CN110849389A - External parameter calibration method for two three-dimensional point cloud acquisition systems based on space sphere - Google Patents

External parameter calibration method for two three-dimensional point cloud acquisition systems based on space sphere Download PDF

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CN110849389A
CN110849389A CN201911018195.1A CN201911018195A CN110849389A CN 110849389 A CN110849389 A CN 110849389A CN 201911018195 A CN201911018195 A CN 201911018195A CN 110849389 A CN110849389 A CN 110849389A
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point cloud
dimensional point
cloud acquisition
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CN110849389B (en
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汪霖
潘庆曼
彭进业
廖成峰
李艳艳
姜博
周延
汪照阳
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Northwestern University
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Abstract

The invention discloses a method for calibrating external parameters of two three-dimensional point cloud acquisition systems based on a space sphere, which comprises the following steps: s1: establishing an external parameter calibration model according to the positions of the two three-dimensional point cloud acquisition systems; s2: acquiring three-dimensional point cloud data of a preset calibration position in each three-dimensional point cloud acquisition system; s3: establishing a nonlinear target function of external parameter calibration according to the external parameter calibration model and the three-dimensional point cloud data; s4: the method for calibrating the external parameters of the two three-dimensional point cloud acquisition systems based on the space sphere solves the problem that the dimensional parameters of the calibration object are difficult to accurately measure in the existing method, and improves the accuracy of external parameter estimation.

Description

External parameter calibration method for two three-dimensional point cloud acquisition systems based on space sphere
Technical Field
The invention belongs to the technical field of surveying and mapping, and particularly relates to a method for calibrating external parameters of two three-dimensional point cloud acquisition systems based on a space sphere.
Background
With the increasing demand of various industries in the information era on spatial data, the conventional data acquisition mode cannot meet the informatization demand, measured data is converted from a two-dimensional form to a three-dimensional form in a mapping system, digital city three-dimensional reconstruction and reverse engineering, three-dimensional point cloud data acquisition becomes an indispensable part as the basis of the system, and the data acquisition precision directly influences the overall precision of the system. The three-dimensional point cloud acquisition system based on the Kinect sensor is a commonly used acquisition system at present, and the calibration of external parameters between two three-dimensional point cloud acquisition systems is used for estimating rigid body transformation parameters between coordinate systems of the three-dimensional point cloud acquisition systems and is a basis for carrying out information fusion on point cloud data acquired by different three-dimensional point cloud acquisition systems.
At present, two external parameter calibration methods of a three-dimensional point cloud acquisition system based on Kinect are fewer, and most of the existing methods aim at external parameter calibration methods of a camera and a three-dimensional laser scanner. For example, Zhao Song et al propose a method for calibrating external parameters of a camera and a three-dimensional laser scanner based on a three-dimensional calibration target, which uses the three-dimensional calibration target as a calibration object and utilizes a Newton iteration method to perform nonlinear parameter optimization.
However, the calibration precision of the method is influenced by the precision of the mark characteristic point of the three-dimensional calibration target, and the Newton iteration method is greatly influenced by the initial value; meanwhile, most of the existing methods need to give the relevant size of the calibration object, and the actual calibration process is usually difficult to accurately measure the relevant size of the calibration object, so that the estimation accuracy of external parameters of the existing calibration methods is low.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method for calibrating external parameters of two three-dimensional point cloud acquisition systems based on a space sphere.
The technical problem to be solved by the invention is realized by the following technical scheme:
a method for calibrating external parameters of two three-dimensional point cloud acquisition systems based on a space sphere comprises the following steps:
s1: establishing an external parameter calibration model according to the positions of the two three-dimensional point cloud acquisition systems;
s2: acquiring three-dimensional point cloud data of a preset calibration position in each three-dimensional point cloud acquisition system;
s3: establishing a nonlinear target function of external parameter calibration according to the external parameter calibration model and the three-dimensional point cloud data;
s4: and optimizing the nonlinear objective function to obtain external parameter estimation values of the two three-dimensional point cloud acquisition systems.
In an embodiment of the present invention, the external parameter calibration model is:
Figure RE-GDA0002357345580000021
wherein ,(x1,y1,z1)TRepresenting the coordinates of the scanning point P under the coordinate system of the first three-dimensional point cloud acquisition system, (x)2,y2,z2)TThe coordinate of the scanning point P under the coordinate system of the second three-dimensional point cloud acquisition system is shown, R is a rotation matrix of 3 multiplied by 3, the posture relation from the coordinate system of the second three-dimensional point cloud acquisition system to the coordinate system of the first three-dimensional point cloud acquisition system is shown, and t ═ t (t ═ tx,ty,tz)TThe translation vector is 3 multiplied by 1 and represents the position relation from the coordinate system of the second three-dimensional point cloud acquisition system to the coordinate system of the first three-dimensional point cloud acquisition system.
