CN113298951A - Three-dimensional frequency surface digitization and model comparison method - Google Patents
Three-dimensional frequency surface digitization and model comparison method Download PDFInfo
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Abstract
The invention relates to the technical field of digital detection, in particular to a three-dimensional frequency surface digitalization and model comparison method, S1, using a three-dimensional measurement and three-dimensional reconstruction algorithm to obtain three-dimensional measurement point cloud data; s2, feature extraction; s3, extracting CAD model data; s4, point cloud matching; and S5, displaying error calculation. The invention has the beneficial effects that: the invention can realize direct detection of three-dimensional FSS form and position parameters, realize measurement of three-dimensional FFS space characteristics by two-dimensional image high-precision dimension measurement and combining with space characteristic information of three-dimensional structured light, and make up for the defect that the traditional three-dimensional structured light measurement has low precision in measuring the space characteristics in a large-size range.
Description
Technical Field
The invention relates to the technical field of digital detection, in particular to a three-dimensional frequency surface digitization and model comparison method.
Background
At present, the precision of the shape and the size of a unit in a frequency selection surface is improved mainly by using a Hakstan three-coordinate measuring instrument to sample and take points, and then comparing the points with a design value.
The FSS is a single-screen or multi-screen periodic array structure consisting of a large number of passive resonance units and is composed of periodically arranged metal patch units or periodically arranged aperture units on a metal screen. Such surfaces may exhibit total reflection (patch type) or full transmission characteristics (aperture type) near the resonant frequency of the cell, referred to as band stop or band pass FSS, respectively. Currently, FSS is widely applied to various stealth technologies of aircraft, and the shape and size of FSS are extremely important for stealth characteristics of aircraft, so that it is a very critical technology to realize high-precision configuration detection of three-dimensional FSS.
Therefore, key technologies such as digital detection of a three-dimensional Frequency Selective Surface (FSS) and the like are researched, so that the quality control of the production process is better, and the form and position parameter errors caused by the three-dimensional FSS manufacturing process are reduced.
Disclosure of Invention
The invention provides a method for making up for the defects in the prior art.
The invention is realized by the following technical scheme:
a three-dimensional frequency surface digitization and model comparison method is characterized by comprising the following steps:
s1, obtaining three-dimensional measurement point cloud data by using a three-dimensional measurement and three-dimensional reconstruction algorithm;
s2, extracting features, preprocessing point clouds to obtain necessary effective data in the registration process;
s3, extracting CAD model data, and uniformly sampling the CAD model to obtain an STL triangular grid data model;
s4, point cloud matching, namely registering the three-dimensional measurement point cloud and the CAD model data to achieve optimal fitting;
and S5, calculating errors, displaying, calculating the Euclidean distance between each actual measurement point in the three-dimensional measurement point cloud and the surface of the CAD model to obtain an error analysis structure, and displaying the error distribution condition of the workpiece by using the gray cloud picture.
Further, in order to better implement the present invention, in S1, a binocular optical module is used for three-dimensional measurement, the binocular optical module uses a three-dimensional optical measurement principle, two cameras are used to calibrate spatial positions of the two cameras, a spatial relationship is established, a phase principal value is calculated according to a grating image projected onto the surface of an object according to grating transformation, and a time difference value is obtained by extracting a point with the same name according to a phase feature of the object to be measured, so as to measure the height of the point.
Further, in order to better implement the present invention, the step of preprocessing the point cloud in S2 includes:
s21, establishing a point cloud data topological relation, and improving algorithm efficiency;
s22, point cloud denoising, namely denoising the ordered or partially ordered point cloud data types by a wiener filtering method, a smooth filtering method, a Kalman filtering method and a least square filtering method, and denoising the scattered and unordered point cloud data types by a Laplacian operator, an average curvature flow method and a moving minimum quadric surface;
and S23, point cloud data are simplified, and data points capable of representing scene characteristics or measured entity surface characteristics are reserved.
