A Review of Point Cloud Registration Algorithms for Laser Scanners: Applications in Large-Scale Aircraft Measurement

Abstract

As 3D acquisition equipment picks up steam, point cloud registration has been applied in ever-increasing fields. This paper provides an exhaustive survey of the field of point cloud registration for laser scanners and examines its application in large-scale aircraft measurement. We first researched the existing representative point cloud registration algorithms, such as hierarchical optimization, stochastic and probability distribution, and feature-based methods, for analysis. These methods encompass as many point cloud registration algorithms as possible; typical algorithms of each method are suggested respectively, and their strengths and weaknesses are compared. Lastly, the application of point cloud registration algorithms in large-scale aircraft measurement is introduced. We discovered that despite the significant progress of point cloud registration combining deep learning and traditional methods, it is still difficult to meet realistic needs, and the main challenges are in the direction of robustness and generalization. Furthermore, it is impossible to extract accurate and comparable features for alignment from large-scale aircraft surfaces due to their relative smoothness, lack of obvious features, and abundance of point clouds. It is necessary to develop lightweight and effective dedicated algorithms for particular application scenarios. As a result, with the development of point cloud registration technology and the deepening into the aerospace field, the particularity of the aircraft shape and structure poses higher challenges to point cloud registration technology.

1. Introduction

The typical three-dimensional data collecting approach, which is inefficient and time-consuming in complicated settings, obtains three-dimensional coordinates primarily through a single station, making detailed descriptions of complex structural planes and entities impossible. Additionally, there are certain issues with data collecting and post-processing hardware, such as laborious operation, high inaccuracy, and instability. In comparison with the commonly used single-point measurement approach, laser scanners may employ a significant number of three-dimensional coordinate data to swiftly measure and describe the object’s surface, acquiring the target object’s three-dimensional coordinate data set. Point clouds are another name for three-dimensional coordinate data. TLS technology has the advantages of fast speed, multiple data sampling rate, high data acquisition accuracy, low external impact, non-contact measurement, high degree of digitization, and the ability to be utilized in combination with GPS (global positioning system) and high-definition digital cameras. It can capture dangerous targets and environmental data more effectively, as well as gain more objective geographical information, resulting in more comprehensive information data collection. Once the point cloud data have been spliced, it may be possible to reconstruct a three-dimensional model for the next stage of analysis and investigation. Active acquisition equipment represented by laser scanning is maturing in terms of simplicity of operation, adaptability, intelligence, and efficiency. It can rapidly and accurately reconstruct the three-dimensional entity of the measured item by accurately capturing the spatial coordinates, color texture, reflection intensity, and other information of dense spots. Engineering measurements include forest structure assessments [1,2,3,4,5,6,7,8,9,10], landslide surveillance [11,12,13,14,15,16], and 3D model reconstruction [17,18,19,20,21,22,23,24,25], which play a critical role in scientific and engineering research. However, due to the effect of measurement environment, instruments and equipment, etc., the acquired point cloud in each frame only comprises a portion of the point cloud information about the measured object when carrying out the actual measurement. Therefore, to obtain the whole point cloud of the measured object, it is often essential to carry out multi-site and multi-angle measurements of the object and register the point cloud recorded from multiple angles to the same coordinate system.

This paper aims to provide a comprehensive survey of the field of point cloud registration for laser scanners and discuss its application in large-scale aircraft measurement. At present, there have been many surveys about point cloud registration. Pomerleau et al. [26] provided an overview of ICP and its improved algorithm. Díez et al. [27] concentrated on non-learning rough point cloud registration algorithms. Cheng et al. [28] classified point cloud registration techniques as fine or rough, although neither of them involved learning-based methods. Similarly, Dong et al. [29] categorized point cloud registration methods into fine and rough registration methods, with some rough methods based on learning involved, although space was restricted. Huang et al. [30] conducted a comprehensive survey of the point cloud registration algorithm and summarized the relationship between optimization-based and deep learning methods, plus the application across various domains about benchmark data sets in point cloud registration, to provide further research insight.

The remainder of this review is organized as follows. We subdivide the existing point cloud registration methods into three categories in Section 2, Section 3 and Section 4, respectively: hierarchical optimization, stochastic and probability distribution, and feature-based methods for analysis. Section 2 introduces ICP and its variants along with graph matching-based algorithms. Section 3 introduces RANSAC and its variants, NDT and its variants, and GMM -based algorithms. Then, the strengths and weaknesses of typical algorithms in Section 2 and Section 3 are compared separately. Section 4 presents feature extraction and feature matching methods. Section 5 details the application of point-cloud registration algorithms on large aircraft measurements. Finally, Section 6 presents the findings of this study, discusses the existing challenges of point cloud registration, and gives the prospects for future research directions.

2. Registration Algorithms Based on Hierarchical Optimization

The critical idea of hierarchical optimization-based algorithms is to develop a sophisticated optimization strategy for achieving the optimal solution to a nonlinear problem. Based on the optimization strategy, this section presents a relatively comprehensive overview of two types of optimization methods: ICP-based variations and graph-based methods. Milestone algorithms are listed in Figure 1.

2.1. Iterative Closest Point (ICP)-Based

The point-to-point iterative closest point algorithm is the most classical approach for registering point clouds, which has historically been a significant research topic in the field of computer vision. The P2P-ICP [31], which leverages the transformation connection discovered in two sets of data from distinct coordinate systems to match data, is usually referred to as the ICP algorithm. The basic principle is presented in Figure 2, that is, solving the spatial transformation between the source point cloud P and the target point cloud Q in the overlapping region of two pieces of point clouds, to minimize the distance between them. Suppose E (R, t) is the error between Q and P in the rotation and translation; then the problem of solving the optimal transformation matrix can be transformed into the optimal solution satisfying min E (R, t). It can be expressed by the following formula:

$$E(R,t)={\displaystyle \sum _{i=1}^n{\Vert Q_i-(P_i\times R+t)\Vert }^2}$$

(1)

where R is rotation, t is translation, and the source point cloud P_i corresponds to the target point cloud Q_i.