In an embodiment of the present invention, the expression of the rotation matrix R is:
R＝R(φ,θ,ψ)＝Rot(Z,φ)Rot(Y,θ)Rot(X,ψ)；
where φ represents roll angle, θ represents pitch angle, ψ represents yaw angle, X, Y, Z represents coordinate axes, Rot (X, ψ) represents rotation by ψ angle about the X axis, Rot (Y, θ) represents rotation by θ angle about the Y axis, Rot (Z, φ) represents rotation by φ angle about Z axis, φ, θ, ψ take values in the ranges of φ e [ -180 °, θ e [ -90 °, and ψ e [ -180 °,180 °).
In one embodiment of the present invention, step S2 includes:
s21: fixedly placing a calibration ball at a preset calibration position, and centering the calibration ball on a ball center OSThe coordinate in the coordinate system of the first three-dimensional point cloud acquisition system is represented as ps＝(xS,yS,zS)TSetting the radius of the calibration sphere as r;
s22: acquiring three-dimensional point cloud data { P) of the calibration ball in a first three-dimensional point cloud acquisition systemi1} (i＝1,2,…,N1), wherein ,N1The number of scanning points on the calibration sphere, the point P on the calibration sphere, acquired by the first three-dimensional point cloud acquisition systemi1The three-dimensional coordinate measurement value under the coordinate system of the first three-dimensional point cloud acquisition system is represented as pi1＝(xi1,yi1,zi1)T；
S23 obtaining different tilt head deflection angles αk(k-1, 2, …, N) three-dimensional point cloud data { P) of the calibration sphere in the second three-dimensional point cloud acquisition systemjk2}(j＝1,2,…,Nk2) Wherein N is the number of different tripod head deflection angles of the second three-dimensional point cloud acquisition system, and Nk2Scanning points on the calibration sphere acquired by the second three-dimensional point cloud acquisition system under the k-th tripod head deflection angle; point P on the calibration spherejk2The three-dimensional coordinate measurement value under the coordinate system of the second three-dimensional point cloud acquisition system is represented as pjk2＝(xjk2,yjk2,zjk2)T。
In one embodiment of the present invention, step S3 includes:
calibrating the model according to the external parameters and the spherical center O of the calibration ballSCoordinate p under the coordinate system of the first three-dimensional point cloud acquisition systemsRadius r of the calibration sphere, point P on the calibration spherei1Three-dimensional coordinate measurement under first three-dimensional point cloud acquisition system coordinate systemValue pi1And a point P on said calibration spherejk2Three-dimensional coordinate measured value p under second three-dimensional point cloud acquisition system coordinate systemjk2And establishing a nonlinear objective function calibrated by the external parameters.
In one embodiment of the present invention, the nonlinear objective function is:
Figure RE-GDA0002357345580000041
wherein, | | · | | represents the euclidean norm.
In one embodiment of the present invention, step S4 includes:
s41: optimizing the model parameters in the nonlinear objective function by using a SHADE algorithm to obtain an optimization result;
s42: and taking the optimization result as an estimation value of the rotation matrix R and the translational vector t to obtain external parameter estimation values of the two three-dimensional point cloud acquisition systems.
In one embodiment of the present invention, step S41 includes:
s411: initializing a SHADE algorithm;
s412: setting successful cross probability set
Figure RE-GDA0002357345580000042
Set of success scale factors
Figure RE-GDA0002357345580000043
Fitness function value deviation set
Figure RE-GDA0002357345580000044
S413: calculating each individual of the current generation
Figure RE-GDA0002357345580000045
Cross probability of
Figure RE-GDA0002357345580000046
And a scale factor Fi GAnd
Figure RE-GDA0002357345580000047
wherein ,NmaxRepresenting the population quantity;
s414: for the current generation individuals
Figure RE-GDA0002357345580000048
Performing mutation operation to generate NmaxIndividual variation
Figure RE-GDA0002357345580000049
(i＝1,2,…,Nmax)；
S415: subjecting the variant individual to
Figure RE-GDA00023573455800000410
Its father generation individual
Figure RE-GDA00023573455800000411
Performing crossover operation to generate new crossover individual
S416: for the current generation individuals
Figure RE-GDA00023573455800000413
Cross individuals generated correspondingly to the cross individuals
Figure RE-GDA00023573455800000414
Selecting and reserving the individual with the smaller fitness function value to form a next generation population;
s417: updating the population and increasing the iteration times by 1;
s418: if the current iteration times G reach the preset maximum iteration times GmaxThen output the G thmaxAll individuals after the second iterationOtherwise, steps S412 to S417 are repeated.