Further, in order to better implement the present invention, S3 includes a method for finding a corresponding point based on the STL triangulation of the CAD model, and the closest point from the point cloud of the original measurement point to the corresponding triangulation is quickly obtained by using the normal vector information carried by the triangulation itself, and is used as the target corresponding point, so that the problem of finding a corresponding point in the matching of the point cloud and the CAD model by the ICP algorithm can be effectively solved.
Further, in order to better implement the present invention, the point cloud matching in S4 includes coarse registration and precise registration, a point set is found based on an STL triangular mesh formed in an engineering model of a three-dimensional product for an obtained three-dimensional point cloud data model, a closest point from the measured point cloud to the corresponding triangular mesh is found by using normal information of the STL triangular mesh itself, and is used as a target corresponding point, and based on the initial target corresponding point, registration of an ICP algorithm model is adopted to reduce difficulty in finding corresponding points in registration of point cloud data and the engineering model by an original ICP algorithm, and time for model registration is reduced.
Further, in order to better realize the method, the rough registration is to rotate the three-dimensional measurement point cloud and the engineering model to approximately coincide through a rough registration algorithm so as to provide an initial value of successive iteration in accurate matching, and a principal component analysis method is adopted for rough matching; the algorithm applied to the accurate registration is an ICP algorithm, corresponding matching points in two point sets to be matched are searched through a step-by-step iteration method, rigid body transformation parameters between the two point sets are calculated until error measure meets given convergence accuracy or reaches the maximum iteration times, and the rigid body transformation parameters between the two point sets are finally obtained, so that the whole registration process is completed.
Further, in order to better implement the present invention, the principal component analysis method in the coarse registration specifically includes setting
Two corresponding point sets are provided, the number of points in the point sets is N, the point set P represents an original measurement point cloud, the point set Q is a corresponding target point set in the engineering model, and the initial rigid body transformation parameter between the point sets is (R)0,T0) (ii) a The method for calculating the rigid body transformation initial value matched with the point cloud and the engineering model by the principal component analysis method comprises the following steps:
s41, covariance matrixes C of the point sets P and Q are respectively calculatedpAnd Cq；
Wherein the content of the first and second substances,
is the center of the set of points P,
is the center of the point set Q
S42, by fitting covariance matrix CpAnd CqSVD analysis can be performed in the following format:
wherein the feature vector UpIs the principal direction of the set of measurement points P, and the eigenvector UqIs the main direction of the corresponding engineering model point set Q, the point set P and Q are direct rotation matrix R0And the translation vector is T0The following were used:
further, in order to better implement the present invention, the ICP algorithm for accurate registration specifically includes:
is provided with
For two-piece point cloud set to be registered, the ICP algorithm firstly points each point P in the point set PiSearching for its closest point q on the set of points XiAs corresponding points, set to be searched
Is set of corresponding points of
The IPC algorithm establishes the following error measures:
then, the above formula is solved to minimize the value, and the value is recorded as
(q,d)＝M(P,Q)
Wherein M represents the minimizing operation; d is the corresponding root mean square error, i.e. d ═ e (q); q is the rigid body transformation vector resulting from the minimization operation, i.e., q ═ R (q) T (q)]TR (q) represents the optimal rotation, and t (q) is the optimal translation vector;
applying rigid body transformation parameters obtained by algorithm calculation to the original measurement point cloud, recording as q (P), and executing the operation in ICP algorithm iteration each time until a certain set convergence criterion is met;
to minimize E (Q), a minimization operation M is performed by first computing the center of gravity u of the set of points P and the set of model points Qp、uq：
And (3) calculating a cross covariance matrix of the point sets P and Q by the obtained gravity center:
use of
Is a reverse symmetric matrix
Construct column vector Δ ═ a23 A31 A12]TAnd from the symmetric matrix 4 x 4 can be obtained
In the formula I3Represents a 3 x 3 identity matrix, tr is the product of the matrices:
and matrix
The unit feature vector r (q) corresponding to the maximum feature value of (a), (b), and (c) is [ q ]0 q1 q2 q3]Which is the optimal rotation expressed by unit quaternion, the corresponding rotation matrix r (q) and translation matrix t (q) can be obtained according to the following formula:
T(q)＝uq-R(q)up；
the specific steps of the ICP algorithm are as follows,
during initial iteration, the initial position P of the measured point cloud is ordered0P, rigid body transformation vector q 1000000]T，K＝0；
Iteratively performing the following steps until convergence at a given threshold:
a, searching a corresponding point set and calculating PkSet of closest points Qk：Qk＝C(PkX), where C is the search operation for the closest point;
b, calculating registration parameters, (q)k,dk)＝Q(P0,Qk)；
c, applying the registration parameters to P0Obtaining a new position, Pk+1＝qk(P0)；
d, error d obtained if two adjacent iterations are performedkIs smaller than a given threshold value tau, i.e. dk-dk+1If tau is less, the iteration is terminated; otherwise k equals k +1, go to step a.
