex or a surface; iteratively updating the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, and taking the attribute values of the elements obtained when iteration is finished as the characteristics of the elements; the elements are classified using a classifier based on the characteristics of each element. The method effectively utilizes regional information of elements in the feature calculation process, and continuously optimizes the feature calculation result through iteration, so that the accuracy, reliability and robustness of element classification of the mesh surface can be obviously improved.

Description

Element classification method and device for mesh curved surface and storage medium
Technical Field
The invention relates to the technical field of three-dimensional modeling, in particular to a method and a device for classifying elements of a mesh curved surface and a storage medium.
Background
With the development of three-dimensional optical scanning technology, more and more entities are scanned as digital models. The optical scanning technology is an important technology for acquiring three-dimensional surface data of an object, and based on a triangulation or raster projection method, point cloud data of a model surface can be acquired and converted into a mesh (e.g., a triangular mesh), the mesh generally consists of vertices, edges and faces, the edges represent the connection relationship between two vertices, and the faces represent the connection relationship between a plurality of vertices (e.g., the faces represent the connection relationship between three vertices if the faces are triangles).
Mesh vertex classification is an important application based on meshes, and aims to classify mesh vertices into different categories, each of which may correspond to a component of an entity. For example, a mesh for a human body may have its vertices divided into vertices belonging to the head, vertices belonging to the torso, vertices belonging to the limbs, and so on. However, in the prior art, mesh vertices are generally regarded as unordered point clouds, and the vertex attributes are directly used for classification, so that the classification result is difficult to achieve high accuracy, reliability and robustness.
Disclosure of Invention
An object of the embodiments of the present application is to provide a method, an apparatus, and a storage medium for classifying elements of a mesh surface, so as to solve the above technical problem.
In order to achieve the above purpose, the present application provides the following technical solutions:
in a first aspect, an embodiment of the present application provides a method for classifying elements of a mesh surface, including: acquiring an attribute value of each element of the mesh surface, wherein the element is a vertex or a surface; iteratively updating the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, and taking the attribute values of the elements obtained when iteration is finished as the features of the elements; classifying each element using a classifier based on the characteristics of the element.
The method is not to directly use the attribute values of the elements (vertexes or surfaces) of the mesh curved surface for classification, but only uses the attribute values of the elements as original input, iteratively updates the attribute values of the elements by using the attribute values of the elements in the neighborhood of the elements, and classifies the elements by using the characteristics of the elements obtained when iteration is finished. Because regional information (neighborhood) of elements is effectively utilized in the feature calculation process, namely, the topological structure among the elements is fully considered, and the feature calculation result is continuously optimized through iteration, the accuracy, reliability and robustness of element classification of the mesh surface can be obviously improved.
In an implementation manner of the first aspect, the iteratively updating the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element includes: determining a multi-ring neighborhood of each element, and respectively counting each attribute value of the elements in each ring neighborhood to obtain an attribute statistical value matrix of each ring neighborhood; wherein, the 0 th ring neighborhood of any element is the element itself, the 1 st ring neighborhood is a set formed by elements directly adjacent to the element, the k-th ring neighborhood is a set formed by removing the elements in the k-1 st ring neighborhood and the k-2 nd ring neighborhood from the elements directly adjacent to the k-1 st ring neighborhood, and k is more than 1; a vertex directly adjacent to one vertex means a vertex directly connected to the vertex through an edge, and a face directly adjacent to one face means a face having a common vertex with the face; forming an extended attribute matrix based on the attribute statistic value matrix of each ring neighborhood of each element; calculating a new attribute value of each element according to the extended attribute matrix, and updating the attribute value of the element by using the new attribute value; and iteratively updating the attribute value of each element in an attribute expansion mode.
The above implementation mode provides a specific definition mode of the element neighborhood, that is, the neighborhood of an element can be divided into multiple rings, wherein the 0 th ring neighborhood is the central element itself, and the number of rings of other ring neighborhoods represents the distance between the element in the ring neighborhood and the central element in the topological sense. Under the definition mode, elements with the same distance in the topological sense as the central element are classified into the same ring neighborhood of the central element, and the topological relation among the elements is fully explored, so that the subsequent feature calculation result is reasonable.
In an implementation manner of the first aspect, the calculating a new attribute value of each element according to the extended attribute matrix includes: processing the extended attribute matrix by utilizing a pre-trained network layer to obtain a new attribute value of each element; wherein, the network layer is a convolution layer or a full connection layer.
In an implementation manner of the first aspect, in a process of iteratively updating an attribute value of each element in an attribute extension manner, network layers used in each iteration are independent from each other, and the network layers used in each iteration form a pre-trained neural network.
In the two implementation modes, the machine learning method is introduced into the feature extraction process of the elements by setting the network layer or the neural network formed by the network layer, and the network layer is embodied to have learnable parameters (such as weight, bias and the like of the convolutional layer), so that parameter values can be continuously optimized for the feature extraction task in the training process, the parameter values can effectively reflect the distribution mode of features in the neighborhood, the feature extraction process of the elements is more intelligent, the feature extraction result is favorably improved, and finally the element classification result of the grid curved surface is improved.
In one implementation of the first aspect, the determining a multi-ring neighborhood for each element includes: the multiple ring neighborhood is continuously selected from the total ring neighborhood of each element, or the multiple ring neighborhood is intermittently selected from the total ring neighborhood of each element.
The multi-ring neighborhood of each element is selected flexibly, and can be selected continuously or discontinuously from all the ring neighborhoods of the elements. For example, when the mesh vertices are dense, the mesh vertices may be selected discontinuously to reduce the amount of subsequent operations, and since the vertex positions of neighboring ring neighbors are not greatly different, the final vertex classification result is not significantly affected by the discontinuous selection of the multi-ring neighbors.
