Captured Point Clouds Research Articles

Non-contact measurement of conveyor belt speed based on fast point cloud registration of feature block

Abstract Non-contact, real-time measurement of conveyor belt speed is critical for energy-saving speed regulation and efficient development of coal mine conveyor systems. Existing speed measurement technologies for conveyor systems are often limited by the slippage and wear in contact measurement and complex environmental disturbance. This study introduces three-dimensional point cloud technology into coal flow information detection and innovatively presents a non-contact measurement method of conveyor belt speed based on fast point cloud registration of feature blocks. In the proposed method, a three-dimensional camera is used to capture point cloud data of the dynamically running conveyor belt, and the raw point cloud is preprocessed and segmented into blocks. Then, the C-MANV (curvature and mean angle of normal vectors) features of block point clouds are constructed based on the point cloud neighborhood curvature and the mean angle of neighborhood normal vectors. Finally, an improved block point cloud registration method based on C-MANV features is adopted to achieve the accurate measurement of the dynamic running speed of conveyor belt. Experimental results demonstrate that the proposed method achieves an average relative error of less than 1.8% in high-speed conveyor belt operation with an average processing time of less than 35 ms, which fulfils the accuracy and real-time requirements for conveyor belt speed detection in coal mines. This study provides an effective technical solution for the speed monitoring of coal mine conveyor systems.

Safe and Reliable Movement of Fast LiDAR-based Self-driving Vehicle

Classification of objects is an important technique for autonomous ground vehicles to identify a surrounding environment and execute safe path planning. In this paper, a method based on horizontal segmentation is proposed to detect cone-shaped objects in vehicle’s vicinity using a LiDAR sensor. A captured point cloud is divided into five layers based on height information, and the division of detected objects into two groups, cones and others, has been made using classifiers available in MATLAB toolboxes. To separate the classified conical objects into four types used to mark the route, an algorithm for their recognition was developed and used. The proposed solution, verified by navigation experiments in real conditions using an unmanned racing car, has gave good results, i.e., a high rate of cone-shaped objects classification, a short processing time and a low computational load. The performed tests have allowed also to diagnose the causes of incorrect classification of objects. Thus, the experimental results indicated that the approach presented in this work can be used in real time for autonomous, collision-free driving along marked routes.

Algorithm-Driven Extraction of Point Cloud Data Representing Bottom Flanges of Beams in a Complex Steel Frame Structure for Deformation Measurement

Laser scanning has become a popular technology for monitoring structural deformation due to its ability to rapidly obtain 3D point clouds that provide detailed information about structures. In this study, the deformation of a complex steel frame structure is estimated by comparing the associated point clouds captured at two epochs. To measure its deformations, it is essential to extract the bottom flanges of the steel beams in the captured point clouds. However, manual extraction of numerous bottom flanges is laborious and the separation of beam bottom flanges and webs is especially challenging. This study presents an algorithm-driven approach for extracting all beams’ bottom flanges of a complex steel frame. RANdom SAmple Consensus (RANSAC), Euclidean clustering, and an originally defined point feature is sequentially used to extract the beam bottom flanges. The beam bottom flanges extracted by the proposed method are used to estimate the deformation of the steel frame structure before and after the removal of temporary supports to beams. Compared to manual extraction, the proposed method achieved an accuracy of 0.89 in extracting the beam bottom flanges while saving hours of time. The maximum observed deformation of the steel beams is 100 mm at a location where the temporal support was unloaded. The proposed method significantly improves the efficiency of the deformation measurement of steel frame structures using laser scanning.

ICP registration with SHOT descriptor for arresters point clouds

Abstract Arresters are one of the critical components of the power system.
However, due to the arrester’s regular and uniform umbrella skirt, both traditional
manual detection methods and existing computer vision approaches exhibit limitations
in accuracy and efficiency. This paper proposes an automatic, robust, efficient arrester
point cloud registration method to address this problem. First, a robotic arm
maneuvers a depth camera to capture point cloud data from various perspectives.
Then, the fast global registration (FGR) point cloud coarse registration method
based on the signature of histograms of orientations (SHOT) descriptor to produce
preliminary registration results. This result is ultimately used as the initial value of
the improved iterative closest point (ICP) algorithm to refine the registration further.
Experimental results on various data sets collected from arrester and public data sets
show that the algorithm’s root mean square error(RMSE) is less than 0.1mm, meeting
the requirements of the engineering application of arrester detection.