The invention has the beneficial effects that:
the invention can realize direct detection of three-dimensional FSS form and position parameters, realize measurement of three-dimensional FFS space characteristics by two-dimensional image high-precision dimension measurement and combining with space characteristic information of three-dimensional structured light, and make up for the defect that the traditional three-dimensional structured light measurement has low precision in measuring the space characteristics in a large-size range.
Drawings
FIG. 1 is a technical roadmap for the present invention;
FIG. 2 is a general technical roadmap for the present invention;
fig. 3 is a schematic view of a binocular structure optical module according to the present invention;
FIG. 4 is a flow chart of structured light three-dimensional reconstruction according to the present invention;
FIG. 5 is a flow chart of a point cloud reduction algorithm of the present invention;
FIG. 6 is a flow chart of a point cloud stitching algorithm of the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
Some embodiments of the invention are described in detail below with reference to the accompanying drawings. The embodiments described below and the features of the embodiments can be combined with each other without conflict.
Fig. 1 to 6 show a specific embodiment of the present invention, which is a three-dimensional frequency surface digitization and model comparison method, wherein a three-dimensional structured light scanning system is used to restore curved surface three-dimensional information of a three-dimensional FSS, unit point cloud data at different positions of the three-dimensional FSS are sampled to splice a point cloud model of the three-dimensional FSS, and a real error between the actual three-dimensional FSS and the CAD model is calculated by comparison with the CAD model. The method specifically comprises the following steps:
the first step is as follows: and acquiring three-dimensional measurement point cloud data by using a three-dimensional measurement technology and a three-dimensional reconstruction algorithm.
The second step is that: and (4) feature extraction, namely, carrying out a series of preprocessing on the point cloud to obtain necessary effective data in the registration process.
The third step: and extracting CAD model data. And uniformly sampling the CAD model with proper density to obtain the STL triangular grid data model.
The fourth step: and point cloud matching. And registering the three-dimensional measurement point cloud and the CAD model data to achieve the best fitting. The registration process comprises two steps, wherein the first step is coarse registration, and the second step is accurate registration.
The fifth step: and calculating and displaying errors. And calculating the Euclidean distance from each actual measurement point in the three-dimensional measurement point cloud to the surface of the CAD model to obtain an error analysis result, and displaying the error distribution condition of the workpiece by using a gray cloud picture and other modes.
For the first step, the experimental system using the three-dimensional measurement technology consists of six parts, namely a power supply module, a structured light projection module (DLP), a binocular optical imaging system, data acquisition, a CPU (image processing), an electromechanical control module and a display module. As shown in fig. 1, a binocular optical imaging system (binocular structure optical module) uses a stereoscopic three-dimensional optical measurement principle, uses two cameras to calibrate the spatial positions of the two cameras by a certain calibration method, establishes a spatial relationship, calculates a phase principal value according to a grating image projected onto the surface of an object according to grating transformation, extracts a homonymous point according to the phase characteristics of the object to be measured, and obtains a time difference value, thereby measuring the height of the point.
