The Iterative Closest Point Registration Algorithm Based on the Normal Distribution Transformation

Laser three-dimensional (3D) image is a novel non-cooperative target 3D image acquisition technology, and the improvements in detection capability and imaging accuracy of the system are critically dependent on efficient echo-signal processing technique and 3D reconstruction method. The registration process is an essential step in array 3D imaging laser point cloud data processing. Registration of point clouds is an effective method that solves the problem caused by the target self-occlusion in the laser 3D imaging system. The accurate registration result will help provide better support for subsequent applications, such as object reconstruction and target recognition. In this study, a set of thresholds in the iterative closest point (ICP) algorithm is analysed on the basis of the characteristics of the laser array 3D imaging system and is combined with the range error and visual lateral resolution of the system, which are both important parameters in the imaging system. To improve the accuracy and speed of registration, the stop threshold of the iterative algorithm and the corresponding point-distance threshold in the algorithm are established in a novel way based on the range error and visual lateral resolution of the system. This forms the foundation, based on which an adaptive threshold ICP algorithm is proposed. The principal idea of the algorithm is to improve the threshold set that has a considerable effect on the accuracy and speed of registration. At first, the characteristics of the imaging point clouds of the laser array 3D imaging system are analysed in the algorithm. Based on this analysis, the distance between the two point clouds and corresponding points with ideal registrations are estimated theoretically, according to the range error and visual lateral resolution of the system. The simulation results show that the theoretically estimated results and actual results have the same variation tendency, thus providing a theoretical basis for subsequent improvements. Next, the estimated results are added according to the iterative closest point algorithm. This implies that the registration thresholds are capable of changing and adapting under different iterations and imaging systems, thus improving the speed and accuracy of registrations. This phenomenon is not seen in other algorithms. Experiments involving laser array imaging of a point cloud and laser scanning of depth imaging data show that the algorithm is practical and effective for both imaging types of point clouds and can improve the speed and accuracy of registration notably. The effectiveness and feasibility of the proposed algorithm are thus verified. In addition, for its full consideration of the imaging system, the basic idea of the proposed algorithm can be used for designing future applications as required.

The iterative closest point (ICP) algorithm is widely used in three-dimensional (3D) point cloud registration, and it is very stable and robust. However, its biggest drawback is being easily trapped in a local optimal solution, which results in the incorrect registration result. Currently, there is neither a clear effective range to define whether the ICP algorithm will fall into a local optimum nor a study providing a comprehensive evaluation of the ICP algorithm. In this paper, we take the overlap ratio, angle, distance, and noise as the influencing factors of ICP and evaluate the validity, robustness, accuracy, and efficiency of point-to-point and point-to-plane ICP by using four datasets. We first analyze the effective ranges of the two ICP algorithms with respect to overlap ratio, angle, and distance and then propose a universal effective range for the three factors. Next, the effect of Gaussian noise on the validity and accuracy of two ICPs is evaluated. We also analyze the factors influencing ICP accuracy and explain their changing rules. We finally study the effect of different parameters on the efficiency. All results are compared by using point-to-point and point-to-plane ICP algorithms. The results show that the overlap ratio has no effect on validity, but it has a significant influence on accuracy. The angle has a great impact on the validity and efficiency of ICP but has no effect on accuracy. The distance only affects validity, has a limited effect on efficiency and no effect on accuracy. Meanwhile, Gaussian noise has a little effect on the validity. In addition, the general effective range of point-to-point ICP is larger than that of point-to-plane ICP, but the point-to-plane ICP algorithm presents a better efficiency. The point-to-point ICP is more robust to Gaussian noise with respect to validity, while the point-to-plane is more resistant in terms of accuracy.

