CN112991521B - Point cloud anisotropic neighborhood searching method based on entropy energy - Google Patents

Abstract

The invention provides a point cloud anisotropic neighborhood search method based on entropy energy, which belongs to the field of three-dimensional signal processing. For each point to be searched in the point cloud data, the method first searches the K neighborhood formed by the K points closest to the point to be measured as the initial neighborhood, and then selects a combination of different points from the initial neighborhood to calculate The eigenvalues of the structure tensor of the point to be searched under the corresponding combination, and the eigenvalues are used to calculate geometric features including linearity and three-dimensional divergence, and the eigenvalues of the structure tensor and the geometric features form an entropy energy function, and the genetic algorithm is used to search such that The combination of points within the initial neighborhood with the smallest entropy energy function constitutes the final neighborhood. The invention can improve the accuracy of the point cloud neighborhood search, make the neighborhood focus on the same plane, and avoid the deviation of solving related geometric features such as normal vector caused by the existence of multiple planes in the neighborhood. Navigation, positioning, virtual reality and other fields have great application prospects.

Description

An Anisotropic Neighborhood Search Method for Point Clouds Based on Entropy Energy

technical field

The invention belongs to the field of three-dimensional signal processing, and in particular relates to a point cloud anisotropic neighborhood search method based on entropy energy.

Background technique

Point cloud refers to a collection of points obtained by 3D scanning equipment, stereo vision technology or 3D model technology, representing a certain 3D coordinate system, and each point contains at least 3D coordinates X, Y, Z. Its essence is to discretize the real world or 3D model, and restore objects in the form of points. It is widely used in 3D reconstruction, navigation, positioning, virtual reality, and augmented reality.

Since it usually only contains spatial coordinate information, the point cloud data often needs to obtain additional geometric information such as the normal vector of each point for subsequent surface reconstruction, noise reduction, navigation and positioning. There is no clear geometric topological relationship between points in the point cloud. When solving geometric information such as the normal vector of a point, it is necessary to search the entire point cloud data to find points with similar characteristics to the point to form the neighbors of the point. domain, and then solve the geometric information such as normal vector in the neighborhood.

The traditional neighborhood search method uses distance as the basis for neighborhood search. Cheng Xiaojun pointed out in his work that the neighborhood of a point cloud is generally obtained by sorting the Euclidean distance between points and surrounding points. Jiang Xiaotong et al. used a binary octree search method to quickly sort and search the distance between point cloud data to realize the fast search of the point cloud K neighborhood. Zhao Yuehua et al. divided the scattered point cloud into cubic grids of equal size, and then based on the distance from the point to the six sides of the cubic grid to realize the fast search of the point cloud neighborhood. The distance information is sometimes insufficient to fully describe the characteristics of the point cloud and is easily disturbed by noise. As an improvement, Weinmann et al. obtained the normalized covariance matrix eigenvalues from the K neighborhood of the point cloud, and used the information of these eigenvalues. The minimum entropy is the optimization goal, and the optimization of the K neighborhood is iteratively constructed to realize the search of the point cloud neighborhood.

The above methods are all isotropic search methods. In the fields of 3D reconstruction, navigation, positioning, etc., artificial objects such as vehicles and buildings are the main objects in the scene. These artificial objects have sharp boundary points or corners, and are isotropic. The neighborhood search method of , will cause multiple planes in the neighborhood of these boundary points or corner points. When solving the normal vector from the neighborhood containing multiple planes, the normal vector will tend to the mean value of the normal vectors of each plane, resulting in blurring and affecting Accuracy of 3D reconstruction, navigation, and positioning.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a point cloud anisotropic neighborhood search method based on entropy energy in order to overcome the shortcomings of the prior art. The invention combines the structural tensor feature of the point with the geometric feature, and performs the anisotropic neighborhood search of the point cloud, so that there is only a single plane in the neighborhood, so as to solve the problem of existence in the neighborhood in the isotropic neighborhood search method. Multiple planes cause problems such as blurred normal vectors. The invention has universality, can be directly used for point cloud neighborhood search, and has great application prospects in the fields of three-dimensional reconstruction, navigation, positioning and virtual reality.