The P2P-ICP algorithm is simple, intuitive, and easy to implement. However, its running speed and the convergence of the global optimum depend largely on the given initial transformation estimation and the establishment of the corresponding relationship throughout the iteration. As a result, establishing the correct corresponding point set during iteration to avoid falling into the local extreme value becomes the key to various ICP improvement algorithms. Blais and Levine [32] determined the corresponding point set by the projection of p in the source point cloud P via the viewpoint direction of the target point cloud q on the target point cloud Q. This algorithm eliminates the phase of searching for corresponding points, which considerably shortens the calculation time, but it does not achieve high registration accuracy. The iterative closest compatible point (ICCP) [33] is calculated by comparing the curvature of points on the point cloud surface and angle between point normal vectors and other related features. Additionally, it seeks corresponding points between point clouds based on these features, considerably reducing the ICP algorithm’s spatial search time. Rusinkiewicz and Levoy [34] replace the calculated point-to-point distance with the point-to-surface distance, which can reduce the number of iterations and makes it difficult to fall into the local extremum. To verify the correctness of point-to-point correspondence, Sharp et al. [35] introduced the ICP-IF algorithm to linearly weight numerous Euclidean invariant features, such as curvature and spherical hue. This method successfully improved the local optimum problem and decreased the initial value requirements of the method, although the noise was not eradicated. Fitzgibbon [36] took advantage of the Levenberg–Marquardt algorithm to estimate the transformation by adding a damping factor to the original LK algorithm.

On the basis of enhancing the robustness, the speed of this strategy will not slow down, and the effect is particularly noticeable for point clouds with a high overlap rate. Bae and Lichti [37] proposed a GP-ICPR method by incorporating RANSAC into the ICP algorithm. It searches for probable matching locations employing changes in the estimated normal vector of the surface generated by the neighborhood, considerably decreasing the computing cost and improving registration speed and accuracy. Censi [38] suggested the PL-ICP by adopting the point-to-line measuring approach, which will enhance the iterative efficiency to a certain extent. However, due to the discreteness of laser measurement, there are not actually existing two matching measurement points. Therefore, problems like matching failure may occur during positioning, but the robustness is deteriorated, and it is more susceptible to the influence of the initial pose error. In this way, PL-ICP is less robust and more vulnerable to initial pose errors. Segal et al. [39] introduced the General-ICP algorithm as a probabilistic framework. It integrates the point-to-point ICP and the point-to-line ICP into the uniform framework. Furthermore, the measurement weights of point-to-point and point-to-line distances will be adjusted to make effective use of the point cloud information, hence avoiding incorrectly matched points. This method ensures the ICP’s speed and simplicity while boosting the matching accuracy. Unfortunately, it still does not address the issue of local optimum. Ying et al. [40] put forward a scale-ICP algorithm based on seven-dimensional spatial iterations that has a certain degree of improvement in iteration speed and alignment accuracy and has better alignment robustness. Bouaziz et al. [41] presented a sparse ICP to enhance the robustness of the alignment algorithm against noise by modeling the alignment problem as an Lp minimization problem. This sparse ICP can control the effect of outliers on the alignment results by modifying parameter p. However, the algorithm converges slowly because of tackling the nonconvex optimization problem. To some extent, this strategy addresses the problem of ICP slipping into local optimum, but the basis of optimization remains local search. Yang et al. [42] developed a global optimal solution (Go-ICP) algorithm to accomplish global registration by combining the branch and bound (BnB) framework. The method boosts registration speed by raising registration efficiency, preventing the ICP algorithm from slipping into the local optimum. Nevertheless, one shortcoming is poor velocity.

He et al. [43] introduced a GF-ICP algorithm based on point cloud features that seeks the correspondence between registered objects by point cloud geometric properties, such as curvature and surface normal. Features are also added to the error function for accurate registration. Pavlov et al. [67] proposed the use of Anderson’s technique in ICP, which accelerates the convergence process by locating a fixed point in the shrinkage map that satisfies the required quality. This method takes fewer iterations than simple iterations to converge to the same error. Wang and Solomon [44] suggested a deep closest point (DCP) based on machine learning. In this method, the dynamic graph convolution network, attention mechanism, and singular value decomposition matrix are utilized to mine the robustness point features, calculate the correlations of points in the deep features, and estimate the affine transformation, respectively, resulting in the accurate registration of unknown category point cloud data. The training samples are ideal three-dimensional objects. Hence, if the method is directly applied to real problems, the effect is not outstanding. Wang and Solomon [45] introduced a PRNet based on the DCP in the following year that determined the correspondence between point clouds by incorporating Gumbel-Softmax and emulated the iterative process of ICP to increase accuracy. PRNet, on the other hand, presently requires inference-time fine-tuning on real-world scans to acquire usable data-dependent representations, which makes PRNet sluggish during inference. Koide et al. [46] proposed a voxelized generalized iterative closest point (VGICP) that extends the voxelization of the GICP to avoid costly nearest neighbor searches while maintaining algorithm accuracy. Li et al. [68] developed a binocular stereo camera point cloud registration method based on IWOA (improved whale optimization algorithm) and improved ICP to address the problems of low accuracy and low efficiency of point cloud registration.

2.2. Graph Matching (GM)-Based

From the perspective of mathematical optimization, the graph matching problem is a discrete combinatorial optimization problem, which makes the problem essentially a non-deterministic polynomial (NP) problem. Therefore, researchers usually seek approximate solutions to this problem. The majority of these approximation algorithms partly relax the discrete constraints of the matching problem, allowing for the employment of optimization techniques on the relaxed problem. Its central concept is to employ a nonparametric model to handle point cloud registration. Figure 3 is an example of GM. A graph consists of vertices and edges that will be adopted with feature descriptors to identify correspondences between two graphs. In the form of the objective function, GM methods can be divided into three categories: first-order, second-order and higher-order GM methods. First-order GM methods, which are comparable with ICP and its variants, only evaluate local feature descriptors with vertex information. Vertex-to-vertex and edge-to-edge similarities are combined in second-order GM methods. Higher-order GM methods involve information about hypergraphs, which are hyperedges containing the angles of vertex tuples. Second-order or higher-order GM methods are expressed as quadratic assignment problems [69]. Currently, the majority of GM algorithms are second-order or higher-order GM methods.