Affine iterative closest point algorithm for point set registration

In response to the issues of slow convergence and the tendency to fall into local optima in traditional iterative closest point (ICP) point cloud registration algorithms, this study presents a fast registration algorithm for laser point clouds based on 3D scale-invariant feature transform (3D-SIFT) feature extraction. First, feature points are preliminarily extracted using a normal vector threshold; then, more high-quality feature points are extracted using the 3D-SIFT algorithm, effectively reducing the number of point cloud registrations. Based on the extracted feature points, a coarse registration of the point cloud is performed using the fast point feature histogram (FPFH) descriptor combined with the sample consensus initial alignment (SAC-IA) algorithm, followed by fine registration using the point-to-plane ICP algorithm with a symmetric target function. The experimental results show that this algorithm significantly improved the registration efficiency. Compared with the traditional SAC-IA+ICP algorithm, the registration accuracy of this algorithm increased by 29.55% in experiments on a public dataset, and the registration time was reduced by 81.01%. In experiments on actual collected data, the registration accuracy increased by 41.72%, and the registration time was reduced by 67.65%. The algorithm presented in this paper maintains a high registration accuracy while greatly reducing the registration speed.

The problem of aligning of 3D point data is the known registration task. The most popular registration algorithm is the Iterative Closest Point (ICP) algorithm. The traditional ICP algorithm is a fast and accurate approach for rigid registration between two point clouds but it is unable to handle affine case. Recently, extension of the ICP algorithm for composition of scaling, rotation, and translation is proposed. A generalized ICP version for an arbitrary affine transformation is also suggested. In this paper, a new iterative algorithm for registration of point clouds based on the point-to-plane ICP algorithm with affine transformations is proposed. At each iteration, a closed-form solution to the affine transformation is derived. This approach allows us to get a precise solution for transformations such as rotation, translation, and scaling. With the help of computer simulation, the proposed algorithm is compared with common registration algorithms.

Differential LiDAR (Light Detection and Ranging) from repeated surveys has recently emerged as an effective tool to measure three-dimensional (3D) change for applications, such as quantifying slip and spatially distributed warping associated with earthquake ruptures, and examining the spatial distribution of beach erosion after hurricane impact. Currently, the primary method for determining 3D change from LiDAR is through the use of the iterative closest point (ICP) algorithm and its variants. However, all current studies using ICP have assumed that all LiDAR points in the compared point clouds have uniform accuracy. This assumption is simplistic given that the error for each LiDAR point is variable, and dependent upon time varying factors such as target range, angle of incidence, and aircraft trajectory accuracy. Therefore, to rigorously determine spatial change, it would be ideal to model the random error for every LiDAR observation in the differential point cloud, and use these error estimates as apriori weights in the ICP algorithm. To test this approach, we implemented a rigorous LiDAR observation error propagation method to generate estimated random error for each point in a LiDAR point cloud, and then determine 3D displacements between two point clouds using an anisotropic weighted ICP (A-ICP) algorithm. The algorithm was evaluated by qualitatively and quantitatively comparing point clouds with synthetic fault ruptures between a uniform weight and anistropically weighted ICP algorithm. Then post-earthquake slip is estimated for the 2010 El Mayor-Cucapah Earthquake (EMC), using pre- and post-event LiDAR. Based on the analysis, Moving Window A-ICP is able to better estimate the synthetic surface ruptures, and provides a smoother estimate of actual displacement for the EMC earthquake.

Airborne light detection and ranging (LiDAR) data are increasingly used in various fields such as topographic mapping, urban planning, and emergency management. A necessary processing step in the application of airborne LiDAR data is the elimination of mismatch errors. This paper proposes a new method for airborne LiDAR strip adjustment based on point clouds with planar neighborhoods; this method is intended to eliminate errors in airborne LiDAR point clouds. Initially, standard pre-processing tasks such as denoising, ground separation, and resampling are performed on the airborne LiDAR point clouds. Subsequently, this paper introduces a unique approach to extract point clouds with planar neighborhoods which is designed to enhance the registration accuracy of the iterative closest point (ICP) algorithm within the context of airborne LiDAR point clouds. Following the registration of the point clouds using the ICP algorithm, tie points are extracted via a point-to-plane projection method. Finally, a strip adjustment calculation is executed using the extracted tie points, in accordance with the strip adjustment equation for airborne LiDAR point clouds that was derived in this study. Three sets of airborne LiDAR point cloud data were utilized in the experiment outlined in this paper. The results indicate that the proposed strip adjustment method can effectively eliminate mismatch errors in airborne LiDAR point clouds, achieving a registration accuracy and absolute accuracy of 0.05 m. Furthermore, this method’s processing efficiency was more than five times higher than that of traditional methods such as ICP and LS3D.