Collaborative Completion and Segmentation for Partial Point Clouds With Outliers.

Outliers will inevitably creep into the captured point cloud during 3D scanning, degrading cutting-edge models on various geometric tasks heavily. This paper looks at an intriguing question that whether point cloud completion and segmentation can promote each other to defeat outliers. To answer it, we propose a collaborative completion and segmentation network, termed CS-Net, for partial point clouds with outliers. Unlike most of existing methods, CS-Net does not need any clean (or say outlier-free) point cloud as input or any outlier removal operation. CS-Net is a new learning paradigm that makes completion and segmentation networks work collaboratively. With a cascaded architecture, our method refines the prediction progressively. Specifically, after the segmentation network, a cleaner point cloud is fed into the completion network. We design a novel completion network which harnesses the labels obtained by segmentation together with farthest point sampling to purify the point cloud and leverages KNN-grouping for better generation. Benefited from segmentation, the completion module can utilize the filtered point cloud which is cleaner for completion. Meanwhile, the segmentation module is able to distinguish outliers from target objects more accurately with the help of the clean and complete shape inferred by completion. Besides the designed collaborative mechanism of CS-Net, we establish a benchmark dataset of partial point clouds with outliers. Extensive experiments show clear improvements of our CS-Net over its competitors, in terms of outlier robustness and completion accuracy.

Latent Space Representations for Marker-Less Realtime Hand-Eye Calibration.

Marker-less hand-eye calibration permits the acquisition of an accurate transformation between an optical sensor and a robot in unstructured environments. Single monocular cameras, despite their low cost and modest computation requirements, present difficulties for this purpose due to their incomplete correspondence of projected coordinates. In this work, we introduce a hand-eye calibration procedure based on the rotation representations inferred by an augmented autoencoder neural network. Learning-based models that attempt to directly regress the spatial transform of objects such as the links of robotic manipulators perform poorly in the orientation domain, but this can be overcome through the analysis of the latent space vectors constructed in the autoencoding process. This technique is computationally inexpensive and can be run in real time in markedly varied lighting and occlusion conditions. To evaluate the procedure, we use a color-depth camera and perform a registration step between the predicted and the captured point clouds to measure translation and orientation errors and compare the results to a baseline based on traditional checkerboard markers.

Comparison of As-Built Surveys Using Handheld Laser Scanner and Conventional Method

With the advent of laser scanners in general, handheld laser scanners have become a tool used by surveyors to capture point clouds. The handheld laser scanner is useful for tight and confined spaces where a terrestrial laser scanner or a human cannot enter. Many surveyors still rely on the conventional method, which involves using a distometer and measuring tape for their strata as-built surveys. This is due to the simplicity and cost-effectiveness of the equipment. However, the conventional method is highly susceptible to human errors, unlike the laser scanner, which captures all features in point clouds without human intervention. In this research, data collected from both handheld laser scanners and conventional methods are compared. The handheld laser scanner captured a total of three levels. After collecting data at the site, the GeoSLAM Hub software processed the point clouds. This software helps convert the 3D point clouds into a 2D plan, with dimensions listed for the subsequent comparison process. The comparison focuses on the X and Y dimensions of the unit, with a tolerance of ±0.1m as per the circular KPUP-1-2015-JILID-I-v2016 provided by JUPEM. Following the comparison, the Root Mean Square Error (RMSE) is determined, with the lowest and highest values being 0.018m and 0.024m, respectively. In conclusion, the results show a minimum difference of 0.001m and a maximum difference of 0.049m, which falls within the provided tolerance. The handheld laser scanner offers visual aids to surveyors, enabling them to identify discrepancies' locations quickly. However, its drawback lies in the equipment's cost. Ultimately, the strata as-built plan is prepared for the three surveyed levels.

Crop Leaf Phenotypic Parameter Measurement Based on the RKM-D Point Cloud Method.

