# Two-Dimensional Shape Analysis of Complex Geometry Based on Photogrammetric Models of Iconostases
## 1 Introduction
The aim of this study is to numerically describe and classify the stylistic characteristics of the shapes of the main parts of an iconostasis, concerning the artistic period to which it belongs. The working hypothesis was defined as follows: Two-dimensional (2D) shape analysis techniques may be used to numerically describe the stylistic characteristics of the considered shape features of the main parts of the iconostases (icons and constructive elements), derived from their photogrammetric models. For that purpose, shape description techniques were used to mathematically characterize shapes of the main architectural elements of the iconostases, concerning its style origins. The particular shape descriptors and measurements associated with them were conceptually conceived. The shape measurements were based on the objects' dimensions and were designed to reflect the main attributes of the real shapes. For numerical characterization of such shape attributes, the shape descriptors were applied to the particular 2D shapes extracted from the digitized 3D models. The research presented in this paper focuses on the basic application of mathematical shape descriptors, while working with digitized data of cultural heritage inside a computer aided design (CAD) environment. The framework of this study refers to the concepts of the contour-based and region-based shape descriptors [17] as one of the possible methods for analyzing complex or unknown geometric characteristics from the digitized cultural heritage data. The concept was applied to the technical drawings of contours of the characteristic shapes extracted from the digitized 3D models of the iconostases. Regarding the archiving of the technical data on iconostases, the project documentation is based either on the hand-drawings created prior to the iconostasis construction or on the traditional CAD drawings resulting from the on-site measurements. The existing hand-drawings created prior to the iconostasis construction were mostly based on simplified schemes that do not contain enough details. This is caused by the long historical origins of iconostases, but also by the fact that iconostases were developed as a result of exceptional knowledge and skills of craftsmen, with no previously created detailed project documentation. Conversely, due to the complex geometry of iconostases, manual CAD drawings based on the current object state may suffer from errors in measurement and imprecise interpretation of irregular and organic shapes of iconostasis' ornamental elements. The lack of technical documentation complicates preservation, archiving, and restoration processes. Nevertheless, creating the technical 2D documentation for the iconostasis' complex geometry with many small and irregular details is a challenging task. Producing detailed CAD drawings based on on-site measurements would be an imprecise, demanding, and time-consuming work. The detailed CAD models of such a complex geometry should be based on the different views of the same model, as well as on the different levels of detail and abstraction [18]. The research presented in this paper addresses the challenge of reverse modeling, which is the creation of CAD-like documentation, and contour detection for the complex geometry from digitized 3D models of iconostases. To detect contours and extract understandable plane sections from unstructured point clouds derived from photogrammetric modeling, the method for point segmentation based on the verticality geometric feature was developed. The obtained results illustrated that the proposed method provides detailed 2D visualization of complex geometry that is not easily recognizable from the colored point cloud. The paper describes an interdisciplinary approach to distinguish different style characteristics of the iconostases. For this purpose, the representative examples of iconostases from the Baroque and Classicism art movements on the territory of Vojvodina (Serbia), that were previously digitized, were compared using the mathematical method of shape analysis.