Point set registration is significant for many applications such as recognition and reconstruction problems in computer science, and localization and mapping problems in robotic science. Traditional iterative closest point (ICP) algorithm is fast, but it is only suitable for registration of rigid motions. Traditional affine ICP algorithm is fast enough and can match the shapes non-rigidly transformed, but it is not robust for noises and outliers. In this study, we propose a new affine ICP variant using correntropy criterion and point-to-line metric. Correntropy is a similarity measure between two random variables and it has outlier rejection property. By maximizing the objective function defined, the registration performance of affine ICP is increased. The method proposed is also find transformation as fast as traditional affine ICP algorithm. Experimental studies on 2D shapes show that our method is quite good in affine registration with noise and outliers in terms of accuracy and speed. The results are compared with state-of-the-art methods.

In this study, a new automatic point cloud registration algorithm based on point cloud registration is proposed to broaden registration ways. The proposed method extracts features of point cloud region for performing the coarse registration. Based on the coarse registration results, the Iterative Closest Point (ICP) algorithm is used for performing the fine registration to restore the measured model. The proposed registration approach is able to do automatic registration without any assumptions about initial positions, and avoid the problems of traditional ICP algorithm in the bad initial estimation. The proposed method along with ICP algorithm provides efficient 3D modeling for computer-aided engineering, computer-aided design and application with Kinect.

<title>Abstract</title> Wheels are critical components of railway vehicles, and the dynamic measurement of wheel parameters is of paramount importance for the safe operation of trains.To enhance the matching accuracy in the existing dynamic measurement processes for train wheel parameters, this paper proposes an improved point cloud registration algorithm based on key point fusion of the Super-4PCS(Super Four-Points Congruent Sets) and ICP (Iterative Closest Point) algorithm. Firstly, point cloud filtering and normal estimation are performed on the wheel point cloud data to obtain source and target point clouds with normal information. Subsequently, the ISS algorithm is employed to extract key points, and the FPFH(Fast Point Feature Histograms) point cloud feature descriptor is utilized to characterize the extracted key points. Then, a two-level registration strategy is used to improve registration accuracy, in which the Super-4PCS algorithm is applied for primary coarse registration and the ICP algorithm is used for the secondary fine registration, respectively. Finally, the experiment is conducted to validate the proposed algorithm and the performance of the algorithm is further comparative analyzed through the listed registration evaluation metrics. Experimental results demonstrate that the proposed algorithm exhibits significant improvements in registration accuracy and robustness for wheel point cloud data compared to the traditional algorithms.

Reduction is a crucial stage in the surgical treatment of bone fractures.The detailed fracture information of the patient can be obtained from computed tomography (CT) scans before surgery and enable physicians to plan preoperative reduction, to reduce the operation time and thus increase the probability of getting satisfactory results. The primary purpose of this paper is to design a computer-aided automatic registration method of fracture point cloud data, so as to simplify the fracture reduction process. In this paper, we propose an integrated fracture reduction system was introduced. The system enables direct semi-automatic processing from CT images to fracture reduction. First, a 3D fracture models is reconstructed from CT images by using the modified Marching Cube (MC) algorithm and is discretized to generate a point cloud. Second, the K-dimensional (KD) tree algorithm is used to cluster and segment the point clouds to identify different fracture fragments. Last, through the combination algorithm of Normal Distributions Transform(NDT) and modified Iterative Closest Point(ICP), the coarse alignment and fine registration of point clouds are achieved step by step. This method has been successfully applied to the reduction of tibial fracture. In the tests performed, the processing time of each step, the point cloud and the 3D model after registration are displayed. The semi-automatic integrated system based on preoperative CT scanning is used to realize fracture reduction，which provides a feasible foundation for minimally invasive and accurate fracture reduction surgery.