In one implementation of the first aspect, the attribute value statistics include at least one of: taking the maximum value, taking the minimum value, taking the mean value, taking the median, taking the upper quartile and taking the lower quartile.
In an implementation manner of the first aspect, if the element is a vertex, the attribute value of the vertex includes at least one of the following: coordinates, curvature and normal of the vertex; if the element is a surface, the attribute value of the surface comprises at least one of the following: the coordinates of the apex of the face, the coordinates of the center of the face, and the normal to the face.
In an implementation manner of the first aspect, the iteratively updating the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element includes: determining an attribute matrix
Figure BDA0002376464680000041
Wherein v isjFor the elements of the mesh surface, Ft (v)j) Representing element vjJ is any integer from 1 to N, both N and M are positive integers, and N represents the total number of elements of the mesh surface; determining a continuous K ring neighborhood of each element from the 0 th ring neighborhood; if K is 0, the kth ring neighborhood of any element is the element itself, if K is 1, the kth ring neighborhood of any element is a set formed by elements directly adjacent to the element, if 1 < K, the kth ring neighborhood of any element is a set formed by elements directly adjacent to the kth ring neighborhood, except for a set formed by elements in the kth-1 ring neighborhood and the kth-2 ring neighborhood, and K is a positive integer; a vertex directly adjacent to one vertex means a vertex directly connected to the vertex through an edge, and a face directly adjacent to one face means a face having a common vertex with the face; determining any value of the adjacency matrix A, A
Figure BDA0002376464680000042
Wherein the content of the first and second substances,
Figure BDA0002376464680000043
is an element viWhen element v is the k-th ring neighborhood ofjIs a neighborhood
Figure BDA0002376464680000044
When element(s) is (are), Ak,i,jGet 1, otherwise Ak,i,jTaking 0, wherein i is any integer from 1 to N; calculating any value B in the complete attribute matrix B, Bk,i,m,j＝Ak,i,j*Xj,m(ii) a Wherein, when the element vjIs a neighborhood
Figure BDA0002376464680000045
When element(s) is (B)k,i,m,jRepresenting element viOf the kth ring neighborhood of (1)jWhen the element v is the m-th attribute value ofjIs not a neighborhood
Figure BDA0002376464680000046
When element(s) is (B)k,i,m,j0, M is any integer from 1 to M; calculating any value C in the fully extended attribute matrix C, Ck,i,p,m＝Sp(Bk,i,m,j) (ii) a Wherein, Ck,i,p,mRepresenting element viThe mth attribute value of the element in the kth ring neighborhood adopts an attribute value statistical mode SpPerforming statistics, wherein P is any integer from 1 to P, P is a positive integer, and P represents the total number of attribute value statistics modes; determining a set of numerical values corresponding to the specified ring neighborhood in the fully extended attribute matrix C as an extended attribute matrix; calculating a new attribute value of each element according to the extended attribute matrix, and updating the attribute value of the element by using the new attribute value; and iteratively updating the attribute value of each element in an attribute expansion mode.
The implementation mode provides a method for calculating the extended attribute matrix, the calculation process is simple and quick, and the definition of the extended attribute matrix is consistent with the foregoing.
In a second aspect, an embodiment of the present application provides an apparatus for classifying elements of a mesh surface, including: the attribute value acquisition module is used for acquiring the attribute value of each element of the mesh curved surface, wherein the element is a vertex or a surface; the attribute value iteration module is used for carrying out iteration updating on the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, and taking the attribute values of the elements obtained when the iteration is finished as the features of the elements; and the element classification module is used for classifying the elements by utilizing a classifier based on the characteristics of each element.
In a third aspect, an embodiment of the present application provides a computer-readable storage medium, where computer program instructions are stored on the computer-readable storage medium, and when the computer program instructions are read and executed by a processor, the computer program instructions perform the steps of the method provided in the first aspect or any one of the possible implementation manners of the first aspect.
In a fourth aspect, an embodiment of the present application provides an electronic device, including: a memory in which computer program instructions are stored, and a processor, where the computer program instructions, when read and executed by the processor, perform the steps of the method provided by the first aspect or any one of the possible implementations of the first aspect.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
FIG. 1 is a flowchart illustrating an element classification method for a mesh surface according to an embodiment of the present application;
fig. 2 is a flowchart illustrating step S110 of a method for classifying elements of a mesh surface according to an embodiment of the present application;
FIG. 3 is a functional block diagram of an apparatus for classifying elements of a mesh surface according to an embodiment of the present application;
fig. 4 shows a schematic diagram of an electronic device provided in an embodiment of the present application.
Detailed Description
The technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures. The terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The inventor has found that, in the method for classifying mesh vertices provided in the comparison embodiment, since the mesh vertices are regarded as unordered point clouds and are classified by directly using the attribute values of the vertices, the topological structure between the mesh vertices cannot be considered, so that the regional characteristics of the mesh surface cannot be effectively captured, and the classification result cannot achieve high accuracy, reliability and robustness. On this basis, embodiments of the present application provide a method, an apparatus, a storage medium, and an electronic device for classifying elements of a mesh surface, where an attribute value of each element in a neighborhood of each element is used to perform iterative update on the attribute value of the element to extract features of the element, and the extracted features are used to classify the element. The regional information around the elements is fully utilized in the calculation process of the features, so that the obtained classification result has higher accuracy, reliability and robustness.
Fig. 1 shows a flowchart of an element classification method for a mesh surface provided in an embodiment of the present application, which may be performed by an electronic device, and fig. 4 shows a possible structure of the electronic device, which may be referred to as described later. Referring to fig. 1, the element classification method of the mesh surface includes:
step S100: an attribute value of each element of the mesh surface is obtained.
