WO2023226429A1 - 基于设计-实测点云模型的预制梁体数字预拼装匹配方法 - Google Patents

基于设计-实测点云模型的预制梁体数字预拼装匹配方法 Download PDF

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WO2023226429A1
WO2023226429A1 PCT/CN2022/142697 CN2022142697W WO2023226429A1 WO 2023226429 A1 WO2023226429 A1 WO 2023226429A1 CN 2022142697 W CN2022142697 W CN 2022142697W WO 2023226429 A1 WO2023226429 A1 WO 2023226429A1
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point cloud
point
slice
matching
design
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熊文
徐畅
朱彦洁
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东南大学
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
    • G06T7/33—Determination of transform parameters for the alignment of images, i.e. image registration using feature-based methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/70—Denoising; Smoothing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/70—Determining position or orientation of objects or cameras
    • G06T7/73—Determining position or orientation of objects or cameras using feature-based methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/40—Extraction of image or video features
    • G06V10/44—Local feature extraction by analysis of parts of the pattern, e.g. by detecting edges, contours, loops, corners, strokes or intersections; Connectivity analysis, e.g. of connected components
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10028—Range image; Depth image; 3D point clouds
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20021—Dividing image into blocks, subimages or windows

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  • the invention relates to digital pre-assembly matching of three-dimensional digital point clouds of bridge engineering components, and specifically relates to a digital pre-assembly matching method for prefabricated beams based on a design-measured point cloud model.
  • Three-dimensional laser scanning technology directly and quickly obtains massive three-dimensional coordinate data on the surface of objects. It has the advantages of high measurement efficiency, high degree of automation, low work intensity for inspection personnel, large data volume, and high data processing efficiency. Compared with traditional measurement technology, it has broader application prospects. .
  • the 3D point cloud data collected by the 3D laser scanner can present the point coordinate information on the surface of the measured object in the form of a 3D digital point cloud, which is not only intuitive and easy to read, but also breaks through the traditional single-point detection.
  • 3D laser scanning technology and 3D digital point cloud are increasingly used in the field of bridge engineering. By identifying the geometric characteristics of components in the 3D digital point cloud, prefabricated component manufacturing quality inspection, construction monitoring, and bridge operation status can be realized.
  • the present invention proposes a prefabricated beam digital pre-assembly matching method based on the most iterative closest point method, Platts analysis algorithm and feature fitting algorithm. It is easy to program and implement. Compared with traditional methods, it improves Computational efficiency and automation.
  • the steps of the prefabricated beam digital pre-assembly matching method based on the design-measured point cloud model of the present invention are as follows:
  • Step (1) Calculate directed bounding boxes for the three-dimensional digital point clouds of the two prefabricated beam bodies that have an assembly relationship, and implement three-dimensional coordinate calibration based on the geometric characteristics of the three-dimensional digital point clouds of the two prefabricated beam bodies; for the calibrated For the three-dimensional digital point clouds of the two prefabricated beams, two point cloud slices were made on the assembly interface of the two prefabricated beams; based on the assembly interface contained in the two point cloud slices, the design information contained in the assembly interface was Generate discrete design point clouds;
  • Step (2) Use the iterative closest point algorithm to register the point cloud slices of the assembly interface of the two prefabricated beams in step (1) with the generated design point cloud respectively; set on the basis of the coordinate range of the design point cloud Distance threshold is used to denoise the two assembled interface point cloud slices;
  • Step (3) based on the design point cloud coordinate range in step (2), divide the two denoised point cloud slices into blocks; select the fitting function and fitting algorithm according to the features required to be fitted, and fit Extract the boundary features and corner features of the assembly interface of the two components to be assembled;
  • Step (4) based on the fitted boundary features and corner features in the pre-assembled interface of the two components to be assembled in step (3), first use the Platts analysis algorithm to achieve rough matching of the assembly interface, and then use the iterative nearest point algorithm to achieve The assembly interface is precisely matched, the point cloud is adjusted to the final assembly posture, the matching error of the assembly interface is calculated and the assembly results are evaluated.
  • step (1) of the prefabricated beam digital pre-assembly matching method based on the design-measured point cloud model of the present invention are as follows:
  • Step 1.1 Calculate directed bounding boxes for the three-dimensional digital point clouds of the two prefabricated beams with assembly relationships, so that the X-axis, Y-axis, and Z-axis directions of the three-dimensional coordinate system are respectively consistent with the component beam width, beam length, and beam height directions. Parallel to achieve coordinate calibration;
  • Step 1.2 Based on the assembly interface characteristics of the two prefabricated beams, make point cloud slices parallel to the XOZ coordinate plane at the assembly interface of the two three-dimensional digital point clouds after coordinate calibration, that is, slice point cloud P 1 , slice point Cloud Q 1 ;
  • the slice thickness is taken as twice the measured point cloud density; the expression is as follows:
  • Step 1.3 Generate a discrete design point cloud D based on the design information and design drawings of the assembly interface contained in the slice point cloud P 1 and the slice point cloud Q 1 .
  • the expression is as follows:
  • step (2) the design point cloud D is used as the benchmark, and based on the iterative closest point algorithm, the slice point cloud P 1 and the slice point cloud are respectively Point cloud Q 1 is registered with the design point cloud D.
  • the registration method is as follows:
  • Step 2.1 Move the centroids of the slice point cloud P 1 , the slice point cloud Q 1 and the design point cloud D to the coordinate origin respectively, that is:
  • P c is the moved slice point cloud P 1 , is the coordinate average of slice point cloud P 1 ;
  • Q c is the moved slice point cloud Q 1 , is the coordinate average of slice point cloud Q 1 ;
  • D c is the moved design point cloud D, is the coordinate average of the design point cloud D;
  • Step 2.2 In the moved design point cloud D c , find the closest points to each point in the moved slice point cloud P c and the moved slice point cloud Q c respectively. Through the orthogonal rotation matrix and rigid translation matrix, Minimize the variance of the distance between corresponding points, that is:
  • m is the number of points of the moved slice point cloud P c .
  • n is the number of points in the moved slice point cloud Q c .
