CN113345005A - Finite random search method suitable for target ball center resolving - Google Patents
Finite random search method suitable for target ball center resolving Download PDFInfo
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Abstract
The invention discloses a finite random search method suitable for target sphere center solution, which mainly comprises the following steps: (1) acquiring a target ball point cloud by using a three-dimensional laser scanning system; (2) setting an initial constraint condition; (3) setting an error measurement criterion of the target ball center; (4) computing an initial search space R3(ii) a (5) Randomly searching to find an optimal center; (6) optimizing constraint conditions and updating a search space; (7) searching again to find an optimal value; (8) detecting an ending condition, and ending the circulation; and step 9: and finishing the search, and determining the center and the radius of the target ball. According to the method, the problem of fitting the central coordinate and the radius of the target ball point cloud is solved by combining the target ball point cloud and the geometric characteristics of the target ball and utilizing a limited random search method, the precision loss in the linearization process is avoided, the high-precision calculation of the central coordinate and the radius of the target ball point cloud is realized, and the efficiency is high.
Description
Technical Field
The invention belongs to the field of engineering measurement and three-dimensional laser scanning, and particularly relates to a finite random search method suitable for target sphere center solution.
Background
Due to the limitation of the scanning visual field and the external environment of the three-dimensional laser scanning system, the scanner can only acquire a part of data of a scanned object under a single visual angle. To acquire the integral model of the scanned object, the scanned object needs to be scanned in multiple viewing angles, and the data at different viewing angles are converted into the same coordinate system, so that the complete geometric model of the scanned object can be acquired, which is the registration problem of the multi-station point cloud. The point cloud registration method based on the homonymous points is a method commonly adopted in high-precision three-dimensional laser scanning at present, and the point cloud registration under different visual angles is realized by resolving seven variable transformation parameters (three rotation amounts, three displacement amounts and a scaling factor) by means of the homonymous points of the overlapped parts of different scanning areas. In actual work, the same-name points of the overlapped parts are mostly set as spherical targets (also called target balls), and the calculation precision of the central coordinates directly influences the registration precision of the point cloud.
The method for solving the central coordinate of the target ball surface scattered point cloud obtained based on three-dimensional laser scanning is a nonlinear problem, at present, linear solving is usually carried out by means of various least square methods, such as a classical least square method, an integral least square method and the like, but most of the methods are based on simple measuring point data solving, the problems that the precision is greatly influenced by an initial value, the local optimum is easy to sink and the like easily occur, and precision loss is inevitably caused. Meanwhile, the number of target ball measuring points obtained by three-dimensional laser scanning is usually more than thousands of, and the adoption of various adjustment methods can cause huge calculation matrixes and low operation efficiency. Furthermore, the target ball is usually of a certain geometric size, for example, the geometric radius of a regular target ball is usually 7.25cm, and this information is not used in the calculation of the target ball center. However, when the center coordinate is actually solved, the information can be utilized, and the information is added into the solving process to serve as constraint, so that not only can the solving precision of the center coordinate be improved, but also the operation efficiency is improved. Therefore, in order to fully utilize the measuring point information and the geometric characteristic information of the target ball and avoid the problem of linearization precision loss of the nonlinear problem, the invention provides a limited random search method suitable for target ball center calculation.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a finite random search method suitable for target ball center solution.
The technical scheme adopted by the invention is as follows: a finite random search method suitable for target ball center solution comprises the following steps:
step 1: acquiring a target ball point cloud by using a three-dimensional laser scanning system;
step 2: setting an initial constraint condition;
and step 3: setting an error measurement criterion of the target ball center;
and 4, step 4: computing an initial search space R3(ii) a Search space R3For the random point p { (x, y, z) ∈ R generated in random search3The space is formed by the point cloud P of the target sphere and the geometric radius R of the target spheresetJointly determining;
and 5: randomly searching to find an optimal center; to search the space R3With (X, Y, Z) as a constraint, a center point (a) is randomly generatedrand，brand，crand) And radius RrandUsing the error metric criterion of step 3, passing NloopSearching for the optimal center point and radius at a second random;
step 6: optimizing constraint conditions and updating a search space;
and 7: searching again to find an optimal value; with new search space
And search radiusRnewThe random search in the step 5 is carried out again for the constraint condition, and the optimal value is searched;
and 8: detecting an ending condition, and ending the circulation; after a predetermined NrefineAfter the secondary iterative optimization, gradually determining the optimal values of the central point and the radius;
and step 9: and finishing the search, and determining the center and the radius of the target ball.