The elements of the mesh surface refer to basic geometric elements forming the mesh surface, and the mesh surface generally comprises three elements of a vertex, an edge and a surface. In the solution of the present application, the elements to be classified are vertices or faces of the mesh surface, and thus reference to the elements hereinafter refers only to the vertices or faces of the mesh surface, and does not include edges. Moreover, it should be further noted that, when the element classification method for mesh surfaces provided in the embodiments of the present application is used for classifying vertices, all elements mentioned in the method refer to vertices (and none of the elements refer to faces); when the element classification method for the mesh surface provided by the embodiment of the application is used for face classification, all elements mentioned in the method refer to faces (and none of the elements refer to vertices).
If an element is a vertex, its attribute values include at least one of: coordinates of the vertex, curvature of the vertex, and a normal direction of the vertex; if an element is a surface, its attribute values include at least one of: the coordinates of the apex of the face, the coordinates of the center of the face, and the normal to the face. Wherein, the attribute related to the coordinate, for example, the coordinate of the vertex, may include three coordinate values in the three-dimensional space, and the three coordinate values may be respectively used as one attribute value, for a total of three attribute values. It will be appreciated that elements may also include other attribute values, by way of example only. For a certain mesh surface, the above attribute values of the elements can be obtained by simple calculation, and the specific method can refer to the prior art and is not described here.
Step S110: and iteratively updating the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, and taking the attribute values of the elements obtained when the iteration is finished as the characteristics of the elements.
A neighborhood of an element in a mesh surface is a set of elements (possibly including the element itself) that are adjacent to the element in a manner that, when the content related to the neighborhood is described later, the element is sometimes referred to as a central element, which is convenient for distinguishing from other elements in the neighborhood. The proximity in the above sense may be in a spatial sense, e.g. within a certain distance from the element, or in a topological sense, e.g. directly or indirectly adjacent to the element.
Since the attribute value of each element of the mesh surface has already been acquired in step S100, the attribute values of the elements in the neighborhood of each element are known. Based on the attribute values of the elements in the neighborhood, a preset algorithm is used to calculate a new attribute value of the central element of the neighborhood, and then the new attribute value is used to update the original attribute value of the central element in step S100, i.e. one iteration is completed. Updating here is to be understood as replacing all original attribute values with all new attribute values as a whole, since the number of new attribute values and original attribute values is not necessarily the same and therefore not necessarily a simple numerical update. After one iteration is completed, whether an iteration ending condition is met or not can be judged, if yes, the iteration is ended, step S120 is executed, if not, the iteration is continued, namely, a new attribute value of a central element of a neighborhood is calculated by using a preset algorithm based on the attribute value of an element in the neighborhood of each element (the neighborhood of the element can be determined again and can also be used in the previous iteration), then, the attribute value of the central element after the previous iteration is updated by using the new attribute value, and the process is repeated until the iteration ending condition is met. The above-mentioned predetermined algorithm is not limited, and specific examples will be given later. The iteration ending condition is not limited, and may be, for example, ending after a preset number of iterations, ending after a preset time of iterations, ending after no change or no change substantially of an attribute value generated by the iterations, and the like.
After the iteration is completed, the attribute value of the element obtained at the end of the iteration is used as the feature of the element, and if the iteration is performed a plurality of times, the feature can be regarded as a high-level attribute value.
Fig. 2 shows one possible implementation manner of step S110, and referring to fig. 2, step S110 may further include:
step S200: a multi-ring neighborhood for each element is determined.
Step S200 gives a way to define the neighborhood of each element: defining the neighborhood of each element according to a ring mode, and specifically operating according to the following rules:
(1) the 0 th ring neighborhood is the element itself.
(2) The 1 st ring neighborhood is a set of elements immediately adjacent to the element. For example, if an element is a vertex, vertices directly adjacent to a vertex refer to those vertices that are directly connected to the vertex by an edge; if the elements are faces, the faces directly adjacent to a face refer to those faces that have a common vertex (at least one common vertex) with the face.
(3) The k-th ring neighborhood is a set of elements immediately adjacent to the k-1-th ring neighborhood excluding elements in the k-1-th ring neighborhood and the k-2-th ring neighborhood. Wherein k > 1.
The following further describes the above rules by mathematical expressions:
for a three-dimensional mesh surface, it is assumed that it has N elements (N vertices or N surfaces) in total, and these N elements form a set V, and for the element Vie.V (i is an arbitrary integer from 1 to N), usingIs represented by the formulaiA set of directly adjacent elements. If element viIs a vertex, then
Figure BDA0002376464680000092
Representation and vertex viA set of vertices connected directly by edges; if the element viIs a surface, then
Figure BDA0002376464680000093
Representation and surface viA collection of faces having a common vertex.
Further, for a set of elements
Figure BDA0002376464680000094
And VsThe set of directly adjacent elements can be represented as:
Figure BDA0002376464680000095
on the basis of the above, the element viIs defined as viBy itself, that is:
Figure BDA0002376464680000096
element viIs defined as the sum of v and 1 ring neighborhood ofiThe set of directly adjacent elements, namely:
Figure BDA0002376464680000097
element viIs defined as a set that is directly adjacent to the 1-ring neighborhood but excludes elements in the 1-ring neighborhood and the 0-ring neighborhood, i.e.:
Figure BDA0002376464680000098
element viIs defined as the set of elements immediately adjacent to the k-1 ring neighborhood but excluding the k-1, k-2, …, 0 ring neighborhoods, i.e.:
Figure BDA0002376464680000099
but since the k-ring neighborhood does not directly neighbor elements in the k-2 ring or smaller neighborhood, i.e.:
Figure BDA00023764646800000910
the definition of the k-ring neighborhood can be simplified as:
Figure BDA00023764646800000911
i.e., in accordance with rule (3) above.