For the second step, the pre-processing of the point cloud comprises:
point cloud data topological relation establishment
The point cloud data acquired by the structured light three-dimensional data scanner are scattered points and have no obvious geometric characteristics. When faced with a huge amount of data, the workload of the computer is undoubtedly increased. If a topological relation is established for the point cloud data in advance, the search range of the K neighbor is greatly reduced, and therefore the efficiency of the algorithm is greatly improved.
Point cloud denoising
The point cloud data collection process is influenced by various privacy to generate errors of different degrees, namely noise points. The existence of the noise points can influence the accuracy of point cloud splicing, so that the difference between a reconstructed point cloud model and a real object is large. Aiming at different point cloud data types, corresponding to different denoising methods: for ordered or partially ordered point cloud data types, the commonly used methods are wiener filtering, smooth filtering, kalman filtering and least square filtering; common methods for the random and disordered point cloud data types include disorder denoising methods such as a Laplac ian operator, mean curvature flow, a moving minimum quadric surface and the like.
Simplification of point clouds
When point cloud data is reduced, data points capable of representing scene characteristics or measured entity surface characteristics are reserved to the maximum extent. Due to the fact that the high-precision point cloud acquisition equipment is used, the scale of the point cloud data volume is enlarged day by day, and a plurality of redundant points exist in the large-scale point cloud data, and therefore it is indispensable to firstly simplify the point cloud data before registering the point cloud data.
For the third step, the engineering model is mostly expressed by using a parameterized B-spline surface or a NURBS surface, and different business software basically follows some same basic data formats. Among the many basic data formats, item selection uses STL models for operational analysis. The STL format is relatively simple and has high processing speed. The model is similar to a grid division mode in a finite element, and after the CAD entity model data is triangulated, a plurality of space triangular facets are used for approaching the corresponding CAD entity three-dimensional model. It describes and records each small triangle with the coordinates of the three vertices of the triangle and the outer normal vector of the triangle. But STL format files do not contain contiguous topological relationships between points, edges, and faces.
The method comprises the steps of carrying out uniform sampling on a CAD model with proper density to obtain a target point cloud and an STL triangular grid data model, and rapidly obtaining the closest point from an original measurement point cloud to a corresponding triangular grid by utilizing normal vector information carried by the triangular grid, wherein the closest point is used as the target corresponding point, so that the problem of searching the corresponding point in the matching of the point cloud and the CAD model by an original ICP algorithm is effectively solved.
And for point cloud matching in the fourth step, researching a registration method of the point cloud data of the three-dimensional measuring equipment and the engineering model, and establishing a coordinate transformation relation between the point cloud data and the engineering model, so that various errors of the three-dimensional data can be analyzed and calculated conveniently in the follow-up process. The engineering model of the three-dimensional product and the three-dimensional profile measurement data of the finished product workpiece are subjected to registration comparison and error analysis, the manufacturing precision of the product is given, and links such as design, production, manufacturing assembly and the like of the product can be better guided. For a large amount of point cloud data acquired by three-dimensional structured light, the point cloud data is spliced by adopting an Iterative Closest Point (ICP) algorithm. In the specific implementation, the point cloud splicing process is divided into two steps of rough splicing and accurate splicing, wherein the rough splicing adopts a three-point method or a multi-point method and a manual pre-judgment mode, so that the point cloud has a better initial position, the point cloud is adjusted to a relatively reasonable position, point cloud areas are mutually overlapped, and an ICP algorithm is utilized to iterate to converge, so that the optimal splicing effect is achieved. And aiming at the obtained three-dimensional point cloud data model, searching a point set on the basis of an STL triangular mesh formed in an engineering model of a three-dimensional product, utilizing the normal information of the STL triangular mesh to obtain the closest point from the measured point cloud to the corresponding triangular mesh, and taking the closest point as a target corresponding point. Based on the initial target corresponding point, the ICP algorithm model is adopted for registration, so that the difficulty in finding the corresponding point of the original ICP algorithm in point cloud data and engineering model registration is reduced, and the model registration time is shortened.
