CN113345005B - Finite random search method suitable for target ball center calculation - Google Patents
Finite random search method suitable for target ball center calculation Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/60—Analysis of geometric attributes
- G06T7/66—Analysis of geometric attributes of image moments or centre of gravity
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10028—Range image; Depth image; 3D point clouds
Abstract
The invention discloses a limited random search method suitable for target ball center calculation, which mainly comprises the following steps: (1) acquiring a target ball point cloud by using a three-dimensional laser scanning system; (2) setting initial constraints; (3) setting an error measurement criterion of the center of the target ball; (4) Calculating an initial search space R 3 The method comprises the steps of carrying out a first treatment on the surface of the (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 end condition, ending the cycle; step 9: and finishing searching and determining the center and the radius of the target ball. According to the method, the problem of fitting the center coordinates and the radius of the target ball point cloud is solved by combining the target ball point cloud with the geometric characteristics of the target ball by utilizing a limited random search method, the precision loss in the linearization process is avoided, the high-precision calculation of the center coordinates and the radius of the target ball point cloud is realized, and the efficiency is higher.
Description
Technical Field
The invention belongs to the field of engineering measurement and three-dimensional laser scanning, and particularly relates to a limited random search method suitable for target ball center calculation.
Background
Due to the limitations of the scan field of view 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 view angle. To obtain the whole model of the scanned object, the scanned object needs to be scanned at multiple angles, and data under different angles of view are converted into the same coordinate system to obtain the complete geometric model of the scanned object, which is the registration problem of the multi-site 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 method realizes point cloud registration under different visual angles by solving seven variable transformation parameters (three rotation amounts, three displacement amounts and one scaling factor) through homonymous points of overlapping parts of different scanning areas. In actual work, the homonymy points of the overlapped part are set as spherical targets (also called target balls), and the resolving precision of the center coordinates of the homonymy points directly influences the registering precision of the point cloud.
The method solves the central coordinate of the scattered point cloud on the surface of the target ball, which is a nonlinear problem, and at present, linearization solution is usually carried out by means of various least square methods, such as classical least square methods, integral least square methods and the like, but the method is mostly based on simple measuring point data solution, so that the problems of large influence of initial values on precision, easy subsidence, local optimization and the like are easy to occur, and the precision loss is unavoidable. Meanwhile, the number of target ball measuring points obtained by three-dimensional laser scanning is generally more than thousands, and various adjustment methods can cause huge calculation matrix and low operation efficiency. In addition, the target sphere is typically of a certain geometry, such as a regular target sphere of 7.25cm in geometric radius, which is often not used in solving the center of the target sphere. However, when the central coordinate is actually solved, the information can be utilized, and the information is added into the solving process to be used as constraint, so that the solving precision of the central coordinate can be improved, and the operation efficiency is improved. Therefore, in order to fully utilize the measurement 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 solving the center of the target ball.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a limited random search method suitable for target ball center calculation.
The technical scheme adopted by the invention is as follows: a finite random search method suitable for target sphere center resolution, comprising the steps of:
step 1: acquiring a target ball point cloud by using a three-dimensional laser scanning system;
step 2: setting initial constraint conditions;
step 3: setting an error measurement criterion of the center of the target ball;
step 4: calculating an initial search space R 3 The method comprises the steps of carrying out a first treatment on the surface of the Search space R 3 For random points p= { (x, y, z) ∈r generated during random search 3 Space where the target ball is located, the space is formed by the point cloud P of the target ball and the preset radius R of the target ball set Jointly determining;
step 5: randomly searching to find an optimal center; in search space R 3 Taking X, Y, Z as constraint, randomly generating a center point (a rand ,b rand ,c rand ) And radius R rand By using the error measurement criterion of the step 3, the method uses N loop Searching for optimal center point and radius by sub-random;
step 6: optimizing constraint conditions and updating a search space;
step 7: searching again to find an optimal value; with new search spacesAnd search radius R new Carrying out random search in the step 5 again for searching an optimal value for constraint conditions;
step 8: detecting an ending condition, ending the cycle; after passing through a predetermined N refine After iterative optimization, gradually determining the optimal values of the center point and the radius;
step 9: and finishing searching and determining the center and the radius of the target ball.
Further, in the step 1, the ground three-dimensional laser scanning system or the vehicle-mounted three-dimensional laser scanning system is used for collecting the point cloud p= { (x) of the target ball i ,y i ,z i ) I=1, 2, …, n, the target sphere point cloud consists of measurement point data of the target sphere surface, and each measurement point consists of X, Y, Z three coordinate components.
Further, in the step 2, the initial constraint condition is mainly composed ofNumber of single random searches N loop Number of iterative optimizations N refine Preset radius R of target ball set Total error constraint threshold E threshold Four parts.