Crop leaf length, perimeter, and area serve as vital phenotypic indicators of crop growth status, the measurement of which is important for crop monitoring and yield estimation. However, processing a leaf point cloud is often challenging due to cluttered, fluctuating, and uncertain points, which culminate in inaccurate measurements of leaf phenotypic parameters. To tackle this issue, the RKM-D point cloud method for measuring leaf phenotypic parameters is proposed, which is based on the fusion of improved Random Sample Consensus with a ground point removal (R) algorithm, the K-means clustering (K) algorithm, the Moving Least Squares (M) method, and the Euclidean distance (D) algorithm. Pepper leaves were obtained from three growth periods on the 14th, 28th, and 42nd days as experimental subjects, and a stereo camera was employed to capture point clouds. The experimental results reveal that the RKM-D point cloud method delivers high precision in measuring leaf phenotypic parameters. (i) For leaf length, the coefficient of determination (R2) surpasses 0.81, the mean absolute error (MAE) is less than 3.50 mm, the mean relative error (MRE) is less than 5.93%, and the root mean square error (RMSE) is less than 3.73 mm. (ii) For leaf perimeter, the R2 surpasses 0.82, the MAE is less than 7.30 mm, the MRE is less than 4.50%, and the RMSE is less than 8.37 mm. (iii) For leaf area, the R2 surpasses 0.97, the MAE is less than 64.66 mm2, the MRE is less than 4.96%, and the RMSE is less than 73.06 mm2. The results show that the proposed RKM-D point cloud method offers a robust solution for the precise measurement of crop leaf phenotypic parameters.

Norest-Net: Normal Estimation Neural Network for 3-D Noisy Point Clouds.

The widely deployed ways to capture a set of unorganized points, e.g., merged laser scans, fusion of depth images, and structure-from- x , usually yield a 3-D noisy point cloud. Accurate normal estimation for the noisy point cloud makes a crucial contribution to the success of various applications. However, the existing normal estimation wisdoms strive to meet a conflicting goal of simultaneously performing normal filtering and preserving surface features, which inevitably leads to inaccurate estimation results. We propose a normal estimation neural network (Norest-Net), which regards normal filtering and feature preservation as two separate tasks, so that each one is specialized rather than traded off. For full noise removal, we present a normal filtering network (NF-Net) branch by learning from the noisy height map descriptor (HMD) of each point to the ground-truth (GT) point normal; for surface feature recovery, we construct a normal refinement network (NR-Net) branch by learning from the bilaterally defiltered point normal descriptor (B-DPND) to the GT point normal. Moreover, NR-Net is detachable to be incorporated into the existing normal estimation methods to boost their performances. Norest-Net shows clear improvements over the state of the arts in both feature preservation and noise robustness on synthetic and real-world captured point clouds.

EXPLORING THE LIMITS OF TERRESTRIAL LASER SCANNERS ON AEROSPACE MATERIALS

Abstract. Terrestrial laser scanners are powerful measurement devices commonly used for 3D modelling tasks generating large volumes of data with fast acquisition as a first priority. However, these scanners can alternatively be used to produce near real-time, engineering quality spatial data concerning the changing state of manufactured components. This paper provides a comprehensive analysis of two terrestrial laser scanners capturing aerospace materials and components, and their associated quality measures. In order to explore the limitations of the tested TLS instruments, a mechanical jig was designed incorporating both a rotation and translation stage. This study involved three elements of a point cloud processing workflow: data capture, registration and feature extraction. Sphere-based 7DoF registration is applied using two different commercially available software packages with varying levels of user control. To analyse the quality of the registration, control points extracted from captured point clouds were compared to nominal values measured using a laser tracker. The quality of the registration was consistent, with differences kept between 0.4 mm and 0.6 mm. To evaluate the quality of the captured point clouds, two different tests were conducted. This included planar fit tests on an aluminium drilling template, and sphere fitting tests on white 1.5” spherical targets in magnetic nests. One half of the aluminium drilling template was coated with matte spray to reduce erroneous laser reflections. Finally, the registered point clouds were input to a developed algorithm which automatically extracted drilling holes from the drilling template. Previous scanning work performed on aerospace materials showed evidence of optical rattling caused by high intensity reflections from the interior holes in a drilling template. Further exploration showed that the amount of optical rattle varies systematically with incidence angle. This work demonstrates a systematic offset in the location of extracted hole centres in the drilling template. This offset is dependent on laser incidence angle, and can therefore be accounted for when locating manufacturing components from a known scanning position.