For coarse registration, the coarse registration is to rotate the three-dimensional measurement point cloud and the engineering model to approximately coincide through a coarse registration algorithm to provide an initial value of successive iterations in the precise matching. In this document, three-dimensional measurement point clouds and engineering models are matched, all the measured three-dimensional point clouds are overlapped with the engineering models, and if the measurement method is proper, the shape difference of main axes of two point sets can be ensured to be small, the characteristics are very consistent with the matching conditions of a principal component analysis method, and the principal component analysis method is high in solving speed and simple in principle, so that the principal component analysis method is adopted for rough matching.
Is provided with
Two corresponding point sets (the number of points in the point set is N). The point set P represents the original measurement point cloud, the point set Q is the corresponding target point set in the engineering model, and the initial rigid body transformation parameter between the point set P and the target point set is (R)0,T0). The method for calculating the rigid body transformation initial value matched with the point cloud and the engineering model by the principal component analysis method comprises the following steps:
first, covariance matrices C of point sets P and Q are calculated respectivelypAnd Cq：
Wherein the content of the first and second substances,
is the center of the set of points P,
is the center of the point set Q
Secondly, by fitting the covariance matrix CpAnd CqSVD analysis can be performed in the following format:
wherein the feature vector UpIs the principal direction of the set of measurement points P, and the eigenvector UqIs the principal direction of the corresponding set of engineering model points Q.
The point set P and Q are directly rotated by the matrix R0And the translation vector is T0The following were used:
for accurate registration, in accurate matching, the most commonly used algorithm is the closest point iterative algorithm proposed by Besl and the like, also commonly referred to as an original ICP algorithm, and the method finds corresponding matching points in two point sets to be matched by a stepwise iterative method, calculates rigid body transformation parameters between the two point sets until an error measure meets given convergence accuracy or reaches the maximum iteration number, and finally obtains rigid body transformation parameters (translation and rotation parameters) between the two point sets to complete the whole registration process, and the specific algorithm is as follows:
is provided with
For two-piece point cloud set to be registered, the ICP algorithm firstly points each point P in the point set PiSearching for its closest point q on the set of points XiSet as corresponding point searched
Is set of corresponding points of
The algorithm establishes the following error measures:
then, the above formula is solved to minimize the value, and the value is recorded as
(q,d)＝M(P,Q)
Wherein M represents the minimizing operation; d is the corresponding root mean square error, i.e. d ═ e (q); q is the rigid body transformation vector resulting from the minimization operation, i.e., q ═ R (q) T (q)]TR (q) represents the optimal rotation, and t (q) is the optimal translation vector.
And applying the rigid body transformation parameters obtained by the algorithm calculation to the original measurement point cloud, and recording as q (P). The ICP algorithm iterates each time this operation is performed until some set convergence criterion is met.
To minimize E (Q), a minimization operation M is performed by first computing the center of gravity u of the set of points P and the set of model points Qp、uq：
And (3) calculating a cross covariance matrix of the point sets P and Q by the obtained gravity center:
use of
Is a reverse symmetric matrix
Construct column vector Δ ═ a23 A31 A12]TAnd from the symmetric matrix 4 x 4 can be obtained
In the formula I3Represents a 3 x 3 identity matrix, tr is the trace of the matrix:
and matrix
The unit feature vector r (q) corresponding to the maximum feature value of (a), (b), and (c) is [ q ]0 q1 q2 q3]Which is the optimal rotation expressed by unit quaternion, the corresponding rotation matrix r (q) and translation matrix t (q) can be obtained according to the following formula:
T(q)＝uq-R(q)up
the ICP algorithm steps of Besl and Mckay may be described as follows:
during initial iteration, the initial position P of the measured point cloud is ordered0P, rigid body transformation vector q 1000000]T，K＝0。
The following steps are performed iteratively until convergence at a given threshold.
