A 3D Point Cloud Preprocessing Method for Prefabricated Pavement Based on a Depth Camera

Abstract

The present invention relates to a three-dimensional point cloud preprocessing method for assembled pavements based on a depth camera, including: collecting three-dimensional information of the assembled pavement based on the depth camera; optimizing the camera pose, determining the transformation relationship between the camera coordinate system and the world coordinate system based on the camera pose, and screening key frames of the point cloud image; point cloud denoising: removing abnormal points and outliers at the boundary of the key frame point cloud image; point cloud background point removal: converting the RBG color model of the key frame point cloud image to the HSV color model, and removing background points based on the color distance; point cloud reduction: extracting the plate boundary of the key frame point cloud image, and performing point cloud reduction based on the plate boundary and the point cloud features inside the plate respectively; point cloud stitching and registration: converting the point cloud coordinates of the key frame to the world coordinate system, and performing precise registration of the point cloud based on the ICP algorithm to complete point cloud stitching. Compared with the prior art, the present invention has the advantages of complete retention of point cloud features and facilitation of subsequent point cloud processing, etc.

Description

Technical Field

[0001] The present invention relates to the technical field of road engineering, and in particular to a three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera. Background Art

[0002] The assembled pavement is an excellent rapid paving structure, featuring factory production, standardization, mechanization, etc., and is green, environmentally friendly, fast in construction speed, and high in engineering quality. It is an important paving form for new construction, renovation, and expansion. The assembled pavement can effectively alleviate the contradiction between the relatively long setting and hardening time of cement concrete and the relatively short constructible time in pavement repair.

[0003] The technology of assembled pavement has formed a mature technical system in countries such as the United States and Japan, and has been widely promoted and applied on a large scale. In recent years, certain progress has also been made in China, but the research results are mostly applied to small-scale pilot projects. Currently, scholars at home and abroad often conduct research on aspects such as the design method, structure and construction, and construction technology of assembled pavement, while relatively few studies have been carried out on the three-dimensional size evaluation and quality control methods of assembled pavement. The prerequisite for the three-dimensional size evaluation of assembled pavement is to perform three-dimensional information scanning on the assembled pavement and conduct corresponding point cloud preprocessing.

[0004] The depth camera can obtain the depth information of each pixel point while capturing a two-dimensional image. Its ranging principle is mainly based on technologies such as structured light, TOF, and binocular stereo vision. The scanning range and accuracy of the camera have been continuously improved with the iteration of products, and more and more scholars have attempted to apply the depth camera to the field of road engineering. For the three-dimensional information of the assembled pavement collected by the depth camera, the existing point cloud preprocessing methods are not comprehensive enough, and the processing results have low accuracy, which cannot fully adapt to the application scenario of the assembled pavement point cloud and will have a great impact on subsequent evaluation and quality control. Summary of the Invention

[0005] The purpose of the present invention is to provide a three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera, which can largely retain the plate features and boundary features in the point cloud information, improve the preprocessing effect, and provide a basis for subsequent three-dimensional size evaluation and quality control methods of assembled pavement.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera includes the following steps:

[0008] Collect three-dimensional information of the assembled pavement based on the depth camera to obtain the original point cloud image of the assembled pavement, where the original point cloud image includes structured point cloud and depth image;

[0009] Optimize the camera pose, determine the transformation relationship between the camera coordinate system and the world coordinate system based on the camera pose, and screen the key frames of the point cloud image;

[0010] Point cloud denoising: Remove the abnormal points and outliers at the boundary of the key frame point cloud image;

[0011] Point cloud background point removal: Convert the RGB color model of the key frame point cloud image to the HSV color model, and remove the background points based on the color distance;

[0012] Point cloud simplification: Extract the plate boundaries of the key frame point cloud image, and perform point cloud simplification based on the plate boundaries and the point cloud features inside the plates respectively;

[0013] Point cloud stitching and registration: Convert the point cloud coordinates of the key frame to the world coordinate system, and perform precise registration of the point cloud based on the ICP algorithm to complete point cloud stitching.

[0014] The optimization of the camera pose includes the optimization of the camera displacement based on the Kalman filter and the optimization of the camera rotation based on the Slerp mean filter.

[0015] The determination of the transformation relationship between the camera coordinate system and the world coordinate system based on the camera pose, and the screening of the key frames of the point cloud image include the following steps:

[0016] Record the camera coordinate system at the initial moment as the world coordinate system;

[0017] For any point P in space, its coordinate values in the world coordinate system and the camera coordinate system satisfy:

[0018]

[0019] where, p w =[p1,p2,p3] T is the coordinate of P in the world coordinate system, p k =[p1',p2',p3'] T is the coordinate of P in the camera coordinate system, R and t represent the camera pose, where the translation vector t = [t1,t2,t3] T represents the displacement of the origin of the camera coordinate system relative to the origin of the world coordinate system, and the rotation matrix R describes the rotation angle of the axes of the camera coordinate system in space relative to the world coordinate system;

[0020] Introduce homogeneous coordinates to combine the translation and rotation transformations into the same matrix:

[0021]

[0022] where, T is the transformation matrix, determined according to the camera pose, and the quaternion representation form of T is:

[0023]

[0024] Among them, the unit quaternion q = w + xi + yj + zk;

[0025] Screening key frames of the point cloud image: Taking the first frame and the last frame of the point cloud image as key frames; performing third-order difference operation on the optimized pose data to obtain the differential pose data; screening the data with displacement greater than the pre-configured displacement threshold in the differential pose data, and taking the corresponding frame as a key frame; screening the data with rotation angle greater than the pre-configured angle threshold in the differential pose data, and taking the corresponding frame as a key frame.

[0026] Removing the abnormal points at the boundary of the key frame point cloud image adopts a point cloud smoothing method based on joint bilateral filtering, which specifically includes the following steps:

[0027] Performing bilateral filtering smoothing on the original point cloud image, determining the spatial domain convolution kernel, and calculating the feature domain convolution kernel of the smoothed image based on the gray value of the depth image;

[0028] Multiplying the convolution kernel in the spatial domain by the convolution kernel in the image feature domain and performing normalization processing to obtain the convolution kernel of the joint bilateral filtering;

[0029] Applying the joint bilateral filtering convolution kernel to the structured point cloud, and taking the weighted sum of the neighborhood of the acting point as the updated value of the coordinates of this point.