Further, in the step 3, in order to search the optimal center and radius of the target sphere, a measurement criterion of the optimal center and radius is set to obtain the total error E total Evaluation, which is obtained by summing the errors of all the measuring points, the error E of each measuring point i Assuming the center coordinates of the target sphere to be (a, b, c) and the radius to be R, the total error E is then total Can be calculated by formula (1):
in (x) i ,y i ,z i ) The coordinates of the measuring points of the target ball point cloud are obtained, and n is the number of the measuring points contained in the target ball point cloud.
Further, in the 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 ball center (x center ,y center ,z center ) Calculated from formula (2):
then, from the center of gravity P center Preset radius R with target ball set Determining a search space R 3 Threshold value of= (X, Y, Z) and target sphere geometric radius R, represented by formula (3):
further, in the step 5, in each searching process, the total error E of this time is determined total Whether or not it is smaller than the overall error constraint threshold E threshold If it is smaller than the predetermined value, it indicates that the searched center and radius have reached the predetermined valueThe accuracy can be considered that the coordinates and the radius of the center point at the moment meet the requirements, otherwise, the searching is continued.
Further, in the step 6, it is assumed that the current search space R 3 The scale of each direction of = (X, Y, Z) is (l) X ,l Y ,l Z ) The coordinates of the optimal center point searched at present are (a) current ,b current ,c current ) Radius of R curren That can update the search space R with this as a constraint 3 Is thatUpdate radius R to R new . Here (l) X ,l Y ,l Z ) Can be calculated from formula (4), +.>And R is R new Can be calculated from formula (5):
further, in the step 7, if the total error E is found to be satisfied total Less than the overall error constraint threshold E threshold If not, the cyclic updating and searching in 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 E total Less than the overall error constraint threshold E threshold Ending at the time, or at the completion of the predetermined N refine And after the iterative optimization is finished, the optimal center coordinates and the radius of the point cloud of the target ball can be finally determined.
The beneficial effects of the invention are as follows: according to the method, the problem of fitting the center coordinates and the radius of the target ball point cloud is solved by combining the target ball point cloud with 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, the high-precision calculation of the center coordinates 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 the center calculation of the ground or vehicle-mounted three-dimensional laser scanning target ball, but also can be applied to the center coordinate extraction 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 chart of the present invention.
Fig. 2 is a schematic diagram of an error metric.
Fig. 3 is a simulated cloud of target points.
FIG. 4 is a build diagram of an initial constraint space.
FIG. 5 is a loop iteration optimization constraint space diagram.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples.
As shown in fig. 1 and 2, the present invention provides a finite random search method suitable for calculating the center of a target sphere, which comprises the following specific implementation steps:
step 1: and acquiring a target ball point cloud by using a three-dimensional laser scanning system. Point cloud P= { (x) of target ball is collected by using ground three-dimensional laser scanning system or vehicle-mounted three-dimensional laser scanning system i ,y i ,z i ) I=1, 2, …, n }, the target sphere point cloud consists of measurement point data of the target sphere surface, each measurement point consists of X, Y, Z three coordinate components.
Step 2: initial constraints are set. The initial constraint condition mainly comprises the number N of single random searches loop Number of iterative optimizations N refine Preset radius R of target ball set Total error constraint threshold E threshold And the four parts are formed. Number of single random searches N loop Refers to randomly searching for a possible optimal value secondary in a set limited search spaceA number; number of iterative optimization N refine The method is that after the preset single random search times are completed, the search space is updated again, and the optimization times are carried out; target ball preset radius R set The method is characterized in that the method refers to a preset target ball geometric radius value, in a three-dimensional laser scanning operation, a target ball with the same geometric radius is usually adopted, if a target ball with multiple geometric radii is selected, the target ball can be designated as the maximum radius, and only one estimated value is required to be designated; total error constraint threshold E threshold The method is to judge the total error of the target ball point cloud of the search ending condition, the value can be calculated by the error measurement criterion of the step 3, and the threshold value is set, so that the subsequent search can be directly ended after the preset error is reached, and the algorithm efficiency is improved.
Step 3: setting an error measurement criterion of the center of the target ball. In order to search for the optimum target sphere center and radius, a measurement of the optimum center and radius must be set, here in terms of the total error E total The evaluation is obtained by the error sum of all measuring points. Error E of each measuring point i The distance from the measuring point to the surface of the currently fitting sphere is given. Assuming the center coordinates of the target sphere are (a, b, c) and the radius is R, then the total error E total Can be calculated by formula (1):
in (x) i ,y i ,z i ) The coordinates of the measuring points of the target ball point cloud are obtained, and n is the number of the measuring points contained in the target ball point cloud.