  • p i is the i-th point in the moved slice point cloud P c
  • q i is the i-th point in the moved slice point cloud Q c
  • d i is the i-th point in the moved design point cloud D c ;
  • slice point cloud P 2 and slice point cloud Q 2 are obtained as follows:
  • Step 2.3 Based on the D coordinate of the design point cloud, set the distance threshold, filter the effective point cloud, and regard the points beyond the coordinate range in the point cloud P 2 and Q 2 as invalid points and remove them to obtain the denoised slice point cloud P 3 , denoised slice point cloud Q 3 .
  • step (3) of the prefabricated beam digital pre-assembly matching method based on the design-measured point cloud model of the present invention are as follows:
  • Step 3.1 Based on the coordinates of the design point cloud D c , divide the denoised slice point cloud P 3 and the denoised slice point cloud Q 3 into blocks, and extract boundary features and corner point features respectively;
  • Step 3.2 For boundary features, adopt the method of direct fitting by applying a fitting function or fitting algorithm; for corner point features, adopt the method of first fitting the boundary features and then calculating the intersection point through the intersection of the boundary features.
  • the angle obtained by fitting is For point features, when the corresponding point cannot be found in the measured point cloud, the nearest neighbor search method is used to select the nearest point as the corner feature.
  • step (4) the interface matching degree error is calculated and the assembly results are evaluated.
  • Step 4.1 Based on the three-dimensional coordinate information of the corner point features extracted from the denoised slice point cloud P 3 and the denoised slice point cloud Q 3 , establish a pre-assembled matching point group C P and a pre-assembled matching point group C Q , where C P and C Q are both k*3 matrices, and k is the number of matching points;
  • Step 4.2 Based on the Platts analysis algorithm, take the pre-assembled matching point group C P as the benchmark, and align the pre-assembled matching point group C Q with it.
  • the expression is as follows:
  • the rigid translation matrix T c under rough matching is calculated according to the above formula
  • the denoised slice point cloud Q 3 is adjusted to the roughly matched slice point cloud Q 4 , and the expression is as follows:
  • Step 4.3 Based on the iterative nearest point algorithm, find the points in the roughly matched slice point cloud Q 4 that are closest to each point in the denoised slice point cloud P 3 , and use the orthogonal rotation matrix and the rigid translation matrix to make the corresponding The variance of the distance between points is the smallest, that is:
  • the rigid translation matrix T f under fine matching is calculated according to the above formula
  • the roughly matched slice point cloud Q 4 is adjusted to the final assembled attitude point cloud Q final , and the expression is as follows:
  • the point cloud P final in the final assembly posture is defined as:
  • Step 4.4 In the assembly plane, calculate the distance f between each point in the final assembly attitude point cloud Q final and its closest point in the final assembly attitude point cloud P final :
  • p fi is the i-th point in the final assembled posture point cloud P final
  • q fi is the i-th point in the final assembled posture point cloud Q final , to evaluate the assembly results.
  • the present invention provides a digital pre-assembly matching method for prefabricated beams based on a design-measured point cloud model.
  • the directed bounding box is calculated on the three-dimensional digital point clouds of two prefabricated beams with an assembly relationship, and two points are formed.
  • Cloud slices and design point cloud secondly, the iterative nearest point algorithm is used to register the two point cloud slices with the generated design point cloud respectively, and the point cloud is filtered and denoised based on the distance threshold; then, the fitting extraction Boundary features and corner features of the pre-assembled interface of the two components to be assembled; finally, Platts analysis and iterative closest point algorithm are used to achieve rough matching and fine matching of the assembled surfaces, calculate the interface matching degree error and evaluate the assembly results.
  • This method introduces design point clouds to filter point clouds near the features to be extracted, and uses a combination of multiple algorithms to adjust the posture of the components to be assembled. It not only improves the degree of automation and reduces manual intervention, but also improves virtual pre-assembly matching and saves money. calculating time.
  • Figure 1 is a method flow chart of the prefabricated beam digital pre-assembly matching method based on the design-measured point cloud model of the present invention
  • Figure 2 is a schematic diagram of point cloud slicing of the prefabricated beam digital pre-assembly matching method based on the design-measured point cloud model of the present invention
  • Figure 3 is a schematic diagram of the effective point cloud screening based on the design point cloud and threshold value of the prefabricated beam digital pre-assembly matching method based on the design-measured point cloud model of the present invention
  • Figure 4 is a schematic diagram of corner point fitting of the prefabricated beam digital pre-assembly matching method based on the design-measured point cloud model of the present invention
  • Figure 5 is a schematic diagram of the assembly posture adjustment based on the pre-assembly matching point group of the prefabricated beam body digital pre-assembly matching method based on the design-measured point cloud model of the present invention
  • Figure 6 is a cross-sectional dimension diagram of the simulated box girder used for simulation verification of the present invention.
  • the digital pre-assembly matching method of prefabricated beams based on the design-measured point cloud model of the present invention mainly includes the following steps:
  • Step (1) Calculate directed bounding boxes for the three-dimensional digital point clouds of the two prefabricated beam bodies that have an assembly relationship, and implement three-dimensional coordinate calibration based on the geometric characteristics of the three-dimensional digital point clouds of the two prefabricated beam bodies; for the calibrated For the three-dimensional digital point clouds of the two prefabricated beams, two point cloud slices were made on the assembly interface of the two prefabricated beams; based on the assembly interface contained in the two point cloud slices, the design information contained in the assembly interface was Generate discrete design point clouds;
  • Step 1.1 Calculate directed bounding boxes for the three-dimensional digital point clouds of the two prefabricated beams with assembly relationships, so that the X-axis, Y-axis, and Z-axis directions of the three-dimensional coordinate system are respectively consistent with the component beam width, beam length, and beam height directions. Parallel to achieve coordinate calibration;
  • Step 1.2 Based on the assembly interface characteristics of the two prefabricated beams, make point cloud slices parallel to the XOZ coordinate plane at the assembly interface of the two three-dimensional digital point clouds after coordinate calibration, that is, slice point cloud P 1 , slice point Cloud Q 1 ;
  • the slice thickness is taken as twice the measured point cloud density; the expression is as follows:
  • Step 1.3 Generate a discrete design point cloud D based on the design information and design drawings of the assembly interface contained in the slice point cloud P 1 and the slice point cloud Q 1 . Its point cloud density must be greater than the density of the three-dimensional digital point cloud obtained by actual scanning. , usually, it should be taken as twice the measured point cloud density; the expression is as follows:
  • Step (2) Use the iterative closest point algorithm to register the assembly interface point cloud slices of the two prefabricated beams with the generated design point cloud respectively; set a distance threshold based on the design point cloud coordinate range, and compare the two prefabricated beams.
