## 1. Introduction

The strong urbanization trends of the past few decades are leading to even more complex construction environments, thus raising the demand for dense and accurate three-dimensional (3D) data. For example, the substantial air pollution problems encountered in the world’s megacities [

1] force countries like China to consider alternative solutions to automobile-based transportation. High-speed rail is thus becoming a very attractive option, especially when considered against a backdrop of worsening airport congestion and given its reduced carbon footprint. However, in order to pursue this option we are faced with substantial engineering challenges. Viewed as 3D objects, high-speed rails and their ancillary infrastructure (e.g., tunnels, bridges, and piers) are complex, challenging, and labor-intensive for traditional surveying solutions (e.g., leveling or triangulation). It is becoming even more challenging if one considers the need to regularly monitor these complex structures.

Laser scanning technology offers a quick and low-cost alternative for the acquisition of large amounts of 3D information. In terrestrial applications, laser scanning allows the collection of detailed façade information with high geometric precision. Terrestrial laser scanning (TLS) is a ground-based, active imaging method that rapidly acquires accurate, dense 3D point clouds of object surfaces through laser range finding. The number and variety of applications that benefit from TLS continue to increase, including landscape measurements, measuring and modeling for complex industrial equipment, building and heritage conservation, 3D urban visualization modeling, surveys for forest and agricultural resources, and deformation monitoring [

2,

3,

4,

5].

When applied to elongated features such as high-speed rails, TLS presents challenges as such applications require numerous long-strip scans to complete a scene. The point cloud sets acquired by such successive scans are referenced to different local frames, each associated with a corresponding scanner location. Therefore, a registration process is needed to align and merge these individual scans relative to a common reference frame. This registration results in the generation of long 3D strips, like the long geolocated 2D mosaics derived through image co-registration [

6]. The co-registration of individual point cloud scenes is a prototypical photogrammetric problem, comparable to traditional strip adjustments, and requiring the estimation of transformation parameters describing the relative position of two overlapping 3D models, namely the scale, shifts, and rotation of one 3D scene relative to another. This is the subject of this publication.

The registered TLS data are the final measurement product and are in the form of a point cloud, consisting of a set of data points defined by their X, Y, and Z coordinates. However, these final measurement products are normally distorted due to registration errors and these errors are accumulated in multi-site cloud registration, especially in surveyed areas with limited control points. The resulting compromised accuracy not only affects the reliability but also restricts the applications of TLS data. Overall, the accuracy of the acquired TLS data is affected by two primary aspects: ranging accuracy of the scanner, and registration accuracy among multiple point cloud data [

7,

8]. As a simple and robust method for finding a set of inliers, the popular RANdom Sample Consensus (RANSAC) algorithm (Fischler and Bolles [

9]), can be used to register point clouds. However, the accuracy of RANSAC is affected by determining the assumed noise in the surface direction, a function of the distance from an object to the laser scanner, incident angle, surface texture, and point clouds generated by multiple scan setups. In order to improve the overall accuracy, we propose a RANSAC-based registration that is enhanced through a Closed Constraint Adjustment (CCA). This Closed Constraint Adjustment (CCA) ensures that loops are closed. In the context of this publication we consider as representative objects to be measured the types of bridge piers that are used as basic docks for high speed rail (HSR).

This paper is organized as follows.

Section 2 reviews different registration techniques.

Section 3 describes the proposed registration methods based on the introduction of the registration method using artificial targets and the basic principles of Random sample consensus (RANSAC).

Section 4 discusses the experimental results of the proposed registration methods, followed by

Section 5 with conclusions and recommendations for further research.