Further, in step 1, the point cloud P { (x) of the target ball is collected by using a ground three-dimensional laser scanning system or a vehicle-mounted three-dimensional laser scanning systemi，yi，zi) 1,2, …, n, the target ball point cloud is composed of measured point data of the target ball surface, and each measured point is composed of X, Y, Z three coordinate components.
Further, in step 2, the initial constraint condition mainly consists of the number of single random searches NloopIterative optimization number of times NrefineGeometric radius R of target ballrealOverall error constraint threshold EthresholdThe four parts are formed.
Further, in step 3, in order to search for the optimal center and radius of the target ball, a criterion for measuring the optimal center and radius is set, and the total error E is calculatedtotalEvaluation, which is determined from the sum of the errors at all measuring points, the error E at each measuring pointiAssuming the coordinates of the center of the target sphere are (a, b, c) and the radius is R for the distance of the measured point to the surface of the current fitting sphere, the total error E istotalCan be calculated by equation (1):
in the formula (x)i，yi，zi) The coordinate of the measuring points of the target ball point cloud is shown, and n is the number of the measuring points contained in the target ball point cloud.
Further, in the step 4, firstly, the gravity center P of the existing measurement point set is calculated according to the point cloud data of the target ballcenter(xcenter，ycenter，zcenter) Calculated from equation (2):
then, from the center of gravity PcenterGeometric radius R of target ballsetDetermining a search space R3A threshold of (X, Y, Z) versus target sphere geometric radius R, represented by formula (3):
further, in the step 5, in each search process, the total error E of this time is determinedtotalWhether or not less than the total error constraint threshold EthresholdIf the center point coordinate and the radius of the center point meet the requirement, otherwise, the search is continued.
Further, in step 6, assume that the current search space R is searched3The dimension of each direction of (X, Y, Z) is (l)X，lY，lZ) The coordinate of the optimal center point searched at present is (a)current，bcurrent，ccurrent) Radius RcurrentThat can be used as a constraint to update the search space R3Is composed of
Update radius R as Rnew. Herein (l)X，lY，lZ) Can be calculated by the formula (4),
and RnewCan be calculated from equation (5):
further, in the step 7, if the total error E is found to be satisfiedtotalLess than a total error constraint threshold EthresholdThe coordinates and the radius of the central point at the moment are taken as results, otherwise, the cyclic updating and searching of the step (6) and the step (5) are continuously repeated.
Further, in the step 9, the finite random search is performed to satisfy the total error EtotalLess than a total error constraint threshold EthresholdEnd at time, or at completion of predetermined NrefineAnd finishing the secondary iterative optimization, and finally determining the optimal center coordinates and the optimal radius of the point cloud of the target ball.
The invention has the beneficial effects that: according to the method, the problem of fitting the central coordinate and the radius of the target ball point cloud is solved by combining the target ball point cloud and the geometric characteristics of the target ball and utilizing a limited random search method, the problem of precision loss in the linearization process is avoided, high-precision calculation of the central coordinate and the radius of the target ball point cloud can be realized, and the efficiency is high. In addition, the method is not only suitable for center calculation of the ground or vehicle-mounted three-dimensional laser scanning target ball, but also can be applied to extraction of center coordinates of other spherical objects.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
FIG. 1 is a technical flow diagram of the present invention.
Fig. 2 is a schematic diagram of an error metric.
Fig. 3 is a simulated target sphere cloud.
FIG. 4 is a construction diagram of an initial constraint space.