  • Each assembly interface point cloud slice is denoised;
  • Step 2.1 Move the centroids of the slice point cloud P 1 , the slice point cloud Q 1 and the design point cloud D to the coordinate origin respectively, that is:
  • P c is the moved slice point cloud P 1 , is the coordinate average of slice point cloud P 1 ;
  • Q c is the moved slice point cloud Q 1 , is the coordinate average of slice point cloud Q 1 ;
  • D c is the moved design point cloud D, is the coordinate average of the design point cloud D;
  • Step 2.2 In the moved design point cloud D c , find the closest points to each point in the moved slice point cloud P c and the moved slice point cloud Q c respectively. Through the orthogonal rotation matrix and rigid translation matrix, To minimize the variance of the distance between corresponding points, the following formula is used:
  • m is the number of points in the moved slice point cloud P c
  • n is the number of points in the moved slice point cloud Q c
  • p i is the i-th point in the moved slice point cloud P c
  • q i is the moved slice
  • the i-th point in the point cloud Q c , d i is the i-th point in the moved design point cloud D c ;
  • slice point cloud P 2 and slice point cloud Q 2 are obtained as follows:
  • Step 2.3 Based on the D coordinate of the design point cloud, set the distance threshold, filter the effective point cloud, and regard the points beyond the coordinate range in the point cloud P 2 and Q 2 as invalid points and remove them to obtain the denoised slice point cloud P 3 , denoised slice point cloud Q 3 .
  • Step (3) Based on the design point cloud coordinate range, divide the two denoised point cloud slices into blocks; select the fitting function and fitting algorithm according to the required fitting characteristics, and extract the two components to be assembled by fitting Boundary features and corner features of the assembly interface; the specific steps are:
  • Step 3.1 Based on the coordinates of the design point cloud D c , divide the denoised slice point cloud P 3 and the denoised slice point cloud Q 3 into blocks, and extract boundary features and corner point features respectively;
  • Step 3.2 For boundary features, adopt the method of direct fitting by applying a fitting function or fitting algorithm; for corner point features, adopt the method of first fitting the boundary features and then calculating the intersection point through the intersection of the boundary features.
  • the angle obtained by fitting is For point features, when the corresponding point cannot be found in the measured point cloud, the nearest neighbor search method is used to select the nearest point as the corner feature;
  • the fitting functions include but are not limited to straight line equations, parabolic equations, etc.
  • the fitting algorithms include but are not limited to least squares method, random sampling consensus algorithm, Hough transform, etc.
  • Step (4) Based on the fitted boundary features and corner point features in the pre-assembled interface of the two components to be assembled, first use the Platts analysis algorithm to achieve rough matching of the assembly interface, and then use the iterative nearest point algorithm to achieve fine matching of the assembly interface. Adjust the point cloud to the final assembly posture, calculate the matching error of the assembly interface and evaluate the assembly results.
  • Step 4.1 Based on the three-dimensional coordinate information of the corner point features extracted from the denoised slice point cloud P 3 and the denoised slice point cloud Q 3 , establish a pre-assembled matching point group C P and a pre-assembled matching point group C Q , where C P and C Q are both k*3 matrices, and k is the number of matching points;
  • Step 4.2 Based on the Platts analysis algorithm, taking the pre-assembled matching point group C P as the benchmark, align the pre-assembled matching point group C Q with it, through the following formula:
  • the orthogonal rotation matrix R c under rough matching is obtained; the rigid translation matrix T c under rough matching; the error matrix E c under rough matching;
  • the denoised slice point cloud Q 3 is adjusted to the roughly matched slice point cloud Q 4 , and the expression is as follows:
  • Step 4.3 Based on the iterative nearest point algorithm, find the points in the roughly matched slice point cloud Q 4 that are closest to each point in the denoised slice point cloud P 3 , and use the orthogonal rotation matrix and the rigid translation matrix to make the corresponding
  • the variance of the distance between points is the smallest, according to the following formula:
  • the orthogonal rotation matrix R f under fine matching is calculated; the rigid translation matrix T f under fine matching is calculated;
  • the roughly matched slice point cloud Q 4 is adjusted to the final assembled attitude point cloud Q final , and the expression is as follows:
  • the point cloud P final in the final assembly posture is defined as:
  • Step 4.4 In the assembly plane, calculate the distance f between each point in the final assembly attitude point cloud Q final and its closest point in the final assembly attitude point cloud P final :
  • p fi is the i-th point in the final assembled posture point cloud P final
  • q fi is the i-th point in the final assembled posture point cloud Q final , to evaluate the assembly results.
  • the simulated prefabricated beam section studied is a pair of box beams (box beam 1, box beam 2) with the same spatial geometric characteristics and an assembly relationship.
  • the beam length is 10m
  • the beam width is 10m
  • the beam height is 2m
  • the point cloud density is 1/cm 2 , the detailed dimensions are shown in Figure 6; in order to simulate the digital pre-assembly matching method of prefabricated beams based on the design-measured point cloud model, three environmental noises and four spatial geometric defects are preset on box beam 1, and on box beam 2 Default three-dimensional offset matrix.
  • Preset geometric defect 1 Point J moves to the right by 0.05m; Preset geometric defect 2: Point D moves up by 0.05m; Preset geometric defect 3: Point L moves to the left by 0.05m; Preset geometric defect 4: Edge EF moves overall to the left 0.05m.
