# Two-Dimensional Shape Analysis of Complex Geometry Based on Photogrammetric Models of Iconostases
## 4 Method for 2D Shape Analysis Based on Photogrammetric Models
### Method for Detecting Contours and Extracting Plane Sections Based on Point Segmentation  
In this section, the method that relies on point cloud segmentation techniques has been proposed to detect contours of the shapes representing iconostasis construction and ornamentation and to extract plain sections of the iconostasis' principal structure.  
The aim was to create cross sections through the iconostasis' constructive and ornamental elements, while excluding the points that represent icons as they present flat paintings inserted into frames. To compute geometric features, as well as to extract points of interest and produce the plane sections, the CloudCompare [64] software was used.  
CloudCompare presents an open-source 3D point cloud processing software that provides many options for the handling and analysis of data obtained by remote sensing techniques. There are two common ways for creating sections in CloudCompare: (1) extract cloud sections across polylines and (2) the cross section tool. Both options allow for creating slices of points projected on a flat projection plane. The section through the point cloud extracts all the paints that fit a selected flat plane. Thus, all the visible points that fit a predefined cross-section plane can be extracted as the contours and/or a new cloud subset. This way, the points representing flat icons, which would be normally represented in the technical drawing section as outline contours, remained in the extracted cross-section (Figure 5).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**3D Reconstruction Statistics** & **ICONB** & **ICONC** & **ICONT** \\ \hline GSD (mm) & 2.68 & 1.10 & 1.20 \\ DEM resolution (mm/pix) & 5.36 & 2.10 & 2.35 \\ RMS 1 error (mm) & 5.20 & 2.10 & 2.50 \\ \hline \hline \end{tabular} \({}^{1}\) Round square meter.  
\end{table}
Table 2: Comparison of 3D reconstruction data between the three case studies.  
Figure 4: Textured meshes and the camera positions of the three digitized iconostases: (**a**) ICONB; (**b**) ICONC; and (**c**) ICONT.  
Rather than selecting all the points on the same plane as the cross section tool does, computing the verticality geometric feature allows for filtering points according to the values of surface verticality (Figure 6). This way, segmented classes of points with similar space orientation can be represented as a plain visualization, which is more understandable than a standard flat section extracted from the point cloud. In the following sections, the detailed processes used for point cloud segmentation and representation are described.  
Figure 5: Example of the plain section by using the cross section tool in CloudCompare.  
Figure 6: Workflow of the point cloud segmentation based on the verticality feature (presented on case studies of ICONB and ICONC): (**a**) verticality computed for the original point cloud; (**b**) filtering points on the ones with a mainly horizontal orientation by adjusting the normalized value to the interval 0–0.1 (**top**) and 0–0.05 (**bottom**); and (**c**) filtering points on the ones with a mainly vertical orientation by adjusting the normalized value to the interval of 0.2–1 (**top**) and 0.05–1 (**bottom**).