This paper presents a method for pose estimation of a rigid body using unit dual quaternions where pose measurements from point clouds are filtered with a multiplicative extended Kalman filter (MEKF). The point clouds come from a 3D camera fixed to the moving rigid body, and then consecutive point clouds are aligned with the Iterative Closest Point (ICP) algorithm to obtain pose measurements. The unit constraint of the dual quaternion is ensured in the filtering process with the Dual Quaternion MEKF (DQ-MEKF), where the measurement updates are performed using the dual quaternion product so that the result is a unit dual quaternion. In addition, we use the Cayley transform for the discrete time propagation of the DQ-MEKF estimate, eliminating the need for normalization and projection of the resulting unit dual quaternion. The ICP algorithm is initialized with the time propagated state of the filter to give faster and more accurate pose measurements. To further improve the accuracy of the initialization, angular velocity measurements from a gyroscope fixed to the camera are included in the filter. The proposed method has been tested in experiments using a Kinect v2 3D camera mounted rigidly on a KUKA KR6 robotic arm, while a customized ICP algorithm was successfully implemented on a Graphical Processing Unit (GPU) system.

The accuracy of the iterative closest point (ICP) algorithm, which is widely employed in image registration, depends on the complexity of the shape of the object under registration. Objects with complex features yield higher reliability in estimating registration parameters. For objects with rotation symmetry, a cylinder for example, rotation along the center axis can not be distinguished. We derive the sensitivity of the rotation error of the ICP algorithm from the curvature of the error function near the minimum error position. We approximate the defined error function to a second order polynomial and show that the coefficient of the second-order term is related to the reliability of the estimated rotation angle. Also the coefficient is related to the shape of the object. In the known correspondence case, the reliability can be expressed by the second moment of the input image. Finally, we apply the sensitivity formula to a simple synthetic object and ellipses, and verify that the predicted orientation variance of the ICP algorithm is in good agreement with computer simulations.

Augmented reality (AR) is gaining attention in medicine because of the convenience and innovation that it brings to operating rooms. Furthermore, oral and maxillofacial surgery (OMS), which is one of sensitive and narrow spatial surgery, requires high accuracy in image registration and low processing time of the system. However, the current systems are suffering from image registration problems while matching two different posture images. We thus aimed to increase that overlay accuracy and decrease the processing time. The proposed system consists of an Iterative Closest Point (ICP) algorithm, which is the combination of a rotation invariant and Manhattan error metric, to provide the best initial parameters and to decrease the computational cost by sorting high and low processing pixel images, respectively. The study on maxillary and mandibular jaw bone demonstrates that the proposed work overlay accuracy ranges from 0.22 to 0.30 mm, and processing time ranges from 10 to 14 frames per second as opposed to the 0.23- to 0.35-mm overlay accuracy and the current 8 to 12 frames per second processing time. This research aimed to improve the visualization and fast AR system for the OMS. Thus, the proposed system achieved an improvement in overlay accuracy and processing time by implementing the Rotation Invariant and Manhattan error metric ICP algorithm.

The traditional affine iterative closest point (ICP) algorithm is fast and accurate for affine registration between two point sets, but it is easy to fall into local minimum. This paper proposes a robust Affine ICP algorithm based on corner points. First, an objective function is established under the guidance of corner points, where the corner points as the shape control point guides the affine registration of 2D point sets. Then, at each step of the algorithm, the affine transformation obtained by the last iterative step is used to establish the correspondence of these two point sets. Next, the new affine transformation is solved by using the objective function under the guidance of the corner points. Experimental results demonstrate that the robustness and convergence of our algorithm are greatly improved compared with the traditional affine registration algorithm.