## 2. Literature Review

Several approaches have emerged for the co-registration of laser scans, with each of them distinguished by its particular target functions and objectives. For example, the Iterative Closest Point (ICP) algorithm is based on minimizing the point-to-point distance in the overlapping area between different TLS scans [

10]. Popular variations of ICP include the Iterative Closest Patch (ICPatch) [

11] and the Iterative Closest Projected Point (ICPP) [

12]. Commonly, ICP-based methods require large overlap among the data sets and accurate initial approximations of the transformation parameters. However, even if there is considerable overlap, convergence to a global minimum is not guaranteed. Furthermore, ICP-based methods are computationally intensive and time consuming in their search for conjugate points in overlapping scans using all available points [

13]. As an improvement, Bae and Lichti [

14] proposed a robust automated registration method for unorganized point clouds, namely the Geometric Primitive ICP with RANSAC (GP-ICPR). In that approach, a modified RANSAC algorithm is used for outlier removal. All the possible point-pair matches are used to estimate the transformation parameters between the two data sets.

Another commonly used algorithm (Chen and Medioni [

15]), minimizes the point-to-plane distance in the overlapping area of the TLS scans. It also requires a very good initial alignment to eventually produce a successful solution. This algorithm is generally faster than ICP. However, the point clouds need to be initially more closely aligned to each other compared to the requirements of ICP. ICP, its variants, and Chen and Medioni’s algorithm assume that the closest point in a point cloud is a good estimate of the correct corresponding point. If two point clouds are not approximately aligned using available georeferencing information, this assumption is not necessarily correct. Although initial alignment can be provided by other means (e.g., surveying of the laser scanner locations), this option is not always possible. Although these adjustment algorithms provide a closed-form solution (

i.e., no iteration), one of the reasons for their popularity, these methods cannot provide statistical information of individual parameters of rigid body transformation as conventional least square methods can offer.

Recent efforts have produced approaches that use not only points, but also lines and surfaces as registration primitives [

16,

17,

18]. Various geometric primitives (e.g., planes, lines, spheres) are derived from point clouds and are subsequently used to register TLS scans instead of using all available points. For instance, Rabbani

et al. [

19] registered scans of an industrial site rich in different geometric features by extracting and comparing the site’s features. Using lines as major geometric primitives, Eo

et al. [

20] showed that line-based matching may give better results than point-based matching. The results of Sibel Canaz [

21] indicate that a linear feature-based registration method is more flexible than a planar feature-based registration method. Line features represent geometric evidence of edges, which are quite prominent and extraordinary, and thus matching conjugate line features may produce more robust and reliable results. Nevertheless, due to issues such as completeness and precision of these extracted line features, their direct matching is not trivial. Plane features have also been used for registration. Brenner

et al. [

22] showed that three plane matches can help determine the transformation parameters between two point clouds, and their method was later compared with the point-based Normal Distributions Transform method. The combination of different primitives has also been studied. Jaw and Chuang [

23] used point-based, line-based, and planar-based registration techniques, both individually and collectively and demonstrated that their combination produced more reliable registration results than single features. Similarly, Huang

et al. [

24] presented a method utilizing multiple geometric features for the registration of TLS data. Conjugate planes were used to find the rotation, and the intersections of the axes of the cylinders and planes were used to determine the translation. Although the comprehensive use of multi-features potentially improves the reliability and precision of registration, these algorithms require that such features are discernible in registered point clouds, which cannot always be assumed to be the case. Aiming to improve accuracy, Cheng [

25] proposed and tested a model of multiple registration error propagation, without introducing a method to eliminate the accumulated error. Xu [

26] assigned error for all scanning positions using the final cumulative registration errors, but the method cannot be considered as a real adjustment [

26].

Therefore, despite these prior efforts, we are still lacking an algorithm that facilitates registration with high accuracy, reliability and robustness. Towards this goal, a registration method is proposed herein that uses a random sample consensus (RANSAC) for adjacent scanning positions. RANSAC is an iterative method to estimate parameters of a mathematical model from a set of observed data that contain outliers. It is a non-deterministic algorithm in that it produces a reasonable result only with a certain probability. The advantage of RANSAC is that it allows a robust estimation of the model parameters estimating the parameters with a high degree of accuracy even when a significant number of outliers are present in the data set. Long-strip, terrestrial laser scanning point clouds are registered by the target points, which are detected by RANSAC without requiring precise initial approximations. While RANSAC solves the correspondence problem and ensures correct matches it cannot ensure by itself an acceptable overall accuracy. Due to the particular nature of long-strip adjustments, errors are easily accumulated along the strip, a problem common in traditional photogrammetric strip adjustments [