FIG. 5 is a diagram of a constraint space for loop iterative optimization.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Referring to fig. 1 and 2, the present invention provides a finite random search method suitable for target sphere center solution, which comprises the following steps:
step 1: and acquiring the target ball point cloud by using a three-dimensional laser scanning system. Acquiring point cloud P { (x) of target ball by using ground three-dimensional laser scanning system or vehicle-mounted three-dimensional laser scanning systemi，yi，zi) 1,2, …, n, the target ball point cloud is composed of measured point data of the target ball surface, and each measured point is composed of X, Y, Z three coordinate components.
Step 2: initial constraints are set. The initial constraint condition mainly consists of the number N of single random search timesloopIterative optimization number of times NrefineGeometric radius R of target ballrealOverall error constraint threshold EthresholdThe four parts are divided into equal parts. Number of single random searches NloopThe method is characterized in that the method refers to the times of randomly searching possible optimal values in a set limited search space; number of iterative optimization NrefineThe optimization times are optimized by updating the search space again after finishing the preset single random search times; geometric radius R of target ballsetThe method is characterized in that a set target sphere geometric radius estimated value is adopted, target spheres with the same geometric radius are usually adopted in a three-dimensional laser scanning operation, if target spheres with various geometric radii are selected, the target spheres can be designated as the maximum radius, and only one estimated value needs to be designated; overall error constraint threshold EthresholdThe total error of the target ball point cloud of the search condition is judged to be finished, the value can be calculated by the error measurement criterion in the step 3, and the threshold value is set, so that the subsequent search can be directly finished after the preset error is reached, and the efficiency of the algorithm is improved.
And step 3: and setting an error measurement criterion of the target ball center. In order to search for the optimum center and radius of the target ball, a criterion for measuring the optimum center and radius must be set, wherein the total error E is usedtotalAnd evaluating, wherein the evaluation is obtained by the error sum of all measuring points. Error E of each measurement pointiThe distance from the measured point to the surface of the currently fitted ball. Assuming the target sphere center coordinates are (a, b, c) and the radius is R, the total error EtotalCan be calculated by equation (1):
in the formula (x)i，yi，zi) The coordinate of the measuring points of the target ball point cloud is shown, and n is the number of the measuring points contained in the target ball point cloud.
And 4, step 4: computing an initial search space R3. Search space R3Means that a random point p { (x, y, z) ∈ R generated in random search3The space is formed by the point cloud P of the target sphere and the geometric radius R of the target spheresetAnd (4) jointly determining. Firstly, the gravity center P of the existing measuring point set is calculated according to the point cloud data of the target ballcenter(xcenter，ycenter，zcenter) Calculated from equation (2):
then, from the center of gravity PcenterGeometric radius R of target ballsetDetermining a search space R3A threshold of (X, Y, Z) versus target sphere geometric radius R, represented by formula (3):
and 5: and (6) randomly searching for an optimal center. To search the space R3With (X, Y, Z) as a constraint, a center point (a) is randomly generatedrand，brand，crand) And radius RrandUsing the error metric criterion of step 3, passing NloopAnd performing secondary random search to find the optimal central point and radius. In each searching process, the total error E of the time is judgedtotalWhether or not less than the total error constraint threshold EthresholdIf the center point coordinate and the radius of the center point meet the requirement, otherwise, the search is continued.
Step 6: optimizing constraint conditions and updating the search space. Through a predetermined NloopAfter the secondary search, the coordinates and radius of the center point can be determined substantially, but more accurate determination of the coordinates and radius of the center point requires further optimization of the search space. It is assumed here that the search space R is currently being searched3The dimension of each direction of (X, Y, Z) is (l)X，lY，lZ) The coordinate of the optimal center point searched at present is (a)current，bcurrent，ccurrent) Radius RcurrentThat can be used as a constraint to update the search space R3Is composed of
Update radius R as Rnew. Herein (l)X，lY，lZ) Can be calculated by the formula (4),
and RnewCan be calculated from equation (5):
and 7: and searching again to find the optimal value. With new search space
And search radius RnewFor constraint conditions, the random search of the step 5 is carried out again, the optimal value is searched, and if the optimal value is found to meet the total error EtotalLess than a total error constraint threshold EthresholdThe coordinates and the radius of the central point at the moment are taken as results, otherwise, the cyclic updating and searching of the step (6) and the step (5) are continuously repeated.
