Normal extension point cloud registration method and system based on step-by-step optimization and numerical approximation optimization

Abstract

The invention belongs to the related technical field of point cloud data processing, and discloses a normal extension point cloud registration method and system based on step-by-step optimization and numerical approximation optimization. The method comprises the following steps: S1, aligning geometric centers of an entity point cloud and a digital-analog point cloud; setting an initial expansion distance d0; s2, calculating an optimal pose parameter when the matching error between the expanded digital-analog point cloud and the entity point cloud is minimum under the current expansion distance, and adjusting the pose of the digital-analog point cloud according to the optimal pose parameter; s3, updating the expansion distance, returning to the step S2 until a preset condition is met, and setting the current expansion distance as dfit; and S4, keeping the pose unchanged, solving a corresponding optimal extension distance dfinal between the dfit and the d0 when the matching error is minimum, extending the digital-analog point cloud under the current pose according to the extension distance, and completing registration between the digital-analog point cloud and the entity point cloud. According to the invention, the registration of two weak feature curved surface point clouds and the calculation of the normal extension distance are realized.

Description

Technical Field

[0001] The present invention belongs to the technical field related to point cloud data processing, and more specifically, relates to a normal expansion point cloud registration method and system based on step-by-step optimization and numerical approximation optimization. Background Art

[0002] In recent years, with the rapid development of 3D scanning technology, digital processing technology based on point cloud registration has been widely used, especially in the processing and manufacturing industry. The processing process of some large curved workpieces includes the following three steps: obtaining the physical workpiece based on standard digital models, wrapping the coating on the workpiece surface, and polishing the coating to complete the overall processing process. The current polishing and coating processing process mainly relies on industrial robots to complete the polishing through offline trajectory planning based on standard digital models. Due to the differences between the actual workpiece and the standard digital model, it is difficult to achieve high-precision robot polishing and coating removal processes. Therefore, using 3D scanning technology to obtain the physical point cloud of the workpiece and align it with the point cloud of the standard digital model of the workpiece can accurately calculate the polishing removal amount and improve the processing accuracy.

[0003] After the workpiece substrate is formed, the coating wrapped around its surface can be regarded as a coating of equal thickness. The standard digital model point cloud is extended along the normal vector by the thickness of the coating to obtain the workpiece solid point cloud. The registration of the workpiece solid point cloud and the workpiece standard digital model point cloud can be regarded as the geometric center registration of the two point clouds. The standard digital model point cloud is nested in the workpiece solid point cloud digital model, and the distance between each corresponding point pair is the thickness of the coating. The classic ICP algorithm and its improved variants rely on the matching of local features of the point cloud. In the case of non-overlapping geometric relationships, the normal extension will be misjudged as free deformation, resulting in distortion in the solution of rigid body transformation parameters. Although the deep learning-based registration method can adapt to some deformation scenarios, its data-driven characteristics are fundamentally in conflict with the deterministic geometric constraints of the normal extension. In addition, the surface of the curved workpiece has the characteristics of weak features, which is prone to overfitting and erroneous registration results.

[0004] Existing methods have not yet effectively solved the point cloud registration problem with strict normal extension constraints, and it is difficult to meet the needs of rigid body pose solution in high-precision coating removal processes. Therefore, there is an urgent need for a point cloud registration algorithm for normal extension. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a normal extension point cloud registration method and system based on step-by-step optimization and numerical approximation optimization, which solves the problem in the prior art that it is impossible to solve the geometric center registration and normal extension distance of two point clouds with a normal extension geometric transformation relationship.

[0006] To achieve the above object, according to one aspect of the present invention, a normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization is provided, the method comprising the following steps:

[0007] S1 aligns the geometric centers of the physical point cloud of the coated workpiece and the digital model point cloud of the uncoated workpiece; and sets an initial expansion distance d0 for the digital model point cloud to expand outward.