Second-order GM techniques are classified into three categories: spectral relaxations, bi-stochastic relaxations, and semidefinite programming relaxations. The spectral relaxation method primarily relaxes the permutation constraints of the matching problem, yielding the matching problem’s spectral characteristic solution. Umeyama [47] developed a relaxed representation of the weight graph matching problem under orthogonal constraints and obtained the global optimal solution of the relaxed problem by the spectrum of the adjacency matrix. Although this method has the ability to gain the global optimal orthogonal solution of the matching problem, the nonnegativity of the obtained matching solution is often not guaranteed, the ultimate matching solution must be achieved via the discretization procedure. In addition, this method can only deal with graph matching problems of the same size. Luo and Hancock [48] suggested a structural graph matching method based on expectation maximum algorithm and singular value decomposition theory. The key benefit is that it can match graphs of different sizes and has strong theoretical support for optimization. Caelli and Kosinov [49] raised a graph-based matching algorithm for adjacency matrix spectral embedding. The vertices of a network are first embedded into the spectrum space of its adjacency matrix, and then the clustering method is adopted to match the vertices in the spectral space, thereby indirectly realizing graph vertex matching. Leordeanu and Hebert [50] presented a simple and effective spectral matching (SM) relaxation model to approximate the QAP problem. The method can obtain the global optimal solution of the relaxation model by calculating the principal eigenvector of the affinity matrix of the attribute relationship graph, and the solution also fulfills the criterion of nonnegativity. However, throughout the matching process, the one-to-one matching constraint of graph matching is ignored, that is, each vertex can only be matched with one vertex. Cour et al. [51] investigated affine matching constraints on the basis of the previously described spectral relaxation, which evaluated the one-to-one constraint of the matching problem to some extent and may also search for the global optimal solution. Therefore, this relaxation is theoretically closer to the original attribute relation graph matching problem. However, the optimal solution matrix derived by this approach frequently fail to satisfy the non-negativity constraints of the solution. Accordingly, the final solution in practical applications needs to be further discretized, such as the Hungarian algorithm and the greedy selection algorithm, to obtain the final solution of the problem.

In recent years, one of the most concerned problems in the field of graph matching has been the investigation of optimization methods under double random constraint relaxation. Since the double random constraint is a convex hull representation of the permutation constraint, the permutation matrix constraint is relaxed to a double random constraint. The graph matching problem can be regarded as a non-convex quadratic programming problem with convex constraints, making it a continuous optimization problem. For the past few years, scholars have developed various continuous optimization strategies to get local optimal solutions to this problem. Gold and Rangarajan [52] devised a graduated assignment (GA) algorithm that obtains the final outcome by tackling a series of approximate linear matching problems. Tian et al. [70] proposed a novel gradual assignment algorithm by further analyzing the convergence of GA algorithm. The experiments indicated that the technique outperforms existing methods in the presence of outliers and deformations, especially when the number of graph nodes is considerable. Torresani et al. [53] addressed the problem with a complicated graph matching objective function and a dual decomposition energy optimization approach. Zhou and de la Torre [54] developed a factorized graph matching (FGM) in which the large pairwise affinity matrix is decomposed into smaller matrices and then a path tracking optimization algorithm is provided to increase the matching performance. Jiang et al. [55] suggested a methodology for LaGrange relaxation graph matching.

The approach first embeds the matching problem’s double random constraints into the optimized matching objective function via LaGrange relaxation and then utilizes the multi-multiplier optimization method to establish the relaxation model. Fu et al. [56] originally suggested exploiting depth map matching to overcome the point cloud registration problem. The algorithm consists of four parts: local feature extractor, edge generator, map feature extractor, and AIS module and LAP SVD. During training, we extract local features by a shared local feature extractor for each point in X and Y and take these local features as the node features F of the initial graph; then, we introduce the AIS module to build the reliable correspondence between the nodes of two given graphs. The method achieves state-of-the-art performance on clean, noisy, part-to-part datasets and unknown category datasets. Lai-Dang et al. [71] introduced a framework that efficiently and economically extracts dense features using a graph attention network for point cloud matching and registration (DFGAT).

Another method for approximating the QAP solution is semidefinite programming (SDP) relaxation. The SDP method employs convex semidefinite to slacken the non-convex constraint. Chaudhury et al. [57] were the first to apply the semidefinite programming relaxation algorithm to register point clouds, and in the relaxation gap of the semidefinite programming, the characteristic noise threshold is almost zero (i.e., we are able to solve the original non-convex least squares problem). All in all, the semidefinite programming algorithm outperforms the double stochastic relaxation and spectral relaxation algorithms. Maron et al. [58] achieved better efficiency by minimizing the dimension of semidefinite constraints. However, they only handle medium-sized point cloud registration, and efficiency is still a problem to be studied. Le et al. [59] regarded the point cloud registration as a special case of graph matching and employed a positive semi-definite relaxation principle. The algorithm allows the number of samples larger than that the minimum number of samples required for model estimation, as well as a method of calculating point correspondences that may quickly eliminate erroneous point correspondences, resulting in generating high-quality hypotheses. Heng et al. [60] adopted hierarchical nonconvexity to handle the spinner problem. This strategy utilizes Douglas–Rachford splitting to efficiently prove global optimality. This method resolves the problem of high computational cost in SDP relaxation. Sun [61] presented a novel solution for the correspondence-based rotation search and point cloud registration called random sampling with invariant compatibility (RANSIC), which applies invariant compatibility to locate outliers from random samples.

Higher-order GM methods cast about for correspondences by comparing hyperedges or hypernodes, whose benefit is that these methods are invariant to scale and affine changes. Higher-order GM algorithms are given a probabilistic interpretation by Zass and Shashua [62]. Duchenne et al. [63] expressed the higher-order matching problem as a tensor optimization problem. Lee et al. [64] developed a higher-order GM method by hopping with a reweighting scheme. Ngoc et al. [65] proposed a framework of tensor block coordinate ascent methods for high-order matching. Zhang and Wang [66] introduced a K-nearest-neighbor-pooling matching method that pools features into GMs for second-order GMs, and then constructed sub-pattern structures for higher-order GMs.

Generally speaking, a higher-order graph is a generalization of a graph where a hyperedge can connect any number of vertices. Or rather, it can determine higher-order relationships between pairs of features under certain constraints. Vertices often represent features or object pieces in higher-order graphs, while hyperedges describe connections between vertex tuples. These relationships are multifarious in that they may hold numerous aspects at the same time, whereas graph relationships can only function in pairs.

Table 1. Summary of registration algorithms based on hierarchical optimization.

Classifications	Typical Algorithms	Author	Year	Strengthens	Weaknesses
Iterative Closet Point (ICP)-Based	P2P-ICP [31]	Besl and McKay	1992	High precision; Wide applied range.	Require large overlap area; High requirements for initial position; Prone to local optimal solution.
	Scale-ICP [39]	Segal et al.	2009
	Sparsel-ICP [41]	Bouaziz et al.	2015
	GF-ICP [43]	He et al.	2017
	DCP [44]	Wang and Solomon	2019
	VGICP [46]	Koide et al.	2021
Graph Matching (GM)-Based	SM [50]	Leordeanu and Hebert	2005	High precision; Robust and reli-able results.	Require significant features; Difficult to guarantee extracted feature precision and quality.
	TM [63]	Duchenne et al.	2011
	FGM [54]	Zhou and de la Torre	2016
	SDRSAC [59]	Le et al.	2019
	DGM [56]	Fu et al.	2021
	IRON [61]	Sun	2022

summarizes the typical algorithms based on hierarchical optimization as well as their strengths and weaknesses.