And 8: detecting an end condition, and endingAnd (6) circulating. After a predetermined NrefineAfter the second iteration optimization, the optimal values of the center point and the radius are gradually determined. Generally, through dozens of iterative optimizations, an optimal value can be basically determined.
And step 9: and finishing the search, and determining the center and the radius of the target ball. The finite random search may be performed while satisfying the total error EtotalLess than a total error constraint threshold EthresholdEnd of time, possibly at completion of predetermined NrefineAnd finishing the secondary iterative optimization, and finally determining the optimal center coordinates and the optimal radius of the point cloud of the target ball.
In the embodiment, the accuracy of the center coordinates and the radius calculated by the invention cannot be quantitatively evaluated by considering that the center coordinates of the real target ball point cloud are not easy to accurately obtain, and the implementation method of the invention is further explained by adopting simulation data.
(1) 2000 measurement point data of a simulated target ball are obtained by using real center coordinates (1000, 1000 and 100) and a radius of 0.08m, and are shown in figure 3.
(2) And (5) setting initial constraint conditions according to the method in the step 2. Number of single random searches NloopSet to 1000, iterative optimization times NrefineSet as 16, the geometric radius R of the target ballrealSet to 0.08m, the overall error constraint threshold EthresholdSet to 0.001 m.
(3) An initial constraint space is constructed according to step 4, and the calculation result is as follows, and is shown in fig. 4.
(4) According to the error measurement criterion set in the step 3, the random search in the step 5 is utilized, and the process is carried out by NloopAfter 1000 searches, an approximate target sphere center (1000, 999.98, 100.01) and an approximate radius R of 0.079109 are obtained, and the total error E is obtainedtotal45.709. At this time, the loop iteration is optimized for the number of times NrefineOnly 1 execution time 16, and total error EtotalGreater than a total error constraint threshold EthresholdThe end conditions are not satisfied, so that it is necessaryAnd (6) continuing to execute the step.
(5) Optimizing the constraint space and the radius according to the step 6, and executing the step 7 until the preset loop iteration optimization times or the total error E is executedtotalLess than a total error constraint threshold EthresholdThe loop ends. Based on the simulation data, after 13 suboptimal iterations, the total error EtotalReaches a value of 0.000633, when less than the overall error constraint threshold EthresholdThen the loop can be ended without further loop optimization. The constraint space, total error, target sphere center statistics for each iteration are shown in table 1. As shown in fig. 5.
TABLE 1 Loop iteration result statistics
(6) In satisfying the total error EtotalLess than a total error constraint threshold EthresholdOr a predetermined number of loop iteration optimizations N is performedrefineAnd then, the obtained center coordinates and the radius are used as the optimal center coordinates and the radius of the target ball center. In the calculation example, after 13 suboptimal iterations, the center coordinates of the target sphere are obtained to be (1000, 1000, 100) which are completely the same as the true value, the obtained radius is 0.079996, the difference between the radius and the true value is 0.004mm, and the target sphere can be basically regarded as the true value. Meanwhile, the execution time is counted to be 1.121 seconds.
According to experimental results, the method provided by the invention can accurately calculate the coordinates and the radius of the central point of the target ball, and the execution efficiency is high.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It should be understood by those skilled in the art that the above embodiments do not limit the scope of the present invention in any way, and all technical solutions obtained by using equivalent substitution methods fall within the scope of the present invention.
The parts not involved in the present invention are the same as or can be implemented using the prior art.
