# Two-Dimensional Shape Analysis of Complex Geometry Based on Photogrammetric Models of Iconostases
## 6 Discussion and Future Work  
In this paper, we focused on the shape analysis of photogrammetric models of the iconostases as the specific elements of the Christian Orthodox church heritage. The paper presents photogrammetric digitization applied to the case studies of the three representative examples of iconostases that originated from the Baroque, Classicism, and transition period between these two art movements in the territory of Vojvodina (Serbia). The main idea driving the proposed method for creating CAD-like plane sections based on photogrammetric models was to produce comprehensible auxiliary views of the irregular and organic geometry of the iconostasis' principal structure. The developed semiautomatic point segmentation approach allowed for the detection of exact points defining the contours of the main iconostasis' structural elements. The detected contours were further retraced and used inside a CAD environment in the shape analysis of the iconostasis' complex structure. Based on that, it was possible to perform a 2D shape analysis and to report well-founded conclusions about the iconostases' stylistic characteristics based on numerical descriptors. The significance of this method lies in its contribution to the shape analysis of the iconostasis' main elements that, due to the irregular shapes, cannot be easily classified as belonging to a particular artistic movement. Based on the comparative analysis of the results as reported in Section 5, the parameters for the classification of different iconostasis elements according to the artistic period were established. The range of variations of each shape descriptor for the different artistic movements was determined to provide the classification of iconostasis structural elements. Accordingly, we suggest that the compactness, convexity, solidity, and ellipticity shape descriptors can be used for classifying shapes with respect to the stylistic characteristics when applied to the icon shapes. The numerical results clearly reported the main characteristics of the two analyzed artistic movements. The resulting values for the icon shapes of the iconostasis originated from the Classicism period demonstrate a more compact, convex, and solid shape with the regular boundary, in contrast to those from the Baroque period which were distinguished by more irregular shape boundaries. In the analysis of \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Shape Descriptor** & \multicolumn{8}{c}{**Icon Shapes**} \\ \hline  & **S1** & **S2** & **S3** & **S4** & **S5** & **S6** & **S7** & **S8** & **S9** & **S10** \\ \hline \(Ecc(S)\) & 0.287 & 0.977 & 0.515 & 0.665 & 0.418 & 0.683 & 0.500 & 0.498 & 0.927 & 0.392 \\ \(Elo(S)\) & 0.670 & 0.103 & 0.470 & 0.335 & 0.560 & 0.317 & 0.494 & 0.440 & 0.079 & 0.532 \\ \(Cst(S)\) & 0.403 & 0.811 & 0.489 & 0.621 & 0.677 & 0.648 & 0.687 & 0.737 & 0.714 & 0.616 \\ \(C(S)\) & 0.842 & 0.933 & 0.806 & 0.874 & 0.994 & 0.872 & 0.989 & 0.967 & 0.886 & 0.961 \\ \(S(S)\) & 0.854 & 0.957 & 0.891 & 0.887 & 0.988 & 0.912 & 0.942 & 0.963 & 0.932 & 0.900 \\ \(R(S)\) & 0.792 & 0.817 & 0.745 & 0.764 & 0.953 & 0.795 & 0.892 & 0.772 & 0.754 & 0.738 \\ \(Ell(S)\) & 0.697 & 0.753 & 0.761 & 0.655 & 0.825 & 0.645 & 0.807 & 0.833 & 0.660 & 0.806 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental results of the calculated shape descriptors for ICONT. the third case study as used for the methodology assessment, the obtained quantitative results for the same descriptors tended to the values related to the iconostasis from the Baroque period. The behavior of the results for the third case study reflects its origins from the end of the Baroque period. For the descriptors listed above, the obtained results are in accordance with the general characteristics of the analyzed artistic movements. This proved the working hypothesis that the 2D shape analysis techniques may numerically describe the stylistic characteristics of the considered shape features when applied to 2D elements such as icon shapes.