In one embodiment of the present invention, step S42 includes:
the G thmaxAll individuals after the second iteration
Figure RE-GDA0002357345580000052
Of individuals with minimum fitness
Figure RE-GDA0002357345580000053
An optimal solution as a minimization objective function; wherein,the first 3-dimensional components are estimated values of three RPY attitude angles (phi, theta, psi) corresponding to the rotation matrix R in the external parameters of the two three-dimensional point cloud acquisition systems,
Figure RE-GDA0002357345580000055
the 4 th to 6 th dimensional components of (a) are translation vector t estimated values in the external parameters.
The invention has the beneficial effects that:
1. the method for calibrating the external parameters of the two three-dimensional point cloud acquisition systems based on the space sphere, provided by the invention, has the advantages that the nonlinear objective functions of the external parameters of the two three-dimensional point cloud acquisition systems are established, and then optimization is carried out, so that the estimation of the external parameters of the two three-dimensional point cloud acquisition systems is realized, the problem that the size parameters of a marker in the existing method are difficult to accurately measure is solved, and the estimation precision of the external parameters is improved;
2. the calibration ball point cloud data under different deflection angles are obtained through the deflection motion of the holder, so that the influence of the noise measured by the two three-dimensional point cloud acquisition systems on the external parameter calibration precision can be effectively inhibited, and the calibration precision of the method on the external parameters of the two three-dimensional point cloud acquisition systems is further improved.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flow chart of an external parameter calibration method for two three-dimensional point cloud acquisition systems based on a space sphere according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of external parameter calibration of two three-dimensional point cloud acquisition systems according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating an external parameter calibration problem of two three-dimensional point cloud acquisition systems according to an embodiment of the present invention;
fig. 4 is a flow chart of the jump optimization algorithm provided in the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
Referring to fig. 1, fig. 1 is a schematic flow chart of an external parameter calibration method for two three-dimensional point cloud collection systems based on a space sphere according to an embodiment of the present invention; the method comprises the following steps:
s1: establishing an external parameter calibration model according to the positions of the two three-dimensional point cloud acquisition systems;
in the embodiment, external parameter calibration between two three-dimensional point cloud acquisition systems, a first three-dimensional point cloud acquisition system and a second three-dimensional point cloud acquisition system is involved. Referring to fig. 2, fig. 2 is a schematic diagram of external parameter calibration of two three-dimensional point cloud acquisition systems according to an embodiment of the present invention; the three-dimensional point cloud collection system 1 in the figure is a first three-dimensional point cloud collection system, and the coordinate system is represented as O1X1Y1Z1The system only comprises a Kinect sensor and can acquire three-dimensional point cloud of a scene in a field range; the three-dimensional point cloud collection system 2 in the figure is a second three-dimensional point cloud collection system, and the coordinate system is represented as O2X2Y2Z2The system consists of a high-precision holder and a Kinect sensor, and collects three-dimensional point cloud of a scanning scene through deflection motion of the high-precision holder.
In this embodiment, the objective of the extrinsic parameter calibration is to estimate an extrinsic parameter between two coordinate systems of the three-dimensional point cloud collection system, i.e. a pose relationship between the two coordinate systems. Establishing an external parameter calibration model according to the positions of the two three-dimensional point cloud acquisition systems, namely establishing problem description of external parameter calibration of the two three-dimensional point cloud acquisition systems,namely establishing two coordinate systems O of the three-dimensional point cloud acquisition system1X1Y1Z1 and O2X2Y2Z2And transforming the coordinates of the lower scanning points.
