# Two-Dimensional Shape Analysis of Complex Geometry Based on Photogrammetric Models of Iconostases
## 4 Method for 2D Shape Analysis Based on Photogrammetric Models
### Iconostases' Photogrammetric Digitization
#### 4.1.1 Photogrammetric Surveying  
Designing the on-site surveying plan is necessary to obtain highly accurate 3D reconstruction results in terms of the relationship between the texture resolution and the ground sample distance (GSD). The GSD represents the distance between adjacent pixel centers expressed in an object scale. Considering the specific iconostasis shape, distinguished by significantly lower object depth compared to its width, as well as the highly detailed ornamentation, the goal of the surveying process was to achieve the highest possible resolution of the smallest object details. The quality of surveying directly impacts the precision of the 3D reconstruction, therefore high-resolution measures were required. The surveying plan was designed according to the iconostasis' shape as well as the specific church location and lighting conditions and constraints. The surveying was conducted using a tripod and a DSLR camera D7000 (NIKON, Tokyo, Japan, pixel number: 4928 \(\times\) 3275; pixel size: 4.78 \(\upmu\)m; sensor size: 23.6 \(\times\) 15.6 mm; focal length: 18-109 mm).  
The strategy was based on calculating several main parameters. The first part of the surveying plan referred to determining camera parameters and locations according to the object geometry and dimensions. We used a wide-angle lens with a 24 mm focal length (\(c\)) and the maximum possible distance of the camera to the object (\(h\)) that allowed for covering the whole iconostasis height with one stripe of photographs. By determining these parameters, the object scale and the GSD were calculated as follows:  
\[m=\frac{h}{c}, \tag{1}\]  
\[\text{whereGSD}=m\times\text{pixel size}. \tag{2}\]  
To select an appropriate camera mode (landscape or portrait), the object space covered by a photograph (\(D\)) was calculated in the following way:  
\[D=\text{GSD}\times\text{pixel number (width)}, \tag{3}\]  
\[D=\text{GSD}\times\text{pixel number (height)}, \tag{4}\]  
where the pixel number width and height are defined by the camera model: 4928 \(\times\) 3275.  
The explained method could be applied in the reverse mode as well by calculating the GSD according to the dimensions of the desired space covered by a photograph in a predefined camera mode.  
Due to the nature of the iconostasis' shape, photographs were taken in a parallel fashion, combined with divergent camera locations. The camera was rotated in the right and left direction by the angle of approximately 10\({}^{\circ}\) to introduce detailed iconostasis depth into the 3D model. To provide an average overlapping of 80% between consecutive photographs, the baseline (\(b\)) was calculated as follows:  
\[b=0.20\times(\text{pixel number (width)}\times\text{GSD}). \tag{5}\]  
The calculated parameters for the three case studies of the iconostases' digitization are shown in Table 1.  
The second part of the surveying plan implied setting appropriate image exposure parameters to achieve the highest image quality and sharpness. First, the automatic camera mode was used to measure the church interior light. Furthermore, the measured in-site image exposure parameters such as aperture and ISO speed were manually set and the aperture priority mode was employed to determine the correct shutter speed. The lighting conditions of the church interior are usually characterized by a very low illumination which resulted in a long shutter speed (Table 1). For that reason, it was essential to use a tripod and delayed shutter to avoid camera shaking. Considering the shooting distances and the aperture, the focus point was fixed and the depth of field (DoF) was checked to achieve the correct sharpness of the photographs.  
Table 1 shows that the surveying parameters do not vary significantly between the case studies, which suggests that the proposed methodology for the iconostasis surveying could be repeated in digitization scenarios of other iconostases.