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

Point cloud anisotropic neighborhood searching method based on entropy energy Download PDF

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CN112991521B
CN112991521B CN202110326588.XA CN202110326588A CN112991521B CN 112991521 B CN112991521 B CN 112991521B CN 202110326588 A CN202110326588 A CN 202110326588A CN 112991521 B CN112991521 B CN 112991521B
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邓博文
孟子阳
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Abstract

The invention provides a point cloud anisotropic neighborhood searching method based on entropy energy, and belongs to the field of three-dimensional signal processing. For each point to be searched in point cloud data, searching a K neighborhood formed by K points nearest to the point to be searched as an initial neighborhood, selecting different combinations of points from the initial neighborhood to calculate a structure tensor eigenvalue of the point to be searched under corresponding combinations, calculating geometric characteristics including linearity and three-dimensional divergence by using the eigenvalue, forming an entropy energy function by using the structure tensor eigenvalue and the geometric characteristics, and searching a combination of points in the initial neighborhood which enables the entropy energy function to be minimum through a genetic algorithm to form a final neighborhood. The method can improve the accuracy of point cloud neighborhood search, enables neighborhoods to be concentrated on the same plane, avoids solving deviation of relevant geometric characteristics such as normal vectors and the like caused by the existence of multiple planes in the neighborhoods, has universality, and has a wide application prospect in the fields of three-dimensional reconstruction, navigation, positioning, virtual reality and the like.

Description

Point cloud anisotropic neighborhood searching method based on entropy energy
Technical Field
The invention belongs to the field of three-dimensional signal processing, and particularly relates to a point cloud anisotropic neighborhood searching method based on entropy energy.
Background
The Point Cloud (Point Cloud) is a set of points representing a three-dimensional coordinate system, which are obtained by a three-dimensional scanning device, a stereo vision technology or a three-dimensional model technology, and each Point at least comprises three-dimensional coordinates X, Y and Z. The essence of the method is discretization of a real world or a three-dimensional model, an object is restored in a point form, and the method is widely applied to the fields of three-dimensional reconstruction, navigation, positioning, virtual reality, reality augmentation and the like.
Because only the spatial coordinate information is usually contained, the point cloud data often needs to additionally obtain additional geometric information such as normal vectors of all points for subsequent curved surface reconstruction, noise reduction, navigation, positioning and the like. There is no definite geometric topological relation between each point in the point cloud, when solving the geometric information such as normal vector of a certain point, it needs to search in the whole point cloud data, find the point with similar characteristic to the point to form the neighborhood of the point, and then solve the geometric information such as normal vector in the neighborhood.
The traditional neighborhood searching method carries out neighborhood searching by taking distance as a judgment basis, and the Chengxiang army indicates in works thereof that the neighborhood of point cloud is generally obtained by sorting the Euclidean distance between a point and a peripheral point. Jiangxiantong et al use a binary octree search method to perform rapid ordering search of distances between point cloud data, and achieve rapid search of K neighborhoods of point clouds. The Zhao Yuanhi et al divides scattered point clouds into cubic grids with equal size, and then realizes the quick search of the point cloud neighborhood by taking the distance from the point to six sides of the cubic grids as the basis. Distance information is sometimes insufficient to completely describe the characteristics of point cloud and is easily interfered by noise, as improvement, Weinmann et al obtain normalized covariance matrix eigenvalues from K neighborhood of the point cloud, and iteratively perform optimization construction of the K neighborhood by taking minimum information entropy of the eigenvalues as an optimization target to realize searching of the point cloud neighborhood.