Intelligent inspection of appearance quality for precast concrete components based on improved YOLO model and multi-source data

PurposeMonitoring of the quality of precast concrete (PC) components is crucial for the success of prefabricated construction projects. Currently, quality monitoring of PC components during the construction phase is predominantly done manually, resulting in low efficiency and hindering the progress of intelligent construction. This paper presents an intelligent inspection method for assessing the appearance quality of PC components, utilizing an enhanced you look only once (YOLO) model and multi-source data. The aim of this research is to achieve automated management of the appearance quality of precast components in the prefabricated construction process through digital means.Design/methodology/approachThe paper begins by establishing an improved YOLO model and an image dataset for evaluating appearance quality. Through object detection in the images, a preliminary and efficient assessment of the precast components' appearance quality is achieved. Moreover, the detection results are mapped onto the point cloud for high-precision quality inspection. In the case of precast components with quality defects, precise quality inspection is conducted by combining the three-dimensional model data obtained from forward design conversion with the captured point cloud data through registration. Additionally, the paper proposes a framework for an automated inspection platform dedicated to assessing appearance quality in prefabricated buildings, encompassing the platform's hardware network.FindingsThe improved YOLO model achieved a best mean average precision of 85.02% on the VOC2007 dataset, surpassing the performance of most similar models. After targeted training, the model exhibits excellent recognition capabilities for the four common appearance quality defects. When mapped onto the point cloud, the accuracy of quality inspection based on point cloud data and forward design is within 0.1 mm. The appearance quality inspection platform enables feedback and optimization of quality issues.Originality/valueThe proposed method in this study enables high-precision, visualized and automated detection of the appearance quality of PC components. It effectively meets the demand for quality inspection of precast components on construction sites of prefabricated buildings, providing technological support for the development of intelligent construction. The design of the appearance quality inspection platform's logic and framework facilitates the integration of the method, laying the foundation for efficient quality management in the future.

MInet: A Novel Network Model for Point Cloud Processing by Integrating Multi-Modal Information.

Three-dimensional LiDAR systems that capture point cloud data enable the simultaneous acquisition of spatial geometry and multi-wavelength intensity information, thereby paving the way for three-dimensional point cloud recognition and processing. However, due to the irregular distribution, low resolution of point clouds, and limited spatial recognition accuracy in complex environments, inherent errors occur in classifying and segmenting the acquired target information. Conversely, two-dimensional visible light images provide real-color information, enabling the distinction of object contours and fine details, thus yielding clear, high-resolution images when desired. The integration of two-dimensional information with point clouds offers complementary advantages. In this paper, we present the incorporation of two-dimensional information to form a multi-modal representation. From this, we extract local features to establish three-dimensional geometric relationships and two-dimensional color relationships. We introduce a novel network model, termed MInet (Multi-Information net), which effectively captures features relating to both two-dimensional color and three-dimensional pose information. This enhanced network model improves feature saliency, thereby facilitating superior segmentation and recognition tasks. We evaluate our MInet architecture using the ShapeNet and ThreeDMatch datasets for point cloud segmentation, and the Stanford dataset for object recognition. The robust results, coupled with quantitative and qualitative experiments, demonstrate the superior performance of our proposed method in point cloud segmentation and object recognition tasks.

THE VAULTING SYSTEM OF THE PALATINE CHAPEL: THE AACHEN CATHEDRAL WORLD HERITAGE SITE DOCUMENTATION PROJECT

Abstract. As part of a comprehensive survey and modelling project involving the Aachen Cathedral, this paper focuses on its oldest part, the Palatine Chapel, a domed octagonal hall supported by eight piers and enveloped by a sixteen-sided outer wall. Working on the data collected during an extensive 3D capturing campaign conducted between 2022 and 2023, this paper will focus on the conic vaults covering the ambulacrum of the 1st floor that represent quite a peculiar architectural and structural solution considering the VIII/IX century building know-how. In this framework, the Chapel's 3D point cloud has been analysed to extract the main 2D generative elements of the conic surfaces and then construct the corresponding 3D geometric models. These outputs have been compared against the captured point cloud to assess the differences between the actual vault data and the reconstructed ideal conic shapes. Finally, the method used to unfold the vaults' surfaces and create high-resolution ortho-images has been displayed.