Step 4: calculating an initial search space R 3 . Search space R 3 Refers to a random point p= { (x, y, z) ∈r generated during random search 3 Space where the target ball is located, the space is formed by the point cloud P of the target ball and the preset radius R of the target ball set And (5) jointly determining. Firstly, calculating the center of gravity P of the existing measurement point set according to the point cloud data of the target ball center (x center ,y center ,z center ) Calculated from formula (2):
then, from the center of gravity P center Preset radius R with target ball set Determining a search space R 3 Threshold value of= (X, Y, Z) and target sphere geometric radius R, represented by formula (3):
step 5: and randomly searching to find the optimal center. In search space R 3 Taking X, Y, Z as constraint, randomly generating a center point (a rand ,b rand ,c rand ) And radius R rand By using the error measurement criterion of the step 3, the method uses N loop And searching for the optimal center point and radius by using the secondary random search. In each searching process, judging the total error E of the time total Whether or not it is smaller than the overall error constraint threshold E threshold If the search result is smaller than the preset precision, the searched center and radius are indicated to reach the preset precision, the coordinates of the center point and the radius at the moment can be considered to meet the requirements, otherwise, the search is continued.
Step 6: optimizing constraint conditions and updating the search space. Through a predetermined N loop After a search, the coordinates and radius of the center point can be determined substantially, but to more accurately determine the coordinates and radius of the center point, further optimization of the search space is required. Assume here that the current search space R 3 The scale of each direction of = (X, Y, Z) is (l) X ,l Y ,l Z ) The coordinates of the optimal center point searched at present are (a) current ,b current ,C current ) Radius of R current That can update the search space R with this as a constraint 3 Is thatUpdate radius R to R new . Here (l) X ,l Y ,l Z ) Can be calculated from formula (4), +.>And R is R new Can be calculated from formula (5):
step 7: searching again to find the optimal value. With new search spacesAnd search radius R new The random search in the step 5 is carried out again for constraint conditions, the optimal value is found, if the total error E is found to be satisfied total Less than the overall error constraint threshold E threshold If not, the cyclic updating and searching in the step (6) and the step (5) are continuously repeated.
Step 8: the end condition is detected and the cycle is ended. After passing through a predetermined N refine After the iterative optimization, the optimal values of the center point and the radius are gradually determined. In general, the optimal value can be basically determined after ten times of iterative optimization.
Step 9: and finishing searching and determining the center and the radius of the target ball. The finite random search may be under the condition of meeting the total error E total Less than the overall error constraint threshold E threshold Ending at the time, possibly also at the completion of the predetermined N refine And after the iterative optimization is finished, the optimal center coordinates and the radius of the point cloud of the target ball can be finally determined.
In this embodiment, the implementation method of the present invention is further described by adopting analog data, considering that the center coordinates of the real target ball point cloud are not easy to be accurately obtained, and the accuracy of the calculated center coordinates and radius of the present invention cannot be quantitatively evaluated.
(1) The data of 2000 measuring points of the target ball were simulated with a true center coordinate (1000,1000,100) and a radius of 0.08m, as shown in fig. 3.
(2) And (3) setting initial constraint conditions according to the method of the step (2). Number of single random searches N loop Setting to 1000, iterative optimization times N refine Set to 16, geometric radius R of target ball real Set to 0.08m, the total error constraint threshold E threshold Set to 0.001m.
(3) The initial constraint space is constructed according to step 4, and the calculation result is as follows and 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 to pass through N loop After 1000 searches, an approximate target sphere center (1000,999.98,100.01) and an approximate radius r= 0.079109 can be obtained, and the total error E total = 45.709. At this time, the number of loop iteration optimization times N refine =16 is performed only 1 time, and total error E total Greater than the overall error constraint threshold E threshold Since the end condition is not satisfied, the step (6) needs to be continued.
(5) Optimizing the constraint space and radius according to the step 6, executing the step 7 until the preset loop iteration optimization times are executed, or the total error E total Less than the overall error constraint threshold E threshold The cycle is ended. Based on the simulation data, after 13 optimization iterations, the total error E total The value of (2) reaches 0.000633, which is less than the overall error constraint threshold E threshold The cycle can be ended without further subsequent cycle optimisation. Constraint space, total error and target sphere center statistics in each iteration are shown in table 1. As shown in fig. 5.
TABLE 1 statistics of loop iteration results
(6) In the case of meeting the total error E total Less than the overall error constraint threshold E threshold Or a predetermined number of loop iteration optimizations N has been performed refine And then, taking the obtained center coordinates and radius as the optimal center coordinates and radius of the center of the target ball. In the calculation example, after 13 optimization iterations, the center coordinate of the target ball is (1000,1000,100), which is completely the same as the true value, the radius is 0.079996, which is different from the true value by 0.004mm, and the target ball can be basically regarded as the true value. Meanwhile, the execution time was counted as 1.121 seconds.