According to the above definition of each ring neighborhood, the number of rings in the neighborhood actually represents the distance between the element in the ring neighborhood and the central element in the topological sense. Taking a vertex as an example, the distance is that the elements in the neighborhood can be connected with the central vertex through several edges, for example, the elements in the 0-ring neighborhood can be connected with the central vertex without edges, the vertices in the 1-ring neighborhood can be connected with the central vertex by 1 edge, the vertices in the 2-ring neighborhood can be connected with the central vertex by 2 edges, and so on. It can be seen that, in the definition mode, the elements with the same distance in the topological sense as the central element are classified into the same ring neighborhood of the central element, and the local topological relation of the elements is fully explored, so that the subsequent calculation result about the element characteristics is reasonable.
The multi-ring neighborhood determined in step S200 may be continuously selected from all ring neighborhoods of the element, for example, ring neighborhoods 0, 1, 2, …, ring neighborhoods 2, 3, 4, …, etc., or may be intermittently selected from all ring neighborhoods of the element, for example, ring neighborhoods 0, 2, 4, …, ring neighborhoods 0, 4, 8, …, ring neighborhoods 2, 4, 6, etc. (when intermittently selected, the ring neighborhoods may be equally spaced or unequally spaced), which is more flexible, and how to select the multi-ring neighborhood may be determined according to the requirement.
For example, assuming that the elements are vertices, the case of discontinuous selection can be used when the vertices of the mesh are dense (for example, the collected point cloud data is densely distributed, and thus the vertices of the mesh are also very dense). The discontinuous selection of the multi-ring neighborhood can obtain a larger neighborhood range by comparing a small number of rings, so that the regional information in a larger range near the vertex can be utilized as much as possible for vertex classification on the premise of saving the operation amount. And at the moment, because the vertex positions of the adjacent ring neighborhoods are not greatly different, the accuracy of the final vertex classification result is not obviously influenced by discontinuously selecting the multiple ring neighborhoods.
Step S210: and respectively counting each attribute value of the element in each ring neighborhood of each element to obtain an attribute statistical value matrix of each ring neighborhood.
There are usually multiple elements in a ring neighborhood, so even if only one attribute value is considered, there are multiple attribute values, and the statistical operation in step S210 can calculate one attribute value based on these multiple attribute values, which is not referred to as an attribute statistical value of the ring neighborhood. The statistical manner of the attribute values may include, but is not limited to, at least one of the following: taking the maximum value, taking the minimum value, taking the mean value, taking the median, taking the upper quartile and taking the lower quartile.
Step S210 is explained below by a mathematical expression:
assuming that each element of the mesh surface has M attribute values, element viIs a collection of attribute valuesCan be expressed as follows:
Ft(vi)＝[ft1(vi)ft2(vi)…ftM(vi)
wherein ftm(vi) Denotes viM is any integer from 1 to M.
Assuming that the statistical modes of the attribute values include three modes of taking a Mean value (marked as Mean), a maximum value (marked as Max) and a minimum value (marked as Min), then for the element set VsThe average value is adopted for counting all attribute values of all elements in the data to obtain VsSet of attribute mean values of:
Figure BDA0002376464680000111
wherein S is a set VsThe number of elements in (1) is similarly, respectively, for VsThe attribute values of all the elements in the system are counted by adopting a maximum value taking mode and a minimum value taking mode, and V can be obtainedsProperty maximum value set of (1):
Figure BDA0002376464680000112
and, VsProperty minimum value set of (1):
Figure BDA0002376464680000113
v can be formed based on the three setssThe attribute statistic value matrix of (2):
Figure BDA0002376464680000114
the ellipses below indicate that other statistics of attribute values may also exist.
Obviously, the above VsAny ring neighborhood that can be any element of a mesh surface
Figure BDA0002376464680000115
(Note that the value range of k here is relaxed to be a non-negative integer, slightly different from the previous one), so that
Figure BDA0002376464680000116
Can be recorded as
Figure BDA0002376464680000117
Step S220: and forming an extended attribute matrix based on the attribute statistic value matrix of each ring neighborhood of each element.
Each value in the extended attribute matrix (each value in the matrix is generally referred to as an element of the matrix, but the term value in the matrix is used herein to avoid confusion with elements of the mesh surface) corresponds to an attribute statistics matrix (obtained in step S210) of a certain ring neighborhood of a certain element.
Step S220 is described below by a mathematical expression:
for a mesh surface comprising N elements, each element having M attributes, an attribute matrix X may be defined as follows:
Figure BDA0002376464680000121
wherein, Ft (v)i) The definitions of (a) and (b) have already been given above.
On this basis, an attribute statistic matrix of a k-ring neighborhood (k is a non-negative integer) of the mesh surface may be defined, that is, a matrix formed by attribute statistic matrices of k-ring neighborhoods of all elements of the mesh surface, as follows:
Figure BDA0002376464680000122
obviously, XkAll values in (a) can be calculated in step S210.
Further, based on XkThe extended attribute matrix Expand can be obtained by calculation0,1,…,K-1(X) as follows:
Figure BDA0002376464680000123
the Expand represents an attribute expansion algorithm, the upper right corner of Expand represents the multi-ring neighborhood acquired in step S200, for example, the above formula represents that a K ring neighborhood (K is a positive integer) is continuously selected from the 0 th ring neighborhood, and of course, as described above, the K ring neighborhood may also be selected discontinuously, and at this time, the above formula is only slightly adjusted.