In the fields of three-dimensional reconstruction, navigation, positioning and the like, artifacts such as vehicles and buildings are main objects in a scene, the artifacts have sharp boundary points or angular points, the isotropic neighborhood search method enables multiple planes to exist in neighborhoods of the boundary points or the angular points, and when a normal vector is solved from a neighborhood containing the multiple planes, the normal vector tends to the mean value of normal vectors of the planes, blurring is generated, and the precision of three-dimensional reconstruction, navigation and positioning is influenced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a point cloud anisotropic neighborhood searching method based on entropy energy. According to the invention, the structure tensor characteristics and the geometric characteristics of the points are combined to perform the anisotropic neighborhood search of the point cloud, so that only a single plane exists in the neighborhood, and the problems of fuzzy normal vectors and the like caused by the existence of a plurality of planes in the neighborhood in the isotropic neighborhood search method are solved. The method has universality, can be directly used for point cloud neighborhood search, and has a wide application prospect in the fields of three-dimensional reconstruction, navigation, positioning and virtual reality.
The invention provides a point cloud anisotropic neighborhood searching method based on entropy energy, which is characterized in that for each point to be searched in point cloud data, K points closest to the point to be searched are firstly searched to form a K neighborhood, the K neighborhood is used as an initial neighborhood, then different point combinations are selected from the initial neighborhood to calculate the structure tensor characteristic value of the point to be searched under corresponding combinations, the geometric characteristics including linearity and three-dimensional divergence are calculated according to the characteristic value, the structure tensor characteristic value and the geometric characteristics form an entropy energy function, and the combination of the points in the initial neighborhood which enables the entropy energy function to be minimum is searched through a genetic algorithm to form a final neighborhood of the point to be searched. The method comprises the following steps:
1) acquiring three-dimensional point cloud data and determining a point to be searched in the point cloud data;
wherein, the point cloud data is P ═ { P ═ Pi,i＝1,2,…M,pi∈R3}，piThe point is the ith point in the point cloud data, and M is the number of the points;
2) for any point Q to be searchediX, y, z is the three-dimensional coordinates of the point; extracting the point Q to be searched from PiK neighborhood of NB (Q)i,K)＝{pi1,pi2,pi3,…,piKIn which p isiKIs QiK is the number of neighborhood points;
3) carrying out anisotropic neighborhood search on the point to be searched by a genetic algorithm; the method comprises the following specific steps:
3-1) initializing a genetic algorithm;
setting the number of populations in a genetic algorithm as M and the length of each individual in the populations as K; randomly initializing the code of each bit of each body in the population to be 0 or 1, wherein 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; setting variation probability PM and cross probability PC, wherein the maximum genetic iteration number is T; making the current iteration time t equal to 1; taking the initialized population as a current population;
3-2) calculating the individual fitness of each individual in the current population, and the specific steps are as follows:
3-2-1) making the individual serial number j equal to 1;
3-2-2) forming a point neighborhood NB (Q) to be searched by corresponding points selected by individuals j in the populationiN), wherein N is the total number of positions in the individual encoded as 1; calculating a point Q to be searchediStructure tensor C ofiAs shown in formula (1):
Figure BDA0002994887560000021
wherein, PijIs a neighborhood NB (Q)iThe j-th point within N),
Figure BDA0002994887560000022
is a neighborhood NB (Q)iN) geometric center point;
3-2-3) pair of structure tensors CiAnd (3) decomposing the characteristic values, and sequencing the characteristic values from small to large to obtain a characteristic value sequencing result as follows: lambda is more than or equal to 00≤λ1≤λ2；
3-2-4) pairs of eigenvalues lambda0,λ1,λ2Respectively carrying out normalization to obtain corresponding normalized characteristic values gamma0,γ1,γ2；
3-2-5) calculating the linearity alpha of the point to be measured1DAs shown in formula (2):
Figure BDA0002994887560000031
3-2-6) calculating three-dimensional divergence alpha of points to be measured3DAs shown in formula (3):
Figure BDA0002994887560000032
3-2-7) calculating an entropy energy function E2DThe reciprocal of which is taken as the individual fitness F of the individual jjAs shown in formula (4):
Figure BDA0002994887560000033
wherein, omega and mu are respectively control factors;
3-2-8) making j equal to j +1, then returning to the step 3-2-2) to calculate the individual fitness of the next individual until the individual fitness of all the individuals in the current population is completely calculated, and entering the step 3-3);
