A method for registering a curved surface point cloud based on a secant characteristic correlation
Point cloud registration is performed using secant feature correlation. Principal component analysis and singular value decomposition are used to solve the problems of high computational cost and low efficiency in existing technologies, thus achieving efficient and accurate point cloud registration.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-07-28
- Publication Date
- 2026-03-27
AI Technical Summary
Existing point cloud registration methods are computationally intensive and inefficient, especially in the complex extraction of feature points and construction of feature descriptors. Furthermore, ICP registration has high requirements for pose, resulting in high computational intensity and low efficiency.
Principal component analysis is used to establish a secant feature model. Correlation analysis is performed using the features on the secant. Singular value decomposition is used to solve the rotation and translation matrices for point cloud registration. Only the points on the secant need to participate in the calculation, which reduces the amount of computation and improves the registration speed.
It significantly reduces computational load, increases registration speed, and maintains high registration accuracy, achieving efficient point cloud registration.
Smart Images
Figure CN116934817B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to the technical field of point cloud registration, and particularly relates to a curved surface point cloud registration method based on secant feature correlation. BACKGROUND
[0002] Point cloud registration technology is widely used in the fields of three-dimensional reconstruction, target tracking and identification, cultural relic restoration and the like, and has high application value and broad application prospect. How to improve the accuracy and real-time performance of the tracking technology to adapt to various requirements in actual application fields is a key problem in the current point cloud registration field.
[0003] A Chinese patent with the publication number CN115861397A and the name "point cloud registration method based on improved FPFH-ICP" is disclosed. The method first performs voxel filtering on the point cloud for downsampling, extracts feature points through an ISS3D algorithm, introduces a point cloud barycenter to constrain the feature points, and eliminates error points. Then, an improved fast point feature histogram (FPFH) is used to construct a feature descriptor for the feature points, a SCA-IA algorithm is used for coarse registration of the point cloud, and finally, an improved ICP algorithm is used for accurate registration of the point cloud after coarse registration. The method has a large amount of calculation due to global search calculation in feature point extraction, and the FPFH algorithm has high calculation complexity when constructing a feature descriptor for the feature points, and the amount of calculation increases with the increase in the number of feature points. The method uses an improved ICP algorithm for global registration, which has certain requirements for the poses of the two point clouds after coarse registration, and has the problems of large amount of calculation and low efficiency. SUMMARY
[0004] The application provides a curved surface point cloud registration calculation method based on secant feature correlation to solve the problems of large amount of calculation and low registration efficiency in the prior art.
[0005] The technical solution of the application to solve the technical problem is as follows:
[0006] A curved surface point cloud registration calculation method based on secant feature correlation comprises the following steps:
[0007] Step 1: Given a triangular mesh target point cloud P and a point cloud Q to be registered;
[0008] Step 2: Obtain the secant of the target point cloud P and the point cloud Q to be registered;
[0009] Firstly, principal component analysis (PCA) is performed on the target point cloud P to obtain three principal components N1(x1, y1, z1), N2(x2, y2, z2) and N3(x3, y3, z3), and the mean point C(c x ,c y ,c z ) is calculated by formula (1). x y z ) is calculated by formula (1).
[0010]
[0011] Where: p i Let n be the i-th point in the target point cloud P, and n be the value of p. i The number of;
[0012] Then, the equations of planes A and B are established through point C with N1 and N2 as normal vectors, as shown in equation (2);
[0013]
[0014] The equation of line Z passing through point C with direction vector N3 is as follows:
[0015]
[0016] The equation of the cylindrical surface L is established with the line Z as the axis and R as the radius as follows:
[0017] (xx m ) 2 +(yy m ) 2 +(zz m ) 2 =R 2 (4)
[0018] Where: (x m ,y m ,z m Let (x, y, z) be the coordinates of the projection of the point (x, y, z) on the cylindrical surface onto the axis Z.
[0019] Finally, let e be the edge in the triangular meshed point cloud that intersects the plane. i e i 0 and e i 1 For e i The two endpoints of the edge, If the intersection of the point cloud and the plane is the point, then the coordinates of the intersection point can be obtained by combining equation (5) and equation (2). After finding all the intersection points, the intersection lines of plane A and B with point cloud P and Q can be obtained.
