# Two-Dimensional Shape Analysis of Complex Geometry Based on Photogrammetric Models of Iconostases
## 4 Method for 2D Shape Analysis Based on Photogrammetric Models  
The proposed method is divided into three main phases:  
1. iconostases photogrammetric digitization;
2. contour detection and extraction of the plane sections of the iconostasis' complex geometry based on point segmentation; and
3. shape analysis of the detected 2D contours through the application of shape descriptors and the measurements associated with them. In the first phase, a strategy for iconostasis photogrammetric digitization has been developed in order to produce detailed and accurate digital 3D models. The strategy is mainly based on designing a surveying plan that is applicable in the general case of the iconostasis photogrammetric 3D reconstruction. For the data processing, the professional photogrammetric software Agisoft Metashape was used. Photogrammetric 3D digitization consists of two main steps:  
* surveying, which implies on-site planning and recording, and the result of the surveying process is a set of photographs and
* data processing, which implies 3D reconstruction of the object using photogrammetric software, and the data processing product is a point cloud and a textured polygonal mesh. To produce comprehensible CAD-like plane sections, in the second phase, we developed a method for extracting characteristic auxiliary views of object geometry based on point segmentation. The semiautomatic point segmentation approach has been developed to create understandable plane sections of the iconostasis' complex geometry from the unstructured point cloud derived using photogrammetric 3D reconstruction. Instead of extracting pure plane sections through the point cloud, the idea was to obtain more understandable and readable plane visualizations with the reduced number of points that can serve to retrace the exact contours of the irregular shapes of the iconostasis' structural elements within the CAD environment. To extract plain sections of the iconostasis' principal structure, the verticality geometric feature extraction by using CloudCompare was applied to detect contours of object elements distinguished by their spatial orientation. The verticality of the geometric feature extraction of the 3D point cloud distinguishes a geometric shape around a point based on its local point neighborhood radius. Using this geometric feature, the points can be described with respect to their normal orientation, i.e., the position at right angles to the referent plane (in this case it was XY-plane). The angle between the XY-plane and the normal vector is computed using 3D surface normal values of each point [44; 45; 46; 47]. For example, the verticality can be well-suited to distinguish between facades and the ground [45]. The concept based on verticality geometric feature extraction is equal to the method of slope analysis which can also be defined as the angle between the vector normal to the surface at that point and the vertical [50]. However, instead of working with the rasterized image data, the method proposed in this paper is established on point cloud 2D CAD-like  
Figure 3: Examples of the archived technical drawings for the iconostases [60]. visualization. The idea driving the methodology was to create comprehensible 2D plane visualizations of complex geometry by extracting points that define contours distinguished by their spatial orientation. The 3D model was first segmented on the basis of its Digital Elevation Model (DEM) in order to sort the detected contours according to their depth values within the object. Then, the verticality feature extraction was performed. The proposed method for detecting contours and extracting plane sections covers processes from point cloud preparation and segmentation, up to the 2D CAD-like visualization.