Referring to fig. 3, fig. 3 is a schematic diagram illustrating an external parameter calibration problem of two three-dimensional point cloud acquisition systems according to an embodiment of the present invention; in the present embodiment, the pose relationship between the two coordinate systems is represented by a rotation matrix R and a translation vector t. Suppose that a certain scanning point P is in the coordinate system O of the three-dimensional point cloud acquisition system 11X1Y1Z1The coordinates of (x) below1,y1,z1)TIn a three-dimensional point cloud acquisition system 2 coordinate system O2X2Y2Z2The lower coordinate is (x)2,y2,z2)TThen, the transformation relationship from the three-dimensional point cloud collection system 2 to the three-dimensional point cloud collection system 1, that is, the external parameter calibration model, is:
Figure RE-GDA0002357345580000071
wherein, R is a 3 × 3 rotation matrix representing the attitude relationship from the coordinate system of the three-dimensional point cloud acquisition system 2 to the coordinate system of the three-dimensional point cloud acquisition system 1, and t ═ t (t ═ t)x,ty,tz)TThe translation vector is 3 × 1, and indicates the positional relationship.
In this embodiment, the rotation matrix R can be described by three RPY attitude angles of Roll angle (Roll), Pitch angle (Pitch), and Yaw angle (Yaw), i.e., the rotation matrix R represents a combined transformation of three rotations of Roll, Pitch, and Yaw, first rotating by an angle ψ about the X-axis, then by an angle θ about the Y-axis, and finally by an angle Φ about the Z-axis. Thus, the rotation matrix R is defined as:
R＝R(φ,θ,ψ)＝Rot(Z,φ)Rot(Y,θ)Rot(X,ψ)；
further, the rotation matrix R can be expressed as:
Figure RE-GDA0002357345580000072
wherein, the roll angle phi, the pitch angle theta and the deflection angle psi are respectively in the value ranges of phi epsilon-180 DEG and 180 DEG, theta epsilon-90 DEG and psi epsilon-180 DEG and 180 deg.
S2: acquiring three-dimensional point cloud data of a preset calibration position in each three-dimensional point cloud acquisition system;
in this embodiment, a calibration sphere is used as a calibration object, and two three-dimensional point cloud acquisition systems are used to respectively acquire three-dimensional point cloud data of the calibration sphere, including:
s21: fixedly placing a calibration ball at a preset calibration position, and centering the calibration ball on a ball center OSThe coordinate in the coordinate system of the three-dimensional point cloud acquisition system 1 is represented as ps＝(xS,yS,zS)TSetting the radius of the calibration sphere as r;
in this embodiment, the calibration ball may be placed at a position in front of the two three-dimensional point cloud collection systems, and the spherical center coordinate p of the calibration ball issAnd the radius r are not given.
S22: obtaining three-dimensional point cloud data { P) of the calibration sphere in the three-dimensional point cloud acquisition system 1i1} (i＝1,2,…,N1), wherein ,N1The number of scanning points on the calibration sphere, the point P on the calibration sphere, acquired by the three-dimensional point cloud acquisition system 1i1The three-dimensional coordinate measurement value under the coordinate system of the three-dimensional point cloud acquisition system 1 is represented as pi1＝(xi1,yi1,zi1)T；
S23 obtaining different tilt head deflection angles αk(k ═ 1,2, …, N) three-dimensional point cloud data { P) of the calibration sphere in the three-dimensional point cloud collection system 2jk2}(j＝1,2,…,Nk2) Wherein N is the number of different tilt head deflection angles of the three-dimensional point cloud acquisition system 2, and Nk2Scanning points on a calibration sphere obtained by the three-dimensional point cloud collection system 2 under the k-th tripod head deflection angle; point P on the calibration spherejk2The three-dimensional coordinate measurement value under the 2 coordinate system of the three-dimensional point cloud acquisition system is represented as pjk2＝(xjk2,yjk2,zjk2)T。
In this embodiment, the three-dimensional point cloud data of the calibration ball under different pan-tilt angles can be respectively obtained through the horizontal deflection of the pan-tilt in the three-dimensional point cloud acquisition system 2, so that the influence of the measurement noise of the two three-dimensional point cloud acquisition systems on the external parameter calibration precision can be effectively inhibited, and the calibration precision of the method on the external parameters of the two three-dimensional point cloud acquisition systems is improved.
S3: establishing a nonlinear target function of external parameter calibration according to the external parameter calibration model and the three-dimensional point cloud data;
in this embodiment, the calibration model and the calibration sphere center O are based on the external parametersSCoordinate p under coordinate system of three-dimensional point cloud acquisition system 1sRadius r of the calibration sphere, point P on the calibration spherei1Three-dimensional coordinate measured value p under three-dimensional point cloud acquisition system 1 coordinate systemi1And a point P on said calibration spherejk2Three-dimensional coordinate measured value p under three-dimensional point cloud acquisition system 2 coordinate systemjk2And establishing a nonlinear objective function calibrated by the external parameters.