One of the most straightforward implementations of the above-described attribute expansion algorithm Expand is to calculate strictly according to the above formula, for example, for Expand0,1,…,k-1(X), can be calculated first
Figure BDA0002376464680000131
Recalculate XkAnd finally obtaining Expand0,1,…,k-1(X) (or directly by
Figure BDA0002376464680000132
Obtaining Expand0,1,…,k-1(X) may be used). Besides the strict definition formula of the extended attribute matrix, other algorithms can be used to quickly calculate the extended attribute matrix, such as the following calculation method, but it should be noted that the calculation result of the extended attribute matrix is consistent no matter which algorithm is used.
Step A: determine the shape of the attribute matrix X, X as [ N, M ] (each value in square brackets represents the size of the matrix in one dimension):
Figure BDA0002376464680000133
wherein v isjBeing an element of a mesh surface, Ft (v)j) Representing element vjJ is any integer from 1 to N.
And B: and determining continuous K ring neighborhoods (namely 0 ring neighborhood to K-1 ring neighborhood) of each element from the 0 ring neighborhood, wherein K is a positive integer.
And C: determining the shape of the adjacency matrix A, A as [ K, N, N ], wherein any value in A is defined as follows:
Figure BDA0002376464680000134
wherein the content of the first and second substances,
Figure BDA0002376464680000135
is an element viIn the k-th ring neighborhood of (c), the above formula means if the element vjIs a neighborhood
Figure BDA0002376464680000136
Of (1), then Ak,i,jGet 1, otherwise Ak,i,jTaking 0, K is any integer from 0 to K-1, and i is any integer from 1 to N.
Step D: calculating the shape of the complete attribute matrix B, B as [ K, N, M, N ], wherein any value in B is defined as follows:
Bk,i,m,j＝Ak,i,j*Xj,m
wherein, if the element vjIs the element vjIn the k-th ring neighborhood of (2)
Figure BDA0002376464680000141
When element in (1) is (B)k,i,m,jRepresenting element viOf the kth ring neighborhood of (1)jIf the element v is the mth attribute value ofjIs not a neighborhood
Figure BDA0002376464680000142
Of (1), then Bk,i,m,jAnd M is any integer from 1 to M.
Step E: calculating the shape of the fully extended attribute matrix C, C as [ K, N, P, M ], wherein any value in C is defined as follows:
Ck,i,p,m＝Sp(Bk,i,m,j)
wherein, Ck,i,p,mRepresenting element viThe mth attribute value of the element in the kth ring neighborhood adopts an attribute value statistical mode SpAnd (3) performing a statistical result (counting the dimension of j is performed) (M attributes of the elements can be arranged according to a uniform preset sequence, so that the mth attribute values of all the elements in the kth ring neighborhood are the same attribute value, and statistics can be performed), wherein P is any integer from 1 to P, P is a positive integer, and P represents the total number of attribute value statistical modes. Statistical method S of attribute valuespOne of the above-mentioned ways of taking the maximum value, taking the minimum value, taking the mean value, taking the median, taking the upper quartile, taking the lower quartile, etc., taking the mean value, taking the maximum value, taking the minimum value as an example, Ck,i,p,mIt can be calculated as follows:
Spto take an average (p ═ 1):
Figure BDA0002376464680000143
wherein the symbol ∑jMeaning that j takes 1 through N, the contents after the symbol are summed.
SpTo get maximum (p ═ 2):
Figure BDA0002376464680000144
wherein, the symbol
Figure BDA0002376464680000145
Means j is taken over to satisfy Ak,i,jAll values of 1 (i.e. satisfy
Figure BDA0002376464680000146
The value set of all j) and the content after the symbol is maximized. The reason why the value set is limited to j is that a value of 0 is artificially set in the matrix B, and if the attribute values are all negative values, the obtained attribute statistic may be an artificially set value of 0 instead of a true attribute value.
SpTaking the size (p ═ 3):
Figure BDA0002376464680000151
wherein, the symbol
Figure BDA0002376464680000152
Means j is taken over to satisfy Ak,i,jAll values of 1 (i.e. satisfy
Figure BDA0002376464680000153
The value set of all j) and the minimum value is calculated for the content after the symbol.
Step F: and determining a set of numerical values corresponding to the specified ring neighborhood in the fully extended attribute matrix C as an extended attribute matrix.
The specified ring neighborhoods herein refer to those ring neighborhoods that are ultimately to be included in the extended attribute matrix, e.g., for Expand0,1,…,K-1(X), the designated ring neighborhood is the 0 th, 1 st, … th, K-1 st ring neighborhood, i.e.:
Expand0,1,…,K-1(X)＝C
for Expand0,2,4(X), the designated ring neighborhood is the 0 th, 2 th, 4 th ring neighborhood, i.e.:
Expand0,2,4(X)＝C[0,2,4],:,:,:
for Expand0,4,8(X), the designated ring neighborhood is the 0 th, 4 th, 8 th ring neighborhood, i.e.:
Expand0,4,8(X)＝C[0,4,8],:,:,:
for Expand0,2,4(X) and Expand0,4,8(X) can be obtained directly from C by means of slicing.
If the extended attribute matrix is calculated by the above steps a to F, the steps S200 to S220 do not need to be executed, but since the algorithm does not affect the calculated extended attribute matrix, the step S230 can be continuously executed after the step S220 or the step F is executed.
Step S230: and calculating a new attribute value of each element according to the extended attribute matrix, and updating the attribute value of the element by using the new attribute value.
In one implementation, the extended attribute matrix may be processed using a pre-trained convolutional layer to obtain a new attribute value for each element, and then the attribute value is updated. The convolutional layer or the fully-connected layer may also be referred to as a network layer.
For example, if the attribute matrix Expand is extended0,1,…,k-1(X) is C, then its shape is [ K, N, P, M]For example, in the case of using a convolutional layer, C can be first reshaped (reshaped) to [ K, NxP, M ]]Then using the convolution kernel size of [ K, P ]]M number of channels, convolution step length [ P, 1 ]]Convolving the reshaped C with convolution layers having R convolution kernels and VALID convolution filling mode to obtain X' with the shape of [ N, R]Each value in X' is a new attribute value, and it is easy to see that, since R is not necessarily equal to M, the number of attribute values of each element is changed from M to R after the attribute values are updated.