[0008] S2 calculates the optimal pose parameters of the expanded digital model point cloud when the matching error between the expanded digital model point cloud and the physical point cloud is minimized at the current expansion distance, and adjusts the pose of the digital model point cloud according to the optimal pose parameters;

[0009] S3 updates the extended distance and returns to step S2 until the extended distance meets the preset conditions or reaches the number of iterations, thereby achieving the position adjustment of the digital and analog point cloud in the matching process. The current extended distance is d fit ;

[0010] S4 keeps the posture of the digital point cloud adjusted in step S3 unchanged, and solves the problem in step d fit The optimal expansion distance d between d0 and d1 is the distance between the expanded digital point cloud and the physical point cloud that minimizes the matching error. final , the digital model point cloud in the current posture is expanded according to the expansion distance to complete the alignment between the digital model point cloud and the physical point cloud.

[0011] Further preferably, the matching error is calculated according to the following formula:

[0012]

[0013] Among them, R is the rotation matrix of the rigid body transformation, t is the translation vector of the rigid body transformation, q i It is the entity point cloud Q{q i Point coordinates, p′ i is the digital point cloud P{p i} Extend distance d along the normal direction i The point cloud P′{p′ i}, N is the number of corresponding point pairs between the physical point cloud and the digital model point cloud, and E is the mean Euclidean distance between the corresponding point pairs of the two point clouds.

[0014] More preferably, the p i The calculation formula of ′ is as follows:

[0015] p i ′=p i +d i n pi

[0016] Among them, p i is the digital point cloud P{p i} point coordinates, p′ i is the digital point cloud P{pi} Extend distance d along the normal direction i The point cloud P′{p′ i} point coordinates, d i is the normal extension distance, n pi is the p in the digital point cloud i The normal vector of the point.

[0017] Further preferably, in step S3, the updating of the extension distance is performed according to the following formula:

[0018]

[0019] Among them, p i new is the point cloud P′{p′ i After registration, shrink in the reverse direction along the normal direction d i The coordinates of the point after q i It is the entity point cloud Q{q i}Point coordinates, n qi It is q in the digital point cloud i The normal vector of the point, It is p i new To the entity point cloud Q{q i} corresponding point q i Distance to the tangent plane, d j are all corresponding point pairs of two point clouds The mean of .

[0020] Further preferably, in step S3, the preset condition is that the extension distance converges.

[0021] More preferably, the p i new The calculation formula is as follows:

[0022] p i new =(Rp i ′+t)-d j n pi new

[0023] Among them, p′ i is the coordinate of the digital point cloud point after normal expansion, R is the rigid body transformation rotation matrix transformed to the target pose, t is the rigid body transformation translation vector transformed to the target pose, d j is the current normal expansion distance, is p′ i Normal vector after reaching the target pose, p i new is p′ iAfter reaching the target pose through pose transformation, the point cloud coordinates are restored to the initial digital model point cloud shape by shrinking in the reverse direction along the normal direction.

[0024] Further preferably, in step S2, the optimal pose parameters of the digital-analog point cloud at the current extended distance are calculated using an improved closest point iterative algorithm.

[0025] Further preferably, in step S4, a numerical approximation optimization method is adopted when calculating the optimal expansion distance.

[0026] Further preferably, the optimal posture parameters include a rotation matrix and a translation vector.

[0027] According to another aspect of the present invention, a normal expansion point cloud registration system based on step-by-step optimization and numerical approximation optimization is provided, which includes an executor for executing the above-mentioned normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization.

[0028] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0029] 1. In the present invention, the optimal posture for matching the digital-analog point cloud and the physical point cloud is first determined, and then the extended distance under the optimal posture is determined. The precise matching between the digital-analog point cloud and the physical point cloud is achieved in two parts. The optimal analytical solutions of the two coupling variables, the rotation matrix and the extended distance, are solved through step-by-step optimization. The value range of the analytical solution of the extended distance is determined through numerical approximation optimization, and the update step size of the analytical solution of the extended distance is further refined. The problem of geometric center alignment and normal extended distance of two point clouds with normal extended geometric transformation relationship is solved, and the solution accuracy of the rotation matrix, translation vector and extended distance is improved.

[0030] 2. In the present invention, by setting the initial normal extension distance, solving the optimal posture transformation, updating the normal extension distance, and iteratively obtaining the final optimal position, this method can quickly obtain the optimal posture matching between the digital point cloud and the physical point cloud.