The invention proposes a point cloud anisotropic neighborhood search method based on entropy energy, which is characterized in that, for each point to be searched in the point cloud data, the method first searches for the K points closest to the point to be measured. K neighborhood, take the K neighborhood as the initial neighborhood, and then select different combinations of points from the initial neighborhood to calculate the eigenvalues of the structure tensor of the point to be searched under the corresponding combinations, and use the eigenvalues to calculate the linearity and The geometric features of the three-dimensional divergence, the structure tensor eigenvalues and the geometric features form an entropy energy function, and the combination of points in the initial neighborhood that minimizes the entropy energy function through the genetic algorithm constitutes the final neighborhood of the point to be searched. The method includes the following steps:

1) Acquire three-dimensional point cloud data, and determine the point to be searched in the point cloud data;

Among them, the point cloud data is recorded as P={pi, _i =1,2,...M,pi ^∈R3 }, _{pi is the ith point} in the point cloud data, and M is the number of points;

2) For any point to be searched Qi ={x, y, z}, x, y, z are the three-dimensional coordinates of the point; extract the K neighborhood NB ₍ Q _{i ,} K)={ _pi1 , _pi2 , _pi3 ,..., _{piK }} , where _piK is the Kth point in the K neighborhood of Qi, and K is the number of neighborhood points;

3) Anisotropic neighborhood search is performed on the search points to be searched by genetic algorithm; the specific steps are as follows:

3-1) Initialize the genetic algorithm;

The number of populations in the genetic algorithm is set to M, and the length of each individual in the population is K; the code of each individual in the population is randomly initialized as 0 or 1, where 0 means that the corresponding point of the position in the K field is not selected. , 1 represents the corresponding point of the selected position in the K field; set the mutation probability PM, the crossover probability PC, and the maximum number of genetic iterations T, ; let the current iteration number t=1; take the initialized population as the current population;

3-2) Calculate the individual fitness of each individual in the current population, the specific steps are as follows:

3-2-1) Let the individual serial number j=1;

3-2-2) Compose corresponding points selected by individual _j in the population into the neighborhood of points to be searched NB(Q _i ,N), where N is the total number of positions coded as 1 in the individual; calculate the number of points to be searched for Qi The structure tensor C _i , as shown in formula (1):

为邻域NB(Q_i,N)的几何中心点；Among them, P _ij is the jth point in the neighborhood NB(Q _i ,N),

is the geometric center point of the neighborhood NB(Q _i ,N);

3-2-3) Decompose the eigenvalues of the structure tensor C _i , and sort the eigenvalues from small to large, and obtain the eigenvalue sorting result: 0≤λ ₀ ≤λ ₁ ≤λ ₂ ;

3-2-4) Normalize the eigenvalues λ ₀ , λ ₁ , and λ ₂ respectively to obtain the corresponding normalized eigenvalues γ ₀ , γ ₁ , γ ₂ ;

3-2-5) Calculate the linearity α _1D of the point to be measured, as shown in formula (2):

3-2-6) Calculate the three-dimensional divergence α _3D of the point to be measured, as shown in formula (3):

3-2-7) Calculate the entropy energy function E _2D , the reciprocal of which is taken as the individual fitness F _{j of individual j} , as shown in formula (4):

Among them, ω and μ are control factors, respectively;

3-2-8) Let j=j+1, then go back to step 3-2-2) to calculate the individual fitness of the next individual, until the individual fitness of all individuals in the current population has been calculated, go to step 3-3 );

3-3) According to the individual fitness of all individuals obtained in step 3-2), select population individuals to generate a new population; the specific steps are as follows:

3-3-1) According to the individual fitness F _j of each individual, calculate the probability ρ _j of the individual being selected, j=1,2,...M, as shown in formula (5):

3-3-2) Using the result of step 3-3-1), select the individuals in the population through the probability selection method, and select M individuals to copy into the new population;

3-4) According to the crossover probability PC, cross the new population individuals obtained in step 3-3) to obtain an updated new population;

3-5) According to the mutation probability PM, mutate the updated new population in step 3-4) to obtain the updated new population;

3-6) Let the number of iterations t=t+1, take the updated new population obtained in step 3-5) as the current population, and then return to step 3-2); until t reaches the maximum number of genetic iterations T, the population is updated Finished, get the final population;

其中L为最终个体选中的K邻域点个数，完成该待搜索点的邻域搜索；3-7) Repeat step 3-2), calculate the individual fitness of each individual in the final population, and select the individual with the smallest entropy energy function value as the final individual; The selected points form the final neighborhood of the point Qi to be _searched

Among them, L is the number of K neighborhood points selected by the final individual to complete the neighborhood search of the point to be searched;

4) Determine whether there are other points to be searched: if so, return to step 2); if not, the search is completed.