[0030] Removing the outliers at the boundary of the key frame point cloud image adopts an outlier removal algorithm based on radius neighborhood, screening out the outliers far from the main body of the point cloud based on the k-neighborhood, and removing the outliers by radius filtering.

[0031] The method for converting the RBG color model of the key frame point cloud image into the HSV color model is as follows:

[0032] v = max(r, g, b)

[0033]

[0034]

[0035] Among them, r, g, b ∈ [0, 1], respectively representing the normalized red, green, and blue values; h, s, v respectively represent the converted HSV values, and h ∈ [0°, 360°], s, v ∈ [0, 1].

[0036] The specific method for removing background points based on color distance is as follows:

[0037] Filter the gray area in the point cloud image according to the HSV color model of the point cloud image, and store the filtering result using a binary image;

[0038] Calculate the color distances of each pixel in the point cloud image from the upper and lower limits of the HSV color threshold of the gray area in turn:

[0039] dis = ((v1 × s1 × cosh1 - v2 × s2 × cosh2) 2

[0040] +(v1 × s1 × sinh1 - v2 × s2 × sin h2) 2 +(v2 - v1) 2 ) 1 / 2

[0041] where dis is the color distance between (h1, s1, v1) and (h2, s2, v2);

[0042] Judge whether the color distance corresponding to each pixel is less than a pre-configured threshold. If so, set the pixel at the corresponding position in the binary image to black, otherwise keep it white to obtain the filtered binary image;

[0043] Perform morphological processing on the filtered binary image;

[0044] Obtain the point cloud image with background points removed according to the pixel index of the binary image.

[0045] The extraction of the plate boundary from the key frame point cloud image includes the following steps:

[0046] Scan the image row by row to determine the initial points of the plate boundary;

[0047] Based on the Moore neighborhood, track and mark the boundaries corresponding to each initial point to complete the search for multiple boundaries;

[0048] Remove the outer boundaries of the background area according to the boundary perimeter to obtain the plate boundary.

[0049] The point cloud reduction based on the plate boundary and the point cloud features inside the plate respectively includes:

[0050] Point cloud reduction inside the plate: Reduce the evenly distributed point cloud inside the plate by equidistant uniform sampling;

[0051] Point cloud reduction of the plate boundary: Resample the boundary using a pre-configured size grid. When the original boundary point passes through the resampled grid, mark the resampled grid as the simplified boundary point and store it using the 8-direction chain code. Based on the resampled boundary index, extract the reduced boundary point cloud;

[0052] Among them, the size of the resampled grid for the point cloud reduction at the plate boundary is smaller than the sampling interval for the point cloud reduction inside the plate.

[0053] The accurate registration of the point cloud based on the ICP algorithm includes the following steps:

[0054] Step 6-2-1): Input the source point cloud P and the target point cloud Q of the key frame to be registered, and use the grid method to find the point clouds P0 and Q0 within the overlapping area of the two.

[0055] Step 6-2-2): For each point p i ∈P0 in the point cloud P0, search for the matching point q i with the closest distance to p i ∈Q0 in the point cloud Q0;

[0056] Step 6-2-3): Use the following formula as the objective function to calculate the rotation matrix R and the translation vector t;

[0057]

[0058] where n is the number of point clouds in P0;

[0059] Step 6-2-4): Perform coordinate transformation on Q0 based on the rotation matrix R and the translation vector t, and denote the point cloud obtained in the k-th iteration as

[0060] Step 6-2-5): Calculate the average distance between the matching points in the point clouds P0 and :

[0061]

[0062] Step 6-2-6): If d is less than the pre-configured distance threshold or the maximum number of iterations has been reached, stop the iteration and complete the accurate registration of the point cloud; otherwise, update the point cloud Q0 and return to Step 6-2-2).

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] (1) The present invention realizes the preprocessing of the point cloud data captured by the depth camera through point cloud denoising, background point removal, point cloud reduction, and stitching registration. The processing result can greatly retain the feature information related to the prefabricated pavement plate and remove the invalid information, providing a good data basis for the subsequent three-dimensional size evaluation and quality control method of the prefabricated pavement.

[0065] (2) The point cloud smoothing method of the present invention adopts a combined bilateral filtering method, combines structured point cloud and depth image information for point cloud denoising, eliminates the noise points in the image, not only smooths the noise inside the point cloud, but also well preserves the boundary information of the plate, overcoming the defect that the traditional bilateral filtering algorithm cannot well remove the abnormal points at the point cloud boundary.

[0066] (3) The point cloud reduction method proposed by the present invention first uses the image to divide the plate boundary and the internal area, then reduces them respectively according to the requirements of the two types of point clouds, and further reduces the number of point clouds as much as possible while retaining the point cloud boundary, and the point cloud reduction effect is good.

[0067] (4) The present invention optimizes the camera pose, makes the point cloud coordinate transformation more accurate, and improves the accuracy of registration.

[0068] (5) The present invention effectively reduces the redundant point cloud and improves the stitching efficiency by selecting appropriate key frame point clouds for stitching registration.

[0069] (6) The present invention adopts an improved ICP algorithm for accurate point cloud registration, which can eliminate the search for irrelevant point clouds, improve the point cloud registration accuracy, and overcome the defects that the existing ICP algorithm consumes a lot of time in finding the nearest matching point in the global point cloud during the iteration process and is prone to falling into the local optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is the method flow chart of the present invention;

[0071] Figure 2 is the schematic diagram of background point removal of the point cloud of the present invention. Among them, (a) is the image obtained by the depth camera, (b) is the binary image processed based on color distance, (c) is the binary image after morphological processing, and (d) is the background point removal result;

[0072] Figure 3 is the point cloud boundary extraction result of the embodiment of the present invention;

[0073] Figure 4 is the point cloud reduction result of the embodiment of the present invention. Among them, (a) is the original point cloud, and (b) is the point cloud reduction result;

[0074] Figure 5 is the accurate point cloud registration result of the embodiment of the present invention;

[0075] Figure 6 is the point cloud stitching result of the embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0076] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and gives detailed implementation manners and specific operation processes, but the protection scope of the present invention is not limited to the following embodiments.