  • step 1.1 calculate the directed bounding boxes of simulated box girder 1 and box girder 2 respectively, so that the X-axis, Y-axis, and Z-axis directions of the three-dimensional coordinate system are parallel to the component beam width, beam length, and beam height directions respectively; according to Step 1.2, make point cloud slices with a thickness of 0.02m (slice point cloud 1, slice point cloud 2) at the assembly interface of the simulated box girder 1 and box girder 2 respectively; according to step 1.3, generate the design point cloud D;
  • step 2.1 move the centroids of slice point cloud 1, slice point cloud 2, and design point cloud D to the coordinate origin respectively;
  • step 2.2 take the design point cloud as the benchmark and based on the iterative closest point algorithm, move the preset Slice point cloud 1 with environmental noise is registered with the design point cloud;
  • step 2.3 set the distance threshold to 0.02m to filter the noise, and all three environmental noises are well filtered;
  • step 3.1 extract the outer boundaries of slice point cloud 1 and slice point cloud 2 respectively. Based on the coordinate range, divide slice point cloud 1 and slice point cloud 2 into blocks respectively. Use the RANSAC algorithm to fit the boundaries and divide the two adjacent points into blocks. The intersection points of the boundaries are regarded as corner points, and corner points A1, B1, C1, D1, E1, F1, A2, B2, C2, D2, E2, and F2 are extracted respectively.
  • step 4.1 based on the extracted corner points of slice point cloud 1 and corner point of slice point cloud 2, a pre-assembled matching point group 1 and a pre-assembled matching point group 2 are formed;
  • step 4.2 based on the Platts analysis algorithm, taking the pre-assembled matching point group 1 as the benchmark, align the pre-assembled matching point group 2 with it, and obtain the rotation matrix and translation matrix corresponding to the rough matching:
  • step 4.3 based on the iterative nearest point algorithm, find the closest point to each point in slice point cloud 2 in the roughly matched slice point cloud 1, and obtain the rotation matrix and translation matrix corresponding to the fine matching:
  • slice point cloud 2 is adjusted to the assembly posture.
  • step 4.4 calculate the distance between each point in slice point cloud 2 and its closest point in slice point cloud 1. It is calculated that at the assembly interface, box beam 1: Point D has an upward offset of 0.049m, point J has an offset of 0.052m to the right, EF side has an offset of 0.05m to the left, point L has an offset of 0.047m to the left, and The default geometric defects are consistent.

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Abstract

本发明涉及桥梁工程构件基于三维点云的数字预拼装匹配领域，具体涉及到基于设计-实测点云模型的预制梁体数字预拼装匹配方法。对具有拼装关系的两个预制梁体的三维数字点云计算有向包围盒，并形成两个点云切片及设计点云；采用迭代最近点算法，将两个点云切片分别与所生成的设计点云作配准；拟合提取两个待拼装构件的预拼装界面的边界特征、角点特征；先后使用普氏分析、迭代最近点算法实现拼装面的粗略匹配与精细匹配，计算界面匹配度误差并评价拼装结果。本发明引入设计点云以实现对欲提取特征附近点云的筛选，采用多种算法结合的方式进行待拼装构件姿态调整，不仅提高了自动化程度减少人工干预，而且提高了数字预拼装匹配精度，节省计算时间。