27]. Through the use of target points and the relationship among adjacent scanning positions one can maintain the overall stability of the solution. This joint use of RANSAC for targets correspondence, and of CCA can offer a reliable and robust solution of the co-registration problem, eliminating misclosures caused by registration errors and ensuring the reliability of the overall registration results.

Table 1 shows the difference of these methods generally.

An approach comparable to this was offered by Ji

et al. [

28]. The difference between this paper and that of Ji

et al. [

28] is threefold. First, the objectives of the two papers differ. Ji

et al. [

28] discuss the investigation of fine registration and compare the impact of different registration methods on the overall precision of the registration process. Conversely, this paper is focused on the complete procedure of registration from target correspondence to fine registration with closing condition. Second, Ji

et al. [

28] propose a registration method without using a control network, which affords a complete control with sufficient control points. Ji

et al. [

28] set a limited number of control points but the number is insufficient for a control network to form an overall constraint. After all, the method used in Ji

et al. [

28] is without a control network. However, this paper utilizes the adjacency of scanning positions, visibility of control points from different scanning positions, and closing condition formed by local scanning positions to conduct an overall adjustment without control points. The results are an improvement in the precision of joint with reduced distortion, thus addressing the long strip registration challenge to a certain extent. Third, this paper further extends Ji

et al. [

28] by integrating in the approach the use of RANSAC for the automatic identification of correspondences. RANSAC is robust in terms of gross errors but only handles the correspondence problem without guaranteeing the overall precision. Due to the characteristics of long-strip, it is easy to accumulate error and create a distorted result. In this paper, the promise of precision is supported by the adjacency of scanning positions, visibility of target points from different scanning positions, and closing condition formed by local scanning positions. Therefore, the approach presented in this paper offers the potential of both high robustness and precision of the overall automatic long-strip registration.

## 5. Concluding Remarks

A RANSAC-based TLS registration algorithm and an indirect adjustment principle were presented to co-register scanned data. In large-scale target scanning position registration, the accumulation of errors has a significant impact on data usage and produces a distorted final registration result. For a pier feature in particular, a layout method for the target points is presented that is suitable for registration of long-strip pier data. The closing condition adjustment significantly reduces the accumulated error and produces useful results. In addition, a closing condition for the complete adjustment methodology was introduced and experiments were conducted to verify the method’s efficiency.

Using RANSAC to register point cloud generally meets the corresponding accuracy requirements. The registration precision for the adjacent scanning positions can achieve 1 mm–6.5 mm. Due to the spread of registration errors, the misclosure is accumulated rapidly up to 0.6 m with the increase of the number of measurement scanning positions in the closed loop, which hampers the merger of the scanning data and leads to dislocation. The pier model has major deformities at the start and end of the measurements, which affects the data’s utility. Here, the RANSAC-based registration, combined with CCA to eliminate the accumulated registration errors, is proposed. The effectiveness of the adjustment process by comparison experiments shows that the RMSEM with CCA is less than 0.01 m, far less than 0.59 m before adjustment. In addition, all cloud point data of the piers are merged without rough surface or obvious dislocation. The experimental registration shows that the method significantly improves the long-strip registration. This methodology is a better solution to eliminate accumulated error within a certain length. When it is longer (more than 30 scanning positions), this constraint is not strong enough and needs to be controlled by the external control points.

Future research issues that emerge from our approach include the fully automated high-precision registration without using artificial targets. Regarding this particular application of real-time online bridge monitoring, it is critical to reduce the time cost of the automatic registration process. Since laser-scanning instruments are often equipped with an additional image sensor, benefiting from this opportunity to improve registration is another emerging research direction.