Claims (9)
1. A finite random search method suitable for target ball center solution is characterized by comprising the following steps:
step 1: acquiring a target ball point cloud by using a three-dimensional laser scanning system;
step 2: setting an initial constraint condition;
and step 3: setting an error measurement criterion of the target ball center;
and 4, step 4: computing an initial search space R3(ii) a Search space R3For the random point p { (x, y, z) ∈ R generated in random search3The space is formed by the point cloud P of the target sphere and the geometric radius R of the target spheresetJointly determining;
and 5: randomly searching to find an optimal center; to search the space R3With (X, Y, Z) as a constraint, a center point (a) is randomly generatedrand,brand,crand) And radius RrandUsing the error metric criterion of step 3, passing NloopSearching for the optimal center point and radius at a second random;
step 6: optimizing constraint conditions and updating a search space;
and 7: searching again to find an optimal value; with new search space
And search radius RnewThe random search in the step 5 is carried out again for the constraint condition, and the optimal value is searched;
and 8: detecting an ending condition, and ending the circulation; after a predetermined NrefineAfter the secondary iterative optimization, gradually determining the optimal values of the central point and the radius;
and step 9: and finishing the search, and determining the center and the radius of the target ball.
2. A method according to claim 1The finite random search method for resolving the target sphere center is characterized in that in the step 1, a ground three-dimensional laser scanning system or a vehicle-mounted three-dimensional laser scanning system is used for collecting point cloud P { (x) of the target spherei,yi,zi) 1,2, …, n, the target ball point cloud is composed of measured point data of the target ball surface, and each measured point is composed of X, Y, Z three coordinate components.
3. The method for finite random search of target sphere center solution according to claim 1, wherein in the step 2, the initial constraint condition mainly consists of the number of single random searches NloopIterative optimization number of times NrefineGeometric radius R of target ballrealOverall error constraint threshold EthresholdThe four parts are formed.
4. The method according to claim 1, wherein in step 3, in order to search for the optimal target ball center and radius, a metric of the optimal center and radius is set, and the total error E is calculatedtotalEvaluation, which is determined from the sum of the errors at all measuring points, the error E at each measuring pointiAssuming the coordinates of the center of the target sphere are (a, b, c) and the radius is R for the distance of the measured point to the surface of the current fitting sphere, the total error E istotalCan be calculated by equation (1):
in the formula (x)i,yi,zi) The coordinate of the measuring points of the target ball point cloud is shown, and n is the number of the measuring points contained in the target ball point cloud.
5. The finite random search method suitable for target sphere center solution according to claim 1, wherein in step 4, first, the center of gravity P of the existing measurement point set is calculated according to the point cloud data of the target spherecenter(xcenter,ycenter,zcenter) Calculated from equation (2):
then, from the center of gravity PcenterGeometric radius R of target ballsetDetermining a search space R3A threshold of (X, Y, Z) versus target sphere geometric radius R, represented by formula (3):
6. the finite random search method for target sphere center solution according to claim 1, wherein in step 5, the total error E of this time is determined during each searchtotalWhether or not less than the total error constraint threshold EthresholdIf the center point coordinate and the radius of the center point meet the requirement, otherwise, the search is continued.
7. The finite random search method for target sphere center solution according to claim 1, wherein in step 6, the current search space R is assumed3The dimension of each direction of (X, Y, Z) is (l)X,lY,lZ) The coordinate of the optimal center point searched at present is (a)current,bcurrent,ccurrent) Radius RcurrentThat can be used as a constraint to update the search space R3Is composed of
Update radius R as Rnew(ii) a Herein (l)X,lY,lZ) Can be calculated by the formula (4),
and RnewCan be calculated from equation (5):
8. the finite random search method for target sphere center solution according to claim 1, wherein in step 7, if the total error E is found, the total error E is satisfiedtotalLess than a total error constraint threshold EthresholdThe coordinates and the radius of the central point at the moment are taken as results, otherwise, the cyclic updating and searching of the step (6) and the step (5) are continuously repeated.
9. The method for finite random search of target sphere center solution according to claim 1, wherein in step 9, the finite random search is performed while satisfying the total error EtotalLess than a total error constraint threshold EthresholdEnd at time, or at completion of predetermined NrefineAnd finishing the secondary iterative optimization, and finally determining the optimal center coordinates and the optimal radius of the point cloud of the target ball.
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