Description

基于设计-实测点云模型的预制梁体数字预拼装匹配方法 技术领域
本发明涉及桥梁工程构件三维数字点云的数字预拼装匹配，具体涉及到基于设计-实测点云模型的预制梁体数字预拼装匹配方法。
背景技术
三维激光扫描技术直接快速获取物体表面海量三维坐标数据，具有测量效率高、自动化程度高、检测人员工作强度低、数据量大、数据处理效率高等优点，相比传统测量技术更具有广阔的应用前景。由三维激光扫描仪采集的三维点云数据能够将被测物体表面点坐标信息以三维数字点云的形式呈现，不仅直观易读，而且突破了传统单点式检测。基于上述优点，三维激光扫描技术和三维数字点云被越来越多的应用在桥梁工程领域，通过识别三维数字点云中的构件几何特征，实现预制构件制造质量检测、施工监控、桥梁运营状态监控等，然而如何从包含海量三维坐标信息的数字点云中快速识别所需特征，如何基于三维数字点云实现预制梁体数字预拼装、面对复杂的几何特征如何实现精准地拟合，提高计算效率与自动化程度，亟待解决。
发明内容
本发明针对桥梁工程构件的三维数字点云，提出基于最迭代最近点法、普氏分析算法及特征拟合算法的预制梁体数字预拼装匹配方法，易于编程实现，相较于传统方法，提高计算效率与自动化程度。
本发明采用如下技术方案：
本发明所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，步骤如下：
步骤(1)、分别对具有拼装关系的两个预制梁体的三维数字点云计算有向包围盒，基于两个预制梁体的三维数字点云的几何特征实现三维坐标校准；针对校准后的两个预制梁体的三维数字点云，在两个预制梁体的拼装界面分别作两个点云切片；基于所作两个点云切片共同包含的拼装界面，针对该拼装界面所包含的 设计信息生成离散的设计点云；
步骤(2)、采用迭代最近点算法，将步骤(1)中两个预制梁体的拼装界面点云切片分别与所生成的设计点云作配准；在设计点云坐标范围的基础上设置距离阈值，对两个拼装界面点云切片进行去噪；
步骤(3)、基于步骤(2)中的设计点云坐标范围，对去噪后的两个点云切片进行分块；根据所需拟合的特征选取拟合函数与拟合算法，拟合提取两个待拼装构件拼装界面的边界特征、角点特征；
步骤(4)、基于步骤(3)中两个待拼装构件的预拼装界面中拟合的边界特征、角点特征，首先采用普氏分析算法实现拼装界面粗略匹配，随后采用迭代最近点算法实现拼装界面精细匹配，将点云调整至最终拼装姿态，计算拼装界面匹配度误差并评价拼装结果。
本发明所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，步骤(1)具体步骤如下：
步骤1.1、分别对具有拼装关系的两个预制梁体的三维数字点云计算有向包围盒，使三维坐标系X轴、Y轴、Z轴方向分别与构件梁宽、梁长、梁高方向平行，实现坐标校准；
步骤1.2、针对两个预制梁体的拼装界面特征，分别在坐标校准后的两个三维数字点云的拼装界面处作平行于XOZ坐标平面的点云切片，即切片点云P 1、切片点云Q 1；
其中切片厚度取两倍实测点云密度；表述式如下：
P 1＝{p 1,p 2,…,p m},Q 1＝{q 1,q 2,…,q n}
步骤1.3、基于切片点云P 1、切片点云Q 1共同包含的拼装界面的设计信息、设计图纸生成离散的设计点云D，表述式如下：
D＝{d 1,d 2,…,d j}
本发明所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，步骤(2)中以设计点云D为基准，基于迭代最近点算法，分别将切片点云P 1、切片点云Q 1与设计点云D配准，其配准方法如下：
步骤2.1、分别将切片点云P 1、切片点云Q 1、设计点云D的形心移动至坐标原点，即：
Figure PCTCN2022142697-appb-000001
P c为移动后的切片点云P 1,
Figure PCTCN2022142697-appb-000002
为切片点云P 1的坐标平均值；
Q c为移动后的切片点云Q 1,
Figure PCTCN2022142697-appb-000003
为切片点云Q 1的坐标平均值；
D c为移动后的设计点云D,
Figure PCTCN2022142697-appb-000004
为设计点云D的坐标平均值；
步骤2.2、在移动后的设计点云D c中分别找到与移动后的切片点云P c、移动后的切片点云Q c中各点最近的点，通过正交旋转矩阵与刚性平移矩阵，使对应点间距离的方差最小，即：
Figure PCTCN2022142697-appb-000005
Figure PCTCN2022142697-appb-000006
m为移动后的切片点云P c的点数，
n为移动后的切片点云Q c的点数，
p i为移动后的切片点云P c中第i个点，q i为移动后的切片点云Q c中第i个点，d i为移动后的设计点云D c中第i个点；
根据上式计算得到的移动后的切片点云P c与移动后的设计点云D c配准时的正交旋转矩阵R p与刚性平移矩阵T p；
根据上式计算得到的移动后的切片点云Q c与移动后的设计点云D c配准时的正交旋转矩阵R q与刚性平移矩阵T q；
配准后得到切片点云P 2、切片点云Q 2表述式如下：
P 2＝R p·P c+T p
Q 2＝R q·Q c+T q
步骤2.3、基于设计点云D坐标，设置距离阈值，筛选有效点云，将点云P 2、Q 2中超出坐标范围的点视为无效点并去除，得到去噪后的切片点云P 3、去噪后的切片点云Q 3。
本发明所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，步骤(3)具体步骤如下：
步骤3.1、基于设计点云D c的坐标，对去噪后的切片点云P 3、去噪后的切片 点云Q 3进行分块，分别提取边界特征、角点特征；
步骤3.2、针对边界特征，采取应用拟合函数或拟合算法直接拟合的方法；对于角点特征，采用先拟合边界特征，再通过边界特征相交计算交点的方法，当拟合得到的角点特征，无法在实测点云中找到对应点时，采取最近邻搜索法，选取最近点为角点特征。
本发明所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，步骤(4)中计算界面匹配度误差并评价拼装结果，具体步骤如下：
步骤4.1、基于去噪后的切片点云P 3、去噪后的切片点云Q 3中提取到的角点特征的三维坐标信息，建立预拼装匹配点组C P、预拼装匹配点组C Q，其中，C P、C Q均为k*3矩阵，k为匹配点个数；
C p＝{C p1,C p2,…,C pk},C Q＝{C Q1,C Q2,…,C Qk}