3. Registration Algorithms Based on Probability Stochastic Distribution Model

The critical idea of probability stochastic distribution model-based algorithms is to employ the probability density function of the point cloud to complete the point cloud registration without extracting feature points in the alignment process, and there is no need to establish an explicit relationship between the corresponding points through iteration. This section presents an overview of three optimization methods: RANSAC-based, NDT-based, and GMM-based variations. Milestone methods are listed in Figure 4.

3.1. Random Sample Consensus (RANSAC)-Based

The RANSAC algorithm [72] has been applied universally in various modeling problems, particularly in the field of computer vision. The algorithm is straightforward and well-suited for the problem of robust estimation. Figure 5 illustrates a conceptual diagram of the RANSAC algorithm in a unidimensional modeling problem. The RANSAC algorithm seeks to identify models that are resistant to noise. By extracting the smallest sample, the algorithm calculates the feasible model parameters, then returns the model parameters to all data samples and calculates the associated inlier rate until the number of iterations exceeds the set number. If the current optimum model’s interior point rate exceeds a predefined threshold, the current optimal result is taken as the final model and sampling is terminated; otherwise, sampling continues. Since the maximum number of iterations N guarantees that at least one set of sampled data is full of interior points under a certain confidence probability, the calculation formula of N is derived as follows:

$$N=\frac{\log (1-p)}{\log (1-1{(1-v)}^m)}$$

(2)

where v is the outlier rate of sample; m is the minimum amount of data required to calculate the model parameters, p is the confidence probability set in advance, that is, the probability of p is guaranteed by N times of sampling, making the samples drawn are all interior points.

However, the performance of the RANSAC algorithm in high-dimensional spaces degrades because the likelihood of sampling a set consisting entirely of interior points decreases exponentially. To overcome this, the NAPSAC algorithm [73] was devised. Chum et al. [74] discovered that selecting more points than the minimum subset necessary for model estimate results in more accurate model parameters (for example, homography parameter estimation requires at least four pairs of matching points). On this premise, the LO-RANSAC algorithm was proposed to raise the registration accuracy by resampling the tentative interior point set. To enhance the effectiveness over time, Matas and Chum [100] designed a pre-check-based RANSAC-Tdd. As a whole, the algorithm can indeed save the time required to execute. If the inlier rate is high, the algorithm does have an ideal effect, but when the inlier rate is very low, the algorithm tends to slip into the infinite sampling and testing process. Unlike RANSAC, which treats all correspondences equally, PROSAC [75] does not uniformly draw random samples from the complete set but rather linearly ranks the corresponding sets by building a similarity function using correspondences. As a result, the PROSAC algorithm provides considerable computational savings under the moderate assumption that similarity measurements predict the validity of a match better than random guesses. Aiming at the problem of low matching accuracy caused by the failure of the PROSAC computational model, Ma et al. [76] improved the PROSAC algorithm and adopted the spectral clustering algorithm to filter the mismatches in the subset, thus accelerating the computational efficiency.

Similarly, Aiger et al. [77] decreased spatial matching operations within the RANSAC basic framework by generating and matching congruent 4-points, and presented 4-points congruent sets for robust pairwise surface registration, thereby expediting the registration process. Specifically, a coplanar 4-point set is constructed in the input point clouds P and Q of any pose, and the affine invariance constraint is used to match the eligible corresponding point pairs in the coplanar 4-points set. The largest common pointset (LCP) strategy is employed to find the maximum overlap of 4-points after registration to obtain the optimal matching result and accomplish point cloud registration. Subsequently, Mellado et al. [78] introduced the Super-4PCS algorithm, which simplified the process of discovering congruent 4-points sets, and made use of angle and distance as constraints. This successfully decreased the number of congruent 4-points sets, reduced the time complexity and increased the registration efficiency. The SC-RAMSAC, created by Sattler et al. [79], was founded on spatial consistency checks. It enabled RANSAC to operate on more secure correspondences with lower inlier ratios. RANSAC’s runtime is considerably improved under the same accuracy and robustness conditions. By enhancing sample efficiency and employing grouping algorithms, Kai et al. [80] lowered overall running time.

Although this method combines benefits of PROSAC [75] and NAPSAC [73], it incorporates some of their drawbacks, especially that the Group-SAC algorithm depends on the description between data points and the aggregate of interior points. By creating a sample sphere model, Meng and Zhang [81] put forth a sampling sphere registration technique based on RANSAC that enhances the search efficiency of corresponding points, cuts down on the amount of time it takes to do so, and lowers the time complexity. Synthesizing the advantages of the NAPSAC, LO-RANSAC, PROSAC, and GroupSAC algorithms, Raguram et al. [101] optimized each step of the RANSAC algorithm and suggested a universal RANSAC framework that subjects each (non-minimum) sample to an iterative refinement process during model estimation, decreasing the number of RANSAC iterations and being consistent with theoretical expectations. Many existing algorithms, however, either fail or have extremely high computational cost due to the presence of outliers, sometimes even occupying the vast majority of assumed correspondences. For the issue of outliers in conjunction with the RANSAC algorithm, Li et al. [82] and Sun [83] proposed OP-RANSAC and RANSIC for outliers respectively. In addition to being quick, they can withstand outliers by over 95%. In particular, RANSIC outperforms other state-of-the-art algorithms on point cloud registration problems by recalling nearly all outliers.

To sum up, RANSAC-based registration methods frequently avoid the need to calculate intricate geometric features and have high robustness to noise, but the selection of corresponding points is a very challenging operation. Generally speaking, when point cloud features are highly obvious, additional geometric feature constraints may be introduced to minimize the time complexity of finding related connections.

3.2. Normal Distribution Transform (NDT)-Based

The normal distribution transform (NDT) approach published by Biber [84] is the most classical of the probability statistics-based registration algorithms. It uniformly voxels the 3D point cloud and determines the best match between the two pieces of point clouds by computing the probability density function of the points in each volume. The specific process is depicted in Figure 6.