[0020]
[0021] Where: 0≤λ≤1, let B be the edge in the triangular meshed point cloud at the intersection with the cylindrical surface. E B E Let E be the two endpoints of the side. A and E B P EFor the intersection of point cloud and cylindrical surface, the intersection coordinates are obtained by formula (6) and formula (4) together, and the intersection line of cylindrical surface L and point cloud P, Q is obtained after all intersection points are obtained.
[0022]
[0023] Wherein: 0≤k≤1, the intersection line obtained here is the secant line;
[0024] Step three, resample the secant line;
[0025] The pair of secant lines obtained by A plane are A P and A Q . P Q are represented by matrix G P and matrix G Q , and the principal component analysis is performed on the matrix G P and G Q as a whole, and the local coordinate system is established with the barycentric point as the origin and the three principal components as the coordinate axes, and the secant line is converted from the world coordinate system to the local coordinate system by formula (7) to obtain matrix J P , J Q .
[0026]
[0027] Wherein: R A is a rotation matrix, and T A is a translation matrix; the secant line is in the plane, and the z value of the secant line point in the local coordinate system is 0, so only the x coordinate needs to be resampled in the first principal component direction, i.e. x axis direction, by formula (8) to obtain y value, and finally the resampled secant line point in the local coordinate system is obtained.
[0028] y i = f(x i +i×λ) (8)
[0029] Wherein: i=(1, 2,..., s), s is the number of resampled points, and f(x) is a resampling function.
[0030] Step four, construct a secant line feature model for the resampled secant line;
[0031] Let the resampled secant line point set be D, and the features of the elements in set D are obtained by formula (9);
[0032]
[0033] Wherein: D i is the i-th element in D, e i is the i-th element feature value, and Dpre and D next For D i Center R C Let the points where the radius circle intersects the secant be the points where the secant intersects the circle. The characteristic descriptor of the secant is then E = {e1, e2, ..., e...}. l The paired secant feature descriptors obtained from the same face are then the secant feature model G = {E} of that plane. AP E AQ};
[0034] Step 5: Perform correlation analysis on the secant feature model;
[0035] In the secant feature model of plane A, the line feature descriptor of the target point cloud is E. AP The point cloud descriptor to be registered is E. AQ First, the model is decentralized using equation (10) to obtain...
[0036]
[0037]
[0038] Then, using equation (11) and Correlation analysis was performed to obtain the correlation coefficient ε, where 0 ≤ ε ≤ 1; next, E AP and E AQ Relative phase shifts are performed according to a step size λ. The correlation coefficient is calculated for each step λ, and the step size S at which the correlation coefficient is maximized is obtained. λ And the correlation coefficient ε, at which the correlation coefficient is the largest, the two secant lines are in one-to-one correspondence, find the overlapping part and select three corresponding point pairs from each secant line to obtain the set of corresponding point pairs T, O;
[0039] Step 6: Solve for the registration rotation and translation matrices of the corresponding point pairs using singular value decomposition;
[0040] First, the centroids of the two corresponding point pairs T and O are obtained according to equation (12), and then the centroids are decentered.
[0041]
[0042] Where: t i Let o be the i-th point in set T. i Let T be the i-th point in set O, and let T and O be the centroids of sets T and O, respectively. Let T′ and O′ be the results of decentering sets T and O, respectively.
[0043] Then, construct the H matrix: Then, singular value decomposition is performed on the H matrix to obtain the U matrix and the V matrix;
[0044] Finally, the rotation matrix of the point cloud registration is R=UV -1 , and the translation matrix is
[0045] Step seven, judge whether the iteration number or the adjacent error difference and the error are less than the threshold value;
[0046] If the iteration number δ or the adjacent error difference and the error τ are not less than the threshold value, then the coordinates of the point cloud Q are updated according to formula (13) and returned to step two, and the steps two to seven are iterated until the iteration condition is reached to complete the point cloud registration.