After the updating of the attribute value is completed, it may be determined whether an iteration end condition is satisfied, if so, the iteration is ended and step S120 is executed, otherwise, the iteration continues in the attribute value expansion manner. That is, if the extended attribute matrix is calculated in steps S200 to S220, the process may jump to step S200 to continue the process (step S200 may be skipped if the multi-ring neighborhood determined before is used), or, if the extended attribute matrix is calculated in steps a to F, the process may jump to step a to continue the process (likewise, some steps, such as step B, may be skipped if repeated execution is not needed). And continuing iteration until an iteration ending condition is met, and taking the attribute value of the element obtained when the iteration ends as the feature of the element, so that the whole iteration process can also be regarded as a process for extracting the feature of the element.
In each iteration, if a network layer is used to calculate the new attribute value, the network layers used in each iteration may be independent from each other, and these network layers may form a pre-trained neural network. In the above implementation manner, the machine learning method is introduced into the feature extraction process of the element by setting the network layer or the neural network formed by the network layer, and is embodied that the network layer has learnable parameters (such as weight, bias and other parameters), so that parameter values can be continuously optimized for the feature extraction task in the training process, the parameter values can effectively reflect the distribution pattern of features in the neighborhood of the element, the feature extraction process of the element is more intelligent, the feature extraction result is improved, and finally the element classification result of the grid curved surface is improved.
Step S120: the elements are classified using a classifier based on the characteristics of each element.
The type of the classifier in this step is not limited, and may be, for example, a softmax classifier, an SVM classifier, etc., and the specific process of classifying by the classifier may refer to the prior art, which is not specifically described here, and as the classification result, the category and the corresponding confidence of each element may be given.
In summary, the method for classifying elements of a mesh surface provided in the embodiment of the present application does not directly use the attribute values of the elements of the mesh surface for classification, but only uses the attribute values of the elements as original inputs, iteratively updates the attribute values of the elements by using the attribute values of the elements in the neighborhood of the elements, and classifies the elements by using the features of the elements obtained when iteration is finished. Because regional information (referring to topological relations such as connection relations among elements in a neighborhood) of the elements is effectively utilized in the feature calculation process, and the feature calculation result is continuously optimized through iteration, the accuracy, reliability and robustness of element classification of the mesh surface can be obviously improved.
In some implementation modes of the method, trainable neural network can be introduced to assist iterative updating of element attribute values, so that the extraction process of element features is more intelligent, and the element classification result is further improved.
In addition, the method can be used for classifying the vertexes of the mesh curved surface and classifying the surface of the mesh curved surface, and is wide in application range and high in use value.
Fig. 3 is a functional block diagram of an element classification apparatus 300 for mesh surfaces according to an embodiment of the present application. Referring to fig. 3, the element classification apparatus 300 for mesh surfaces includes:
an attribute value obtaining module 310, configured to obtain an attribute value of each element of the mesh surface, where the element is a vertex or a surface;
an attribute value iteration module 320, configured to iteratively update the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, and use the attribute values of the elements obtained when the iteration is finished as features of the elements;
an element classification module 330, configured to classify each element using a classifier based on a feature of the element.
In one implementation of the apparatus 300 for classifying elements of a mesh surface, the attribute value iteration module 320 iteratively updates the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, including: determining a multi-ring neighborhood of each element, and respectively counting each attribute value of the elements in each ring neighborhood to obtain an attribute statistical value matrix of each ring neighborhood; wherein, the 0 th ring neighborhood of any element is the element itself, the 1 st ring neighborhood is a set formed by elements directly adjacent to the element, the k-th ring neighborhood is a set formed by elements directly adjacent to the k-1 st ring neighborhood except the k-1 st ring neighborhood and the k-2 nd ring neighborhood, and k is more than 1; a vertex directly adjacent to one vertex means a vertex directly connected to the vertex through an edge, and a face directly adjacent to one face means a face having a common vertex with the face; forming an extended attribute matrix based on the attribute statistic value matrix of each ring neighborhood of each element; calculating a new attribute value of each element according to the extended attribute matrix, and updating the attribute value of the element by using the new attribute value; and iteratively updating the attribute value of each element in an attribute expansion mode.
In one implementation of the apparatus 300 for classifying elements of a mesh surface, the attribute value iteration module 320 calculates a new attribute value of each element according to the extended attribute matrix, including: processing the extended attribute matrix by utilizing a pre-trained network layer to obtain a new attribute value of each element; wherein, the network layer is a convolution layer or a full connection layer.
In one implementation of the device 300 for classifying elements of a mesh surface, in the process of iteratively updating the attribute value of each element in an attribute expansion manner, the network layers used in each iteration are independent from each other, and the network layers used in each iteration form a pre-trained neural network.
In one implementation of the apparatus 300 for classifying elements of a mesh surface, the attribute value iteration module 320 determines a multi-ring neighborhood of each element, including: the multiple ring neighborhood is continuously selected from the total ring neighborhood of each element, or the multiple ring neighborhood is intermittently selected from the total ring neighborhood of each element.
In one implementation of the apparatus 300 for classifying elements of mesh surfaces, the attribute value statistical method includes at least one of the following: taking the maximum value, taking the minimum value, taking the mean value, taking the median, taking the upper quartile and taking the lower quartile.
In one implementation of the apparatus 300 for classifying elements of a mesh surface, if the element is a vertex, the attribute value of the vertex includes at least one of the following: coordinates, curvature and normal of the vertex; if the element is a surface, the attribute value of the surface comprises at least one of the following: the coordinates of the apex of the face, the coordinates of the center of the face, and the normal to the face.
