CN110288636B - LiDAR point cloud non-initial value registration method based on plane feature constraint - Google Patents

LiDAR point cloud non-initial value registration method based on plane feature constraint Download PDF

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CN110288636B
CN110288636B CN201910368059.9A CN201910368059A CN110288636B CN 110288636 B CN110288636 B CN 110288636B CN 201910368059 A CN201910368059 A CN 201910368059A CN 110288636 B CN110288636 B CN 110288636B
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王永波
郑南山
张秋昭
杨化超
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China University of Mining and Technology CUMT
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Abstract

The invention discloses a LiDAR point cloud non-initial value registration method based on plane feature constraint, which adopts a four-parameter method to realize the expression of plane features in a three-dimensional space, takes the parameter equality of the homonymous plane features of adjacent observation stations after registration as constraint conditions, constructs a three-dimensional space similarity transformation target function based on dual quaternion description under the constraint of the plane features according to a least square criterion, and realizes the non-initial value solution of registration parameters through the extreme value analysis of the target function. The four-parameter expression of the planar features provides a simpler and more effective way for comparison of homonymous features; compared with vector algebra, the expression form of the space similarity transformation model based on dual quaternion description is simpler, and the additional constraint conditions in the registration process are fewer; compared with an iterative method, the algorithm realizes direct solution of parameters on the premise of not determining initial values of parameters of the spatial similarity transformation model in advance, and has better stability and higher reliability.

Description

LiDAR point cloud non-initial value registration method based on plane feature constraint
Technical Field
The invention particularly relates to a LiDAR point cloud non-initial value registration method based on plane feature constraint.
Background
By virtue of the excellent characteristics of rapidness, high efficiency, high precision and the like, the LiDAR (LiDAR) provides reliable data guarantee for comprehensively, truly, rapidly and accurately reproducing the geospatial entity and the environmental information thereof. However, due to the reasons that the spatial complexity of the geographic entity is generally high, the visual surface of the LiDAR sensor is generally narrow, and the like, in order to acquire surface feature data capable of comprehensively representing the geographic entity and surrounding ground objects thereof, a spatial three-dimensional data acquisition method based on a ground LiDAR technology generally needs to aim at objects along a plurality of different visual directions, acquire LiDAR point cloud data capable of describing the surface features of a target geographic entity and surrounding ground objects thereof, and splice originally independent stations together based on a point cloud registration algorithm to realize comprehensive expression of the geographic entity and surrounding environment information thereof.
The essence of LiDAR point cloud registration is to seek and establish a characteristic corresponding relation between LiDAR point clouds of adjacent survey stations, describe a relative position relation between coordinate references of the adjacent survey stations based on a space similarity transformation model, and calculate rotation, scaling and translation parameters for describing the relative position relation between the two coordinate references, so that mutual conversion between coordinate systems of different survey stations and unification of the coordinate references are realized. At present, a model parameter solving method commonly used in LiDAR point cloud registration is to expand a spatial similarity transformation formula by using a taylor formula of a multivariate function, apply linearization processing to the spatial similarity transformation formula, and further realize the solution of the spatial similarity transformation parameter based on an iteration mode. However, the iterative method has its own disadvantages as follows: 1) the initial values of the transformation parameters need to be determined in advance, and therefore linearization of a nonlinear objective function model is realized, and incorrect selection of the initial values may cause incorrect results or non-convergence of functions; 2) under the constraint of the linearization process, the method is only suitable for the condition of small corner coordinate transformation essentially, and in the registration process of the LiDAR point cloud, if the initial value of the similarity transformation model parameter between two coordinate systems cannot be provided or the initial value of the provided similarity transformation model parameter is not ideal, the accuracy and reliability of the calculation result will be seriously influenced. In comparison, the analytic method obtains parameters of a spatial similarity transformation model through calculation of an optimized error function, and avoids the problem of initial value calculation and iterative convergence caused by the initial value calculation, so that the research of the analytic solution method (also called direct solution method or direct method) of LiDAR point cloud registration is of great significance.