[0031] 3. After determining the optimal matching posture, the present invention performs secondary optimization through the numerical approximation method while keeping the optimal posture unchanged. Under the optimal alignment posture optimized in step-by-step, the update step size of the d value is refined to make up for the defect that the d value update step size is too large and the optimal solution is missed during the step-by-step optimization solution process.

[0032] 4. The method for updating the extended distance constructed by the present invention is calculated based on the average of the tangent plane distances from each point in the digital-analog point cloud to the corresponding point in the physical point cloud after the pose is updated. This update method takes into account that after the two point clouds are aligned, the normal vectors of the corresponding point pairs are in the same direction, that is, the direction of the normal vector of the point in the physical point cloud. Therefore, the process of updating and calculating the extended distance is based on the average of the projection distances of the vectors from each point in the digital-analog point cloud to the corresponding point in the physical point cloud in the direction of the normal vector of the corresponding point in the physical point cloud, that is, the average of the distances from each point in the digital-analog point cloud to the tangent plane of the corresponding point in the physical point cloud, rather than the Euclidean distance between the two. This makes the updated extended distance more accurate and improves the iterative convergence speed.

[0033] 5. Compared with the existing point cloud registration method, the method provided by the present invention does not require the two point clouds to have the same overlapping area and significant surface features, and can complete the registration of two weak-feature surface point clouds and the calculation of the normal extension distance. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a simplified flow chart of a normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization constructed according to a preferred embodiment of the present invention;

[0035] Figure 2 It is a detailed flow chart of a normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization constructed according to a preferred embodiment of the present invention;

[0036] Figure 3 Schematic diagram of optimal pose matching between a physical point cloud and a digital model point cloud constructed according to a preferred embodiment of the present invention;

[0037] Figure 4 This is a result diagram of the registration of a physical point cloud and a digital model point cloud constructed according to a preferred embodiment of the present invention at an optimal posture and extended distance. DETAILED DESCRIPTION

[0038] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0039] like Figure 1 and Figure 2As shown in the figure, a normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization is used to solve the analytical solution of the coupling variables. This method uses the numerical approximation method to perform secondary optimization on the solution of the step-by-step optimization. Specifically, the d value that minimizes the point cloud registration error during the step-by-step optimization process is taken, and a quantized interval of d values is generated between the initial value of d. The endpoints of each interval are taken as the quantized value of d. After the digital-analog point cloud is expanded along the normal direction by a quantized distance of d using the numerical approximation method, the IICP algorithm is used to update the rigid body transformation solution R and t. The d value and rigid body transformation solution R and t that minimize the registration error are obtained, which is the final solution.

[0040] The above method specifically comprises the following steps:

[0041] S1 aligns the geometric centers of the physical point cloud of a coated workpiece and the digital model point cloud of the uncoated workpiece. The physical point cloud is 3D point cloud data obtained by scanning the coated workpiece surface, while the digital model point cloud is 3D point cloud data extracted by meshing the workpiece's 3D model using software. Theoretically, the 3D point cloud shape of the workpiece can be obtained by extending the digital model point cloud along the normal distance d.

[0042] Determination of the optimal pose for S2 matching

[0043] (1) Initialize the normal extension distance d0 and the initial registration pose of the point cloud

[0044] The optimization objective function solved by this algorithm is defined as follows:

[0045]

[0046] In the formula, R is the rotation matrix of the rigid body transformation, t is the translation vector of the rigid body transformation, d is the normal extension distance, and q i For the entity point cloud Q{q i} point coordinates, p i For the digital point cloud P{p i} point coordinates, (q i ,p i ) are the corresponding point pairs in the two point clouds, n pi is the normal vector of the digital-analog point cloud. The variable R is coupled to the variable d, so an analytical solution is not possible. The objective function is to expand the digital-analog point cloud along the normal vector d and then perform a rigid body transformation to minimize the Euclidean distance between corresponding point pairs.