[0077] A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera includes the following steps:

[0078] Step 1) Collect three-dimensional information of the assembled pavement based on the depth camera to obtain the original point cloud image of the assembled pavement

[0079] In this embodiment, a ZED depth camera is used. This camera does not require an external power supply and can work after being connected to a computer through a USB interface. However, the large volume of the external laptop computer brings inconvenience to mobile operations. To further improve the mobility and convenience of three-dimensional data collection, in this embodiment, a Jetson Nano embedded development board is used to replace the laptop computer, and a lightweight three-dimensional scanning system for assembled pavement is built in combination with the depth camera. Its main features are as follows:

[0080] ① Small size: The size of the Jetson Nano is only 70×45mm, with excellent portability;

[0081] ② Low energy consumption: The power consumption of the device is only 5-10 watts, and it can be directly powered by a battery without an external power supply;

[0082] ③ Strong computing power: The Jetson Nano supports CUDA, and its computing performance meets the task requirements such as point cloud processing and three-dimensional reconstruction;

[0083] ④ High degree of modularity: It supports users to customize and install components to meet specific needs.

[0084] The applicable embedded development board can greatly reduce the volume of the scanning system and improve the convenience of operation. The programs developed therefrom also have better consistency and performance. The ZED SDK provides support for the Jetson Nano and can be directly connected through a USB interface. To make the system run normally, other hardware devices such as a cooling fan, Wi-Fi and Bluetooth modules, and a power supply module are installed, and the development board is encapsulated by an external metal shell. Its volume is much smaller than that of a laptop computer. When collecting data on-site, the display screen and keyboard can be removed, and the ZED camera can be remotely controlled by a mobile phone to further improve the mobility of the system.

[0085] In this embodiment, a parallel scanning method is adopted. The plane of the depth camera is approximately parallel to the plane of the prefabricated pavement. Before each scan, the position of the camera needs to be adjusted using a spirit level. At this time, the distance between each point and the camera can be regarded as the distance between the plate and the camera. Compared with the inclined scanning, the point cloud obtained by the parallel scanning is more evenly distributed and has higher point cloud quality. The point cloud of the background area included in the scanning range is less, and it can be separated from the point cloud of the plate main body by distance. During parallel scanning, the features between each frame of point cloud have good consistency, which can ensure the accuracy of point cloud registration.

[0086] Based on the disparity of binocular images, the ZED camera will calculate the corresponding depth data, including three types: scattered point cloud, structured point cloud and depth image.

[0087] The scattered point cloud is a collection of discrete points within the scanning range, and the points in the point cloud are disordered. In addition to the three-dimensional coordinates, the point cloud obtained by the ZED camera also includes the color information of the point. The camera supports various point cloud formats such as xyz, ply, obj, and pcd. Usually, the number of points corresponding to a single-frame image is 800,000 - 1,200,000.

[0088] Each point in the structured point cloud corresponds one-to-one with the pixel in the left-eye image. The coordinates of the point in the three-dimensional space can be read from the structured point cloud according to the pixel index of the image. Therefore, many algorithms in image processing can be extended to the structured point cloud. Due to the different positions of the two cameras, there are some areas in the left and right-eye images that cannot be matched, and the corresponding points of the above pixels in the structured point cloud have no measured values.

[0089] The depth image shows the depth of each pixel point in the left-eye image in the form of a grayscale image, and the value of each pixel is the normalized result of the depth value. The depth image has poor accuracy and cannot be used for three-dimensional reconstruction, but only as a reference.

[0090] For different stages of the design and evaluation of the prefabricated pavement, different settings are adopted to obtain the three-dimensional point cloud:

[0091] (1) Design stage

[0092] In the design stage of the prefabricated repair project, it is necessary to detect the plane position and elevation of the existing road surface to assist in the design of the repair plan. During scanning, the installed camera is placed above the repair area, the camera is parallel to the existing road surface, and scans along the boundary of the repair area plate.

[0093] (2) Prefabrication stage

[0094] During the prefabrication stage, it is necessary to complete the verification of the planar dimensions and thickness of the prefabricated plates. Since three-dimensional information of multiple surfaces of the plate cannot be obtained simultaneously in a single scan, it is necessary to scan the plate surface and the side of the plate separately. When scanning the plate surface, place the camera and the bracket on the plate and adjust the camera to be parallel to the plate surface. Continuously move the camera until the depth information of the entire area of the plate surface is collected. When scanning the side of the plate, place the camera at the stacking height of the plate and adjust the camera plane to be parallel to the side plane of the plate. Move the camera along the boundary of the plate to complete the collection of side data.

[0095] (3) Construction stage

[0096] During the construction stage, the objects for collecting three-dimensional information include the surrounding existing plates and the top surface of the base course. When scanning the existing plates, place the camera on the existing plates, adjust the camera plane to be horizontal, and continuously scan along the boundary of the plates. When collecting the elevation data of the top surface of the base course, place the camera on the surface of the base course and move the camera until the collection is completed.

[0097] (4) Acceptance stage

[0098] When collecting three-dimensional data at the joints during the acceptance stage, there is no need to continuously scan the joints. Several sampling areas can be selected along the joints. Only the point cloud data of the joint points within the sampling areas are collected and analyzed. This not only reduces the workload of data collection but also eliminates the steps of camera pose data processing and point cloud registration and stitching, improving the efficiency of joint evaluation.

[0099] Step 2) Optimize the camera pose, determine the transformation relationship between the camera coordinate system and the world coordinate system based on the camera pose, and screen the key frames of the point cloud images;

[0100] For any point P in space, its coordinate values in the world coordinate system and the camera coordinate system satisfy:

[0101]

[0102] where, p w =[p1,p2,p3] T is the coordinate of P in the world coordinate system, p k =[p1',p2',p3'] T is the coordinate of P in the camera coordinate system, R and t represent the camera pose, where the translation vector t = [t1,t2,t3] T represents the displacement of the origin of the camera coordinate system relative to the origin of the world coordinate system, and the rotation matrix R describes the rotation angle of the coordinate axes of the camera coordinate system in space relative to the world coordinate system;

[0103] Introduce homogeneous coordinates to combine the translation and rotation transformations into the same matrix:

[0104]

[0105] Among them, T is the transformation matrix.