3-3) selecting population individuals according to the individual fitness of all the individuals obtained in the step 3-2) to generate a new population; the method comprises the following specific steps:
3-3-1) Individual fitness F according to each individualjCalculating the probability ρ of the individual being selectedjJ is 1,2, … M, as shown in equation (5):
Figure BDA0002994887560000034
3-3-2) selecting individuals in the population by using the result of the step 3-3-1) through a probability selection method, and selecting M individuals to copy into a new population;
3-4) crossing the new population individuals obtained in the step 3-3) according to the crossing probability PC to obtain an updated new population;
3-5) carrying out variation on the new population updated in the step 3-4) according to the variation probability PM to obtain an updated new population;
3-6) enabling the iteration time t to be t +1, taking the updated new population obtained in the step 3-5) as the current population, and then returning to the step 3-2); until T reaches the maximum genetic iteration time T, finishing population updating to obtain a final population;
3-7) repeating the step 3-2), calculating the individual fitness of each individual in the final population, and selecting the individual with the minimum entropy energy function value as the final individual; according to the code value of each digit of the final individual, the selected points in the individual are formed into the point Q to be searchediFinal neighborhood of
Figure BDA0002994887560000035
Wherein L is the number of K neighborhood points selected by the final individual, and the neighborhood search of the point to be searched is completed;
4) judging whether other points to be searched exist: if yes, returning to the step 2) again; if not, the search is complete.
The invention has the characteristics and beneficial effects that:
the method comprises the steps of firstly establishing a point cloud K neighborhood, calculating geometrical characteristics such as structure tensor eigenvalue, linearity, flatness, three-dimensional divergence and the like in the neighborhood, forming the structure tensor eigenvalue, the linearity, the flatness and the three-dimensional divergence into an entropy energy function, solving a neighborhood point combination which enables the entropy energy function to be minimum through a genetic algorithm, and realizing point cloud anisotropic neighborhood search. The method can be directly used for point cloud neighborhood search, and has a wide application prospect in the fields of three-dimensional reconstruction, navigation, positioning, virtual reality and the like.
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FIG. 1 is an overall flow diagram of the method of the present invention.
FIG. 2 is a schematic diagram of a point cloud data of a flange workpiece and a position of a point to be searched according to an embodiment of the present invention.
FIG. 3 is a diagram of neighborhood of points to be searched along the upper edge of the step surface in the embodiment of the present invention.
FIG. 4 is a diagram of a neighborhood of a point to be searched along a lower edge of a step surface in the embodiment of the present invention.
FIG. 5 is a diagram of the neighborhood of the point to be searched on the chamfer of the threaded hole in the embodiment of the present invention.
FIG. 6 is a diagram of a neighborhood of a point to be searched on the lower edge of a chamfer of a threaded hole in the embodiment of the present invention.
Detailed Description
The invention provides a point cloud anisotropic neighborhood searching method based on entropy energy, which is further described in detail below by combining the accompanying drawings and specific embodiments.
The invention provides a point cloud anisotropic neighborhood searching method based on entropy energy, which is characterized in that for each point to be searched in point cloud data, K points closest to the point to be searched are firstly searched to form a K neighborhood, the K neighborhood is used as an initial neighborhood, then different point combinations are selected from the initial neighborhood to calculate the structure tensor characteristic value of the point to be searched under corresponding combinations, the geometric characteristics including linearity and three-dimensional divergence are calculated according to the characteristic value, the structure tensor characteristic value and the geometric characteristics form an entropy energy function, and the combination of the points in the initial neighborhood which enables the entropy energy function to be minimum is searched through a genetic algorithm to form a final neighborhood of the point to be searched. The overall flow of the method is shown in fig. 1, and comprises the following steps:
1) acquiring three-dimensional point cloud data and determining a point to be searched in the point cloud data;
wherein, the cloud number is countedAccording to the formula P ═ Pi,i＝1,2,…M,pi∈R3}，piThe point is the ith point in the point cloud data, and M is the number of the points.