[0047] Q=R×P+T (13)
[0048] The application has the advantages that: the application establishes a standard plane and a cylindrical surface by using principal component directions, obtains a secant line of each surface and a curved surface point cloud, calculates the curvatures of points on the secant line, and establishes a secant line feature model by taking the curvatures as features to perform correlation analysis to perform registration, only part of the points on the secant line are required to participate in the registration, instead of all the points, the calculation amount is greatly saved, the registration speed is improved, and higher registration accuracy can be obtained. BRIEF DESCRIPTION OF DRAWINGS
[0049] Figure 1 It is a flowchart of the curved surface point cloud registration method based on secant line feature correlation of the application;
[0050] Figure 2 It is a schematic diagram of an initial state of the point cloud before registration;
[0051] Figure 3 It is a schematic diagram of a secant line of each surface;
[0052] Figure 4 It is a feature schematic diagram of the application;
[0053] Figure 5 It is a schematic diagram of an A plane feature descriptor before correlation analysis;
[0054] Figure 6 It is a schematic diagram of an A plane feature descriptor after correlation analysis;
[0055] Figure 7 It is a schematic diagram of an A plane registration result;
[0056] Figure 8 It is a schematic diagram of a point cloud registration error change;
[0057] Figure 9 It is a schematic diagram of a point cloud registration result. DETAILED DESCRIPTION
[0058] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings. The following examples are used to illustrate the present application, but not to limit the scope of the present application.
[0059] As shown in Figure 1 , a curved surface point cloud registration method based on secant characteristic correlation includes the following steps:
[0060] Step one, given a triangular mesh target point cloud P and a point cloud to be registered Q.
[0061] A 200x300 size target point cloud P is established by a two-dimensional normal distribution probability density function equation, wherein the curved surface equation is as follows:
[0062]
[0063] Wherein: k=30, p=0, m1=0, m2=0, s1=50, s2=100. Then, the point cloud P is translated by 10 units along the x direction, 5 units along the y direction, and rotated by 15 degrees around the z axis to obtain the point cloud to be registered Q. The initial state of P and Q is shown in Figure 2 .
[0064] Step two, obtain the secant of the target point cloud P and the point cloud to be registered Q.
[0065] First, principal component analysis (PCA) is performed on the target point cloud P to obtain three principal components N1(x1, y1, z1), N2(x2, y2, z2), and N3(x3, y3, z3), and the mean point C(c x ,c y ,c z ) is calculated by equation (1).
[0066]
[0067] Wherein: p i is the i-th point in the point cloud P, and n is the size of the point cloud P. Then, the A and B plane equations are established by passing through the point C and taking N1 and N2 as the normal vectors, as shown in equation (2).
[0068]
[0069] The straight line Z equation is established by passing through the point C and taking N3 as the direction vector as follows:
[0070]
[0071] The cylindrical surface L equation is established by taking the straight line Z as the axis and R as the radius as follows:
[0072] (x-x m )2 +(yy m ) 2 +(zz m ) 2 =R 2 (4)
[0073] Where: (x m ,y m ,z m Let be the coordinates of the projection of a point on the cylindrical surface onto the Z-axis; finally, let e be the edge in the triangular meshed point cloud that intersects the plane. i e i 0 and e i 1 For e i The two endpoints of the edge, If the intersection point is the point cloud and the plane, then the coordinates of the intersection point can be obtained by combining equation (5) and equation (2). After finding all the intersection points, the intersection lines of plane A and B with point cloud P and Q can be obtained.
[0074]
[0075] Where: 0≤λ≤1, let B be the edge in the triangular meshed point cloud that intersects the cylindrical surface. E B E Let E be the two endpoints of the side. A and E B P E Let L be the intersection point of the point cloud and the cylindrical surface. Then, we can obtain the coordinates of the intersection point by combining equation (6) and equation (4). After finding all the intersection points, we can obtain the intersection line between the cylindrical surface L and the point cloud P and Q.
[0076]
[0077] Where: 0≤k≤1, the intersection line obtained here is the secant line, such as Figure 3 As shown.
[0078] Step 3: Resample the secant lines.
[0079] The paired secant lines A obtained from plane A P A Q For example, let's take secant A as an example. P A Q Using matrix G P And matrix G Q To represent, and for matrix G P and G Q Principal component analysis is performed on the whole system, and a local coordinate system is established with the centroid as the origin and the three principal components as the coordinate axes. The secant is transformed from the world coordinate system to the local coordinate system using equation (7) to obtain matrix J. P JQ .
[0080]
[0081] where: R A is a rotation matrix, T A is a translation matrix. Because the secant lines are in the plane, the z value of the secant point in the local coordinate system is 0, so only the x coordinate of the coincident part in the first principal component direction, i.e., the x-axis direction, is resampled by step λ to obtain the y value through equation (8), and finally the resampled secant point in the local coordinate system is obtained.