In the existing analytical solving algorithm for LiDAR point cloud registration, the method can be divided into 3 types according to different mathematical description methods of the rotation transformation process in the point cloud registration algorithm: 1) the description of a rotation transformation process is realized by utilizing vector algebra, and a direct solution method of transformation parameters is realized based on the orthogonalization and Singular Value Decomposition (SVD); 2) realizing the description of the rotary transformation process based on the unit quaternion and realizing a direct solution method of transformation parameters based on the description; 3) the description of the rotary transformation process is realized based on dual quaternion, and the direct solving method of the transformation parameter is realized based on the description. The unit quaternion can realize concise description of the rotation transformation process by only utilizing 4 parameters, and compared with a vector algebra method (describing the rotation transformation process by utilizing a rotation matrix or a rotation angle), the calculation is simpler, however, in the process of solving the space similarity transformation parameters, the calculation of the translation vector is established on the basis of the result of the rotation transformation parameters, so the precision of the result is influenced by the rotation transformation parameters to a certain extent, and the influence has error transmission and accumulation phenomena; in contrast, dual quaternions enable a direct description of the rotation and translation parameters, without any correlation between the rotation and translation parameter solving processes, and therefore, in recent years, much attention has been paid to their research in LiDAR point cloud registration and related applications thereof.
The method comprises the following steps of classifying the existing LiDAR point cloud registration algorithm into 4 types according to different choices of registration primitives in a registration process, namely LiDAR point cloud registration based on point feature constraint, LiDAR point cloud registration based on linear feature constraint, LiDAR point cloud registration based on planar feature constraint and LiDAR point cloud registration based on point, line and plane common constraint, analysis shows that the LiDAR point cloud registration algorithm is influenced by LiDAR point cloud sampling resolution, generally speaking, the extraction precision of linear features and planar features is higher than that of the point features, theoretically, the LiDAR point cloud registration algorithm applied to the LiDAR point cloud registration is beneficial to improving the registration quality, however, linear features and planar features in a three-dimensional space are described by using vector algebra, the diversity and complexity of expression forms directly result in the construction of a linear/planar feature constraint-based point cloud registration model, the phenomenon is more obvious in the design of an analytic registration model, the linear coordinates of Pl ü, the linear coordinates overcome the defects of linear features in the linear feature registration process in the registration process, the linear feature orientation and the linear feature are more obviously described by iteration, the iterative algorithm of linear and the linear coordinates, the linear feature is more reasonable and the linear feature is more reliable than the linear feature of the existing LiDAR linear feature.
Based on the analysis, the method selects plane features as elements of LiDAR point cloud registration, uses a Pl ü cker linear coordinate as a reference, proposes a four-parameter method (combination of a plane normal vector and the distance from an origin to a plane) to realize description of the plane features in a three-dimensional space, and uses dual quaternions to realize description of a plane feature space similarity transformation process, on the basis, constructs a corresponding target function according to a least square criterion, and further develops the LiDAR point cloud non-initial value registration method based on dual quaternion description under plane feature constraint.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a LiDAR point cloud non-initial value registration method based on plane feature constraint, which overcomes the dependence of an iterative method on parameter initial value selection and further improves the stability of an algorithm.
The technical scheme is as follows: the invention discloses a LiDAR point cloud non-initial value registration method based on plane feature constraint, which comprises the following steps:
(1) using a plane fitting algorithm to respectively extract homonymous plane features from point clouds of a reference station and a LiDAR station to be registered, and respectively representing as follows:
Figure GDA0002291178650000031
wherein the content of the first and second substances,and
Figure GDA0002291178650000033
normal vectors of homonymous plane features respectively
Figure GDA0002291178650000034
And moment
Figure GDA0002291178650000035
Figure GDA0002291178650000036
The corresponding quaternion;
(2) describing a space similarity transformation process of the three-dimensional plane features based on dual quaternions, and constructing a space similarity transformation target function based on dual quaternion description according to a least square criterion by taking parameter equality of homonymous features after space similarity transformation as a precondition;
(3) respectively solving rotation quaternion in sequence by using extreme value analysis method
Figure GDA0002291178650000037
Scaling factor mu and translation quaternion
Figure GDA0002291178650000038
And realizing the unification of the coordinate systems of the reference station and the station to be registered based on the parameters, thereby realizing the seamless splicing of the LiDAR point clouds of the two survey stations.
The step (1) comprises the following steps:
(11) unitizing the normal to the plane, i.e.