[0047] By measuring the workpiece entity with a vernier caliper, we can obtain an initial value of the extended distance d0 with an error, and then use the formula p i ′=p i +d0n piObtain the coordinate p of the digital point cloud after the initial value d0 is extended along the normal vector i ′, at this time, the normal extension distance d is fixed, in order to optimize R and t in the next step. The optimization objective function at this time becomes:

[0048]

[0049] Once the objective function is converted to the above form, the covariance matrix can be decomposed using SVD singular value decomposition to obtain a single-step analytical solution for the rotation matrix R and the translation vector t. The solution formula is as follows:

[0050]

[0051] R=VU T

[0052]

[0053] formula, in It is the center point of the digital point cloud after expansion along the normal direction. is the center point of the entity point cloud, It is the point set after the digital model point cloud is expanded and centralized along the normal direction. is the point set after the entity point cloud is centralized, p i ′=p i +d0n pi is the coordinate point of the digital point cloud after the distance d0 is extended in the direction of the normal vector, H is the covariance matrix, UΣV T is the singular value decomposition result of the matrix H. The above iterative solution process for the rotation matrix R and the translation vector t is performed using the IICP (Improved Iterative Closest Point algorithm) registration algorithm. The point-to-surface error and the angle between the normal vectors of the corresponding point pairs are used as the threshold to determine the exit from the iterative solution process. The IICP algorithm is disclosed in the doctoral dissertation "Research on Point Cloud Stitching Methods for Mobile Measurement of Large Surface Robots, Wangjinshan, 2022" and will not be repeated here. After reaching the threshold, the iteration is exited, and the rigid body transformation solutions R and t with the minimum error under the initial measurement extension value d0 are obtained.

[0054] (2) Update the normal extension distance d

[0055] After optimizing and updating R and t, the digital analog point cloud with a normal extension distance of d0 is subjected to a rigid body transformation with a rotation matrix and a translation vector as the updated R and t, and shrunk d0 in the opposite direction along the new normal vector direction, and the optimal solution of the rigid body transformation of the original digital analog point cloud with a normal extension distance of d0 is obtained, that is, p i new =(Rp i ′+t)-d0n pinew On this basis, we need to further update the normal extension distance d j The update formula of the normal extension distance d is as follows:

[0056] d i =(p i new -q i )·n qi

[0057]

[0058] where d i is the projection of the coordinate point of the digital point cloud in the normal direction of the corresponding coordinate point of the physical point cloud, d j is the mean of the absolute values of the projections of all corresponding point pairs, representing the mean of the distances along the normal direction. Update optimization d j After that, the digital-analog point cloud is expanded again along the normal vector to obtain the expanded digital-analog point cloud coordinates p i ′=p i new +d j n pi_new , which is used to update and optimize the rigid body transformation R and t again.

[0059] (3) Update and solve the rigid body transformation rotation matrix R and translation vector t

[0060] The iterative solution process of the rotation matrix R and the translation vector t is performed using the IICP registration algorithm. The point-to-surface error and the angle between the normal vectors of the corresponding point pairs are used as thresholds to determine when to exit the iterative process. When the threshold is reached, the iteration is exited, and the expansion value d is obtained. j Under the condition of the smallest error, the rigid body transformation solution R and t will be extended along the normal distance d j The digital point cloud shrinks in the opposite direction along the new normal vector direction d j Repeat steps (2) and (3) until the expansion distance converges or the maximum number of iterations is reached.

[0061] Determination of the optimal expansion distance of S3

[0062] Select the normal extension distance d that minimizes the error of the IICP registration algorithm calculation result fit And the rigid body transformation solution R at this time fit With t fit , the initial digital point cloud is R fit With t fit Rigid body transformation.

[0063] In d fit Generate a quantized interval with d0, each normal extension distance d iTo quantify the endpoint value of the interval, use the digital point cloud in the current pose and expand the distance d along the normal vector direction i , and then calculate the rigid body transformation through the IICP registration algorithm, and select the expansion distance d that minimizes the error after registration min , that is, through numerical approximation, the normal extension distance d is completed final Quantitative optimization, selection and expansion distance d final Coupled rigid body transformation R final With t final , at this time R final , t final with d final This is the final solution result.

[0064] like Figure 3 and 4 The figure shows the result of a specific embodiment of the present invention, where the red point cloud is the physical point cloud and the blue point cloud is the digital model point cloud. There are visible rotation and translation errors between the two point clouds after rough registration. After the registration is performed using the normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization proposed by the present invention, the registration result is as follows: Figure 4 As shown in the figure, the average error of the two point clouds after registration is 0.3 mm, and the deviation between the calculated value of the normal extension distance and the standard value is 0.014 mm, indicating that the point cloud registration method has a high solution accuracy.