In this embodiment, the external parameter calibration of the two three-dimensional point cloud acquisition systems aims at estimating pose parameters R and t from the three-dimensional point cloud acquisition system 2 to the three-dimensional point cloud acquisition system 1, and the external parameter calibration problem can be converted into a nonlinear optimization problem to be solved. Respectively scanning the calibration ball by using two three-dimensional point cloud acquisition systems to obtain point cloud data comprising O acquired by the three-dimensional point cloud acquisition system 11X1Y1Z1Three-dimensional point cloud data { P) under coordinate systemi1}(i＝1,2,…,N1) And the three-dimensional point cloud collection system 2 at different pan-tilt angles αkO obtained under (k ═ 1,2, …, N)2X2Y2Z2Three-dimensional point cloud data { P) under coordinate systemjk2}(j＝1,2,…,Nk2). And establishing a nonlinear objective function of external parameters of the two three-dimensional point cloud acquisition systems by using a distance constraint condition that the distance from each point on the calibration sphere to the sphere center is equal to the radius.
The point P is obtained by calibrating a model formula according to the pose relationship, namely the external parameter, of the two three-dimensional point cloud acquisition systemsjk2Coordinate p under coordinate system of three-dimensional point cloud acquisition system 1jk1＝(xjk1,yjk1,zjk1)TComprises the following steps:
due to the point Pi1And point Pjk2Are all located at the center of the sphere and are OSRadius r, thus point Pi1And point Pjk2All distances to the centre of the sphere are r, i.e.
Figure RE-GDA0002357345580000092
Wherein, | | · | | represents the euclidean norm.
According to the least square sum principle, two external parameters R (phi, theta, psi) and t (t) of the three-dimensional point cloud acquisition system are establishedx,ty,tz)TThe non-linear objective function of (a) is:
Figure RE-GDA0002357345580000093
wherein the decision variables in the non-linear objective function are (phi, theta, psi, tx,ty,tz,xS,yS,zSR) including three RPY attitude angles (phi, theta, psi) corresponding to the rotation matrix R, and a translation vector t ═ t (t)x,ty,tz)TCalibrating the coordinate p of the sphere center under the coordinate system of the three-dimensional point cloud acquisition system 1s＝(xS,yS,zS)TAnd a nominal spherical radius r.
Therefore, the calibration problem of the external parameters R (phi, theta, phi) and t is converted into a minimum optimization problem of a nonlinear objective function, and the decision variables are (phi, theta, phi, t)x,ty,tz,xS,yS,zS,r)。
S4: and optimizing the nonlinear objective function to obtain external parameter estimation values of the two three-dimensional point cloud acquisition systems.
In the present embodiment, step S4 includes:
s41: and optimizing the model parameters in the nonlinear objective function by using a SHADE algorithm to obtain an optimized result.
In this embodiment, it is preferable to optimize the established objective function by using a Success-based parameter differential evolution (shadow) algorithm with strong global optimization capability, so as to realize the estimation of external parameters of the two three-dimensional point cloud acquisition systems. The SHADE algorithm is firstly proposed by Ryoji and Alex in 2013, and is an improved differential evolution method based on probability, and the method comprises four parts of population initialization, mutation, crossing and selection. The SHADE algorithm has the advantages of simplicity and easiness in implementation, strong global optimization capability, strong robustness and the like. Therefore, the method uses the SHADE algorithm for optimizing the objective function, thereby realizing the accurate estimation of the external parameters of the two three-dimensional point cloud acquisition systems.
Referring to fig. 4, fig. 4 is a flowchart of a shadow optimization algorithm according to an embodiment of the present invention; the method comprises the following steps:
s411: initializing a SHADE algorithm;
firstly, the solution space dimension D is given as 10, and the value range [ x ] of the feasible solution of the nonlinear objective functionmin,xmax]The number of the groups is NmaxMaximum number of iterations GmaxHistory parameter vector MCR＝(MCR，1，MCR，2，…，MCR，H) and MF＝(MF,1,MF,2,…,MF,H) Dimension H of (A);
setting the current iteration number G as 0, taking the nonlinear objective function as the fitness function of the problem to be solved, and randomly initializing N in uniform distribution within the feasible solution value rangemaxIndividual one
History parameter vector MCR and MFAll values in the set are set to 0.5, and the Archive (Archive) set A is made to be an empty set
Figure RE-GDA0002357345580000112
Let index counter h be 1.