From experimental results, the method designed by the invention can accurately calculate the coordinates and the radius of the center point of the target ball, and has higher execution efficiency.
The foregoing has shown and described the basic principles, principal features and advantages of the 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 equivalent substitution and the like fall within the scope of the present invention.
The invention is not related in part to the same as or can be practiced with the prior art.
Claims (7)
1. The finite random search method suitable for target sphere center calculation 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 initial constraint conditions; the initial constraint condition is that the number of times of single random search is N loop Number of iterative optimizations N refine Preset radius r of target ball set Total error constraint threshold E threshold Four parts;
step 3: setting an error measurement criterion of the center of the target ball;
step 4: calculating an initial search space R 3 The method comprises the steps of carrying out a first treatment on the surface of the Search space R 3 For random searchRandom point p= { (x, y, z) ∈r generated at that time 3 Space where the target ball is located, the space is formed by the point cloud P of the target ball and the preset radius R of the target ball set Jointly determining;
step 5: randomly searching to find an optimal center; in search space R 3 = (X, Y, Z) as constraint, randomly generates a center point (a rand ,b rand ,c rand ) And radius R rand By using the error measurement criterion of the step 3, the method uses N loop Searching for optimal center point and radius by sub-random;
step 6: optimizing constraint conditions and updating a search space; assuming the current search space R 3 The scale of each direction of = (X, Y, Z) is (l) X ,l Y ,l Z ) The coordinates of the optimal center point searched at present are (a) current ,b current ,c current ) Radius of R current That can update the search space R with this as a constraint 3 Is thatUpdate radius R to R new The method comprises the steps of carrying out a first treatment on the surface of the Here (l) X ,l Y ,l Z ) Calculated from formula (4), a->And R is R new Can be calculated from formula (5):
step 7: searching again to find an optimal value; with new search spacesAnd search radius R new For restraining stripsCarrying out random search in the step 5 again to find an optimal value;
step 8: detecting an ending condition, ending the cycle; after passing through a predetermined N refine After iterative optimization, gradually determining the optimal values of the center point and the radius;
step 9: and finishing searching and determining the center and the radius of the target ball.
2. The finite random search method for target sphere center calculation according to claim 1, wherein in the step 1, a ground three-dimensional laser scanning system or a vehicle-mounted three-dimensional laser scanning system is used to collect a point cloud p= { (x) of the target sphere i ,y i ,z i ) I=1, 2, …, n }, the target sphere point cloud consists of measurement point data of the target sphere surface, each measurement point consists of X, Y, Z three coordinate components.
3. The finite random search method for target sphere center calculation according to claim 1, wherein in step 3, in order to search for optimal target sphere center and radius, a criterion of optimal center and radius is set to total error E total Evaluation, which is obtained by summing the errors of all the measuring points, the error E of each measuring point i Assuming the center coordinates of the target sphere to be (a, b, c) and the radius to be R, the total error E is then total Can be calculated by formula (1):
in (x) i ,y i ,z i ) The coordinates of the measuring points of the target ball point cloud are obtained, and n is the number of the measuring points contained in the target ball point cloud.
4. The finite random search method for target sphere center calculation according to claim 1, wherein in step 4, first, the center of gravity P of the existing set of measurement points is calculated from the point cloud data of the target sphere center (x center ,y center ,z center ) Calculated from formula (2):
then, from the center of gravity P center Preset radius R with target ball set Determining a search space R 3 Threshold value of= (X, Y, Z) and target sphere geometric radius R, represented by formula (3):
5. the finite random search method for target ball center calculation according to claim 1, wherein in said step 5, in each search process, the total error E of the time is determined total Whether or not it is smaller than the overall error constraint threshold E threshold If the search result is smaller than the preset precision, the searched center and radius are indicated to reach the preset precision, the coordinates of the center point and the radius at the moment can be considered to meet the requirements, otherwise, the search is continued.
6. The finite random search method for target sphere center calculation according to claim 1, wherein in said step 7, if the total error E is found to be satisfied total Less than the overall error constraint threshold E threshold If not, the cyclic updating and searching in the step 6 and the step 5 are continuously repeated.
7. The finite random search method for target sphere center calculation according to claim 1, wherein in the step 9, the finite random search is performed while satisfying the total error E total Less than the overall error constraint threshold E threshold Ending at the time, or at the completion of the predetermined N refine Sub-stackAnd after the generation of optimization, finally, the optimal center coordinates and the radius of the point cloud of the target ball can be determined.
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