In the embodiment, when a flange workpiece is subjected to three-dimensional reconstruction, firstly, the workpiece is subjected to shape scanning to obtain point cloud data, then, the normal vectors of all points are solved, and the three-dimensional reconstruction is carried out, the surface of the flange workpiece is provided with a step surface and 8 threaded holes, so that a large number of sharp edges exist, and the neighborhood of the points on the edge obtained by an isotropic neighborhood searching method appears fuzzy normal vectors when solving vectors. In this example, four points to be searched are selected from an upper edge point and a lower edge point of a step surface of a flange workpiece, an upper edge point and a lower edge point of a chamfer of a threaded hole, and neighborhood search is performed on the four points to be searched, as shown in fig. 2, a black large dot is each point to be searched, and a gray dot is point cloud data of the flange workpiece.
2) For any point Q to be searchediX, y, z is the three-dimensional coordinates of the point; extracting the point Q to be searched from PiK neighborhood of NB (Q)i,K)＝{pi1,pi2,pi3,…,piKIn which p isiKIs QiK is the number of the neighborhood points manually set, and this embodiment takes K as 100.
3) Carrying out anisotropic neighborhood search on the point to be searched by a genetic algorithm; the method comprises the following specific steps:
3-1) initializing the genetic algorithm: setting the number of populations in a genetic algorithm as M, wherein M is 200, the length of each individual in the population is K (consistent with the value of K in the K field), and randomly initializing the code of each digit of each individual in the population as 0 or 1 (wherein 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; setting a mutation probability PM, where PM is 0.01 in this embodiment, a cross probability PC, where PC is 0.9 in this embodiment, the maximum number of genetic iterations is T, and T is 300 in this embodiment; making the current iteration time t equal to 1; taking the initialized population as the current population
3-2) calculating the individual fitness of each individual in the current population, and the specific steps are as follows:
3-2-1) making the individual serial number j equal to 1;
3-2-2) forming a point neighborhood NB (Q) to be searched by corresponding points selected by individuals j in the populationiN), where N is the total number of positions in the individual that are encoded as 1 (also the neighborhood NB (Q)iN) the number of inner points, N is less than or equal to K); calculating a point Q to be searchediStructure tensor C ofiAs shown in formula (1), wherein P isijFor the j-th point in the neighborhood,
Figure BDA0002994887560000051
is the geometric center point of the neighborhood;
Figure BDA0002994887560000052
3-2-3) pair of structure tensors CiAnd (3) decomposing the characteristic values, and sequencing the characteristic values from small to large to obtain a characteristic value sequencing result as follows: lambda is more than or equal to 00≤λ1≤λ2；
3-2-4) pairs of eigenvalues lambda0,λ1,λ2Respectively carrying out normalization to obtain corresponding normalized characteristic values gamma0,γ1,γ2；
3-2-5) calculating the linearity alpha of the point to be measured1DAs shown in formula (2):
Figure BDA0002994887560000053
3-2-6) calculating three-dimensional divergence alpha of points to be measured3DAs shown in formula (3):
Figure BDA0002994887560000054
3-2-7) calculating an entropy energy function E2DThe reciprocal of which is taken as the individual fitness F of the individual jjAs shown in formula (4):
Figure BDA0002994887560000055
wherein, ω and μ are control factors, and ω is 0.6 and μ is 0.5 in this example.
