# Two-Dimensional Shape Analysis of Complex Geometry Based on Photogrammetric Models of Iconostases
## 1 Introduction  
Although two decades have passed since the pioneering digital heritage project, the Digital Michelangelo Project [1], three-dimensional (3D) digitization still represents a flourishing field of research and application in cultural heritage. Ever since 3D acquisition and digitizing technologies have been proved as sufficiently developed for extensive application in the field of tangible cultural heritage, they have been used for reconstruction, conservation, digital restoration, and monitoring, as well as for physical replication and remote fruition [2]. Cultural heritage digitization is especially important in the cases of 3D reconstruction, preservation, and conservation of cultural heritage that is in some way unavailable or inaccessible and when no other data about an object is available. One specific branch of such types of cultural heritage is church heritage due to its unique value and context. Church heritage presents a significant type of tangible cultural heritage that can be appreciated only in situ. In the context of the Christian Orthodox church heritage, the iconostasis represents one of the most notable features and the dominating art and architectural element of thechurch interior. The iconostasis, whose name originates from the Greek language and means 'icon stand', represents a highly ornamented element of the Christian Orthodox church interiors, which serves simultaneously as a vertical frame composed of icons and the physical division between a sanctuary containing an altar and a naive in a church. Iconostases initially evolved from a very low altar screen, called Byzantine templon, which was later on lifted higher using columns that supported an overhead, to gradually becoming a high icon screen [3; 4; 5; 6]. Their development into a multi-tier and richly decorated vertical frame, composed of religious paintings usually painted by the most influential artists of that time, made them the most decorative and ornamental elements of the Christian Orthodox churches. The iconostasis construction is characterized by a mainly flat shape but with complex and irregular geometry of rich ornamental carvings, usually made of wood or marble, with the icons placed from behind into highly decorated frames. The unique frame carving works have an equal place with the icons in the whole iconostasis structure. Moreover, the iconostasis' decorative woodcarving and plasterworks represent one of the strongest contributions to European applied arts. In addition, art history has noted that there are no two identical iconostases [7]. Given the heterogeneous nature of the iconostasis shape, the question arises whether it is possible to mathematically perceive common style-related shape characteristics of the iconostasis' main elements. The architectural and visual characteristics of iconostases are mostly related to the period of church origin. Moreover, while the design of the iconostasis' ornamental structure was based on naturalistic floral motifs that symbolized theological themes, the style characteristics mainly depended on the craftsman's skills and imagination [4]. Considering the style characteristics of complex geometry are often difficult to define, the mathematical analysis of the real-world building characteristics helps to cope with data uncertainty in the study of an architectural type [8; 9; 10]. Mathematical methods based on shape analysis techniques have been widely used in the tasks of object identification, recognition, and classification [11; 12; 13; 14; 15]. The shape-based object analysis approach can be used to study, numerically describe, and classify diverse types of engineering and architectural elements [14]. Furthermore, the identification of different components in 3D models of cultural heritage is significant as it can contribute to the more efficient study of digital heritage and integrating it with metric information and attributes [16].