S412: setting successful cross probability set
Figure RE-GDA0002357345580000113
Set of success scale factors
Figure RE-GDA0002357345580000114
Fitness function value deviation set
Figure RE-GDA0002357345580000115
S413: calculating each individual of the current generation
Figure RE-GDA0002357345580000116
Cross probability of
Figure RE-GDA0002357345580000117
And a scale factor Fi GAnd
Figure RE-GDA0002357345580000118
wherein ,NmaxRepresenting the population quantity;
in this example, for each individual in the G-th generation
Figure RE-GDA0002357345580000119
Randomly selecting index value r from 1,2, …, HiCalculating the cross probabilityScale factor
Figure RE-GDA00023573455800001111
And
Figure RE-GDA00023573455800001112
the calculation formulas are respectively as follows:
Figure RE-GDA00023573455800001113
Figure RE-GDA00023573455800001114
Figure RE-GDA00023573455800001115
wherein, randni(μ,σ2) The mean is μ and the variance is σ2Normally distributed random number, randic(μ,σ2) The mean is μ and the variance is σ2Cauchy distribution random number of (c).
In this embodiment, μ is
Figure RE-GDA00023573455800001116
σ2Respectively 0.1, 0.1 and 0.2.
S414: performing mutation operation; for the current generation of individuals xi GPerforming mutation operation to generate NmaxIndividual variation
Figure RE-GDA00023573455800001117
In this example, to generate more excellent individuals, N was generated from the G-th generation individuals by mutationmaxIndividual variation
Figure RE-GDA00023573455800001118
The current-to-pbest/1 mutation strategy used is as follows:
Figure RE-GDA0002357345580000121
wherein ,
Figure RE-GDA0002357345580000122
is the current G generation before
Figure RE-GDA0002357345580000123
Randomly selected individuals from the optimal individuals,
Figure RE-GDA0002357345580000124
randomly selected individuals from the G-th generation individuals,
Figure RE-GDA0002357345580000125
randomly selected individuals in all the individuals set and the archiving set A in the G generation.
S415: performing cross operation; subjecting the variant individual to
Figure RE-GDA0002357345580000126
Its father generation individual
Figure RE-GDA0002357345580000127
Performing crossover operation to generate new crossover individual
Figure RE-GDA0002357345580000128
In this embodiment, the interleaving policy used in the interleaving operation is:
Figure RE-GDA0002357345580000129
wherein ,jrandIs [1, D ]]Random integers within the range.
S416: selecting operation; for the current generation individuals
Figure RE-GDA00023573455800001210
Cross individuals generated correspondingly to the cross individuals
Figure RE-GDA00023573455800001211
Selecting and reserving the individual with the smaller fitness function value to form a next generation population;
in this example, the G-th generation individuals are
Figure RE-GDA00023573455800001212
Cross individuals generated correspondingly to the cross individuals
Figure RE-GDA00023573455800001213
Comparing the fitness function values, and reserving the individuals with smaller fitness function values to form a next generation population so as to control the population quantity, wherein the selection strategy is as follows:
Figure RE-GDA00023573455800001214
s417: updating the population and increasing the iteration times by 1;
in this embodiment, if
Figure RE-GDA00023573455800001215
Then will beFi GAnd
Figure RE-GDA00023573455800001217
are added to the collection A, S respectivelyCR、SF and SΔfIn (1). When the potential of A is | A | > NmaxWhen the method is used, a plurality of individuals in A are randomly deleted to ensure that | A | is less than or equal to Nmax(ii) a If it isThen M will beCR,h and MF,hThe updating is as follows:
Figure RE-GDA0002357345580000131
Figure RE-GDA0002357345580000132
wherein the weight factor is represented by SΔfIs obtained from an element, i.e.
The current iteration number G is increased by 1.
S418: if the current iteration times G reach the preset maximum iteration times GmaxThen output the G thmaxAll individuals after the second iterationOtherwise, steps S412 to S417 are repeated.
In this embodiment, if G < GmaxIf yes, the index counter h is increased by 1, and h is satisfied>H is set to H as 1, go to step S412; otherwise, if G is greater than or equal to GmaxIf true, the SHADE method terminates the iteration and proceeds to step S42.
S42: and taking the optimization result as an estimation value of the rotation matrix R and the translational vector t to obtain external parameter estimation values of the two three-dimensional point cloud acquisition systems.