[0065] A normal expansion point cloud registration system based on step-by-step optimization and numerical approximation optimization, the system includes an executor, which is used to execute the above-mentioned normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization. The specific implementation method is as described above and will not be repeated here.

[0066] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization, characterized in that: The method comprises the following steps: S1 aligns the geometric centers of the physical point cloud of the coated workpiece and the digital model point cloud of the uncoated workpiece; Setting the initial expansion distance d0 of the digital-analog point cloud outward; S2 calculates the optimal pose parameters of the expanded digital model point cloud when the matching error between the expanded digital model point cloud and the physical point cloud is minimized at the current expansion distance, and adjusts the pose of the digital model point cloud according to the optimal pose parameters; S3 updates the extended distance and returns to step S2 until the extended distance meets the preset conditions or reaches the number of iterations, thereby achieving the position adjustment of the digital and analog point cloud in the matching process. The current extended distance is d fit ; S4 keeps the posture of the digital point cloud adjusted in step S3 unchanged, and solves the problem in step d fit The optimal expansion distance d between d0 and d1 is the distance between the expanded digital point cloud and the physical point cloud that minimizes the matching error. final , the digital model point cloud in the current posture is expanded according to the expansion distance to complete the alignment between the digital model point cloud and the physical point cloud.

2. The normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization according to claim 1, characterized in that: The matching error is calculated according to the following formula: Among them, R is the rotation matrix of the rigid body transformation, t is the translation vector of the rigid body transformation, q i It is the entity point cloud Q{q i Point coordinates, p′ i is the digital point cloud P{p i } Extend distance d along the normal direction i The point cloud P′{p′ i }, N is the number of corresponding point pairs between the physical point cloud and the digital model point cloud, and E is the mean Euclidean distance between the corresponding point pairs of the two point clouds.

3. The normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization according to claim 2, characterized in that: The p i The calculation formula of ′ is as follows: p i ′=p i +d i n pi Among them, p i is the digital point cloud P{p i } point coordinates, p′ i is the digital point cloud P{p i } Extend distance d along the normal direction i The point cloud P′{p′ i } point coordinates, d i is the normal extension distance, n pi It is the p in the digital point cloud i The normal vector of the point.

4. The normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization according to claim 1 or 3, characterized in that: In step S3, the update extension distance is performed according to the following formula: Among them, p i new is the point cloud P′{p′ i After registration, shrink in the reverse direction along the normal direction d i The coordinates of the point after q i It is the entity point cloud Q{q i }Point coordinates, n qi It is q in the digital point cloud i The normal vector of the point, It is p i new To the entity point cloud Q{q i } corresponding point q i Distance to the tangent plane, d j are all corresponding point pairs of two point clouds The mean of .

5. The normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization according to claim 4, characterized in that: The p i new The calculation formula is as follows: p i new =(Rp i ′+t)-d j n pi new Among them, p′ i is the coordinate of the digital point cloud point after normal expansion, R is the rigid body transformation rotation matrix transformed to the target pose, t is the rigid body transformation translation vector transformed to the target pose, d j is the current normal expansion distance, is p′ i Normal vector after reaching the target pose, p i new is p′ i After reaching the target pose through pose transformation, the point cloud coordinates are restored to the initial digital model point cloud shape by shrinking in the reverse direction along the normal direction.

6. The normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization according to claim 1 or 3, characterized in that: In step S3, the preset condition is that the extension distance converges.

7. The normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization according to claim 1 or 3, characterized in that: In step S2, the optimal pose parameters of the digital-analog point cloud at the current extended distance are calculated using an improved closest point iterative algorithm.

8. The normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization according to claim 7, characterized in that: In step S4, a numerical approximation optimization method is used to calculate the optimal expansion distance.

9. The normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization according to claim 1 or 8, characterized in that: The optimal posture parameters include a rotation matrix and a translation vector.

10. A normal expansion point cloud registration system based on step-by-step optimization and numerical approximation optimization, characterized in that: The system includes an actuator, which is used to execute the normal expansion point cloud registration method based on step-by-step optimization and numerical approximation optimization described in any one of claims 1 to 9.

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