# Mobile LiDAR for Scalable Monitoring of Mechanically Stabilized Earth Walls with Smooth Panels
## 4 Methodology
### Point Cloud Registration  
Several procedures have been introduced in recent literature for the fine registration of point cloud data. According to [PERSON] and [PERSON] [PERSON] and [PERSON] (2018), an automated registration approach should  
Figure 8: Graphical representation of the relationship between \(LF_{\text{cs}}\) and \(P_{\text{cs}}\) for deriving the panel-to-leveled face position and orientation serviceability measures  
address the following four components: (1) the parameters describing the transformation between the reference frames of the respective datasets, (2) the primitives used for the evaluation of the transformation parameters, (3) the mathematical conditions ensuring the alignment of corresponding primitives following the registration, and (4) the matching strategy for the automated identification of corresponding primitives and derivation of transformation parameters. A six-parameter transformation (three shifts and three rotation angles denoted here forwards as XT, YT, ZT, \(\Omega\), \(\Phi\), and K, respectively) can be used for relating the reference frames of acquired point clouds from different drive runs considering the short acquisition period--mainly under 30 s each. In spite of the fact that there is no point-to-point correspondence between overlapping drive runs, point primitives are recommended for the fine registration. This is mainly attributed to the huge redundancy, which will still assure the highest accuracy for the estimated transformation parameters. The similarity metric is based on ensuring that the distance between a point in one drive run and its corresponding point in another drive run is zero. As for the matching strategy, the well-known iterative closest point (ICP) algorithm [25; 26] can be used to establish the correspondences through iterative minimization of the squared sum of point-to-point distances in the common area between neighboring drive runs. [PERSON] et al. [27] proposed an alternative strategy to avoid the underlying assumption of the ICP--i.e., point-to-point correspondence in overlapping point clouds--where the estimation of the transformation parameters is based on a point-to-plane minimization metric. This strategy suffers from computational inefficiency. The iterative closest patch (ICPatch) algorithm [28], which is a variant of ICP, is an alternative strategy that mitigates the point-to-point correspondence assumption. The ICPatch strategy derives point-patch pairs in two overlapping point clouds through an iterative minimization of the squared sum of the normal distances between such pairs (e.g., the points in a drive run are matched to the triangular patches, which are established through a triangular irregular network procedure, in another drive run). In order to avoid the key shortcoming of a TIN generation procedure (namely, inability to represent vertical surfaces), the iterative closest projected point (ICPP) algorithm was developed by [PERSON] and [PERSON] [22]. In the ICPP approach, the triangular patch is defined by the closest three points in the point cloud from another drive run to a transformed point from the first one using the current estimate of the transformation parameters. A modified matching strategy was introduced in this research, where a hybrid implementation of ICPatch and ICPP is utilized [29]. Similar to any fine registration procedure, one needs to start by setting approximate estimates for the transformation parameters between the collected point clouds from different drive runs. Since the available point clouds are assumed to be in good alignment through the system calibration and onboard GNSS/INS direct geo-referencing unit, zero shifts and zero rotation angles can be employed as the starting estimates for the transformation parameters. These values are applied to transform a point from one drive run, which is designated as the source surface, to the reference frame of another drive run, which is referred to as the reference surface.