Magnusson [85] generalized 2D-NDT and extended it to the registration of three-dimensional data, namely 3D-NDT. This improved algorithm would enhance the registration efficiency while ensuring accuracy. The ML-NDT algorithm Cihan and Hakan [86] developed is a multilayer-based normal distribution transformation method. The Gaussian probability function is replaced with the Mahalanobis distance function as the score function, and the Newton and LM methods are used to optimize the score function. The algorithm divides the point cloud into 8n cells (n denotes the number of layers), and the registration speed is faster than with the previous NDT algorithm. Das and Waslander [87] suggested a multi-scale K-means normal distributions transform (MSKM-NDT), which separates point clouds into clusters based on K-means clustering and optimizes at various sizes in order to address the discontinuity problem of the cost function in NDT. Crossing local minima is a benefit of multi-scale optimization, and this approach converges more quickly as a result. Das et al. [88] proposed a segmented region growing normal distributions transform (SRG-NDT), which first removes the ground plane from the scan by a Gaussian-based segmentation algorithm before applying an effective region-growing algorithm to cluster the remaining points. Due to the removal of the ground points, the probability distribution is substantially smaller than that of the voxel method, the discontinuity of the cost function is overcome, and the speed is significantly increased. Lu et al. [89] proposed an NDT algorithm with variable size voxels, and the accuracy of the algorithm was enhanced. Hong and Lee [90] proposed to convert the reference point cloud into a disk-like distribution suitable for point cloud structures to increase the registration accuracy of NDT. The algorithm’s registration speed and accuracy are enhanced on the basis of this by capitalizing on the numerical model of hue and saturation. Zaganidis et al. [91] proposed a semantic-assisted normal distributions transform (SE-NDT). It applies PointNet to offer global features and connects with local features via a segmentation network to provide the category of the point, thus providing classification semantic information.

The NDT’s primary restrictions are comparable with those of the ICP. For one, the NDT is also heavily dependent on accurate initial values. When the estimated transform is updated sequentially, the transform points may pass through PDF cells and end up in the incorrect corresponding PDF cells.

3.3. Gaussian Mixture Model (GMM)-Based

Other statistically based methods transform the registration problem of two pieces of point clouds into the estimation problem of probability density function and take one piece of a point cloud as a template to construct a Gaussian mixture model (GMM) through the maximum likelihood estimation method to fit another piece of the point cloud, thus achieving point cloud registration. These approaches have the benefit of not requiring point-to-point connection to be established between two pieces of point clouds, unlike ICP. Since the approach for local optimization used in this type of registration still relies on the initial value to determine the parameters for the spatial transformation. They are nevertheless prone to falling into local minima even when there is poor initial alignment or little overlap between two pieces of point clouds. GMM is also a popular method for coping with point cloud registration. The main concept behind the GMM-based approach is to convert the registration problem into a maximum likelihood problem of the input data. Afterwards, calculate the transformation matrix and Gaussian mixture model parameters after optimizing the maximum likelihood problem. Figure 7 illustrates the basic principle of GMM-based algorithm. The benefit of the GMM-based method is that it is insensitive to noise and outliers. Furthermore, the research direction of this method is to develop an optimization strategy to optimize the transition matrix by maximizing the likelihood.

To estimate the transformation between point clouds, Myronenko and Song [92] proposed the CPD algorithm based on the GMM model [93], which regards the two pieces of point clouds as the centroid and data of the GMM model and aligns the centroids of point clouds by maximizing the posterior probability. The algorithm has strong noise resistance and robustness, but its high computational complexity makes it less efficient for matching data with higher density. To resolve point sets that are disorganized by noise and outliers, Evangelidis et al. [94] presented the joint registration of multiple point clouds (JRMPC) algorithm, which assumes that multiple point sets are produced by a single GMM. Batch and incremental EM optimization algorithms are also employed. A new convex hull indexed Gaussian mixture model (CH-GMM) [95] point cloud registration algorithm is proposed, which combines the convex hull (a set of original point sets) and GMM to lower the computational complexity. The algorithm could address rigid and non-rigid 3D point cloud registration problems. Ben et al. [96] introduced a hierarchical data structure for 3D point clouds that is based on GMM and includes a compact and generative representation. Model creation is sped up by generating constraints on spatial interactions between points and model. Our model produces findings with better fidelity at smaller sizes, with only moderate trade-offs in construction time, even on mobile devices, compared with discrete techniques or hybrid approaches like the NDT. Min et al. [97] took a probabilistic approach, modeling the problem as a hybrid mixture model with a Von–Mises–Fisher mixture model (FMM) modeling the orientation and a Gaussian mixture model (GMM) modeling the location. Eckart et al. [98] presented hierarchical gaussian mixtures for adaptive 3D registration (HGMR), which builds a top-down multi-scale representation of point cloud by recursively performing the likelihood segmentation of several small-scale data in parallel on the GPU. This approach is more effective and flexible than the prior iterative closest point and GMM-based point association algorithms. Deep GMR [99] replaces the E-step (Expectation-step) in the expectation maximization method with a neural network. Despite its inability to register partially overlapping point clouds, Deep GMR produces good performance in global registration.

Table 2. Summary of registration algorithms based on probability stochastic distribution model.

Classifications	Typical Algorithms	Author	Year	Strengthens	Weaknesses
Random Sample Consensus (RANSAC)-Based	RANSAC [72]	Fischler and Bolles	1981	Low requirements for initial position; Strong robustness and anti-noise capability.	Slow speed; Low precision; Number of iterations required for convergence is difficult to determine.
	NAPSAC [73]	Myatt et al.	2002
	SC-RAMSAC [79]	Sattler et al.	2009
	Super-4PCS [78]	Mellado et al.	2015
	SC-PROSAC [76]	Ma et al.	2021
	RANSIC [83]	Sun	2021
Normal Distribution Transform (NDT)-Based	2D-NDT [84]	Biber	2003	Wide applied range; Fast speed; High efficiency Low requirements for initial position	High requirements for initial position; Poor robustness.
	ML-NDT [86]	Cihan and Hakan	2011
	SRG-NDT [88]	Das et al.	2014
	VSV-NDT [89]	Lu et al.	2015
	HANDT [90]	Hong and Lee	2016
	SE-NDT [91]	Zaganidis et al.	2018
Gaussian Mixture Model (GMM)-Based	GMM [93]	Jian and Vemuri	2005	Good mathematical properties; Better computation performance; Reaches the asymptotic error faster than the deterministic model.	Does not find the global maximum value.
	CPD [92]	Myronenko and Song	2010
	JRMPC [94]	Evangelidis et al.	2014
	CH-GMM [95]	Fan et al.	2016
	HGMR [98]	Eckart et al.	2018
	Deep GMR [99]	Yuan et al.	2020

summarizes typical algorithms based on the probability stochastic distribution model, plus their strengthens and weaknesses.