3-2-8) making j ═ j +1, selecting a new individual in the population, then returning to the step 3-2-2) to calculate the individual fitness of the next individual, and entering the step 3-3) until the individual fitness of all the individuals in the current population is completely calculated;
3-3) selecting population individuals according to the individual fitness of all the individuals obtained in the step 3-2) to generate a new population; the method comprises the following specific steps:
3-3-1) Individual fitness F according to each individualjCalculating the probability ρ of the individual being selectedj(j ═ 1,2, … M), as shown in formula (5):
Figure BDA0002994887560000061
3-3-2) selecting individuals in the population by using the result of the step 3-3-1) through a roulette method or other probability selection methods, and selecting M individuals to be copied into a new population;
3-4) crossing the new population individuals obtained in the step 3-3) to obtain an updated new population; the specific method comprises the following steps:
randomly generating a parent class pair from a new population each time according to a set cross probability PC, randomly selecting coding point positions to perform coding exchange cross operation, generating two new individuals, and replacing the parent class pair with the generated two new individuals; after M operations are carried out, completing new population crossing to obtain an updated new population;
3-5) carrying out variation on the new population updated in the step 3-4) to obtain an updated new population; the specific method comprises the following steps:
randomly selecting individuals from the new population according to the set mutation probability PM, randomly selecting coding point positions to perform coding turnover mutation operation to generate new individuals, and replacing the individuals before mutation with the new individuals after mutation; after M operations are carried out, the new population variation operation is completed, and the updated population is obtained;
3-6) completing population updating through steps 3-3) -3-5), generating a new population, enabling the iteration time T to be T +1, taking the new population as the current population, then returning to the step 3-2), performing fitness calculation again until the maximum genetic iteration time T is reached, and obtaining a final population after population updating is completed;
3-7) repeating the step 3-2), calculating the individual fitness of each individual in the final population, and selecting the individual with the minimum entropy energy function value (namely, the maximum individual fitness) as the final individual; according to the code value of each bit of the final individual, combining the selected points (namely the points in the K neighborhood corresponding to the position coded as 1) in the individual into a point Q to be searchediFinal neighborhood of
Figure BDA0002994887560000062
Wherein L is the number of K neighborhood points selected by the final individual, and the neighborhood search of the point to be searched is completed;
4) judging whether other points to be searched exist: if yes, returning to the step 2) again; if not, the search process is ended.
According to the present invention, neighborhood searching is performed on each point to be searched for on the flange workpiece according to steps 1) -3), and the results are shown in fig. 3-6, where fig. 3 is a neighborhood searching result on the upper edge of the step surface along the point to be searched for, fig. 4 is a neighborhood searching result on the lower edge of the step surface along the point to be searched for, fig. 5 is a neighborhood searching result on the upper edge of the screw hole along the point to be searched for, fig. 6 is a neighborhood searching result on the lower edge of the screw hole along the point to be searched for, in the figure, triangles are neighborhoods searched according to the method of the present invention, small black dots are neighborhood searching results according to Weinmann et al, large black dots are positions to be detected, dots in two ellipses belong to different planes, respectively, and as can be seen from the figures, neighborhoods searched based on Weinmann et al contain two planes, while neighborhoods searched based on the present invention have anisotropy, and contain only a single plane inside, the problem of ambiguity in normal vector solution can be effectively avoided.

