# Spatial Data Analysis for Deformation Monitoring of Bridge Structures
## 2 Deformation Analysis Using TLS  
Laser scanning is a non-selective technique for 3D data collection; therefore, with the exception of special cases of repetition of measurements from a single position of the instrument, it is practically impossible to reproduce the identical position of measured points in point clouds from different epochs of deformation measurements. This fact makes it impossible to directly determine the displacements, therefore the allocation of identical parts of the object is performed in a separate step, which usually involves modeling parts of the point cloud [8]. The approaches for deformation analysis from terrestrial laser scanning results can be divided according to [15] into five categories:  
* Point-based approaches;
* Point cloud-based approaches;
* Surface-based approaches;
* Geometry-based approaches;
* Parameter-based approaches.  
Point-based approaches are based on determination of displacements, which are based on the difference in the coordinates of repeatedly measured points in the clouds [16]. Such an approach can be used only if the scanner allows repeated measurement of points without changing the orientation of the instrument. In practice, this means that, from one position of the instrument, the surface of the monitored object is repeatedly scanned at certain time intervals using identical scanning parameters in each epoch while the stability of the instrument must be ensured during the whole monitoring process.  
Point cloud-based approaches determine the displacements and deformations from the difference of two clouds. The relationship between clouds is determined by their transformation (registration) into a common coordinate system, most often using the ICP algorithm [17]. For example, according to [18], the clouds are divided into clusters after the registration process using hierarchical clustering methods, e.g., octant tree. The displacements between the clouds can then be determined in different ways. One way is to calculate the distance between the nearest neighbors. Another way is to calculate the average distance between corresponding clusters, which is calculated from the distances between identical pairs of points from both clouds, or by calculating the Hausdorff distance (the maximum distance from the set of the distances of nearest neighbors). The angles between the normal vectors of the planar surfaces approximating the points of the cloud in the corresponding clusters can also indicates deformations. A simple determination of the coordinate differences between the corresponding clusters' centroids also belongs to this category.  
The surface-based approaches are based on modeling point clouds by surfaces [19]. The displacements are determined by calculating the distances between the cloud points in the current epoch and the triangular network created in the basic epoch [8]. The second approach is to determine the distances between two surfaces in a defined regular grid of points [20].  
Geometry-based approaches determine changes in the spatial position and orientation of the geometric primitives (planar surface, cylinder, sphere, etc.) modeled from point clouds. Parameter-based approaches are essentially an extension of geometry-based approaches [8]. In this case, displacements and deformations are determined by the statistical testing of changes in the characteristic parameters of geometric primitives in individual epochs [1].