Figure GDA0002291178650000039
(12) Defining the distance m from the coordinate origin to the plane as the mode of the plane feature, and knowing the normal vector of the plane
Figure GDA00022911786500000310
The expression modulo m with any point p, passed by it is as follows:
Figure GDA00022911786500000311
wherein the vector
Figure GDA00022911786500000312
The coordinate of an arbitrary point p in the three-dimensional space;
(13) the mathematical description defining the planar features is in the form of:
Figure GDA00022911786500000313
wherein the content of the first and second substances,
Figure GDA00022911786500000314
Figure GDA00022911786500000315
the step (2) is realized by the following formula:
Figure GDA0002291178650000041
wherein the content of the first and second substances,
Figure GDA0002291178650000042
respectively representing the homonymy plane characteristics P extracted by the reference station and the station to be registereda、PbThe unit normal vector of (a) is,respectively represent Pa、PbThe modulus of (d), mu represents the scaling factor,
Figure GDA0002291178650000044
represents a unit quaternion corresponding to the rotation matrix R,
Figure GDA0002291178650000045
represents the translation quaternion corresponding to the translation vector T, W (-) and Q (-) each represent a function of the quaternion, namely:
Figure GDA0002291178650000046
order:
Figure GDA0002291178650000048
Figure GDA0002291178650000049
according to the least square criterion, when ∑ f1 2+∑f2 2When the minimum value is obtained, the optimal solution of the space similarity transformation parameter can be obtained through an extremum analysis method.
The rotational quaternionThe solution process of (2) is as follows:
for sigma f1 2Is decomposed and makes the expression of
Figure GDA00022911786500000411
Then:
Figure GDA00022911786500000412
based on Lagrange multiplier method, in expression sigma f1 2Adding additional constraint condition
Figure GDA00022911786500000413
The corresponding objective function is constructed as follows:
Figure GDA00022911786500000414
constructing matrices
Figure GDA0002291178650000051
Then there are:
quaternion
Figure GDA0002291178650000053
Is an eigenvector, λ, of the matrix A1Is the corresponding characteristic value when lambda1Taking the maximum eigenvalue of the matrix A, the objective function
Figure GDA0002291178650000054
Is the smallest, at which time the feature vector
Figure GDA00022911786500000517
The corresponding quaternion is the sought, i.e., the optimal rotational quaternion.
The scaling coefficient mu and the translation quaternion
Figure GDA0002291178650000055
The solution process of (2) is as follows:
for sigma f2 2And let:
Figure GDA0002291178650000056
Figure GDA0002291178650000057
Cm1＝2∑I，
Figure GDA0002291178650000058
Figure GDA0002291178650000059
Figure GDA00022911786500000510
the following can be obtained:
Figure GDA00022911786500000511
based on Lagrange multiplier method, in expression sigma f2 2Adding additional constraint condition
Figure GDA00022911786500000512
Construction ofCorresponding objective function, and obtaining corresponding scaling coefficient mu and translation quaternion through extreme value analysis
Figure GDA00022911786500000513
Figure GDA00022911786500000514
Figure GDA00022911786500000515
Wherein the content of the first and second substances,
has the advantages that: compared with the prior art, the invention has the beneficial effects that: 1. the four-parameter expression mode of the plane features in the three-dimensional space provides a simpler and more effective mode for comparison of the homonymous plane features, and compared with expression methods of three-dimensional space rotation transformation such as Euler angles, rotation matrixes and the like, the expression form of quaternions is simpler, and additional constraint conditions in the registration process are fewer; 2. the analytical solution of the spatial similarity transformation parameters is realized based on an extreme value analysis method, the dependency of an iterative method on parameter initial value selection is removed, and the stability of the algorithm is higher.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a cloud of building reference standing surface points acquired using a Riegl VZ-1000 series ground LiDAR facility;
FIG. 3 is a cloud image of elevation points of a station to be registered of a building acquired by a Riegl VZ-1000 series ground LiDAR device;
FIG. 4 is a visual effect diagram before point cloud registration of a reference station and a LiDAR point to be registered;
FIG. 5 is a visual effect diagram of a reference station registered with a point cloud of LiDAR to be registered based on the algorithm of the present patent.