Claims (2)

1. A point cloud anisotropy neighborhood searching method based on entropy energy is characterized in that for each point to be searched in point cloud data, K points closest to the point to be searched are searched firstly to form a K neighborhood, the K neighborhood is used as an initial neighborhood, then different point combinations are selected from the initial neighborhood to calculate a structure tensor characteristic value of the point to be searched under corresponding combinations, geometric features including linearity and three-dimensional divergence are calculated according to the characteristic value, an entropy energy function is formed by the structure tensor characteristic value and the geometric features, and a final neighborhood of the point to be searched is formed by searching the combination of points in the initial neighborhood which enables the entropy energy function to be minimum through a genetic algorithm; the method comprises the following steps:
1) acquiring three-dimensional point cloud data and determining a point to be searched in the point cloud data;
wherein, the point cloud data is P ═ { P ═ Pi,i＝1,2,…M,pi∈R3}，piThe point is the ith point in the point cloud data, and M is the number of the points;
2) for any point Q to be searchediX, y, z is the three-dimensional coordinates of the point; extracting the point Q to be searched from PiK neighborhood of NB (Q)i,K)＝{pi1,pi2,pi3,…,piKIn which p isiKIs QiK is the number of neighborhood points;
3) carrying out anisotropic neighborhood search on the point to be searched by a genetic algorithm; the method comprises the following specific steps:
3-1) initializing a genetic algorithm;
setting the number of populations in a genetic algorithm as M and the length of each individual in the populations as K; randomly initializing the code of each bit of each body in the population to be 0 or 1, wherein 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; setting variation probability PM and cross probability PC, wherein the maximum genetic iteration number is T; making the current iteration time t equal to 1; taking the initialized population as a current population;
3-2) calculating the individual fitness of each individual in the current population, and the specific steps are as follows:
3-2-1) making the individual serial number j equal to 1;
3-2-2) forming a point neighborhood NB (Q) to be searched by corresponding points selected by individuals j in the populationiN), wherein N is the total number of positions in the individual encoded as 1; calculating a point Q to be searchediStructure tensor C ofiAs shown in formula (1):
Figure FDA0003552815900000011
wherein, PijIs a neighborhood NB (Q)iThe j-th point within N),
Figure FDA0003552815900000012
is a neighborhood NB (Q)iN) geometric center point;
3-2-3) pair of structure tensors CiAnd (3) decomposing the characteristic values, and sequencing the characteristic values from small to large to obtain a characteristic value sequencing result as follows: lambda is more than or equal to 00≤λ1≤λ2；
3-2-4) pairs of eigenvalues lambda0,λ1,λ2Respectively carrying out normalization to obtain corresponding normalized characteristic values gamma0,γ1,γ2；
3-2-5) calculating the linearity alpha of the point to be measured1DAs shown in formula (2):
Figure FDA0003552815900000021
3-2-6) calculating three-dimensional divergence alpha of points to be measured3DAs shown in formula (3):
Figure FDA0003552815900000022
3-2-7) calculating an entropy energy function E2DThe reciprocal of which is taken as the individual fitness F of the individual jjAs shown in formula (4):
Figure FDA0003552815900000023
wherein, omega and mu are respectively control factors;
3-2-8) making j equal to j +1, then returning to the step 3-2-2) to calculate the individual fitness of the next individual until the individual fitness of all the individuals in the current population is completely calculated, and entering the step 3-3);
3-3) selecting population individuals according to the individual fitness of all the individuals obtained in the step 3-2) to generate a new population; the method comprises the following specific steps:
3-3-1) Individual fitness F according to each individualjCalculating the probability ρ of the individual being selectedjJ is 1,2, … M, as shown in equation (5):
Figure FDA0003552815900000024
3-3-2) selecting individuals in the population by using the result of the step 3-3-1) through a probability selection method, and selecting M individuals to copy into a new population;
3-4) crossing the new population individuals obtained in the step 3-3) according to the crossing probability PC to obtain an updated new population;
3-5) carrying out variation on the new population updated in the step 3-4) according to the variation probability PM to obtain an updated new population;
3-6) enabling the iteration time t to be t +1, taking the updated new population obtained in the step 3-5) as the current population, and then returning to the step 3-2); until T reaches the maximum genetic iteration time T, finishing population updating to obtain a final population;
3-7) repeating the step 3-2), calculating the individual fitness of each individual in the final population, and selecting the individual with the minimum entropy energy function value as the final individual; according to the code value of each digit of the final individual, the selected points in the individual are formed into the point Q to be searchediFinal neighborhood of
Figure FDA0003552815900000025
Wherein L is the number of K neighborhood points selected by the final individual, and the neighborhood search of the point to be searched is completed;
4) judging whether other points to be searched exist: if yes, returning to the step 2) again; if not, the search is complete.
2. The method of claim 1, wherein the probabilistic selection method is roulette.
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