In one implementation of the apparatus 300 for classifying elements of a mesh surface, the attribute value iteration module 320 iteratively updates the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, including: determining an attribute matrix
Figure BDA0002376464680000191
Wherein v isjFor the elements of the mesh surface, Ft (v)j) Representing element vjJ is any integer from 1 to N, both N and M are positive integers, and N represents the total number of elements of the mesh surface; determining a continuous K ring neighborhood of each element from the 0 th ring neighborhood; wherein if K is 0, the kth ring neighborhood of any element is the element itself, if K is 1, the kth ring neighborhood of any element is a set of elements directly adjacent to the element, and if 1 < K, the kth ring neighborhood of any element is a set of elements directly adjacent to the kth-1 ring neighborhoodRemoving a set formed by elements in a K-1 ring neighborhood and a K-2 ring neighborhood from the set formed by the elements, wherein K is a positive integer; a vertex directly adjacent to one vertex means a vertex directly connected to the vertex through an edge, and a face directly adjacent to one face means a face having a common vertex with the face; determining any value of the adjacency matrix A, A
Figure BDA0002376464680000192
Wherein the content of the first and second substances,
Figure BDA0002376464680000193
is an element viWhen element v is the k-th ring neighborhood ofjIs a neighborhood
Figure BDA0002376464680000194
When element(s) is (are), Ak,i,jGet 1, otherwise Ak,i,jTaking 0, wherein i is any integer from 1 to N; calculating any value B in the complete attribute matrix B, Bk,i,m,i＝Ak,i,j*Xj,m(ii) a Wherein, when the element vjIs a neighborhood
Figure BDA0002376464680000195
When element(s) is (B)k,i,m,jRepresenting element viOf the kth ring neighborhood of (1)jWhen the element v is the m-th attribute value ofjIs not a neighborhood
Figure BDA0002376464680000196
When element(s) is (B)k,i,m,j0, M is any integer from 1 to M; calculating any value C in the fully extended attribute matrix C, Ck,i,p,m＝Sp(Bk,i,m,j) (ii) a Wherein, Ck,i,p,mRepresenting element viThe mth attribute value of the element in the kth ring neighborhood adopts an attribute value statistical mode SpPerforming statistics, wherein P is any integer from 1 to P, P is a positive integer, and P represents the total number of attribute value statistics modes; determining a set of numerical values corresponding to the specified ring neighborhood in the fully extended attribute matrix C as an extended attribute matrix; computing each element from the extended attribute matrixUpdating the attribute value of the element by using the new attribute value; and iteratively updating the attribute value of each element in an attribute expansion mode.
The implementation principle and the resulting technical effect of the device 300 for classifying elements of mesh surfaces provided in the embodiments of the present application have been introduced in the foregoing method embodiments, and for the sake of brief description, reference may be made to the corresponding contents in the method embodiments where no part of the device embodiments is mentioned.
Fig. 4 shows a possible structure of an electronic device 400 provided in an embodiment of the present application. Referring to fig. 4, the electronic device 400 includes: a processor 410, a memory 420, and a communication interface 430, which are interconnected and in communication with each other via a communication bus 440 and/or other form of connection mechanism (not shown).
The Memory 420 includes one or more (Only one is shown in the figure), which may be, but not limited to, a Random Access Memory (RAM), a Read Only Memory (ROM), a Programmable Read-Only Memory (PROM), an Erasable Read-Only Memory (EPROM), an electrically Erasable Read-Only Memory (EEPROM), and the like. The processor 410, as well as possibly other components, may access, read, and/or write data to the memory 420.
The processor 410 includes one or more (only one shown) which may be an integrated circuit chip having signal processing capabilities. The Processor 410 may be a general-purpose Processor, and includes a Central Processing Unit (CPU), a Micro Control Unit (MCU), a Network Processor (NP), or other conventional processors; or a special-purpose Processor, including a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, a discrete Gate or transistor logic device, and a discrete hardware component.
Communication interface 430 includes one or more (only one shown) devices that can be used to communicate directly or indirectly with other devices for data interaction. The communication interface 430 may be an ethernet interface; may be a high-speed network interface (such as an Infiniband network); may be a mobile communications network interface, such as an interface for a 3G, 4G, 5G network; the interface CAN be various bus interfaces, such as USB, CAN, I2C, SPI and the like; or may be other types of interfaces having data transceiving functions.
One or more computer program instructions may be stored in the memory 420 and read and executed by the processor 410 to implement the steps of the element classification method for mesh surfaces provided by the embodiments of the present application and other desired functions.
It will be appreciated that the configuration shown in fig. 4 is merely illustrative and that electronic device 400 may include more or fewer components than shown in fig. 4 or have a different configuration than shown in fig. 4. The components shown in fig. 4 may be implemented in hardware, software, or a combination thereof. The electronic device 400 may be a physical device, such as a PC, a laptop, a tablet, a cell phone, a server, an embedded device, etc., or may be a virtual device, such as a virtual machine, a container, etc. The electronic device 400 is not limited to a single device, and may be a combination of a plurality of devices or a cluster including a large number of devices.
The embodiment of the present application further provides a computer-readable storage medium, where computer program instructions are stored on the computer-readable storage medium, and when the computer program instructions are read and executed by a processor of a computer, the method for classifying elements of a mesh surface provided in the embodiment of the present application is executed. The computer-readable storage medium may be implemented as, for example, memory 420 in electronic device 400 in fig. 4.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
In addition, units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Furthermore, the functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (10)

1. A method for classifying elements of a mesh surface is characterized by comprising the following steps:
acquiring an attribute value of each element of the mesh surface, wherein the element is a vertex or a surface;
iteratively updating the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, and taking the attribute values of the elements obtained when iteration is finished as the features of the elements;
classifying each element using a classifier based on the characteristics of the element.