Detailed Description
The present invention is described in further detail below with reference to the accompanying drawings, in which the present invention includes the following steps, as shown in fig. 1.
1. Plane feature extraction and expression based on LiDAR point cloud
And determining and selecting LiDAR point clouds belonging to the target plane features in a man-machine interaction mode, and realizing the fitting of the plane features according to a least square criterion.
In order to realize the uniqueness of the mathematical expression of the plane features in the three-dimensional space, the extracted plane features are processed as follows:
1) unitizing the normal to the plane, i.e.
Figure GDA0002291178650000061
2) The distance m from the coordinate origin to the plane (also called the mode of the plane) is used as the fourth element of the plane expression, and the normal vector of the plane is known
Figure GDA0002291178650000062
The expression modulo m with any point p, passed by it is as follows:
Figure GDA0002291178650000063
wherein the vector
Figure GDA0002291178650000064
The coordinate of an arbitrary point p in the three-dimensional space;
through the above processing, the extracted planar features can be expressed as:
Figure GDA0002291178650000065
wherein the content of the first and second substances,
through the above processing, the corresponding parameter of any plane in the three-dimensional space is unique.
2. Target function construction based on dual quaternion description
In a vector algebraic space, a normal vector and a module of a plane feature are subjected to space similarity transformation operation respectively, and the corresponding relation between the normal vector and the module before and after transformation is expressed as follows:
Figure GDA0002291178650000071
the spatial similarity transformation process described by equation (3) is described based on dual quaternions, which can be further expressed as:
Figure GDA0002291178650000072
wherein the content of the first and second substances,
Figure GDA0002291178650000073
represents a unit quaternion corresponding to the rotation matrix R,
Figure GDA0002291178650000074
expressing unit quaternion
Figure GDA0002291178650000075
The conjugate of (a) to (b),
Figure GDA0002291178650000076
order:equation (4) can be further rewritten as:
Figure GDA0002291178650000078
wherein the content of the first and second substances,
Figure GDA0002291178650000079
representing quaternion
Figure GDA00022911786500000710
Conjugation of (1).
Each component in the formula (5) is expressed in a matrix form, and it can be obtained:
Figure GDA00022911786500000711
order:
Figure GDA00022911786500000712
Figure GDA00022911786500000713
according to the least square criterion, when ∑ f1 2+∑f2 2When the minimum value is obtained, the optimal solution of the spatial similarity transformation can be obtained.
3. Solving of spatial similarity transformation parameters
(1) Rotating quaternion
Figure GDA00022911786500000714
Is solved for
To realize a pairTo Σ f1 2The expression of (c) is decomposed as follows:
Figure GDA0002291178650000081
order:then:
Figure GDA0002291178650000083
based on Lagrange multiplier method, in expression sigma f1 2Adding additional constraint condition
Figure GDA0002291178650000084
The objective function is defined and constructed as follows:
Figure GDA0002291178650000085
where lambda is1Is the lagrange multiplication constant; optimal rotational quaternion
Figure GDA0002291178650000086
Can be obtained by minimizing the objective function.
Taking the partial derivative of equation (11) has:
Figure GDA0002291178650000087
order:
Figure GDA0002291178650000088
then there are:
Figure GDA0002291178650000089
according to the correlation between the eigenvalue and the eigenvector of the matrix, the following can be known: quaternion
Figure GDA00022911786500000810
Is an eigenvector, λ, of the matrix A1Is the corresponding characteristic value.
By using
Figure GDA00022911786500000811
Multiplication by equation (12) has:
Figure GDA00022911786500000812
substituting equation (11) to obtain
Figure GDA00022911786500000813
It can be seen that when lambda is1Taking the maximum eigenvalue of the matrix A, the objective function
Figure GDA00022911786500000814
Is the smallest, at which time the feature vector
Figure GDA0002291178650000091
The corresponding quaternion is the optimal rotational quaternion.
(2) Scaling factor mu and translation quaternion
Figure GDA0002291178650000092
Is solved for
To realize a pair
Figure GDA0002291178650000093
To Σ f2 2The expression of (c) is decomposed as follows:
Figure GDA0002291178650000094
order:
Figure GDA0002291178650000095
Cm1＝2∑I，
Figure GDA0002291178650000097
equation (17) can be rewritten as:
Figure GDA0002291178650000098
based on Lagrange multiplier method, in expression sigma f2 2Adding additional constraint condition
Figure GDA0002291178650000099
The objective function is defined and constructed as follows:
where lambda is2Is Lagrange multiplied by a constant.