[0082] y i = f(x i +i×λ) (8)
[0083] where: i = (1, 2,..., s), s is the number of resampled points, and f(x) is a resampling function.
[0084] Step four, constructing a secant feature model for the resampled secant line.
[0085] Let the resampled secant point set be D, and the features of the elements in set D are obtained through equation (9).
[0086]
[0087] where: D i is the i-th element in D, e i is the i-th element feature value, D pre and D next are the points of intersection of the circle with radius R i and center D C and the secant line, as shown in Figure 4 , so the feature descriptor of the secant line is E = {e1, e2,..., e l}, and the pair of secant feature descriptors obtained on the same plane are the secant feature model G = {E AP , E AQ} of the plane.
[0088] Step five, correlation analysis of the secant feature model.
[0089] The secant feature descriptor of the target point cloud in the secant feature model of plane A is E AP , the feature descriptor of the point cloud to be registered is E AQ , and the two secant feature descriptors of plane A are shown in Figure 5 , where the horizontal coordinate represents the position of the secant point, and the vertical coordinate represents the feature value at each position. First, the model is decentered through equation (10) to obtain
[0090]
[0091]
[0092] Then, the correlation analysis is performed on and to obtain the correlation coefficient ε, where 0≤ε≤1, and the two feature descriptors of the A plane after the correlation analysis are shown as Figure 6 Next, E AP and E AQ are relatively shifted by a step size λ, and the correlation coefficient is calculated every time the step size λ is moved, to obtain the motion step size S λ =553 and the correlation coefficient ε=0.9997, where the correlation coefficient is the largest, the two secants are one-to-one corresponding, the overlapping part is obtained, and three corresponding point pairs are selected from each secant, to obtain the corresponding point pair set T, O.
[0093] Step six, the rotation matrix and the translation matrix of the registration are solved by singular value decomposition on the corresponding point pairs.
[0094] First, the centroid of the two corresponding point pair sets T, O is solved according to formula (12), and the centering processing is performed.
[0095]
[0096] Then, the H matrix is constructed: and the singular value decomposition is performed on the H matrix to obtain the U matrix and the V matrix; finally, the rotation matrix of the point cloud registration is R=UV -1 , and the translation matrix is The rotation matrix of the A plane registration solved by the svd method is and the translation matrix is
[0097] Step seven, whether the iteration number or the adjacent error difference and the error are smaller than the threshold value is judged.
[0098] If the iteration number δ or the adjacent error difference and the error τ are not smaller than the threshold value, the coordinate of the point cloud Q is updated according to formula (13), and the step two is returned, and the steps two to seven are iterated until the iteration condition is reached to complete the point cloud registration.
[0099] Q=RXP+T (13)
[0100] The root mean square error change result chart in the point cloud registration process is shown as Figure 8 , the final error is 0.0658 mm, the total time is 2.191 s, and the final point cloud registration result chart is shown as Figure 9as shown.
Claims
1. A method for registering surface point clouds based on secant feature correlation, characterized in that, It includes the following steps: Step 1: Given the triangulated target point cloud P and the point cloud to be registered Q; Step 2: Obtain the secant lines of the target point cloud P and the point cloud Q to be registered; Step 3: Resample the secant lines; Step 4: Construct a secant feature model for the resampled secant; Step 5: Perform correlation analysis on the secant feature model; Step 6: Solve for the registration rotation and translation matrices of the corresponding point pairs using singular value decomposition; Step 7: Determine whether the number of iterations has been reached, or whether the difference between adjacent errors and the total error are all less than the threshold. The specific steps of step two are as follows: First, principal component analysis (PCA) is performed on the target point cloud P to obtain three principal components: N1(x1,y1,z1), N2(x2,y2,z2), and N3(x3,y3,z3). The mean point C(c) is then obtained using equation (1). x ,c y ,c z ); Wherein: p i is the i-th point in the target point cloud P, n is the number of p i . Then, the equations of planes A and B are established through point C with N1 and N2 as normal vectors, as shown in equation (2); The equation of line Z passing through point C with direction vector N3 is as follows: The equation of the cylindrical surface L is established with the line Z as the axis and R as the radius as follows: (x - x m ) 2 (y - y m ) 2 (z - z m ) 2 = R 2 (4) where: (x m ,y m ,z m ) are the coordinates of the projection point of the point (x, y, z) on the cylindrical surface on the axis Z, Finally, let e be the edge in the triangular meshed point cloud that intersects the plane. i e i 0 and e i 1 For e i The two endpoints of the edge, If the intersection of the point cloud and the plane is the point, then the coordinates of the intersection point can be obtained by combining equation (5) and equation (2). After finding all the intersection points, the intersection lines of plane A and B with point cloud P and Q can be obtained. Where: 0≤λ≤1, let B be the edge in the triangular meshed point cloud at the intersection with the cylindrical surface. E B E Let E be the two endpoints of the side. A and E B P E Let L be the intersection of the point cloud and the cylindrical surface. Then, we can obtain the coordinates of the intersection by combining equation (6) and equation (4). After finding all the intersection points, we can obtain the intersection line between the cylindrical surface L and the point cloud P and Q. Where: 0≤k≤1, the intersection line obtained here is the secant line.