[0106] Step 2-1) Camera pose optimization

[0107] Due to the limited accuracy of the estimated camera pose data, there will be certain noise in the data. Taking the displacement data as an example, due to the existence of noise, the displacement data has certain fluctuations and needs to be optimized. Since the data types of camera displacement and rotation are different, different optimization methods are adopted here.

[0108] ① Optimization of camera displacement based on Kalman filter

[0109] The translation vector t represents the camera translation very concisely, and only three components of the displacement of the camera relative to the initial moment at each moment need to be recorded. Assume that the displacement of the camera satisfies the Markov property, that is, the position at time k is only related to the position at time k-1 and has nothing to do with the previous moments. To eliminate the influence of noise in the observation process, Kalman filter can be used to perform optimal estimation on the displacement of the camera.

[0110] Kalman filter is a method that uses the linear system state equation and combines the system observation data to perform optimal estimation on the system state. At time k, the state of the camera is x k , including the position p k and the velocity v k , the acceleration is u k , the observed value of the camera position is z k . The time interval between each frame of the camera is Δt. Then according to the Markov hypothesis, we have:

[0111]

[0112] Simplify the above formula and consider the influence of noise to obtain the following formula:

[0113]

[0114] Among them, F k is the state transition matrix, u k is the state control quantity, B k is the control matrix, and W k-1 is the noise.

[0115] Use the covariance matrix P k to describe the uncertainty of the situation at time k.

[0116]

[0117] Combined with the properties of covariance, the covariance matrices of two adjacent moments satisfy:

[0118]

[0119] Among them, Q k is noise.

[0120] Corresponding to the state x k , the observation value obtained by the camera is z k . Considering the influence of noise, the relationship between the observation value and the state satisfies:

[0121] z k = Hx k + y k

[0122] Among them, H is the observation matrix, and y k is noise.

[0123] Define the covariance matrix of the observation noise as R, then the Kalman filter coefficient K is calculated according to the following formula k :

[0124]

[0125] Then the state of the filtered camera can be expressed by the observation result and the Kalman filter coefficient:

[0126]

[0127] Finally, update the covariance matrix for the next round of iteration:

[0128]

[0129] During the movement of the camera, the position p k has three components [p xk , p yk , p zk . Similarly, there is v k = [v xk , v yk , v zk . Since the camera is not equipped with an IMU module, only the relative displacement of the camera can be observed, and the speed of the camera movement cannot be obtained. The state transition matrix F k and the observation matrix H are respectively:

[0130]

[0131] Kalman filtering plays a very good role in smoothing the noise in the displacement.

[0132] ② Optimization of camera rotation based on Slerp mean filtering

[0133] Unlike the translation vector t, although the rotation matrix R can concisely represent the transformation relationship of the camera coordinate system, it is not the best way to represent rotation data. Using a matrix to represent rotation has the following disadvantages: First, rotation itself has only three degrees of freedom, but the rotation matrix requires nine components to be stored. The redundant data will occupy unnecessary storage space and affect the efficiency of pose data processing; Second, there are strict constraint relationships between the components of the matrix to ensure that the rotation matrix is an orthogonal matrix and its determinant is 1, which brings great difficulties to the processing of pose data.

[0134] Therefore, before optimizing the rotation data, it is necessary to first determine a suitable way to represent the camera rotation. In addition to the rotation matrix, the rotation of a rigid body in three-dimensional space can also be described by three-dimensional vectors such as rotation vectors and Euler angles. When using rotation vectors or Euler angles to describe the rotation of three degrees of freedom, the redundancy of the rotation matrix is overcome. However, any rotation description method in the form of a three-dimensional vector will inevitably have singularity problems, resulting in the loss of rotation degrees of freedom in special cases.

[0135] This embodiment selects quaternions in a four-dimensional vector space to represent rotation to overcome the above-mentioned singularity problems. The quaternion q has a real part and three imaginary parts:

[0136] q = w + xi + yj + zk = [w + x + y + z]

[0137] where w is the real part of the quaternion, and i, j, k are the three imaginary parts of the quaternion, satisfying:

[0138]

[0139] Usually, the real part and the imaginary part of the quaternion are separated and rewritten in the form of an ordered pair of a scalar and a vector, q = [s, v], Unit quaternions can represent rotations in three-dimensional space. For a rotation about the unit vector n = [n x , n y , n z T rotated by an angle θ, it can be represented by a unit quaternion as:

[0140]

[0141] From the above formula, the three imaginary parts i, j, k of the quaternion satisfy the cross product rule of the unit vectors of the Cartesian coordinate system. The imaginary quaternion lies on a three-dimensional hyperplane in four-dimensional space. Therefore, the three imaginary parts of the imaginary quaternion can be corresponding to the coordinate axes of the Cartesian coordinate system to represent points in three-dimensional space. For a vector in three-dimensional space, its quaternion form is p = [0, x, y, z] = [0, p]. If p is rotated by an angle θ about the axis n to become the point p', this rotation process can be described by a quaternion as

[0142] p' = qpq* = qpq -1

[0143] where q is the quaternion corresponding to the rotation, and q -1 is the inverse quaternion of q:

[0144]

[0145] The description form of quaternion for rotation is simple, and it occupies less space compared with the rotation matrix. When storing rotation data, only the imaginary part of the unit quaternion is needed. At the same time, the quaternion in four-dimensional space overcomes the singularity problem of three-dimensional vectors, which is convenient for subsequent optimization of pose data.

[0146] To remove the noise in the estimated quaternion, in this embodiment, mean filtering is used to smooth the obtained unit quaternion sequence. The mean calculation of quaternions can be realized by the Slerp interpolation method. Slerp interpolation, that is, spherical linear interpolation, is a linear interpolation operation of quaternions. When the interpolation coefficient is taken as 0.5, the interpolation result can be considered as the average value of the quaternions.

[0147] Let the unit quaternions corresponding to the camera rotation at two moments be q0 and q1 respectively. Assume that the vector v corresponding to the y-axis of the depth camera becomes v0 = q0vq0* and v1 = q1vq1* after being rotated by q0 and q1 respectively. The change amount corresponding to the rotation between q1 and q0 is still a rotation, and this rotation rotates the vector v0 around a fixed rotation axis n by an angle θ to v1. If the rotation angle is changed to θ / 2, at this time the vector v0 rotates to v t at this position, then the quaternion q t corresponding to this rotation can be regarded as the average value of the quaternions q0 and q1.

