# Simplified Scan-vs-BIM Frameworks for Automated Structural Inspection of Steel Structures
## 3 Methodology
### Preprocessing
#### 3.1.3 Extraction of Points Inside Bounding Space  
In this process, all points in the bounding space were collected and a sampling process was included for optimization. A geometric formula was applied to distinguish a point inside the bounding space. The mathematics involved in this step are discussed in the equations (Appendix A). Among the parameters of the target structural object, the \"start point\" and \"end point\" are defined as p1 and p2, respectively; the target point to be checked whether it is within the bounding space is defined as p0. If the calculated shortest distance is smaller than the R value of the bounding space, it is considered an internal point.  
The DNN needs to predefine the size of the input layer. Not all points within the bounding space can be used as indicators of analysis. Therefore, it is necessary to predefine the number of points to be input in the DNN-based integrity evaluation. In general, the DNN uses an input size of the form power of 2 [26]. When the points collected on a general structural column are uniformly arranged in the longitudinal direction, 512 points are 8 mm, 1024 points are 5 mm, and 2048 points are arranged at intervals of 2 mm. Structural integrity can be assessed more accurately and in detail by using as many points as possible and arranging them at small intervals. However, if a large number of points are used, the amount of computations of the DNN increases, thus reducing the efficiency of the framework [38]. Therefore, it is necessary to define the number of points according to the appropriate criteria. Considering the mechanical error of the 3D scanner and the variables of the field conditions, it was determined to configure the input data at intervals of 5 mm and sample 1024 points as a reasonable standard for structural integrity evaluation.  
The simplest way to sample a point cloud is to randomly select 1024 points. However, random selection has a disadvantage in that the data structure is lost because the selected point is concentrated only on a specific part and cannot maintain the data features of the existing point cloud [39]. Therefore, a theoretical methodology for sampling rather than random selection was presented. Farthest Point Sampling (FPS) is the most used  
Figure 3: Extraction of object shape inside bounding space.  
method [40]. FPS works by starting at a point in the set and iteratively selecting the point farthest from an already selected point [41]. These methods do not minimize geometric errors and subsequent processing of a sampled point cloud is not possible, thus leading to sub-optimal results [42]. In a recent study, SampleNet--a new differential relaxation methodology for sampling from a point cloud that approximates the points sampled as a mixture of points in the point cloud--was proposed. The approximation method of SampleNet consistently acquires good results in classification and geometric reconstruction applications [43]. By applying SampleNet to the proposed process, 1024 points were sampled. Through SampleNet, the features of the point cloud can be clearly maintained, and the framework can output consistent and stable results.