In this embodiment, the G-thmaxAll individuals after the second iteration
Figure RE-GDA0002357345580000135
Of individuals with minimum fitnessAn optimal solution as a minimization objective function; wherein,
Figure RE-GDA0002357345580000137
the first 3-dimensional components are estimated values of three RPY attitude angles (phi, theta, psi) corresponding to the rotation matrix R in the external parameters of the two three-dimensional point cloud acquisition systems,the 4 th to 6 th dimensional components of (a) are translation vector t estimated values in the external parameters.
The invention provides a calibration method for external parameters of two three-dimensional point cloud acquisition systems based on a calibration sphere with an unknown radius, aiming at the problem of external parameter estimation of the two three-dimensional point cloud acquisition systems. The method utilizes a distance constraint condition that the distance from each point on a space calibration sphere to the sphere center is equal to the radius, and establishes a nonlinear optimization objective function of external parameters of two three-dimensional point cloud acquisition systems. On the basis, the established objective function is optimized by using a SHADE algorithm to realize the estimation of the external parameters of the two three-dimensional point cloud acquisition systems, so that the problem that the size parameters of the marker are difficult to accurately measure in the existing method is solved, and the accuracy of external parameter estimation is improved.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (9)

1. A method for calibrating external parameters of two three-dimensional point cloud acquisition systems based on a space sphere is characterized by comprising the following steps:
s1: establishing an external parameter calibration model according to the positions of the two three-dimensional point cloud acquisition systems;
s2: acquiring three-dimensional point cloud data of a preset calibration position in each three-dimensional point cloud acquisition system;
s3: establishing a nonlinear target function of external parameter calibration according to the external parameter calibration model and the three-dimensional point cloud data;
s4: and optimizing the nonlinear objective function to obtain external parameter estimation values of the two three-dimensional point cloud acquisition systems.
2. The two three-dimensional point cloud acquisition system extrinsic parameter calibration method according to claim 1, wherein the extrinsic parameter calibration model is:
wherein ,(x1,y1,z1)TRepresenting the coordinates of the scanning point P in the coordinate system of the first three-dimensional point cloud acquisition system (b), (b)x2,y2,z2)TThe coordinate of the scanning point P under the coordinate system of the second three-dimensional point cloud acquisition system is shown, R is a rotation matrix of 3 multiplied by 3, the posture relation from the coordinate system of the second three-dimensional point cloud acquisition system to the coordinate system of the first three-dimensional point cloud acquisition system is shown, and t ═ t (t ═ tx,ty,tz)TThe translation vector is 3 multiplied by 1 and represents the position relation from the coordinate system of the second three-dimensional point cloud acquisition system to the coordinate system of the first three-dimensional point cloud acquisition system.
3. The method for calibrating extrinsic parameters of two three-dimensional point cloud acquisition systems according to claim 2, wherein the expression of the rotation matrix R is:
R＝R(φ,θ,ψ)＝Rot(Z,φ)Rot(Y,θ)Rot(X,ψ)；
where φ represents roll angle, θ represents pitch angle, ψ represents yaw angle, X, Y, Z represents coordinate axes, Rot (X, ψ) represents rotation by ψ angle about the X axis, Rot (Y, θ) represents rotation by θ angle about the Y axis, Rot (Z, φ) represents rotation by φ angle about Z axis, φ, θ, ψ take values in the ranges of φ e [ -180 °, θ e [ -90 °, and ψ e [ -180 °,180 °).
4. The method for calibrating the extrinsic parameters of two three-dimensional point cloud acquisition systems according to claim 2, wherein step S2 comprises:
s21: fixedly placing a calibration ball at a preset calibration position, and centering the calibration ball on a ball center OSThe coordinate in the coordinate system of the first three-dimensional point cloud acquisition system is represented as ps＝(xS,yS,zS)TSetting the radius of the calibration sphere as r;
s22: acquiring three-dimensional point cloud data { P) of the calibration ball in a first three-dimensional point cloud acquisition systemi1}(i＝1,2,…,N1), wherein ,N1The number of scanning points on the calibration sphere, the point P on the calibration sphere, acquired by the first three-dimensional point cloud acquisition systemi1The three-dimensional coordinate measurement value under the coordinate system of the first three-dimensional point cloud acquisition system is represented as pi1＝(xi1,yi1,zi1)T；
S23 obtaining different tilt head deflection angles αk(k-1, 2, …, N) three-dimensional point cloud data { P) of the calibration sphere in the second three-dimensional point cloud acquisition systemjk2}(j＝1,2,…,Nk2) Wherein N is the number of different tripod head deflection angles of the second three-dimensional point cloud acquisition system, and Nk2Scanning points on the calibration sphere acquired by the second three-dimensional point cloud acquisition system under the k-th tripod head deflection angle; point P on the calibration spherejk2The three-dimensional coordinate measurement value under the coordinate system of the second three-dimensional point cloud acquisition system is represented as pjk2＝(xjk2,yjk2,zjk2)T。
5. The method for calibrating the extrinsic parameters of two three-dimensional point cloud acquisition systems according to claim 4, wherein step S3 comprises:
calibrating the model according to the external parameters and the spherical center O of the calibration ballSCoordinate p under the coordinate system of the first three-dimensional point cloud acquisition systemsRadius r of the calibration sphere, point P on the calibration spherei1Three-dimensional coordinate measurement value p under first three-dimensional point cloud acquisition system coordinate systemi1And a point P on said calibration spherejk2Three-dimensional coordinate measured value p under second three-dimensional point cloud acquisition system coordinate systemjk2And establishing a nonlinear objective function calibrated by the external parameters.