The characteristics and beneficial effects of the present invention are:

The present invention firstly establishes the point cloud K neighborhood, calculates geometric features such as the eigenvalue, linearity, flatness and three-dimensional divergence of the structure tensor in the neighborhood, and calculates the eigenvalue, linearity, flatness and three-dimensional divergence of the structure tensor. The entropy energy function is formed, and the neighborhood point combination that minimizes the entropy energy function is solved by genetic algorithm to realize the anisotropic neighborhood search of point cloud. The invention can be directly used for point cloud neighborhood search, and has great application prospects in the fields of three-dimensional reconstruction, navigation, positioning and virtual reality.

Description of drawings

FIG. 1 is an overall flow chart of the method of the present invention.

FIG. 2 is a schematic diagram of the point cloud data of the flange workpiece and the position of the point to be searched in the embodiment of the present invention.

FIG. 3 is a neighborhood diagram of a point to be searched along a step surface in an embodiment of the present invention.

FIG. 4 is a neighborhood diagram of a point to be searched along the lower edge of a step surface in an embodiment of the present invention.

5 is a neighborhood diagram of a point to be searched along the upper edge of a chamfered threaded hole in an embodiment of the present invention.

6 is a neighborhood diagram of a point to be searched along the lower edge of a chamfered threaded hole in an embodiment of the present invention.

Detailed ways

The present invention proposes a method for searching anisotropic neighborhoods of point clouds based on entropy energy, which will be further described in detail below with reference to the accompanying drawings and specific embodiments.

The present invention proposes a point cloud anisotropic neighborhood search method based on entropy energy. For each point to be searched in the point cloud data, the method first searches the K points closest to the point to be measured to form a K neighborhood, Take the K neighborhood as the initial neighborhood, and then select the combination of different points from the initial neighborhood to calculate the eigenvalue of the structure tensor of the point to be searched under the corresponding combination, and use the eigenvalue to calculate the linearity and three-dimensional divergence. Geometric feature, the structure tensor feature value and geometric feature form an entropy energy function, and the combination of points in the initial neighborhood with the smallest entropy energy function is searched by genetic algorithm to form the final neighborhood of the point to be searched. The overall process of the method is shown in Figure 1, which includes the following steps:

1) Acquire three-dimensional point cloud data, and determine the point to be searched in the point cloud data;

Among them, the point cloud data is recorded as P={pi, _i =1,2,...M,pi ^∈R3 }, _{pi is the ith point} in the point cloud data, and M is the number of points.

When 3D reconstruction is performed on a flange workpiece in this embodiment, the workpiece is first scanned for its shape to obtain point cloud data, and then the normal vector of each point is solved and 3D reconstruction is performed. The surface of the flange workpiece has a stepped surface and 8 threads. Therefore, there are a large number of sharp edges, and the neighborhood of the points on the edge obtained by the isotropic neighborhood search method will appear normal vector ambiguity when solving the normal vector. In this example, we select one point along the step surface and one point on the bottom edge of the flange workpiece, one point on the upper edge and one point on the bottom edge of the chamfering of the threaded hole, a total of four points to be searched for neighborhood search, as shown in Figure 2, the black large circle The points are the points to be searched, and the gray points are the point cloud data of the flange workpiece.

2) For any point to be searched Qi ={x, y, z}, x, y, z are the three-dimensional coordinates of the point; extract the K neighborhood NB ₍ Q _{i ,} K)={p _i1 , p _i2 , p _i3 ,...,p _{iK }} , where p _iK is the Kth point in the K neighborhood of Qi, and K is the number of manually set neighborhood points. K=100.

3) Anisotropic neighborhood search is performed on the search points to be searched by genetic algorithm; the specific steps are as follows:

3-1) Initialize the genetic algorithm: set the number of populations in the genetic algorithm to M, in this embodiment, M=200, the length of each individual in the population is K (the value of K in the K field), and the population is randomly initialized The code of each individual is 0 or 1 (where, 0 represents that the corresponding point of the position in the K field is not selected, and 1 represents that the corresponding point of the position in the K field is selected; therefore, each individual in the population represents a kind of The combination of selected points in the K neighborhood); set the mutation probability PM, this embodiment takes PM=0.01, the crossover probability PC, this embodiment takes PC=0.9, the maximum number of genetic iterations is T, this embodiment takes T=300 ; Let the current iteration number t=1; take the initialized population as the current population

3-2) Calculate the individual fitness of each individual in the current population, the specific steps are as follows:

3-2-1) Let the individual serial number j=1;

为该邻域的几何中心点；3-2-2) The corresponding points selected by individual j in the population form the neighborhood NB(Q _i ,N) of the points to be searched, where N is the total number of positions coded as 1 in the individual (also the neighborhood NB(Q _{i )} ,N) the number of inner points, N≤K); calculate the structural tensor C _i of the point Qi to be searched _, as shown in formula (1), where P _ij is the jth point in the neighborhood,

is the geometric center point of the neighborhood;