PRESERVATION THROUGH DIGITIZATION - STANDARDIZATION IN DOCUMENTATION OF BUILD CULTURAL HERITAGE USING CAPTURING REALITY TECHNIQUES AND HERITAGE/HISTORIC BIM METHODOLOGY

Abstract. Building Information Modelling (BIM) is an established approach in the construction industry that enables efficient collaboration between stakeholders and facilitates project management. However, when it comes to historical buildings, the application of BIM can be demanding due to the complex nature of these projects. Although BIM Uses in the construction sector are well-documented (Penn State University, 2013) and we are surrounded by amazing technologies, we do not yet have standardized international workflows on how to use those state-of-the-art techniques with Cultural Heritage Assets (Bruno and Roncella, 2019). Standardizing Cultural Heritage (CH) metric documentation and Heritage/Historic Building Information Modeling (HBIM) is challenging since each CH asset needs different information throughout the whole life cycle of the monument - both their physical and non-physical attributes, such as historical and cultural characteristics. Additionally, every work carried out on CH, such as knowledge acquisition, restoration, adaptation, etc., requires specific data inputs. Although there are guidelines books that offer some general proposals, they represent the maximum effort towards standardization. As a result, the field of HBIM has emerged as a relatively new area of scientific research that focuses on the digital representation of CH assets.This research aims to develop a working method and templates for procurement workflow standardization that will facilitate the documentation of historic buildings and heritage assets in coordination with relevant historic preservation authorities for the BIM use case - asset register. The use of various measurement methods, the registration of captured point clouds, and the transfer of geometry to a BIM-compliant 3D information model and sustainable data storage are important aspects of this project.

Indoor localisation and location tracking in indoor facilities based on LiDAR point clouds and images of the ceilings

Abstract. Localisation and navigation technologies have vastly evolved during the last years, facilitating users’ guidance in various environments. Unlike outdoor environments where GNSS comprises a universal solution, in indoor environments various localisation techniques have been used, each one with its drawbacks. Thus, this research investigates the reliability of the ceilings towards indoor localisation, by using components that are included in a simple mobile device. The choice of ceilings lies in their advantages, which include the incorporation of various characteristic components, as well as the absence of obstacles between them and the sensor. Indoor localisation is achieved based on LiDAR point clouds and images from RGB sensors of mobile devices. Additionally, this research involves location tracking of different users, to discover different movement patterns in an indoor facility. The proposed methodology revealed the robustness of the Coloured ICP algorithm for in-door localisation based on point clouds, both in terms of time efficiency and quality, while the combination of the SURF feature detector and SIFT descriptor provides the optimal indoor localisation results with image data. The proposed pipeline revealed encouraging results for use in emergencies, based on static data acquisition of a user, while it is also suitable for dynamic applications, in case a sensor is mounted on an automated device for indoor mapping operations. The captured point clouds of the ceilings can also be used as a reference to CAD and BIM models, to help the modelling of the existing utilities and their components in an indoor facility.

Multiobjective Optimization-Based Terrestrial Laser Scanning Layout Planning for Landslide Monitoring

Terrestrial laser scanning (TLS) is an important means to monitor landslides, and the layout is the key to guarantee captured point clouds with a high quality and low cost. Nevertheless, TLS layout in landslide monitoring is currently determined by user’s subjective experience, and shows a poor performance in reliability and point accuracy. Therefore, we propose multi-objective optimization based TLS layout planning for landslide monitoring. Three-dimensional (3D) scanning simulation of candidate scan positions is first carried out. A multi-objective optimization problem (MOP) is then constructed according to requirements of landslide TLS monitoring in the coverage, cost, and point accuracy. Finally, the combination of an improved non-dominated sorting genetic algorithm Ⅱ (NSGA-II) and the Pareto-Edgeworth-Grierson (PEG) algorithm is introduced to solve the MOP and obtain the optimal layout. To test the proposed method, experiments were performed in two landslide sites in Wuhan, China. Results showed that the planned TLS layouts reached a trade-off among coverage, point accuracy, and the number of TLS scan positions. Comparison experiments based on simulation demonstrated that the constraints fused into NSGA-II dramatically improved the reliability of the planned TLS layout, and the proposed method improved the coverage and point accuracy by 11.62% and 1.52 times compared to the user’s experience. Real scanning demonstrated the proposed method improved the coverage by 10.48%, and reduced the deformation error by 0.78 mm~7.66 mm compared to the user’s experience. In summary, the proposed method is an efficient approach for TLS layout planning, which can improve the ability of landslide TLS monitoring.

Metrology Benchmarking of 3D Scanning Sensors Using a Ceramic GD&T-Based Artefact.