6. The method for calibrating extrinsic parameters of two three-dimensional point cloud acquisition systems according to claim 5, wherein the nonlinear objective function is:
Figure FDA0002246365360000031
wherein, | | · | | represents the euclidean norm.
7. The method for calibrating the extrinsic parameters of two three-dimensional point cloud acquisition systems according to claim 2, wherein step S4 comprises:
s41: optimizing the model parameters in the nonlinear objective function by using a SHADE algorithm to obtain an optimization result;
s42: and taking the optimization result as an estimation value of the rotation matrix R and the translational vector t to obtain external parameter estimation values of the two three-dimensional point cloud acquisition systems.
8. The method for calibrating the extrinsic parameters of two three-dimensional point cloud acquisition systems according to claim 7, wherein step S41 comprises:
s411: initializing a SHADE algorithm;
s412: setting successful cross probability set
Figure FDA0002246365360000032
Set of success scale factorsFitness function value deviation set
Figure FDA0002246365360000034
S413: calculating each individual of the current generation
Figure FDA0002246365360000035
Cross probability of
Figure FDA0002246365360000036
And a scale factor Fi GAnd
Figure FDA0002246365360000037
wherein ,NmaxRepresenting the population quantity;
s414: for the current generation individuals
Figure FDA0002246365360000038
Performing mutation operation to generate NmaxIndividual variation
Figure FDA0002246365360000039
S415: subjecting the variant individual to
Figure FDA00022463653600000311
Its father generation individual
Figure FDA00022463653600000312
Performing crossover operation to generate new crossover individual
S416: for the current generation individualsCross individuals generated correspondingly to the cross individuals
Figure FDA00022463653600000315
Selecting and reserving the individual with the smaller fitness function value to form a next generation population;
s417: updating the population and increasing the iteration times by 1;
s418: if the current iteration times G reach the preset maximum iteration times GmaxThen output the G thmaxAll individuals after the second iteration
Figure FDA0002246365360000041
Otherwise, steps S412 to S417 are repeated.
9. The method for calibrating the extrinsic parameters of two three-dimensional point cloud acquisition systems according to claim 7, wherein step S42 comprises:
the G thmaxAll individuals after the second iteration
Figure FDA0002246365360000042
Of individuals with minimum fitness
Figure FDA0002246365360000043
An optimal solution as a minimization objective function; wherein,
Figure FDA0002246365360000044
the first 3-dimensional components are estimated values of three RPY attitude angles (phi, theta, psi) corresponding to the rotation matrix R in the external parameters of the two three-dimensional point cloud acquisition systems,
Figure FDA0002246365360000045
the 4 th to 6 th dimensional components of (a) are translation vector t estimated values in the external parameters.
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CN112102415A (en) * 2020-08-25 2020-12-18 中国人民解放军63919部队 Depth camera external parameter calibration method, device and equipment based on calibration ball
CN114739313A (en) * 2022-02-18 2022-07-12 西北大学 Calibration method of three-dimensional laser scanner

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CN107192350B (en) * 2017-05-19 2019-07-12 中国人民解放军信息工程大学 A kind of three-dimensional laser scanner intrinsic parameter scaling method and device
CN110196031B (en) * 2019-04-26 2020-06-09 西北大学 Calibration method of three-dimensional point cloud acquisition system

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CN112102415A (en) * 2020-08-25 2020-12-18 中国人民解放军63919部队 Depth camera external parameter calibration method, device and equipment based on calibration ball
CN114739313A (en) * 2022-02-18 2022-07-12 西北大学 Calibration method of three-dimensional laser scanner

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