## 2 Materials and Methods
### Wedge Iterative (Modified Model)  
The work presented is based upon \"Wedge-filtering of geomorphologic terrestrial laser scan data\" [14], where the general procedure of the Wedge Absolute method is described. In the following, we explain our modifications that led to the Iterative Method while the basic principle of Wedge Absolute is briefly reproduced for understanding.  
In a static terrestrial laser scan, all measured points must be visible from the laser source of the scanner. Figure 1A shows a point cloud of terrain from the view of the laser scanner. Connecting each point with the laser source creates a line between the two (blue line in Figure 1B), given that there were no obstacles along these lines. In the case two connecting lines have the same horizontal angle, the connecting line with the larger vertical angle and smaller measuring distance compared to the connecting line with the smaller vertical angle and greater measuring distance cannot lead to a ground point. Consequently, a point cannot be a ground point if there is a more distant point with a smaller vertical angle in the same direction.  
Of course, it is rare that two connection lines have exactly the same direction. Thus, you need to define a threshold. The basic idea is that, for each point, two adjacent points are searched, which are further from the recording point than the point to be checked. The angle is calculated between the connecting line from the recording centre to the recording point and the connecting lines to the adjacent points. The angles are calculated using Equation (1):  
\[\alpha_{li,re}=\tan^{-1}\left(\frac{\Delta_{vert}}{abs\ (\Delta_{horz})}\right) \tag{1}\]  
where \(\alpha_{li,re}\) is the left or right wedge angle; \(\Delta_{vert}\) is the difference of the vertical angle; and \(\Delta_{horz}\) is the difference of the horizontal angle.  
For the Wedge Absolute method, if the angular values are greater than a previously defined threshold value, the corresponding recording point is recognized as a non-ground point and will be erased (Equation (2)).  
\[\alpha_{li}\cap\alpha_{re}>\lambda_{TLV} \tag{2}\]  
where \(\alpha_{li,re}\) is the left or right wedge angle; and \(\lambda_{TLV}\) is the threshold limit value.  
Because the section for the two angle thresholds looks like a wedge (Figure 1A, blue dashed), we called it the wedge-method. As mentioned in our previous work [14], this filtering method is  
Figure 1: View to terrain from the centre of scanner (**A**); and cross-section of a terrain (**B**).  
not a stand-alone solution for calculating a digital terrain model because it has some weaknesses. The Wedge Absolute method on its own provides satisfactory filtering results only for terrain, without steep inclines.  
In contrast to the absolute method in the iterative method, the angle difference to the two adjacent points is calculated for all points. This angle difference is compared with a predefined threshold value. Therefore, an angle difference of 180\({}^{\circ}\) means that the point lies precisely in a plane with the two adjacent points. A value greater than 180\({}^{\circ}\) indicates that the point is not likely to be deleted. A very small value (acute angle) again indicates a vegetation point. The method to find the two adjacent points is explained in Section 2.3.3. If the angle difference is less than a certain threshold, the point will be erased (Equation (3)):  
\[\theta_{diff}<\lambda_{TLV} \tag{3}\]  
where \(\theta_{diff}\) is the difference of left (from right adjacent point) and right (from left adjacent point) wedge angle; and \(\lambda_{TLV}\) is the threshold limit value.