步骤4.2、基于普氏分析算法，以预拼装匹配点组C P为基准，将预拼装匹配点组C Q与之对齐，表述式如下：
C Q＝R c·C P+T c+E c
根据上式计算得到粗略匹配下的正交旋转矩阵R c；
根据上式计算得到粗略匹配下的刚性平移矩阵T c；
根据上式计算得到粗略匹配下的误差矩阵E c；
将两匹配点组距离最小时，即粗略匹配下的误差矩阵E c最小时对应的姿态，确定为粗略匹配后姿态；
argmin||E c||
基于粗略匹配下的正交旋转矩阵R c、粗略匹配下的刚性平移矩阵T c，将去噪后的切片点云Q 3调整至粗略匹配后的切片点云Q 4表述式如下：
Q 4＝R c·Q 3+T c
实现粗略匹配；
步骤4.3、基于迭代最近点算法，在粗略匹配后的切片点云Q 4中找到与去噪后的切片点云P 3中各点最近的点，通过正交旋转矩阵与刚性平移矩阵，使对应点间距离的方差最小，即：
argmin||R f·Q 4+T f-P 3|| 2
根据上式计算得到精细匹配下的正交旋转矩阵R f；
根据上式计算得到精细匹配下的刚性平移矩阵T f；
基于精细匹配下的正交旋转矩阵R f、精细匹配下的刚性平移矩阵T f，将粗略匹配后的切片点云Q 4调整至最终拼装姿态点云Q final，表述式如下：
Q final＝R f·Q 4+T f
实现精细匹配；
为统一描述，将最终拼装姿态下的点云P final定义为：
P final＝P 3
步骤4.4、在拼装平面中，计算最终拼装姿态点云Q final与中各点距其在最终拼装姿态点云P final中最近点的间距f：
f＝||q fi-p fi||
p fi为最终拼装姿态点云P final中第i个点，q fi为最终拼装姿态点云Q final中第i个点，以此评估拼装结果。
有益效果
本发明提供的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，首先，通过对具有拼装关系的两个预制梁体的三维数字点云计算有向包围盒，并形成两个点云切片及设计点云；其次，采用迭代最近点算法，将两个点云切片分别与所生成的设计点云作配准，基于距离阈值实现点云的筛选与去噪；随后，拟合提取两个待拼装构件的预拼装界面的边界特征、角点特征；最后，依次采用普氏分析、迭代最近点算法实现拼装面的粗略匹配与精细匹配，计算界面匹配度误差并评价拼装结果。本方法引入设计点云以实现对欲提取特征附近点云进行筛选，采用多种算法结合的方式进行待拼装构件姿态调整，不仅提高了自动化程度减少人工干预，而且提高了虚拟预拼装匹配，节省计算时间。
附图说明
图1为本发明基于设计-实测点云模型的预制梁体数字预拼装匹配方法的方法流程图；
图2为本发明基于设计-实测点云模型的预制梁体数字预拼装匹配方法点云切片示意图；
图3为本发明基于设计-实测点云模型的预制梁体数字预拼装匹配方法基于设计点云及阈值的有效点云筛选示意图；
图4为本发明基于设计-实测点云模型的预制梁体数字预拼装匹配方法角点拟合示意图；
图5为本发明基于设计-实测点云模型的预制梁体数字预拼装匹配方法基于预拼装匹配点组的拼装姿态调整示意图；
图6为本发明模拟验证所用的仿真箱梁截面尺寸图。
具体实施方式
为使本发明实施例的目的和技术方案更加清楚，下面将结合本发明实施例的附图，对本发明实施例的技术方案进行清楚、完整地描述。显然，所描述的实施例是本发明的一部分实施例，而不是全部的实施例。基于所描述的本发明的实施例，本领域普通技术人员在无需创造性劳动的前提下所获得的所有其他实施例，都属于本发明保护的范围。
如图1至图5所示，本发明基于设计-实测点云模型的预制梁体数字预拼装匹配方法，主要包括以下几个步骤：
步骤(1)、分别对具有拼装关系的两个预制梁体的三维数字点云计算有向包围盒，基于两个预制梁体的三维数字点云的几何特征实现三维坐标校准；针对校准后的两个预制梁体的三维数字点云，在两个预制梁体的拼装界面分别作两个点云切片；基于所作两个点云切片共同包含的拼装界面，针对该拼装界面所包含的设计信息生成离散的设计点云；
其具体步骤如下：
步骤1.1、分别对具有拼装关系的两个预制梁体的三维数字点云计算有向包围盒，使三维坐标系X轴、Y轴、Z轴方向分别与构件梁宽、梁长、梁高方向平行，实现坐标校准；
步骤1.2、针对两个预制梁体的拼装界面特征，分别在坐标校准后的两个三维数字点云的拼装界面处作平行于XOZ坐标平面的点云切片，即切片点云P 1、切片点云Q 1；
其中切片厚度取两倍实测点云密度；表述式如下：
P 1＝{p 1,p 2,…,p m},Q 1＝{q 1,q 2,…,q n}
步骤1.3、基于切片点云P 1、切片点云Q 1共同包含的拼装界面的设计信息、设计图纸生成离散的设计点云D，其点云密度需大于实际扫测获取的三维数字点云密度，通常地，宜取实测点云密度的两倍；表述式如下：
D＝{d 1,d 2,…,d j}
步骤(2)、采用迭代最近点算法，将两个预制梁体的拼装界面点云切片分别与所生成的设计点云作配准；在设计点云坐标范围的基础上设置距离阈值，对两个拼装界面点云切片进行去噪；
步骤2.1、分别将切片点云P 1、切片点云Q 1、设计点云D的形心移动至坐标原点，即：
Figure PCTCN2022142697-appb-000007
P c为移动后的切片点云P 1,
Figure PCTCN2022142697-appb-000008
为切片点云P 1的坐标平均值；
Q c为移动后的切片点云Q 1,
Figure PCTCN2022142697-appb-000009
为切片点云Q 1的坐标平均值；
D c为移动后的设计点云D,
Figure PCTCN2022142697-appb-000010
为设计点云D的坐标平均值；
步骤2.2、在移动后的设计点云D c中分别找到与移动后的切片点云P c、移动后的切片点云Q c中各点最近的点，通过正交旋转矩阵与刚性平移矩阵，使对应点间距离的方差最小，通过下式：
Figure PCTCN2022142697-appb-000011
Figure PCTCN2022142697-appb-000012
m为移动后的切片点云P c的点数，n为移动后的切片点云Q c的点数，p i为移动后的切片点云P c中第i个点，q i为移动后的切片点云Q c中第i个点，d i为移动后的设计点云D c中第i个点；
计算得到的移动后的切片点云P c与移动后的设计点云D c配准时的正交旋转矩阵R p与刚性平移矩阵T p，移动后的切片点云Q c与移动后的设计点云D c配准时的正交旋转矩阵R q与刚性平移矩阵T q；
配准后得到切片点云P 2、切片点云Q 2表述式如下：
P 2＝R p·P c+T p
Q 2＝R q·Q c+T q
步骤2.3、基于设计点云D坐标，设置距离阈值，筛选有效点云，将点云P 2、Q 2中超出坐标范围的点视为无效点并去除，得到去噪后的切片点云P 3、去噪后的切片点云Q 3。
步骤(3)、基于设计点云坐标范围，对去噪后的两个点云切片进行分块；根据所需拟合的特征选取拟合函数与拟合算法，拟合提取两个待拼装构件拼装界面的边界特征、角点特征；具体步骤为：