The scaling coefficient mu and the translation quaternion can be obtained by solving through extreme value analysis
Figure GDA00022911786500000911
The specific process is as follows:
the partial derivative for equation (19) has:
Figure GDA00022911786500000912
Figure GDA00022911786500000913
according to the formula (21), it is possible to obtain:
Figure GDA00022911786500000914
mu is substituted into formula (20) and item is transposed to obtain
Wherein the content of the first and second substances,
by using
Figure GDA0002291178650000103
By multiplying by equation (23), one can obtain:
Figure GDA0002291178650000104
the above formula is simplified to obtainCoefficient lambda2Expression (c):
because (C)m2 T+Cm3 T) Is an anti-symmetric array, and the array is,
Figure GDA0002291178650000106
the above formula can be further simplified as follows:
Figure GDA0002291178650000107
find out the parameter lambda2Can be obtained according to the formula (23) and the formula (22) in sequenceAnd the value of μ.
To obtain
Figure GDA0002291178650000109
And
Figure GDA00022911786500001010
can be obtained by the following formula
Figure GDA00022911786500001011
Figure GDA00022911786500001012
Table 1 shows experimental data for simulation designed to verify the correctness of the algorithm, in which the homonymous features are 5 planes determined in a three-dimensional space; table 2 shows the spatial similarity transformation parameters set in advance by the experimental data for simulation.
TABLE 1 simulated plane feature data for Algorithm correctness testing
Figure GDA00022911786500001013
TABLE 2 Preset spatial similarity transform parameters
Figure GDA0002291178650000112
Based on the plane characteristic data shown in table 1, the result of the similarity transformation parameter between the station to be registered and the reference survey station calculated by the algorithm of the present patent is shown in table 3:
TABLE 3 deviation of registration results from homonymous features after registration
Figure GDA0002291178650000113
Fig. 2 and 3 respectively show a point cloud of a facade of a building acquired by using VZ-1000 series ground LiDAR equipment manufactured by Riegl corporation of austria, a survey station shown in fig. 2 is taken as a reference station, a survey station shown in fig. 3 is a station to be registered, and plane feature data shown in table 4 are 7 pairs of same-name plane features extracted from the reference station and the station to be registered respectively, and are used for testing feasibility and practicability of an algorithm.
TABLE 4 plane features extracted based on least squares fitting
Figure GDA0002291178650000114
Figure GDA0002291178650000121
TABLE 5 registration parameters based on the algorithm herein and their deviations between homonymous features after registration
Figure GDA0002291178650000122
Based on the registration model parameters obtained by calculation through the patent algorithm shown in table 5, the difference between the homonymous plane feature normal vectors is extremely small from the deviation between homonymous features after registration, the maximum deviation value between the moments of the planes is 0.0394m, and the maximum deviation value is equivalent to the result of the existing LiDAR point cloud registration algorithm based on point feature and linear feature constraint.
The LiDAR point clouds of two adjacent observation stations shown in the figures 2 and 3 are registered by using the algorithm, and the visual effects before and after registration are respectively shown in figures 4 and 5.
In general, under the condition that any initial value of unknown parameters of a three-dimensional space similarity transformation model is not given, the algorithm can realize parameter solving, has correct results, is consistent with the original design purpose, and can be used for registration of LiDAR point clouds of adjacent stations and other fields related to three-dimensional space similarity transformation.