4. Registration Algorithms Based on Feature

The feature-based algorithm only selects a certain portion of the point cloud for registration rather than using all of the points. This approach is robust and does not require the initial pose. Feature extraction and feature matching are common components of feature-based point cloud registration algorithms. Among them, feature extraction decreases the amount of data to be processed. Moreover, it converts difficult-to-compare feature information into easily comparable information, making it easier to match important points; feature matching is used to find the correct correspondence between features of the source and target point cloud to compute the transformation matrix [27]. Figure 8 depicts the flowchart of a typical feature-based point cloud registration method. Milestone methods are listed in Figure 9.

4.1. Feature Extraction

It is not appropriate to register all the points. On the one hand, it will greatly increase the computational workload. On the other hand, it is not particularly helpful for registration since there are numerous comparable point cloud parts. It leads to pointless processing and increases the number of feature matches and the probability of erroneous matches. From the perspective of information theory, it is less informative for the region with low uniqueness to register point clouds. Considering that features produced could be unhelpful for registration, uniqueness additionally takes into account the impacts of noise, occlusion, and outliers.

Therefore, the repetition of features and the uniqueness of extracted features are significant markers for gauging the effectiveness of feature extraction algorithms. To extract the crucial points, Masuda et al. [103] utilized the basic random sampling method. Despite being fairly straightforward and capable of controlling the quantity of points, this technique lacks a mechanism to guarantee that the sampled points are dispersed equally over the point cloud. The spatial difference between the query point and the neighborhood point is parameterized in the Rusu et al. [104]-proposed point feature histogram (PFH), which creates a multidimensional histogram to characterize the geometric attributes of the query point k vicinity. The simplicity and rotational invariance of this type of feature extraction approach, as well as its great resistance to sampling density and noise spots, making it a viable option. However, in response to its comparatively high computational amount, Rusu et al. [105] further proposed the FPFH, which reduces the computational complexity and improves the operation speed while retaining the PFH characteristics. To address the registration problem in current machine vision, Liu et al. [135] presented a new three-dimensional (3-D) point cloud registration algorithm that combines fast point feature histograms (FPFH) and greedy projection triangulation. To increase the likelihood that the key points retrieved would be unique in the point cloud, Zhong [106] advocated extracting key points with the covariance matrix within a certain radius and selecting points in the region where the minimum value of the covariance matrix eigenvalues varied significantly. Ji et al. [107] extracted feature points by FAST feature extractor, then sorted them according to the Harris measure and selected the top-ranked points as feature points. Prakhya et al. [108] introduced the histogram of normal orientations (HoNO) for detecting 3D key points on point clouds by calculating the histogram for each point in the normal orientations. In comparison to previous 3D key point detectors, the identified key points are highly reproducible, successfully avoiding planar regions, and situated in the informative regions of the 3D point cloud. Zeng et al. [109] proposed a 3DMatch network with voxels as input. Prior to using a 3D convolutional neural network to learn local geometric patterns and obtain 512-dimensional feature descriptors, the point cloud is first quantified into a voxel representation.

PointNet [110] is the first network to extract features directly from the input point cloud. PointNet primarily addresses the issues of point cloud disorder, displacement invariance, and rotation invariance. The generality of features is, however, constrained by PointNet’s inability to capture the semantic information of spatial points. As a solution to the aforementioned issues, PointNet++ [111] adds a hierarchical structure made up of the farthest point sampling layer, a grouping layer, and a PointNet layer to capture information at different scales. PointNet and PointNet++ cannot be directly applied to the field of point cloud registration because they do not emphasize the geometric relationship between points, which restricts the representational potential of features. It does, however, provide an excellent reference for tackling the difficulties of disorder, density change, displacement invariance, and rotation invariance in point cloud feature extraction, as well as facilitating subsequent study.

Deng et al. introduced PPFNet [112], which calculates point pair features (PPF) first for the local area around sampling sites [104,105] and merges local and global features of various scales; the final feature is obtained through MLPs coding. PPFNet makes use of global context awareness, encodes features, and increases their resistance to noise. However, the calculation of PPF features necessitates a significant quantity of nearest-neighbor labeled data, and the creation of a local reference frame depends on the estimate of normal vectors, making it sensitive to noise. To improve the disadvantages of PPFNet, Deng et al. also suggested PPF-FoldNet [113]. Before using a framework containing a PointNet encoder, this method will first extract PPF features, and a FoldingNet [136] decoder to produce the final point cloud’s feature representation. PPF-FoldNet performs better in noisy environments, although it is still susceptible to changes in point density. Yew and Lee [114] introduced 3DFeat-Net, which takes into account learning a 3D form feature detector and feature extractor at the same time and exploits weakly supervised training to tackle the relevant point cloud issue. Gojcic et al. [115] suggested 3DSmoothNet, which produced a smoothed density value voxelization (SDV) suitable for convolution operations to encode the original point cloud and learn the ultimate features through the Siamese network architecture. The method enhances the generalization ability. The technique can still gain better results if it is trained on a single scene before being applied to multiple scenarios. Choy et al. [116] proposed fully convolutional geometric features (FCGF), which employ sparse convolution instead of traditional convolution to alleviate the problem of point cloud sparsity. The network architecture is constructed by sparse convolution to extract point cloud’s local geometric properties. FCGF, on the other hand, has a poor generalization impact due to the overfitting of the data sample.

After converting the reflection intensity into 2D images, Zhang et al. [117] applied the scale-invariant feature transform (SIFT) to extract feature. It is essential to select the spatial point that corresponds to the extreme value position of the Gaussian DoG as the feature point. PRNet (partial-to-partial registration network) [45] defines the saliency of points by the two-parametric distance of features, and then selects several key points with high significance according to the size of the two-parametric distance. Yew and Lee [118] proposed RPMNet based on robust point matching (RPM) [52]. The feature extraction phase has a PPFNet-like structure, and hybrid features are created by combining features with 3-dimensional point coordinates. The outlier parameters and annealing parameters are estimated by a parameter prediction network, and the point pair matching is then calculated by merging the mixed features. RPMNet performs admirably in the presence of noise and partial overlap, but the model’s initial input calls for additional label data, so it is not suitable for dense point cloud input. Similar to PRNet, RPMNet necessitates the computation of features again and over in iterations, raising the computational cost. Horache et al. [119] suggested a multi-scale architecture and self-supervised fine-tuning (MS-SV Conv) based on FCGF. MS-SV Conv continues the FCGF’s characteristics like fast operation speed and robustness to rotation, as well as greatly enhances the generalization performance. Ao et al. [120] proposed a new neural network structure SpinNet. A 3D cylindrical convolution operation [137] procedure was applied to extract the final features for each voxel after the initial features for each voxel were retrieved using shared-weight MLPs and a maximum pooling aggregation function. SpinNet guarantees that features are rotationally invariant and perform well in general. Huang et al. [138] supplemented the previous key point extraction methods. Thereafter, they pointed out that the prerequisite for key point extraction is to ensure that key points should be within the overlapping area of the two pieces of point clouds. Ginzburg and Raviv [121] introduced deep weighted consensus (DWC) for global registration. DWC is an unsupervised network that employs two DGCNNs [139] to extract the global and local RI in turn after first extracting rotation-invariant (RI) features in the local neighborhood of the point. The final features are obtained through the global-local fusion network.