2. The method for classifying elements of a mesh surface according to claim 1, wherein the iteratively updating the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element comprises:
determining a multi-ring neighborhood of each element, and respectively counting each attribute value of the elements in each ring neighborhood to obtain an attribute statistical value matrix of each ring neighborhood; wherein, the 0 th ring neighborhood of any element is the element itself, the 1 st ring neighborhood is a set formed by elements directly adjacent to the element, the k-th ring neighborhood is a set formed by elements directly adjacent to the k-1 st ring neighborhood except the k-1 st ring neighborhood and the k-2 nd ring neighborhood, and k is more than 1; a vertex directly adjacent to one vertex means a vertex directly connected to the vertex through an edge, and a face directly adjacent to one face means a face having a common vertex with the face;
forming an extended attribute matrix based on the attribute statistic value matrix of each ring neighborhood of each element;
calculating a new attribute value of each element according to the extended attribute matrix, and updating the attribute value of the element by using the new attribute value;
and iteratively updating the attribute value of each element in an attribute expansion mode.
3. The method for classifying elements of a mesh surface according to claim 2, wherein said calculating a new attribute value for each element according to said extended attribute matrix comprises:
processing the extended attribute matrix by utilizing a pre-trained network layer to obtain a new attribute value of each element; wherein, the network layer is a convolution layer or a full connection layer.
4. The method for classifying elements of a mesh surface according to claim 3, wherein in the process of iteratively updating the attribute value of each element by means of attribute extension, the network layers used in each iteration are independent from each other, and the network layers used in each iteration form a pre-trained neural network.
5. The method of element classification for mesh surfaces as claimed in claim 2, wherein said determining a multi-ring neighborhood for each element comprises:
the multiple ring neighborhood is continuously selected from the total ring neighborhood of each element, or the multiple ring neighborhood is intermittently selected from the total ring neighborhood of each element.
6. The method of classifying elements of a mesh surface according to claim 2, wherein the statistical means of attribute values comprises at least one of: taking the maximum value, taking the minimum value, taking the mean value, taking the median, taking the upper quartile and taking the lower quartile.
7. The element classification method according to claim 1, wherein, if the element is a vertex, the attribute value of the vertex includes at least one of: coordinates, curvature and normal of the vertex; if the element is a surface, the attribute value of the surface comprises at least one of the following: the coordinates of the apex of the face, the coordinates of the center of the face, and the normal to the face.
8. The element classification method according to claim 1, wherein the iteratively updating the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element comprises:
determining an attribute matrix
Figure FDA0002376464670000021
Wherein v isjFor the elements of the mesh surface, Ft (v)j) Representing element vjJ is any integer from 1 to N, both N and M are positive integers, and N represents the total number of elements of the mesh surface;
determining a continuous K ring neighborhood of each element starting from the 0 th ring neighborhood; if K is 0, the kth ring neighborhood of any element is the element itself, if K is 1, the kth ring neighborhood of any element is a set formed by elements directly adjacent to the element, if 1 < K, the kth ring neighborhood of any element is a set formed by elements directly adjacent to the kth ring neighborhood, except for a set formed by elements in the kth-1 ring neighborhood and the kth-2 ring neighborhood, and K is a positive integer; a vertex directly adjacent to one vertex means a vertex directly connected to the vertex through an edge, and a face directly adjacent to one face means a face having a common vertex with the face;
determining any value of the adjacency matrix A, A
Figure FDA0002376464670000031
Wherein the content of the first and second substances,
Figure FDA0002376464670000032
is an element viWhen element v is the k-th ring neighborhood ofjIs a neighborhood
Figure FDA0002376464670000033
When element(s) is (are), Ak,i,jGet 1, otherwise Ak,i,jTaking 0, wherein i is any integer from 1 to N;
calculating any value B in the complete attribute matrix B, Bk,i,m,j＝Ak,i,j*Xj,m(ii) a Wherein, when the element vjIs a neighborhood
Figure FDA0002376464670000034
When element(s) is (B)k,i,m,jRepresenting element viOf the kth ring neighborhood of (1)jWhen the element v is the m-th attribute value ofjIs not a neighborhood
Figure FDA0002376464670000035
When element(s) is (B)k,i,m,j0, M is any integer from 1 to M;
calculating any value C in the fully extended attribute matrix C, Ck,i,p,m＝Sp(Bk,i,m,j) (ii) a Wherein, Ck,i,p,mRepresenting element viThe mth attribute value of the element in the kth ring neighborhood adopts an attribute value statistical mode SpPerforming statistics, wherein P is any integer from 1 to P, P is a positive integer, and P represents the total number of attribute value statistics modes;
determining a set of numerical values corresponding to the specified ring neighborhood in the fully extended attribute matrix C as an extended attribute matrix;
calculating a new attribute value of each element according to the extended attribute matrix, and updating the attribute value of the element by using the new attribute value;
and iteratively updating the attribute value of each element in an attribute expansion mode.
9. An apparatus for classifying elements of a mesh surface, comprising:
the attribute value acquisition module is used for acquiring the attribute value of each element of the mesh curved surface, wherein the element is a vertex or a surface;
the attribute value iteration module is used for carrying out iteration updating on the attribute values of the elements based on the attribute values of the elements in the neighborhood of each element, and taking the attribute values of the elements obtained when the iteration is finished as the features of the elements;
and the element classification module is used for classifying the elements by utilizing a classifier based on the characteristics of each element.
10. A computer-readable storage medium having computer program instructions stored thereon, which when read and executed by a processor, perform the method of any one of claims 1-8.
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