The use of non-contact scanning equipment in metrology and in dimensional and geometric inspection applications is increasing due to its ease of use, the speed and density of scans, and the current costs. In fact, these technologies are becoming increasingly dominant in the industrial environment, thus moving from reverse engineering applications to metrological applications. However, this planned transfer requires actions to ensure the achievable accuracy by providing traceability of measurements. In the present study, a comparison between the devices is carried out and a specific standard artefact is designed, equipped with multiple ceramic optically friendly entities, and allowing a wide variety of geometric dimensioning and tolerancing (GD&T). Four different 3D scanning sensors are used in the experimentation. Three of them are based on laser triangulation, and the fourth is a structured blue light sensor (fringe pattern projection). The standard artefact is calibrated with a high accuracy, using a coordinate measuring machine (CMM) and probing sensors. With this CMM, reference values of multiple predefined GD&T are obtained. The evaluation methodology maximises the accuracy of each device in measuring the dimensions of the artefact due to the good dimensional (milling and turning), surface (control of machining variables), and the dimensional and spatial distribution characteristics. The procedure also includes the same treatment of the captured point clouds (trimming, filtering, and best-fit algorithm, etc.) in each of the four 3D scanning sensors considered. From this process, very reliable measurements of the maximum achievable accuracy of each device (deviations from the CMM measurements) are finally obtained, and a multi-characteristic comparison between the four sensors is performed, also with high reliability.

Tropical Species Classification with Structural Traits Using Handheld Laser Scanning Data

Information about tree species plays a pivotal role in sustainable forest management. Light detection and ranging (LiDAR) technology has demonstrated its potential to obtain species information using the structural features of trees. Several studies have explored the structural properties of boreal or temperate trees from terrestrial laser scanning (TLS) data and applied them to species classification, but the study of structural properties of tropical trees for species classification is rare. Compared to conventional static TLS, handheld laser scanning (HLS) is able to effectively capture point clouds of an individual tree with flexible movability. Therefore, in this study, we characterized the structural features of tropical species from HLS data as 23 LiDAR structural parameters, involving 6 branch, 11 crown and 6 entire tree parameters, and used these parameters to classify the species via 5 machine-learning (ML) models, respectively. The performance of each parameter was further evaluated and compared. Classification results showed that the employed parameters can achieve a classification accuracy of 84.09% using the support vector machine with a polynomial kernel. The evaluation of parameters indicated that it is insufficient to classify four species with only one and two parameters, but ten parameters were recommended in order to achieve satisfactory accuracy. The combination of different types of parameters, such as branch and crown parameters, can significantly improve classification accuracy. Finally, five sets of optimal parameters were suggested according to their importance and performance. This study also showed that the time- and cost-efficient HLS instrument could be a promising tool for tree-structure-related studies, such as structural parameter estimation, species classification, forest inventory, as well as sustainable tree management.

Extraction of Guardrails from MMS Data Using Convolutional Neural Network

Mobile mapping systems can capture point clouds and digital images of roadside objects. Such data are useful for maintenance, asset management, and 3D map creation. In this paper, we discuss methods for extracting guardrails that separate roadways and walkways. Since there are various shape patterns for guardrails in Japan, flexible methods are required for extracting them. We propose a new extraction method based on point processing and a convolutional neural network (CNN). In our method, point clouds and images are segmented into small fragments, and their features are extracted using CNNs for images and point clouds. Then, features from images and point clouds are combined and investigated using whether they are guardrails or not. Based on our experiments, our method could extract guardrails from point clouds with a high success rate.

A transmission model for motion estimation of instability space targets

Motion estimation is an effective way to rectify the distortion caused by motion existed in captured point clouds of space targets. However, the non-cooperative and motion complexity of instability space targets make it difficult to precisely estimate the motion parameters, especially in the linear measurement system with a single sensor. In order to solve this problem, we present a novel motion representation for motion estimation of instability space targets. The motion representation, called the transmission model, converts a nonlinear system of motion parameters into a polynomial system of orthogonal matrices, which improve the efficiency of motion estimation. Moreover, we exploit a self-constrained form to express the target orthogonal matrices, which makes them be further solved efficiently by transferring the constrained optimization problem into a self-constrained one. Additionally, an effective strategy is devised to solve the polynomial system of orthogonal matrices by progressively increasing the consecutive number of point clouds until the precision is attained. Experimental results have demonstrated that our approach achieves a high estimation accuracy and a good performance of reconstruction within few seconds under a variety of motion states in our research background.