[0148] Using the Slerp formula of quaternions and taking the interpolation coefficient as 0.5, the average value of the quaternions q0 and q1 is:

[0149]

[0150] where θ is the angle between q0 and q1 in four-dimensional space, which can be calculated by the dot product of quaternions:

[0151] θ = arccos(q0·q1)

[0152] The above formula may have calculation errors due to the too small angle θ. Therefore, when θ is less than the threshold, this formula can be simplified to a linear expression:

[0153] q t = Slerp(q0,q1,0.5) = 0.5q0 + 0.5q1

[0154] Using the above quaternion mean calculation method, perform one-dimensional mean filtering on the original quaternion sequence.

[0155] Step 2-2) Based on the camera pose, determine the transformation relationship between the camera coordinate system and the world coordinate system, and screen the key frames of the point cloud image

[0156] Step 2-2-1) Denote the camera coordinate system at the initial moment as the world coordinate system;

[0157] Step 2-2-2) Determine the coordinate transformation matrix according to the optimized camera pose

[0158] Quaternions with a simple form have great advantages in data storage and optimization. However, for the coordinate transformation of a large amount of point cloud data, the multiplication operation of quaternions is rather cumbersome. Using the calculated rotation matrix can improve the efficiency of coordinate transformation.

[0159] The multiplication of quaternions can be represented by matrices. Left-multiplying and right-multiplying the quaternion q = w + xi + yj + zk are respectively equivalent to multiplying by the matrices:

[0160]

[0161] Therefore, the transformation relationship of the unit quaternion q = w + xi + yj + zk to the vector p is equivalent to:

[0162]

[0163] The above formula indicates the transformation relationship between the unit quaternion and the rotation matrix. If the pose data of the camera at a certain moment is the translation vector t = [t1, t2, t3] T , and the unit quaternion q = w + xi + yj + zk, then the rotation matrix corresponding to the camera pose at this moment is:

[0164]

[0165] It should be noted that when performing one-dimensional mean filtering on the original quaternion sequence, starting from the second frame, calculate the angle between the quaternion of each frame and the quaternions of its previous and next frames. If the angle is less than 5°, use the rotation matrix corresponding to the camera pose at the above moment to calculate the mean quaternion; otherwise, use the transformation relationship formula of the unit quaternion to the vector p to calculate the mean. Similarly, calculate the mean of the two newly obtained mean quaternions as the updated value of the rotation data for this frame.

[0166] Step 2-2-3) Screen the key frames of the point cloud image

[0167] Most of the scanned content of the frames of the ZED camera has a large overlapping area. If the point cloud data of each frame is stitched and registered, it will cause a large amount of point cloud overlap. Using the pose data to screen each frame and only stitching the point clouds of representative key frames can effectively reduce redundant point clouds and improve the stitching efficiency.

[0168] The selection of key frames has an important impact on the accuracy and efficiency of the 3D reconstruction of the assembled pavement. When the key frames are selected densely, a large amount of redundant point clouds will still be retained, and the algorithm efficiency is too low; when the number of selected key frames is small, the overlapping area between the point clouds of each frame is too small, which may cause some areas of the plate to have no point cloud coverage, affecting the accuracy of modeling.

[0169] The principle for screening key frames in the present invention is: on the basis of uniform sampling, ensure that there is at least a 25% overlapping area (about 20 - 25 cm) between two consecutive key frames, and retain the frames with larger rotation angles; the specific screening method is as follows:

[0170] Take the first frame and the last frame of the point cloud image as key frames; perform third-order difference operation on the optimized pose data to obtain the differenced pose data; screen the data with a displacement greater than 20 cm in the differenced pose data, and take the corresponding frames as key frames; screen the data with a rotation angle greater than 5° in the differenced pose data, and take the corresponding frames as key frames.

[0171] Step 3) Point cloud denoising: Remove the abnormal points and outliers at the boundaries of the key frame point cloud images

[0172] Step 3-1) Use the point cloud smoothing method based on joint bilateral filtering to remove the abnormal points at the boundaries of the key frame point cloud images

[0173] The depth information obtained based on the image disparity will have abnormal value points due to the noise of the image itself, resulting in the distortion of the point cloud boundary information. Bilateral filtering cannot well remove the abnormal points at the boundaries of the point cloud. The present invention uses joint bilateral filtering for processing.

[0174] The weight coefficient of the feature domain of the joint bilateral filtering does not come from the structured point cloud, but is obtained from the gray value of the camera image. The construction method of its spatial domain weight coefficient is the same as that of bilateral filtering, and the difference lies in the weight coefficient of the feature domain. The Gaussian function of the feature domain of the joint bilateral filtering is:

[0175]

[0176] Among them, J(x i ,y i ) and J(x c ,y c ) represent the gray values of the corresponding points in the original image.

[0177] The main steps for point cloud denoising using bilateral joint filtering are as follows:

[0178] Step 3-1-1) Perform bilateral filtering smoothing on the original point cloud image, determine the spatial domain convolution kernel, and calculate the feature domain convolution kernel of the smoothed image based on the gray values of the depth image;

[0179] Step 3-1-2) Multiply the convolution kernel in the spatial domain by the convolution kernel in the image feature domain and perform normalization processing to obtain the convolution kernel for joint bilateral filtering;

[0180] Step 3-1-3) Apply the joint bilateral filtering convolution kernel to the structured point cloud, and use the weighted sum of the neighborhood of the acting point as the updated value of the coordinates of this point.

[0181] Bilateral filtering of the original image eliminates the noise points in the image, making the image edges more prominent. Combining the filtered image with the point cloud for joint bilateral filtering not only smooths the noise inside the point cloud, but also better preserves the boundary information in the feature domain of the camera image.

[0182] Step 3-2) Use an outlier removal algorithm based on the radius neighborhood to remove outliers at the boundary of the key frame point cloud image: Screen out the outliers that are far from the main body of the point cloud based on the k-neighborhood, and use radius filtering to remove the outliers.