It is typical to learn characteristics jointly with crucial points’ saliency. Since the saliency is frequently derived from unique features, this selection method relies on the encoding of the feature learning module, and the adaptive selection by the network is more crucial for the registration task at hand. In addition, proper exchange of information between two pieces of point clouds can make the detection of key points more accurate, for the reason that the alignment process tends to concentrate more on the overlapping regions.

4.2. Feature Matching

Feature matching is also a process of transformation estimation. After extracting the feature points, the transformation matrix can be obtained by the corresponding relationship between feature points. The registration problem turns into a convex problem if it has the corresponding. There are several methods to gain transformation matrix, including SVD (singular value decomposition), least squares method, etc. In contrast to the ICP-like procedure, only one coarse transformation is required in this case, therefore accuracy is not the most crucial factor. Instead, the accurate correspondence might offer a suitable initial value for the subsequent fine registration. The brute force matching method is the most fundamental. Assuming that there exist n features in each of the two-point clouds, it may take up to n6 related feature points needed to detect the rigid transformation between two sets of points, only a tiny portion of which can identify the proper transformation matrix. Direct feature extracting is feasible in the case of a few points in the point cloud. However, it will be a highly time-consuming operation if there are many point clouds. It is possible to develop some search strategies using information from feature extraction that ought to make a substantial speedup in feature matching and a significant reduction in computational cost.

Stamos and Allen [122] designed a transformation matrix that can be determined between two pairs of line features. Those features that do not satisfy the ratio of line length to plane size are filtered by threshold and then other features are verified to discover the best match iteratively. Gelfand et al. [123] proposed using the branch-and-bound method for key point matching to convert the coordinate root mean square error verification into the distance root mean square error, thus verifying the quality of key point matching without computing the transformation matrix. The approach is resistant to outliers, noise, and occlusion, but it has strict constraints for the retrieved feature points. Liu et al. [124] introduced constraints on the polar geometry in determining the matching relationship. They looked for feature matching based on RANSAC that made the majority of feature points adhere to the polar geometry requirements. Brenner et al. [125] estimated the transformation matrix using a triplet of face features, but first they computed and ordered the triple product of the triples. The translation error is reduced and iterations are terminated when the same transformation happens a set number of times respectively, the greater the triple product being the reason for this. Albarelli et al. [126] applied a game-theoretic framework to match key points, where matches that satisfy mutually stiff requirements are allowed to persist and all other correspondences are eliminated via a natural selection process. Yang et al. [127] integrated the resulting semantic line features into triangular pairs, created analogous triangular pairs by combining three constraints on line features, removed some erroneous correspondences with geometric consistency tests and calculated the transformation matrix with the remaining correspondences. Wang et al. [128] used the CTNC (closest to next closest) technique: for each feature, the most similar and second-similar features meet a certain ratio requirement to be deemed as the correct matching feature. Jung et al. [129] created two-dimensional synthetic images with a variety of views using three-dimensional point clouds. He then scaled images to produce them at various resolutions, which produced a huge number of repeated feature-matching relationships. Finally, the most repetitions were voted as feature match. Xu et al. [130] took planes as features of K-4PCS and designed feature matching with angle rather than distance as a metric.

Yang et al. [131] used weights to determine the distance between features by weighing color and spatial characteristics. When the spatial position of two pieces of point clouds differ significantly, color features are more accurate than spatial features. It is preferable to employ spatial characteristics to match the point clouds’ geometric specifics after alignment. Tao et al. [132] traversed to find the best correspondence by the angles of two pairs of straight lines to identify corresponding pairs of straight lines and derive a transformation that does not account for motion in the direction of gravity. By designing surface features that only require a pair of correspondences to determine the transformation matrix, Chen et al. [140] reduced the number of transformations that needed to be verified. They also established a Kd-tree to find approximation features, discovered comparable transformations using the Kd-tree, and calculated the mean of certain related transformations. The majority of models often employ the inner product of feature or two-parametric distance of features to describe the matching similarity between two sets of features due to the K-nearest neighbors’ inadequate computing efficiency in the network model. Nevertheless, this way ignores the difference of features on a certain channel. To improve this situation, Li et al. [133] learned a similarity measure for feature matching using distance-aware similarity matrix convolution to obtain better matching relationships.

The network supports the use of fast point feature histograms (FPFH) or graph neural networks (GNN) to extract rotationally invariant geometric features. Furthermore, the distance augmented feature tensor is obtained by stitching it with a simple point-to-four-dimensional Euclidean feature, and then one-dimensional convolution is applied to the tensor to learn the feature matching metric. To further increase the robustness of the algorithm, the posture is fine-tuned once the initial parameters are obtained using the energy minimization function. Xu et al. [134] suggested an overlapping mask network (OMNet). During each iteration, the overlapping masks of the two source and target point clouds are predicted individually, the non-overlapping parts are filtered. Afterwards, MLPs predict the relative motion parameters from the global features of two pieces of point clouds. OMNet achieves state-of-the-art results by removing the overlapping regions to prevent interference of the global features.

5. Application in Large-Scale Aircraft Measurement

Today, as measurement technology picks up steam, it has become conceivable to scan the entire surface of an aircraft with a 3D laser scanner without traditional contact measurements. This technology is appropriate for aircraft measuring situations due to its non-contact, wide measurement range, and active illumination offered by the scanner. It can instantly deliver millions of high-quality data points to depict the aircraft’s surface. Due to occlusions and equipment restrictions, it is sometimes impractical to obtain the whole surface of huge objects like airplanes at a single location. Multi-station scanning is required when scanning the entire aircraft surface. As a result, a fundamental and crucial component of aircraft detection is learning how to register point clouds in several coordinate systems into the global coordinate system.