(1) Finding corresponding point sets: calculating PkSet of closest points Qk：Qk＝C(PkX), where C is the search operation for the closest point.
(2) Calculating registration parameters: (q) ak,dk)＝Q(P0,Qk)。
(3) Applying registration parameters to P0Obtaining a new position: pk+1＝qk(P0)。
(4) Error d obtained by two adjacent iterationskIs smaller than a given threshold value tau, i.e. dk-dk+1If tau is less, the iteration is terminated; otherwise k equals k +1, go to step (1).
Finally, the above embodiments are only used for illustrating the technical solutions of the present invention and not for limiting, and other modifications or equivalent substitutions made by the technical solutions of the present invention by those of ordinary skill in the art should be covered within the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solutions of the present invention.
Claims (8)
1. A three-dimensional frequency surface digitization and model comparison method is characterized by comprising the following steps:
s1, obtaining three-dimensional measurement point cloud data by using a three-dimensional measurement and three-dimensional reconstruction algorithm;
s2, extracting features, preprocessing point clouds to obtain necessary effective data in the registration process;
s3, extracting CAD model data, and uniformly sampling the CAD model to obtain an STL triangular grid data model;
s4, point cloud matching, namely registering the three-dimensional measurement point cloud and the CAD model data to achieve optimal fitting;
and S5, calculating errors, displaying, calculating the Euclidean distance between each actual measurement point in the three-dimensional measurement point cloud and the surface of the CAD model to obtain an error analysis structure, and displaying the error distribution condition of the workpiece by using the gray cloud picture.
2. The method of claim 1, wherein the method comprises: in S1, the binocular optical module is used for three-dimensional measurement, and the binocular optical module uses a stereoscopic three-dimensional optical measurement principle, calibrates the spatial positions of the two cameras with the two cameras, establishes a spatial relationship, calculates a phase principal value according to a grating image projected onto the surface of an object and a grating transformation, extracts a homonymy point according to the phase characteristics of the object to be measured, and obtains a time difference value, thereby measuring the height of the point.
3. The method of claim 1, wherein the method comprises: the step of preprocessing the point cloud in S2 includes:
s21, establishing a point cloud data topological relation, and improving algorithm efficiency;
s22, point cloud denoising, namely denoising the ordered or partially ordered point cloud data types by a wiener filtering method, a smooth filtering method, a Kalman filtering method and a least square filtering method, and denoising the scattered and unordered point cloud data types by a Laplacian operator, an average curvature flow method and a moving minimum quadric surface;
and S23, point cloud data are simplified, and data points capable of representing scene characteristics or measured entity surface characteristics are reserved.
4. The method of claim 1, wherein the method comprises: s3 includes a method for searching corresponding points based on the CAD model STL triangular mesh, the closest point from the original measurement point cloud to the corresponding triangular mesh is quickly obtained by utilizing the normal vector information carried by the triangular mesh, and the closest point is used as the target corresponding point, so that the problem of searching the corresponding point in the matching of the point cloud and the CAD model by the original ICP algorithm can be effectively solved.
5. The method of claim 1, wherein the method comprises: the point cloud matching in the S4 comprises coarse registration and accurate registration, a point set is searched for the obtained three-dimensional point cloud data model on the basis of an STL triangular mesh formed in an engineering model of a three-dimensional product, the closest point from the measured point cloud to the corresponding triangular mesh is obtained by utilizing the normal information of the STL triangular mesh, the closest point is used as a target corresponding point, and the registration of the ICP algorithm model is adopted on the basis of the initial target corresponding point so as to reduce the difficulty in searching the original ICP algorithm for the corresponding point in the registration of the point cloud data and the engineering model and reduce the time of model registration.