步骤3.1、基于设计点云D c的坐标，对去噪后的切片点云P 3、去噪后的切片点云Q 3进行分块，分别提取边界特征、角点特征；
步骤3.2、针对边界特征，采取应用拟合函数或拟合算法直接拟合的方法；对于角点特征，采用先拟合边界特征，再通过边界特征相交计算交点的方法，当拟合得到的角点特征，无法在实测点云中找到对应点时，采取最近邻搜索法，选取最近点为角点特征；
其中拟合函数包括但不限于直线方程、抛物线方程等，拟合算法包括但不限于最小二乘法、随机抽样一致算法、霍夫变换等；
步骤(4)、基于两个待拼装构件的预拼装界面中拟合的边界特征、角点特征，首先采用普氏分析算法实现拼装界面粗略匹配，随后采用迭代最近点算法实现拼装界面精细匹配，将点云调整至最终拼装姿态，计算拼装界面匹配度误差并评价拼装结果。
步骤4.1、基于去噪后的切片点云P 3、去噪后的切片点云Q 3中提取到的角点特征的三维坐标信息，建立预拼装匹配点组C P、预拼装匹配点组C Q，其中，C P、C Q均为k*3矩阵，k为匹配点个数；
C p＝{C p1,C p2,…,C pk},C Q＝{C Q1,C Q2,…,C Qk}
步骤4.2、基于普氏分析算法，以预拼装匹配点组C P为基准，将预拼装匹配点组C Q与之对齐，通过下式：
C Q＝R c·C P+T c+E c
求得到粗略匹配下的正交旋转矩阵R c；粗略匹配下的刚性平移矩阵T c；粗略匹配下的误差矩阵E c；
将两匹配点组距离最小时，即粗略匹配下的误差矩阵E c最小时对应的姿态，确定为粗略匹配后姿态；
argmin||E c||
基于粗略匹配下的正交旋转矩阵R c、粗略匹配下的刚性平移矩阵T c，将去噪后的切片点云Q 3调整至粗略匹配后的切片点云Q 4表述式如下：
Q 4＝R c·Q 3+T c
实现粗略匹配；
步骤4.3、基于迭代最近点算法，在粗略匹配后的切片点云Q 4中找到与去噪后的切片点云P 3中各点最近的点，通过正交旋转矩阵与刚性平移矩阵，使对应点间距离的方差最小，通过下式：
argmin||R f·Q 4+T f-P 3|| 2
计算得到精细匹配下的正交旋转矩阵R f；精细匹配下的刚性平移矩阵T f；
基于精细匹配下的正交旋转矩阵R f、精细匹配下的刚性平移矩阵T f，将粗略匹配后的切片点云Q 4调整至最终拼装姿态点云Q final，表述式如下：
Q final＝R f·Q 4+T f
实现精细匹配；
为统一描述，将最终拼装姿态下的点云P final定义为：
P final＝P 3
步骤4.4、在拼装平面中，计算最终拼装姿态点云Q final与中各点距其在最终拼装姿态点云P final中最近点的间距f：
f＝||q fi-p fi||
p fi为最终拼装姿态点云P final中第i个点，q fi为最终拼装姿态点云Q final中第i个点，以此评估拼装结果。
实施例一：
如图6所示：案例计算主要基于MATLAB进行算法编程得出计算结果。
研究的仿真预制梁段为一对空间几何特征相同、具有拼装关系的箱梁(箱梁1、箱梁2)，梁长10m，梁宽10m，梁高2m，点云密度为1/cm 2，详细尺寸如 图6所示；为模拟基于设计-实测点云模型的预制梁体数字预拼装匹配方法，在箱梁1上预设三处环境噪声、四处空间几何缺陷，在箱梁2上预设三维偏移矩阵。
预设几何缺陷1：J点右移0.05m；预设几何缺陷2：D点上移0.05m；预设几何缺陷3：L点左移0.05m；预设几何缺陷4：EF边整体左移0.05m。
预设三维偏移矩阵：
Figure PCTCN2022142697-appb-000013
Figure PCTCN2022142697-appb-000014
1、根据步骤1.1，分别计算仿真箱梁1与箱梁2的有向包围盒，使三维坐标系X轴、Y轴、Z轴方向分别与构件梁宽、梁长、梁高方向平行；根据步骤1.2，在仿真箱梁1与箱梁2的拼装界面处分别作厚度为0.02m的点云切片(切片点云1、切片点云2)；根据步骤1.3，生成设计点云D；
2、根据步骤2.1，分别将切片点云1、切片点云2、设计点云D的形心移动至坐标原点；根据步骤2.2，以设计点云为基准，基于迭代最近点算法，将预设有环境噪声的切片点云1与设计点云配准；根据步骤2.3，设置距离阈值为0.02m过滤噪声，三处环境噪声均实现较好滤除；
3、根据步骤3.1，分别提取切片点云1与切片点云2的外边界，基于坐标范围，分别将切片点云1与切片点云2分块，使用RANSAC算法拟合边界，将两相邻边界的交点视为角点，分别提取角点A1、B1、C1、D1、E1、F1，A2、B2、C2、D2、E2、F2。
4、根据步骤4.1，基于所提取到的切片点云1角点、切片点云2角点，构成预拼装匹配点组1与预拼装匹配点组2；
根据步骤4.2，基于普氏分析算法，以预拼装匹配点组1为基准，将预拼装匹配点组2与之对齐，得到粗略匹配对应的旋转矩阵与平移矩阵为：
Figure PCTCN2022142697-appb-000015
Figure PCTCN2022142697-appb-000016
得到粗略匹配下的切片点云2。
根据步骤4.3，基于迭代最近点算法，在粗略匹配后的切片点云1中找到距切片点云2中各点最近的点，得到精细匹配对应的旋转矩阵与平移矩阵：
Figure PCTCN2022142697-appb-000017
与预设三维偏移矩阵一致；根据粗略匹配与精细匹配对应的旋转矩阵与平移矩阵，将切片点云2以将其调整至拼装姿态。
根据步骤4.4，计算切片点云2中各点距其在切片点云1中最近点的间距。计算得到拼装界面处，箱梁1：D点有向上0.049m偏移，J点有向右0.052m偏移，EF边有向左0.05m偏移，L点有向左0.047m偏移，与预设几何缺陷一致。
以上所述，仅为本发明较佳的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到的变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应该以权利要求的保护范围为准。

Claims (5)

  1. 基于设计-实测点云模型的预制梁体数字预拼装匹配方法，其特征在于：步骤如下：
    步骤(1)、分别对具有拼装关系的两个预制梁体的三维数字点云计算有向包围盒，基于两个预制梁体的三维数字点云的几何特征实现三维坐标校准；针对校准后的两个预制梁体的三维数字点云，在两个预制梁体的拼装界面分别作两个点云切片；基于所作两个点云切片共同包含的拼装界面，针对该拼装界面所包含的设计信息生成离散的设计点云；
    步骤(2)、采用迭代最近点算法，将步骤(1)中两个预制梁体的拼装界面点云切片分别与所生成的设计点云作配准；在设计点云坐标范围的基础上设置距离阈值，对两个拼装界面点云切片进行去噪；
    步骤(3)、基于步骤(2)中的设计点云坐标范围，对去噪后的两个点云切片进行分块；根据所需拟合的特征选取拟合函数与拟合算法，拟合提取两个待拼装构件拼装界面的边界特征、角点特征；