To tackle the issue of the poor efficiency of extracting boundary features from thin-walled structural sections of aircraft, Yu et al. [141] suggested a line-by-line processing algorithm of the scan line point cloud based on its distribution characteristics. The boundary feature line is fitted once the local measurement points have been collected by neighborhood search and projected onto the scanning plane. This algorithm can avert several time-consuming and challenging calculations such as point cloud partition surface fitting, thereby improving the processing efficiency of large-scale point clouds. In addition to analyzing point cloud and CAD model registration approaches, Kong [142] also analyzed point cloud sampling, streamlining, denoising feature extraction, and other techniques. The one-time alignment of large-size aeronautical structural parts is achieved through human–machine interaction. The efficiency of point cloud matching and alignment precision may be considerably increased by area mapping to find corresponding points and raising the weight factor of assembly characteristics compared with the traditional ICP. Deng et al. [143] evaluated the coordinate systems between each measurement system and the assembly frame for the measurement of major components in aircraft assemblies. They also accomplished this by improving the alignment of ERS (enhanced reference system) points. Wang [144] introduced a unique ICP algorithm for aircraft parts point cloud by fusing similar feature matching with the weighted Euclidean distance threshold method, which has a superior registration effect for small-sized parts. The alignment effect is not ideal since the approach cannot extract precise comparable characteristics for the registration process owing to the relatively smooth surface of an aircraft and the enormous size of the point cloud. Wang et al. [145] adopted a laser scanner with multiple scanning stations to capture genuine point clouds. In addition, they provided a generic framework for aircraft point cloud registration to concurrently align multiple point cloud stratifications with the global coordinate system. The method estimates the overlapping area based on the density-invariant area method and adopts the hierarchical optimization registration method to realize the multi-view registration of aircraft point clouds, allowing the whole geometry of the aircraft to be precisely acquired.

To address the problem of the low accuracy of aircraft point cloud registration, Li and Wang [146] designed and implemented an accurate multi-view registration algorithm to improve the traditional hierarchical registration method by eliminating the effect of density variation in large-scale point clouds, enabling the segmented point clouds precisely registered and significantly enhancing the alignment accuracy. As a result of gentle, smooth, and few features on the surface of aircraft skin, Jin et al. [147] suggested a contour constraint-based alignment technique for the skin point cloud in response to issues with misalignment and local minima when utilizing the ICP algorithm for number pattern matching. The skin contour, which is applied as a registration constraint, will be matched with the extraction of Ck feature points. This method not only fixes the local convergence problem but also ensures both accuracy and speed in point cloud registration. To detect the deformation of large aircraft skin, Xie et al. [148] suggested a seam structure-aware ICP (SSA-ICP) that is suitable for the original point clouds of aircraft with noise and outliers’ overload. This method can effectively locate the scanning point cloud in the whole aircraft skin directly on the original scanning point cloud. To acquire comprehensive data on the sealing quality of an aviation fuel tank, multiple viewpoints of the aircraft fuel tank point cloud must be registered. Nevertheless, numerous repeating features are found in airplane fuel tanks, including the regularly spaced rivets. They might result in mismatches in the point clouds of the tanks if conventional registration techniques are applied. A unique 3D descriptor named LP-PPF was constructed by Cao et al. [149] employing the point and line characteristics of point clouds created from aviation fuel tanks to overcome the challenge. The suggested descriptor has the ability to achieve precise alignment between neighboring point cloud pairs. This technique handles point cloud registration in recurrent and challenging scenarios well. Furthermore, Cao et al. extended this approach to other scenes in the aerospace area. Figure 10a illustrates the evaluation on the registration of airplane skin, airplane flap, and helicopter skin, respectively. The registration results in Figure 10b further demonstrate the promising results of this approach. Among them, the ground truth of the raw scanned data is obtained by structured-light 3D scanner with laser tracker.

Today, as aircraft manufacturing technology gathers momentum, the demand for large-scale aircraft measurement is rising by leaps and bounds. Accordingly, the registration algorithm of point clouds obtained by the measurement is also playing an increasingly significant role. As far as the measurement of large-scale aircraft is concerned, the registration algorithm of massive point clouds is the core factor affecting the practical application of this technology. In terms of the current research progress, the point cloud registration algorithm for large-scale aircraft is still in the laboratory research stage. Furthermore, there is still a long way to go before it can be applied in aviation manufacturing enterprises.

6. Conclusions and Future Research

In this paper, we compared the current point cloud registration algorithms, which encompass as comprehensively as possible the various algorithms for point cloud alignment. Details of these classical methods and their applications to large-scale aircraft measurements are analyzed. Specifically, we first categorize the existing methods into hierarchical optimization, stochastic and probability distributions, and feature-based methods for analysis. Then, we presented the typical algorithms of each method, along with a summary of their strengths and weaknesses. Ultimately, the application of point cloud registration algorithms in large-size aircraft measurement is discussed.

After many years of research, point cloud registration has achieved many remarkable results. However, more applications put forward greater challenges to point cloud registration as it gradually penetrates into the production life. The main challenges and future research directions are as follows:

(1) Due to the constraint of view angle, realistic sensor-acquired point clouds typically produce partially overlapping point clouds, making the direct registration of these data challenging. Although some researchers have developed algorithms that can be aligned under partial overlap, the overlap rate is frequently constrained. Because of this, finding a fundamental solution to the partial overlap point cloud alignment problem is of great application value and promising area.

(2) At present, although the point cloud registration technique combining deep learning and traditional methods has made significant progress, only simple objects can be solved for alignment now. For example, these approaches fail to achieve the desired results and still rely on the traditional algorithm, RANSAC [72], when dealing with complicated scenarios and large-scale point clouds. RANSAC algorithm, however, is stochastic and the number of iterations increases exponentially with outliers. Better outcomes were achieved by researchers who applied the RANSAC concept to neural networks. These findings demonstrate that the combination of neural networks and traditional techniques have greater potential. Generally speaking, traditional methods have the trait of transparency, while neural networks have strong fitting ability. As a result, how to combine the advantages of both is one of the future trends.

(3) In different application scenarios, the algorithms encounter different obstacles, which demands the generality of point cloud registration algorithms. Nevertheless, it is challenging to propose a general algorithm, from the current research stage. For instance, in the case of aircraft, the aircraft’s skin size is huge, the surface is smooth, and there are few curvature features. Consequently, serious misalignment will occur when employing feature-based methods in the registration process. Therefore, a more well-liked research hotspot is on the creation of focused, lightweight, and effective algorithms for certain application scenarios.