6. The method of claim 5, wherein the three-dimensional frequency surface is digitized and modeled after the three-dimensional frequency surface is scanned by a scanning camera, the method comprising: the rough registration is to rotate the three-dimensional measurement point cloud and the engineering model to approximately coincide through a rough registration algorithm so as to provide an initial value of successive iteration in accurate matching, and a principal component analysis method is adopted for rough matching;
the algorithm applied to the accurate registration is an ICP algorithm, corresponding matching points in two point sets to be matched are searched through a step-by-step iteration method, rigid body transformation parameters between the two point sets are calculated until error measure meets given convergence accuracy or reaches the maximum iteration times, and the rigid body transformation parameters between the two point sets are finally obtained, so that the whole registration process is completed.
7. The method of claim 6, wherein: the principal component analysis method in the coarse registration is specifically to set
Two corresponding point sets are provided, the number of points in the point sets is N, the point set P represents an original measurement point cloud, the point set Q is a corresponding target point set in the engineering model, and the initial rigid body transformation parameter between the point sets is (R)0,T0) (ii) a The method for calculating the rigid body transformation initial value matched with the point cloud and the engineering model by the principal component analysis method comprises the following steps:
s41, covariance matrixes C of the point sets P and Q are respectively calculatedpAnd Cq；
Wherein the content of the first and second substances,
is the center of the set of points P,
is the center of the point set Q
S42, by fitting covariance matrix CpAnd CqSVD analysis can be performed in the following format:
wherein the feature vector UpIs the principal direction of the set of measurement points P, and the eigenvector UqIs the main direction of the corresponding engineering model point set Q, the point set P and Q are direct rotation matrix R0And the translation vector is T0The following were used:
8. the method of claim 6, wherein: the ICP algorithm for accurate registration specifically comprises the following steps:
is provided with
For two-piece point cloud set to be registered, the ICP algorithm firstly points each point P in the point set PiSearching for its closest point q on the set of points XiAs corresponding points, set to be searched
Is set of corresponding points of
The IPC algorithm establishes the following error measures:
then, the above formula is solved to minimize the value, and the value is recorded as
(q,d)＝M(P,Q)
Wherein M represents the minimizing operation; d is the corresponding root mean square error, i.e. d ═ e (q); q is the rigid body transformation vector resulting from the minimization operation, i.e., q ═ R (q) T (q)]TR (q) represents the optimal rotation, and t (q) is the optimal translation vector;
applying rigid body transformation parameters obtained by algorithm calculation to the original measurement point cloud, recording as q (P), and executing the operation in ICP algorithm iteration each time until a certain set convergence criterion is met;
to minimize E (Q), a minimization operation M is performed by first computing the center of gravity u of the set of points P and the set of model points Qp、uq：
And (3) calculating a cross covariance matrix of the point sets P and Q by the obtained gravity center:
use of
Is a reverse symmetric matrix
Construct column vector Δ ═ a23 A31 A12]TAnd from the symmetric matrix 4 x 4 can be obtained
In the formula I3Represents a 3 x 3 identity matrix, tr is the product of the matrices:
and matrix
The unit feature vector r (q) corresponding to the maximum feature value of (a), (b), and (c) is [ q ]0 q1 q2 q3]Which is the optimal rotation expressed by unit quaternion, the corresponding rotation matrix r (q) and translation matrix t (q) can be obtained according to the following formula:
T(q)＝uq-R(q)up；
the specific steps of the ICP algorithm are as follows,
during initial iteration, the initial position P of the measured point cloud is ordered0P, rigid body transformation vector q 1000000]T，K＝0；
Iteratively performing the following steps until convergence at a given threshold:
a, searching a corresponding point set and calculating PkSet of closest points Qk：Qk＝C(PkX), where C is the search operation for the closest point;
b, calculating registration parameters, (q)k,dk)＝Q(P0,Qk)；
c, applying the registration parameters to P0Obtaining a new position, Pk+1＝qk(P0)；
d, error d obtained if two adjacent iterations are performedkIs smaller than a given threshold value tau, i.e. dk-dk+1If tau is less, the iteration is terminated; otherwise k equals k +1, go to step a.
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