[0183] Outliers refer to abnormal point clouds that deviate from the true measured values on the surface of the plate. Using bilateral filtering can remove the outliers caused by shot noise to a certain extent, but the denoising process is mainly based on the position relationship of pixels and does not consider the spatial topological relationship of the point cloud, so it cannot remove the outliers with large offsets. Outliers are usually far from the main body of the point cloud and mostly exist in isolation, and their neighborhood features can be used to screen them out.

[0184] The k-nearest neighbor (k-nearest neighbor) constructs the neighborhood of a point by finding the k points closest to the target point, which is the most commonly used type of point cloud neighborhood. The k-dimension tree (kd-tree) is a data structure for quickly retrieving points in a k-dimensional space and is also an effective method for quickly constructing the k-neighborhood of a point cloud.

[0185] The kd-tree is a special case of a space binary tree. The kd-tree for point cloud data represents a partitioning of the three-dimensional point cloud space. The partitioning of the space by the kd-tree is achieved through several hyperplanes perpendicular to the coordinate axes. Each node on the tree corresponds to a subspace, and its construction method is as follows:

[0186] Step 3-2-1) Create the root node, corresponding to the space composed of all point clouds;

[0187] Step 3-2-2) Select the axis with the largest variance of point cloud distribution. Use the median of all point cloud coordinate values as the splitting point, set a hyperplane perpendicular to this axis, and divide the root node region into two subspaces;

[0188] Step 3-2-3) Generate the left and right child nodes of the root node, corresponding to the subspaces where the coordinate values are less than and greater than the splitting point respectively;

[0189] Step 3-2-4) Repeat the splitting operations in steps 3-2-2) to 3-2-3) within each subspace. Stop splitting when there are no instance points in the subspace, and the kd-tree construction is completed.

[0190] The kd-tree can narrow down the search range of the point cloud to the subspace, thus avoiding the search for most data points and improving the speed of neighborhood retrieval. Taking the nearest neighbor as an example, the method for retrieving the nearest neighbor of a certain point is as follows:

[0191] Step 3-2-5) Starting from the root node, visit each layer of nodes of the kd-tree step by step, and use the leaf node containing the target point as the current nearest point;

[0192] Step 3-2-6) Recursively search for the parent node. If there is a point closer to the target point in the space corresponding to the parent node, update the current nearest point;

[0193] Step 3-2-7) Search for whether there is a closer point in the other branch corresponding to the node. The specific method is to determine whether this space intersects with the sphere centered at the target point with the current nearest distance as the radius: if it does not intersect, continue to recursively search for the parent node; if it intersects, move to the space where this node is located for further search;

[0194] Step 3-2-8) Repeat steps 3-2-6) to 3-2-7) until the root node is searched and the retrieval ends.

[0195] The present invention uses radius filtering to remove outliers, and the search for the radius neighborhood of the point cloud is realized by the kd-tree constructed in the previous section. Since the point cloud of the plate body is densely and evenly distributed, the number of adjacent points of each point cloud within the radius neighborhood of size d is relatively large. For the outlier points in red in the figure, they are far from the plate body, and there are no or only a few points (usually also outlier points) within the radius neighborhood. Therefore, the number of adjacent points within the radius neighborhood of the point cloud can be used as the judgment basis for outlier points. When using radius filtering, appropriate radius thresholds and screening thresholds should be selected in combination with the acquisition density and distribution of the point cloud.

[0196] Using a radius threshold of 10 cm and a screening threshold of 10 for radius filtering to process the point cloud of the plate, the radius filtering effectively removes the outlier points far from the plate.

[0197] Step 4) Removal of point cloud background points

[0198] In the scanning range of the ZED camera, in addition to the prefabricated paving slab itself, a large amount of background information is also included. Accurately screening out the target slab from the original point cloud and eliminating the influence of the background vertex cloud can greatly improve the efficiency and accuracy of subsequent point cloud processing. The main color of the prefabricated paving slab is relatively uniform gray, and there is a large color difference between the background and it. The slab area can be screened out using the color of the image, and then the slab point cloud can be extracted from the structured point cloud.

[0199] Step 4-1): Convert the RBG color model of the key frame point cloud image to the HSV color model;

[0200] The ZED camera image uses the most common RGB color model to represent colors. The RGB color model is also known as the additive primary color light model. By superimposing red, green, and blue in different proportions, different colors are composed.

[0201] As an additive model, the values in the RGB color model are not intuitive, and the distribution of colors in space is also uneven. The RGB values of similar colors may vary greatly, and it is difficult to judge the similarity of colors only based on RGB values. Taking gray as an example, it is mainly distributed on the main diagonal of the cube, and it is difficult to select appropriate RGB thresholds to separate it from the image.

[0202] The HSV color model is a non-linear transformation of the RGB color model. The HSV color space is usually represented by a cone. In the cone, the hue is the angle around the central axis of the cone, the saturation is the distance from the cross-section of the cone to the center of the circle, and the value is the distance from the center of the cross-section of the cone to the vertex of the cone.

[0203] Compared with the RGB model, the HSV model is more in line with the way the human eye perceives colors. Similar HSV values represent similar colors, and most image processing algorithms based on colors are also carried out in the HSV color space. Therefore, before eliminating the background area using color differences, the camera image needs to be converted to the HSV color model first.

[0204] Convert the RGB color model to the HSV color model according to the following formula:

[0205] v = max(r, g, b)

[0206]

[0207]

[0208] Among them, r, g, b ∈ [0, 1], representing the red, green, and blue values after color normalization respectively; h, s, v represent the converted HSV values, where h ∈ [0°, 360°], and s, v ∈ [0, 1].

[0209] Step 4-2) Eliminate background points based on color distance;

[0210] In the HSV color space, color distance can be used to represent the similarity of colors. According to the color distance, pixels with a high degree of similarity can be screened, thereby eliminating background points unrelated to the plate.