    步骤(4)、基于步骤(3)中两个待拼装构件的预拼装界面中拟合的边界特征、角点特征，首先采用普氏分析算法实现拼装界面粗略匹配，随后采用迭代最近点算法实现拼装界面精细匹配，将点云调整至最终拼装姿态，计算拼装界面匹配度误差并评价拼装结果。
  2. 根据权利要求1所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，其特征在于，步骤(1)具体步骤如下：
    步骤1.1、分别对具有拼装关系的两个预制梁体的三维数字点云计算有向包围盒，使三维坐标系X轴、Y轴、Z轴方向分别与构件梁宽、梁长、梁高方向平行，实现坐标校准；
    步骤1.2、针对两个预制梁体的拼装界面特征，分别在坐标校准后的两个三维数字点云的拼装界面处作平行于XOZ坐标平面的点云切片，即切片点云P 1、切片点云Q 1；
    其中切片厚度取两倍实测点云密度；表述式如下：
    P 1＝{p 1,p 2,…,p m},Q 1＝{q 1,q 2,…,q n}
    步骤1.3、基于切片点云P 1、切片点云Q 1共同包含的拼装界面的设计信息、 设计图纸生成离散的设计点云D，表述式如下：
    D＝{d 1,d 2,…,d j}。
  3. 根据权利要求2所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，其特征在于：步骤(2)中以设计点云D为基准，基于迭代最近点算法，分别将切片点云P 1、切片点云Q 1与设计点云D配准，其配准方法如下：
    步骤2.1、分别将切片点云P 1、切片点云Q 1、设计点云D的形心移动至坐标原点，即：
    Figure PCTCN2022142697-appb-100001
    P c为移动后的切片点云P 1,
    Figure PCTCN2022142697-appb-100002
    为切片点云P 1的坐标平均值；
    Q c为移动后的切片点云Q 1,
    Figure PCTCN2022142697-appb-100003
    为切片点云Q 1的坐标平均值；
    D c为移动后的设计点云D,
    Figure PCTCN2022142697-appb-100004
    为设计点云D的坐标平均值；
    步骤2.2、在移动后的设计点云D c中分别找到与移动后的切片点云P c、移动后的切片点云Q c中各点最近的点，通过正交旋转矩阵与刚性平移矩阵，使对应点间距离的方差最小，即：
    Figure PCTCN2022142697-appb-100005
    Figure PCTCN2022142697-appb-100006
    m为移动后的切片点云P c的点数，
    n为移动后的切片点云Q c的点数，
    p i为移动后的切片点云P c中第i个点，q i为移动后的切片点云Q c中第i个点，d i为移动后的设计点云D c中第i个点；
    根据上式计算得到的移动后的切片点云P c与移动后的设计点云D c配准时的正交旋转矩阵R p与刚性平移矩阵T p，
    根据上式计算得到的移动后的切片点云Q c与移动后的设计点云D c配准时的正交旋转矩阵R q与刚性平移矩阵T q；
    配准后得到切片点云P 2、切片点云Q 2表述式如下：
    P 2＝R p·P c+T p
    Q 2＝R q·Q c+T q
    步骤2.3、基于设计点云D坐标，设置距离阈值，筛选有效点云，将点云P 2、Q 2中超出坐标范围的点视为无效点并去除，得到去噪后的切片点云P 3、去噪后的切片点云Q 3。
  4. 根据权利要求3所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，其特征在于：步骤(3)具体步骤如下：
    步骤3.1、基于设计点云D c的坐标，对去噪后的切片点云P 3、去噪后的切片点云Q 3进行分块，分别提取边界特征、角点特征；
    步骤3.2、针对边界特征，采取应用拟合函数或拟合算法直接拟合的方法；对于角点特征，采用先拟合边界特征，再通过边界特征相交计算交点的方法，当拟合得到的角点特征，无法在实测点云中找到对应点时，采取最近邻搜索法，选取最近点为角点特征。
  5. 根据权利要求4所述的基于设计-实测点云模型的预制梁体数字预拼装匹配方法，其特征在于：步骤(4)中计算界面匹配度误差并评价拼装结果，具体步骤如下：
    步骤4.1、基于去噪后的切片点云P 3、去噪后的切片点云Q 3中提取到的角点特征的三维坐标信息，建立预拼装匹配点组C P、预拼装匹配点组C Q，其中，C P、C Q均为k*3矩阵，k为匹配点个数；
    C p＝{C p1,C p2,…,C pk},C Q＝{C Q1,C Q2,…,C Qk}
    步骤4.2、基于普氏分析算法，以预拼装匹配点组C P为基准，将预拼装匹配点组C Q与之对齐，表述式如下：
    C Q＝R c·C P+T c+E c
    根据上式计算得到粗略匹配下的正交旋转矩阵R c；
    根据上式计算得到粗略匹配下的刚性平移矩阵T c；
    根据上式计算得到粗略匹配下的误差矩阵E c；
    将两匹配点组距离最小时，即粗略匹配下的误差矩阵E c最小时对应的姿态，确定为粗略匹配后姿态；
    argmin||E c||
    基于粗略匹配下的正交旋转矩阵R c、粗略匹配下的刚性平移矩阵T c，将去噪后的切片点云Q 3调整至粗略匹配后的切片点云Q 4表述式如下：
    Q 4＝R c·Q 3+T c
    实现粗略匹配；
    步骤4.3、基于迭代最近点算法，在粗略匹配后的切片点云Q 4中找到与去噪后的切片点云P 3中各点最近的点，通过正交旋转矩阵与刚性平移矩阵，使对应点间距离的方差最小，即：
    argmin||R f·Q 4+T f-P 3|| 2
    根据上式计算得到精细匹配下的正交旋转矩阵R f；
    根据上式计算得到精细匹配下的刚性平移矩阵T f；
    基于精细匹配下的正交旋转矩阵R f、精细匹配下的刚性平移矩阵T f，将粗略匹配后的切片点云Q 4调整至最终拼装姿态点云Q final，表述式如下：
    Q final＝R f·Q 4+T f
    实现精细匹配；
    为统一描述，将最终拼装姿态下的点云P final定义为：
    P final＝P 3
    步骤4.4、在拼装平面中，计算最终拼装姿态点云Q final与中各点距其在最终拼装姿态点云P final中最近点的间距f：
    f＝||q fi-p fi||
    p fi为最终拼装姿态点云P final中第i个点，q fi为最终拼装姿态点云Q final中第i个点，以此评估拼装结果。
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