3-2-3) Decompose the eigenvalues of the structure tensor C _i , and sort the eigenvalues from small to large, and obtain the eigenvalue sorting result: 0≤λ ₀ ≤λ ₁ ≤λ ₂ ;

3-2-4) Normalize the eigenvalues λ ₀ , λ ₁ , and λ ₂ respectively to obtain the corresponding normalized eigenvalues γ ₀ , γ ₁ , γ ₂ ;

3-2-5) Calculate the linearity α _1D of the point to be measured, as shown in formula (2):

3-2-6) Calculate the three-dimensional divergence α _3D of the point to be measured, as shown in formula (3):

3-2-7) Calculate the entropy energy function E _2D , the reciprocal of which is taken as the individual fitness F _{j of individual j} , as shown in formula (4):

Among them, ω and μ are control factors respectively, and in this example, ω=0.6 and μ=0.5 are selected.

3-2-8) Set j=j+1, select a new individual in the population, and then return to step 3-2-2) to calculate the individual fitness of the next individual until the individual fitness of all individuals in the current population is fully calculated Finished, go to step 3-3);

3-3) According to the individual fitness of all individuals obtained in step 3-2), select population individuals to generate a new population; the specific steps are as follows:

3-3-1) According to the individual fitness F _j of each individual, calculate the probability ρ _j of the individual being selected, (j=1,2,...M), as shown in formula (5):

3-3-2) Using the result of step 3-3-1), select the individuals in the population by "roulette method" or other probability selection methods, and select M individuals to copy into the new population;

3-4) Crossover the new population individuals obtained in step 3-3) to obtain an updated new population; the specific method is as follows:

According to the set crossover probability PC, the parent class pair is randomly generated from the new population each time, and the coding point is randomly selected to carry out the code exchange crossover operation to generate two new individuals, and the two new individuals generated replace their parent class pair; After a total of M operations, the crossover of the new population is completed, and the updated new population is obtained;

3-5) mutate the updated new population in step 3-4) to obtain the updated new population; the specific method is as follows:

According to the set mutation probability PM, individuals are randomly selected from the new population, and the coding points are randomly selected to perform the coding flip mutation operation to generate new individuals, and the mutated new individuals are used to replace the former individuals; after a total of M operations, the new individual is completed. Population mutation operation to get the updated population;

3-6) Complete the population update through steps 3-3)-3-5), generate a new population, set the number of iterations t=t+1, take the new population as the current population, and then return to step 3-2), again The fitness calculation is performed until the maximum number of genetic iterations T is reached, the population update is completed, and the final population is obtained;

其中L为最终个体选中的K邻域点个数，完成该待搜索点的邻域搜索；3-7) Repeat step 3-2) to calculate the individual fitness of each individual in the final population, and select the individual with the smallest entropy energy function value (that is, the largest individual fitness) as the final individual; Coding value, the selected point in the individual (that is, the point in the K _neighborhood corresponding to the position coded as 1) forms the final neighborhood of the point to be searched Qi

Among them, L is the number of K neighborhood points selected by the final individual to complete the neighborhood search of the point to be searched;

4) Determine whether there are other points to be searched: if so, return to step 2); if not, end the search process.

According to the present invention, according to steps 1)-3), the flange workpiece of the embodiment is searched for the neighborhood of each point to be searched, and the result is shown in Fig. 3-6, wherein Fig. 3 shows the neighbors of the point to be searched along the step surface Domain search results, Fig. 4 is the search result of the neighborhood of the point to be searched along the lower edge of the step surface, Fig. 5 is the search result of the neighborhood of the point to be searched along the upper edge of the threaded hole, Fig. 6 is the search result of the neighborhood of the point to be searched along the lower edge of the threaded hole, Fig. The middle triangle is the neighborhood searched according to the method of the present invention, the small black point is the result of the neighborhood search according to the method of Weinmann et al., the large black dot is the position of the point to be measured, and the points in the two ellipses belong to different planes, respectively. As can be seen from the figure, the neighborhood searched based on the method of Weinmann et al. contains two planes, while the neighborhood searched based on the present invention is anisotropic and only contains a single plane, which can effectively avoid the problem of ambiguity in normal vector solution.