[0211] Step 4-2-1) Screen the gray area in the point cloud image according to the HSV color model of the point cloud image, and store the screening result using a binary image;

[0212] Step 4-2-2) Calculate the color distances between the HSV colors of each pixel in the point cloud image and the upper and lower limits of the HSV color threshold of the gray area in turn:

[0213] dis = ((v1 × s1 × cosh1 - v2 × s2 × cosh2) 2

[0214] + (v1 × s1 × sinh1 - v2 × s2 × sinh2) 2 + (v2 - v1) 2 ) 1 / 2

[0215] Among them, dis is the color distance between (h1, s1, v1) and (h2, s2, v2);

[0216] Step 4-2-3) Determine whether the color distance corresponding to each pixel is less than the pre-configured threshold. If so, set the pixel at the corresponding position in the binary image to black, otherwise keep it white to obtain the screened binary image;

[0217] Step 4-2-4) Perform morphological processing on the screened binary image;

[0218] Step 4-2-5) Obtain the point cloud image with background points eliminated according to the pixel index of the binary image.

[0219] The original image obtained by the depth camera is as shown in Figure 2 (a), the binary image processed based on color distance is as shown in Figure 2 (b), the binary image after morphological processing is as shown in Figure 2 (c), and the background point elimination result is as shown in Figure 2 (d). It can be seen that the method described in the present invention better eliminates the background area, and the complete plate is retained in the result.

[0220] Step 5) Point cloud reduction:

[0221] Step 5-1) Extract the plate boundaries from the key-frame point cloud images;

[0222] Step 5-1-1) Scan the image line by line to determine the initial points of the plate boundaries;

[0223] Step 5-1-2) Track and mark the boundaries corresponding to each initial point based on the Moore neighborhood to complete the search for multiple boundaries;

[0224] Step 5-1-3) Eliminate the outer boundaries of the background area according to the boundary perimeter to obtain the plate boundaries.

[0225] This part of the content refers to the literature Suzuki S, Be K. Topological structural analysis of digitized binary images by border following[J]. Computer Vision Graphics & Image Processing, 1985, 30(1): 32-46., which will not be elaborated in this embodiment. In this embodiment, the boundary extraction results are as Figure 3 shown.

[0226] Step 5-2) Perform point cloud reduction based on the plate boundaries and the point cloud features inside the plates respectively;

[0227] Reduction of the point cloud inside the plate: Reduce the evenly distributed point cloud inside the plate by equidistant uniform sampling; Since the point cloud inside the plate is relatively evenly distributed, the sampling interval can be appropriately increased. In this embodiment, the sampling interval is set to 50 pixels;

[0228] Reduction of the point cloud on the plate boundary: Resample the boundary using a pre-configured size grid. When the original boundary point passes through the resampled grid, mark the resampled grid as the simplified boundary point and store it using the 8-direction chain code. Extract the reduced boundary point cloud based on the resampled boundary index; In this embodiment, the size of the grid for resampling the boundary is 25 pixels.

[0229] The point cloud reduction results of this embodiment are as Figure 4 shown.

[0230] Step 6) Point cloud stitching and registration

[0231] Step 6-1) Convert the point cloud coordinates of the key frame to the world coordinate system through the coordinate conversion method described in step 2);

[0232] Step 6-2) Perform precise registration of the point cloud based on the ICP algorithm;

[0233] The traditional ICP algorithm is not efficient. A large amount of time is consumed in finding the nearest matching points in the global point cloud during the iterative process, and it is easy to fall into a local optimal solution. Usually, only part of the area overlaps between two point clouds. It is obviously inefficient to find matching points in the global point cloud.

[0234] Combined with the pose data of the depth camera, the present invention optimizes the traditional ICP algorithm. The scanning range of each frame of the depth camera is roughly the same, and the position of the overlapping area can be roughly calculated according to the optimized camera pose data. Only the point cloud in the overlapping area is registered using the ICP algorithm, which can save the search for irrelevant point clouds and improve the accuracy of point cloud registration.

[0235] The overlapping area of the two point clouds can be obtained by the grid method. After completing the coordinate transformation of the two frames of point clouds, the point cloud space composed of them is evenly divided into grids. If a grid contains both the target point cloud and the source point cloud at the same time, then this grid is an overlapping grid. The smallest circumscribed cube of all overlapping grids is used as the final overlapping area. Then the input point cloud of the improved ICP algorithm is the intersection of the target point cloud, the source point cloud and the overlapping area.

[0236] The steps of the improved ICP algorithm are as follows:

[0237] Step 6-2-1) Input the source point cloud P and the target point cloud Q of the key frame to be registered, and use the grid method to find the point clouds P0 and Q0 in their overlapping area;

[0238] Step 6-2-2) For each point p i ∈P0 in the point cloud P0, search for the matching point q i with the closest distance to p i ∈Q0 in the point cloud Q0;

[0239] Step 6-2-3) Use the following formula as the objective function to calculate the rotation matrix R and the translation vector t;

[0240]

[0241] where n is the number of point clouds in P0;

[0242] Step 6-2-4) Perform coordinate transformation on Q0 based on the rotation matrix R and the translation vector t, and denote the point cloud obtained in the k-th iteration as

[0243] Step 6-2-5) Calculate the average distance between the matching points in the point cloud P0 and :

[0244]

[0245] Step 6-2-6) If d is less than the pre-configured distance threshold or the maximum number of iterations is reached, stop the iteration and complete the precise registration of the point cloud; otherwise, update the point cloud Q0 and return to Step 6-2-2). In this embodiment, the distance threshold is set to 1 mm and the maximum number of iterations is set to 50 times.

[0246] The precise registration result of the point cloud in this embodiment is as Figure 5 shown.

[0247] Step 6-3) Complete the point cloud stitching to obtain the complete point cloud data of the assembled pavement surface, as Figure 6 shown.

[0248] The above has described in detail the preferred specific embodiments of the present invention. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera, characterized in that, It includes the following steps: Based on a depth camera, three-dimensional information of the prefabricated pavement is collected to obtain the original point cloud image of the prefabricated pavement, and the original point cloud image includes structured point clouds and depth images; Optimize the camera pose, determine the transformation relationship between the camera coordinate system and the world coordinate system based on the camera pose, and screen the key frames of the point cloud image; Point cloud denoising: Remove the abnormal points and outliers at the boundary of the key frame point cloud image; Point cloud background point removal: Convert the RBG color model of the key frame point cloud image to the HSV color model, and remove background points based on the color distance; Point cloud simplification: Extract the plate boundary of the key frame point cloud image, and perform point cloud simplification based on the plate boundary and the point cloud features inside the plate respectively; Point cloud stitching and registration: Convert the point cloud coordinates of the key frames to the world coordinate system, and accurately register the point clouds based on the ICP algorithm to complete point cloud stitching.