2. The method for registering surface point clouds based on secant feature correlation according to claim 1, characterized in that, The specific steps of step three are as follows: The paired secant lines A obtained from plane A P A Q For example, let's take secant A as an example. P A Q Using matrix G P And matrix G Q To represent, and for matrix G P and G Q Principal component analysis is performed on the whole system, and a local coordinate system is established with the centroid as the origin and the three principal components as the coordinate axes. The secant is transformed from the world coordinate system to the local coordinate system using equation (7) to obtain matrix J. P J Q ; Where: R A Let T be the rotation matrix. A For translation matrix; secant lines are all in the plane, and the z value of secant points in the local coordinate system is 0. We only need to resample the x coordinate with step size λ in the first principal component direction, i.e. x-axis direction, for the overlapping part, and finally obtain the resampled secant points in the local coordinate system. y i =f(x i +i×λ) (8) Where: i = (1,2,...,s), s is the number of resampling points, and f(x) is the resampling function.
3. The method for registering surface point clouds based on secant feature correlation according to claim 1, characterized in that, The specific steps of step four are as follows: Let D be the set of resampled secant points. The characteristics of the elements in set D are obtained by equation (9). Where: D i Let e be the i-th element in D. i Let D be the eigenvalue of the i-th element. pre and D next For D i Center R C Let the points where the radius circle intersects the secant be the points where the secant intersects the circle. The characteristic descriptor of the secant is then E = {e1, e2, ..., e...}. l The paired secant feature descriptors obtained from the same face are then the secant feature model G = {E} of that plane. AP E AQ In the secant feature model of plane A, the line feature descriptor of the target point cloud is E. AP The point cloud descriptor to be registered is E. AQ .
4. The surface point cloud registration calculation method based on secant feature correlation according to claim 3, characterized in that, The specific steps of step five are as follows: First, E AP E AQ By decentralizing the model using equation (10), we can obtain the following results. Then, using equation (11) and Correlation analysis was performed to obtain the correlation coefficient ε, where 0 ≤ ε ≤ 1; next, E AP and E AQ Relative phase shifts are performed according to a step size λ. The correlation coefficient is calculated for each step λ, and the step size S at which the correlation coefficient is maximized is obtained. λ And the correlation coefficient ε, at which point the correlation coefficient is the largest, the two secant lines are in one-to-one correspondence, find the overlapping part and select three corresponding point pairs from each secant line to obtain the set of corresponding point pairs T, O.
5. The surface point cloud registration calculation method based on secant feature correlation according to claim 4, characterized in that, The specific steps of step six are as follows: First, the centroids of the two corresponding point pairs T and O are obtained according to equation (12), and then the centroids are decentered. Where: t i Let o be the i-th point in set T. i Let i be the i-th point in set O. and Let T and O be the centroids of sets T and O, respectively, and T′ and O′ be the results of decentering sets T and O, respectively. Then, construct the H matrix: Then, singular value decomposition is performed on the H matrix to obtain the U matrix and the V matrix; Finally, the rotation matrix for point cloud registration is obtained as R = UV. -1 The translation matrix is 6. The method for registering surface point clouds based on secant feature correlation according to claim 2, characterized in that, The specific steps of step seven are as follows: If the iteration number δ or the difference between adjacent errors and the error τ are all less than the threshold condition, then the coordinates of the point cloud Q are updated according to Equation (13) and the process returns to step two. Steps two through seven are iterated until the iteration condition is met and the point cloud registration is completed. Q=R A ×P+T A (13) Where: R A Let T be the rotation matrix. A It is a translation matrix.