Claims (2)

1. a point cloud anisotropic neighborhood search method based on entropy energy, it is characterized in that, this method is to each point to be searched in the point cloud data, first searches the K points that are closest to the point to be searched to form K Neighborhood, take the K neighborhood as the initial neighborhood, and then select a combination of different points from the initial neighborhood to calculate the eigenvalue of the structure tensor of the point to be searched under the corresponding combination, and use the eigenvalue to calculate the linearity and three-dimensional The geometric feature of divergence, the structure tensor feature value and the geometric feature are formed into an entropy energy function, and the combination of points in the initial neighborhood where the entropy energy function is minimized is searched through a genetic algorithm to form the final neighborhood of the point to be searched; the method includes: The following steps: 1) Acquire three-dimensional point cloud data, and determine the point to be searched in the point cloud data; Among them, the point cloud data is recorded as P={pi, _i =1,2,...M,pi ^∈R3 }, _{pi is the ith point} in the point cloud data, and M is the number of points; 2) For any point to be searched Qi ={x, y, z}, x, y, z are the three-dimensional coordinates of the point; extract the K neighborhood NB ₍ Q _{i ,} K)={ _pi1 , _pi2 , _pi3 ,..., _{piK }} , where _piK is the Kth point in the K neighborhood of Qi, and K is the number of neighborhood points; 3) Anisotropic neighborhood search is performed on the search points to be searched by genetic algorithm; the specific steps are as follows: 3-1) Initialize the genetic algorithm; The number of populations in the genetic algorithm is set to M, and the length of each individual in the population is K; the code of each individual in the population is randomly initialized as 0 or 1, where 0 means that the corresponding point of the position in the K field is not selected. , 1 represents the corresponding point of the selected position in the K field; set the mutation probability PM, the crossover probability PC, and the maximum number of genetic iterations T; set the current iteration number t=1; take the initialized population as the current population; 3-2) Calculate the individual fitness of each individual in the current population, the specific steps are as follows: 3-2-1) Let the individual serial number j=1; 3-2-2) Compose corresponding points selected by individual _j in the population into the neighborhood of points to be searched NB(Q _i ,N), where N is the total number of positions coded as 1 in the individual; calculate the number of points to be searched for Qi The structure tensor C _i , as shown in formula (1):

Among them, P _ij is the jth point in the neighborhood NB(Q _i ,N),

is the geometric center point of the neighborhood NB(Q _i ,N); 3-2-3) Decompose the eigenvalues of the structure tensor C _i , and sort the eigenvalues from small to large, and obtain the eigenvalue sorting result: 0≤λ ₀ ≤λ ₁ ≤λ ₂ ; 3-2-4) Normalize the eigenvalues λ ₀ , λ ₁ , and λ ₂ respectively to obtain the corresponding normalized eigenvalues γ ₀ , γ ₁ , γ ₂ ; 3-2-5) Calculate the linearity α _1D of the point to be measured, as shown in formula (2):

3-2-6) Calculate the three-dimensional divergence α _3D of the point to be measured, as shown in formula (3):

3-2-7) Calculate the entropy energy function E _2D , the reciprocal of which is taken as the individual fitness F _{j of individual j} , as shown in formula (4):

Among them, ω and μ are control factors, respectively; 3-2-8) Let j=j+1, then go back to step 3-2-2) to calculate the individual fitness of the next individual, until the individual fitness of all individuals in the current population has been calculated, go to step 3-3 ); 3-3) According to the individual fitness of all individuals obtained in step 3-2), select population individuals to generate a new population; the specific steps are as follows: 3-3-1) According to the individual fitness F _j of each individual, calculate the probability ρ _j of the individual being selected, j=1,2,...M, as shown in formula (5):

3-3-2) Using the result of step 3-3-1), select the individuals in the population through the probability selection method, and select M individuals to copy into the new population; 3-4) According to the crossover probability PC, cross the new population individuals obtained in step 3-3) to obtain an updated new population; 3-5) According to the mutation probability PM, mutate the updated new population in step 3-4) to obtain the updated new population; 3-6) Let the number of iterations t=t+1, take the updated new population obtained in step 3-5) as the current population, and then return to step 3-2); until t reaches the maximum number of genetic iterations T, the population is updated Finished, get the final population; 3-7) Repeat step 3-2), calculate the individual fitness of each individual in the final population, and select the individual with the smallest entropy energy function value as the final individual; The selected points form the final neighborhood of the point Qi to be _searched

Among them, L is the number of K neighborhood points selected by the final individual to complete the neighborhood search of the point to be searched; 4) Determine whether there are other points to be searched: if so, return to step 2); if not, the search is completed. 2. The method of claim 1, wherein the probability selection method is a roulette method.

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