2. The three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera according to claim 1, characterized in that, The optimization of the camera pose includes the optimization of the camera displacement based on the Kalman filter and the optimization of the camera rotation based on the Slerp mean filter.

3. A three-dimensional point cloud preprocessing method for assembled pavements based on a depth camera according to claim 1, characterized in that, The step of determining the transformation relationship between the camera coordinate system and the world coordinate system based on the camera pose and screening the key frames of the point cloud image includes the following steps: Record the camera coordinate system at the initial moment as the world coordinate system; For any point P in space, its coordinate values in the world coordinate system and the camera coordinate system satisfy: where p w = [p1, p2, p3] T is the coordinate of P in the world coordinate system, and p k = [p1', p2', p3'] T is the coordinate of P in the camera coordinate system. R and t represent the camera pose. Among them, the translation vector t = [t1, t2, t3] T represents the displacement of the origin of the camera coordinate system relative to the origin of the world coordinate system, and the rotation matrix R describes the rotation angles of the coordinate axes of the camera coordinate system in space relative to the world coordinate system; Introduce homogeneous coordinates to combine translation and rotation transformations into the same matrix: Among them, T is the transformation matrix, determined according to the camera pose, and the quaternion representation of T is: Among them, the unit quaternion q = w + xi + yj + zk; Screen the key frames of the point cloud image: Use the first frame and the last frame of the point cloud image as key frames; Perform third-order difference operations on the optimized pose data to obtain the differenced pose data; Screen the data with a displacement greater than the pre-configured displacement threshold in the differenced pose data, and use the corresponding frames as key frames; Screen the data with a rotation angle greater than the pre-configured angle threshold in the differenced pose data, and use the corresponding frames as key frames.

4. A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera according to claim 1, characterized in that, The method of removing abnormal points at the boundary of the key frame point cloud image uses a point cloud smoothing method based on joint bilateral filtering, which specifically includes the following steps: Perform bilateral filtering smoothing on the original point cloud image, determine the spatial domain convolution kernel, and calculate the feature domain convolution kernel of the smoothed image based on the gray value of the depth image; Multiply the convolution kernel in the spatial domain by the convolution kernel in the image feature domain and perform normalization processing as the convolution kernel of the joint bilateral filtering; Apply the joint bilateral filtering convolution kernel to the structured point cloud, and use the weighted sum of the neighborhood of the acting point as the updated value of the coordinate of this point.

5. A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera according to claim 1, characterized in that, The method of removing outliers at the boundary of the key frame point cloud image uses an outlier removal algorithm based on the radius neighborhood, screens out the outliers far from the main body of the point cloud based on the k-neighborhood, and uses radius filtering to remove the outliers.

6. A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera according to claim 1, characterized in that, The method of converting the RBG color model of the key frame point cloud image to the HSV color model is: v = max(r, g, b) Among them, r, g, b ∈ [0, 1], respectively representing the normalized red, green, and blue values of the color; h, s, v respectively represent the converted HSV values, and h ∈ [0°, 360°], s, v ∈ [0, 1].

7. A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera according to claim 6, characterized in that The background point elimination based on color distance is specifically as follows: Filter the gray area in the image according to the HSV color model of the point cloud image, and store the filtering result using a binary image; Calculate the color distances between the HSV colors of each pixel in the point cloud image and the upper and lower limits of the HSV color threshold of the gray area in turn: dis = ((v1 × s1 × cos h1 - v2 × s2 × cos h2) 2 + (v1 × s1 × sin h1 - v2 × s2 × sin h2) 2 + (v2 - v1) 2 ) 1 / 2 where dis is the color distance between (h1, s1, v1) and (h2, s2, v2); Judge whether the color distance corresponding to each pixel is less than a pre-configured threshold. If so, set the pixel at the corresponding position in the binary image to black, otherwise keep it white to obtain the filtered binary image; Perform morphological processing on the filtered binary image; Obtain the point cloud image after background point elimination according to the pixel index of the binary image.

8. A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera according to claim 1, characterized in that, The extraction of the plate boundary from the key frame point cloud image includes the following steps: Scan the image line by line to determine the initial points of the plate boundary; Track and mark the boundaries corresponding to each initial point based on the Moore neighborhood to complete the search for multiple boundaries; Eliminate the outer boundaries of the background area according to the boundary perimeter to obtain the plate boundary.

9. A three-dimensional point cloud preprocessing method for assembled pavement based on a depth camera according to claim 1, characterized in that The point cloud reduction based on the point cloud features inside the plate boundary and inside the plate respectively includes: Point cloud reduction inside the plate: Reduce the uniformly distributed point cloud inside the plate by equidistant uniform sampling; Point cloud reduction of the plate boundary: Resample the boundary using a pre-configured size grid. When the original boundary point passes through the resampled grid, mark the resampled grid as the simplified boundary point and store it using the 8-direction chain code. Based on the resampled boundary index, extract the reduced boundary point cloud; Among them, the size of the resampled grid for point cloud reduction of the plate boundary is smaller than the sampling interval for point cloud reduction inside the plate.

10. A three-dimensional point cloud preprocessing method for prefabricated pavement based on a depth camera according to claim 1, characterized in that, The accurate registration of the point cloud based on the ICP algorithm includes the following steps: Step 6-2-1): Input the source point cloud P and the target point cloud Q of the key frame to be registered, and use the grid method to find the point clouds P0 and Q0 in the overlapping area of the two; Step 6-2-2) For each point p i ∈ P0 in the point cloud P0, search for the matching point q i in the point cloud Q0 that is closest to p i ∈ Q0; Step 6-2-3): Use the following formula as the objective function to calculate the rotation matrix R and the translation vector t; where n is the number of point clouds in P0; Step 6-2-4) Perform a coordinate transformation on Q0 based on the rotation matrix R and the translation vector t. Denote the point cloud obtained in the k-th iteration as Step 6-2-5) Calculate the average distance between the point cloud P0 and the matching points in Step 6-2-6): If d is less than the pre-configured distance threshold or the maximum number of iterations has been reached, stop the iteration and complete the accurate registration of the point cloud; otherwise, update the point cloud Q0 and return to Step 6-2-2).

Images