Claims (5)

1. A LiDAR point cloud non-initial value registration method based on plane feature constraint is characterized by comprising the following steps:
(1) using a plane fitting algorithm to respectively extract homonymous plane features from point clouds of a reference station and a LiDAR station to be registered, and respectively representing as follows:
Figure FDA0002291178640000011
wherein the content of the first and second substances,
Figure FDA0002291178640000012
andnormal vectors of homonymous plane features respectively
Figure FDA0002291178640000014
And moment
Figure FDA0002291178640000015
Figure FDA0002291178640000016
To what is providedA corresponding quaternion;
(2) describing a space similarity transformation process of the three-dimensional plane features by using dual quaternions, and constructing a three-dimensional space similarity transformation target function based on dual quaternion description under plane feature constraint according to a least square criterion by using parameter equality of homonymous features after space similarity transformation as a precondition;
(3) respectively solving rotation quaternion in sequence by using extreme value analysis methodScaling factor mu and translation quaternion
Figure FDA00022911786400000116
And realizing the unification of point cloud coordinate systems of the reference station and the LiDAR to-be-registered station based on the obtained parameters, and further realizing the seamless splicing of the LiDAR point clouds of the two survey stations, namely realizing the registration of the LiDAR point clouds of the two survey stations.
2. The method of claim 1, wherein step (1) comprises the steps of:
(11) unitizing normal vectors to planar features in three-dimensional space, i.e.
Figure FDA0002291178640000017
(12) Defining the distance m from the coordinate origin to the plane as the mode of the plane feature, and knowing the normal vector of the plane
Figure FDA0002291178640000018
The expression modulo m with any point p, passed by it is as follows:
Figure FDA0002291178640000019
wherein the vector
Figure FDA00022911786400000110
The coordinate of an arbitrary point p in the three-dimensional space;
(13) the mathematical description defining the planar features is in the form of:
Figure FDA00022911786400000111
wherein the content of the first and second substances,
Figure FDA00022911786400000112
Figure FDA00022911786400000113
3. the method of claim 1, wherein the step (2) is implemented by the following formula:
Figure FDA00022911786400000114
wherein the content of the first and second substances,
Figure FDA0002291178640000021
respectively representing homonymous plane features P extracted based on point clouds of LiDAR of a reference station and a station to be registereda、PbThe unit normal vector of (a) is,
Figure FDA0002291178640000022
respectively represent Pa、PbThe modulus of (d), mu represents the scaling factor,
Figure FDA0002291178640000023
represents a unit quaternion corresponding to the rotation matrix R,representing translation quaternions corresponding to the translation vector T, W (-) and Q (-) each representing a function of a quaternion, a concrete expressionThe formula is as follows:
Figure FDA0002291178640000025
order:
Figure FDA0002291178640000026
Figure FDA0002291178640000027
according to the least square criterion, when ∑ f1 2+∑f2 2When the minimum value is obtained, the optimal solution of the space similarity transformation parameter can be obtained through an extremum analysis method.
4. The method of claim 1, wherein the rotational quaternion is based on a LiDAR point cloud non-initial registration method based on a planar feature constraintThe solution process of (2) is as follows:
for sigma f1 2Is decomposed and makes the expression of
Figure FDA0002291178640000028
Then:
Figure FDA0002291178640000029
based on Lagrange multiplier method, in expression sigma f1 2Adding additional constraint condition
Figure FDA00022911786400000210
The corresponding objective function is constructed as follows:
Figure FDA00022911786400000211
constructing matricesThen there are:
Figure FDA00022911786400000213
quaternion
Figure FDA00022911786400000214
Is an eigenvector, λ, of the matrix A1Is and
Figure FDA00022911786400000215
corresponding characteristic value, when λ1Taking the maximum eigenvalue of the matrix A, the objective function
Figure FDA0002291178640000031
Is the smallest, at which time the feature vector
Figure FDA00022911786400000314
The corresponding quaternion is the sought, i.e., the optimal rotational quaternion.
5. The method of claim 1, wherein the scaling coefficient μ and the translation quaternion are used to determine the location of the LiDAR point cloud based on the planar feature constraintThe solution process of (2) is as follows:
for sigma f2 2And let:
Figure FDA0002291178640000033
Figure FDA00022911786400000312
Cm1＝2∑I，
Figure FDA0002291178640000034
Figure FDA0002291178640000035
the following can be obtained:
Figure FDA0002291178640000036
based on Lagrange multiplier method, in expression sigma f2 2Adding additional constraint condition
Figure FDA0002291178640000037
Constructing corresponding objective function, and obtaining corresponding scaling coefficient mu and translation quaternion through extreme value analysis
Figure FDA0002291178640000038
Figure FDA0002291178640000039
Figure FDA00022911786400000310
Wherein the content of the first and second substances,
Figure FDA00022911786400000311
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