Geometric and topological tools for quantave analysis in archaeology: the Ayia Irini case study A. Scalas 1 , V. Vassallo 2 , M. Mortara 1 , M. Spagnuolo 1 1 Istuto di Matemaca Applicata e Tecnologie Informache “Enrico Magenes”, Consiglio Nazionale delle Ricerche (CNR-IMATI), Italy. 2 The Cyprus Instute—STARC, Cyprus/Department of Ancient History and Archaeology-Lund University, Sweden The GRAVITATE project addresses the world of Cultural Heritage and related science. The innovave aspect of the project is to create a digital plaorm that allows Re-Unificaon, Re-Associaon and Re-Assembly of heritage ar- facts, based on 3D geometry, shape analysis, colour features, semanc metadata and natural language proces- sing. The integraon of these approaches into a single decision support plaorm, with a full suite of visualisa- on tools provides a unique resource for the cultural heritage research community. The aim of the project is to support sciensts to Re-Assemble fragmented and broken heritage arfacts, idenfy and Re-Unify parts that were separated across collecons and to recognise and Re-Associate cultural heritage ar- facts that have common features, allowing new knowledge and understanding of past sociees to be inferred. Among all the collecons which are being studied in the context of GRAVITATE, we are focusing on the Ayia-Irini collecon. The Ayia Irini collecon consists of almost 2000 vove clay statues and stat- uees of different size, shape and style found in a Cypriot sanctuary by a Swedish expedion in the 20th century [1]. Aſter the excavaon, the artefacts were divided between Sweden and Cyprus and they are currently conserved in five different museums. 103 statuees, from the different hosng instuons and belonging to the so called ‘small, human idols’ (max. 27 cm height), have been cho- sen and digized both through laser scanning and photogrammetric technique in order to produce 3D replicas to be quantavely analyzed by the means of geometric and topological tools. The items sampled belong to 3 typological groups created by the archaeologists according to a qualitave stylisc archaeological classificaon. According to the archaeologists who excavated and studied the site, the statuees sampled for this research can be classified into three typological groups: Type 5, 6 and 7. The Type 5 and 6 are characterized by hand-made statuees sharing similar characteriscs which make difficult a definite aribuon to a class respect to another. Moreover, some items present shared features and similaries that make us hypothesize the presence of pro- ducon paerns that could be meaningful for the idenficaon of workshops or even different arsans’ hands. The statuees aributed to Type 7 are made by three integrated techniques (hand-made, wheel-made and moulded) and share more defined characteriscs. The archaeologists state that for these statuees different kind of moulds were used to produce their heads. The 3D analysis aims at quantavely test this infor- maon and to detect other characteriscs that can help us to idenfy further producon paerns and possibly a chronological sequence [2] [3]. Project Funded by The European Commission This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement 665155 Quanty Enty How do we obtain it Already implemented Thickness Transversal slices We slice the base and compute the average distance between the inner and outer boundary. Eccentricity Transversal slices The minimum bounding rectangle of the slice is extracted (following the approach described in [4]) and then the ec- centricity is computed as the rao between the maximal and minimal axis of the rectangle. Circularity Roundness Transversal slices The roundness of a slice measures how much its shape resembles the one of a perfect circle. We obtain such a measure fing a circle [5] to the slice and extracng the distances between each point of the slice and the circle. Distance from the principal axis Mulple transversal slices We extract slices at different heights and compute the average of their barycenter and then, for each one, we com- pute the distance between its barycenter and the average one. The average of this distances is a good approxima- on of the distance from the principal axis. Shape of the head Mulple transversal slices The shape of the head is well approximated by the shape of some of its transversal slices. So, we extract them and compare them, qualitavely by now. Size of the statue Volume An approximaon of the volume of the statue can be given by its oriented bounding box. So, we extract it from the model using MathGeoLib library [6] (which uses the approach described in [7]) and then compute the volume of the obtained parallelepiped (area of the base mes the height). Future works Features posion Surface We are planning to exploit surface informaon (e.g., the curvature ) to find the posion of certain features (e.g., arms) Distance from the principal axis Mulple transversal slices The principal axis can be defined in different ways: 1. Rotaonal simmetry axis; 2. The line passing through the centers of the bases of the best fing cylinder. We will try this possibilies and take the best one. Shape of the head Mulple transversal slices We are planning to define a skeleton based descripon of some well-defined slices, which enclose the principal cha- racteriscs of the head (e.g. the transversal slice through the p of the nose). Size of the statue Volume We will translate the triangular meshes to tethraedral ones and compute a beer approximaon of the volume. The GRAVITATE plaorm is divided into a web-client and a desktop-client, which are connected to each other. The web client allows users to perform semanc and geometric queries. The desktop-client supports analysis and documentaon of the retrieved objects and provides five different views: Inspecon, Fragment, ReAssembly, History and Groups, with tools specific for each view. The Fragment view allows analysis and annotaon of fragments. In parcular, it is possible to visualise geometric properes such as the mean curvature, and detect features such as eyes and mouths in a statue or 2D and 3D paerns. The part-based annotaon of 3D mo- dels takes also place in this view, where a controlled vocabulary, the Cultural Heritage Arfact Partonomy (CHAP), has been defined to an- notate the interesng parts of the fragment under invesgaon. Archaeological quesons 1. Is that possible to idenfy different levels of experse according to the uniformity of the statuees’ clay width and other dimen- sions ? 2. Is the presence of fixed measurements, raos between the parts and geometric similaries expression of a ‘serial’ producon to be aributed to specific workshops or arsans’ hands? 3. How many moulds can be idenfied in our sample? How many artefacts come from the same mould? Is it possible to idenfy a ‘chronological sequence’ through the comparison of the heads which seem to come from the same mould? 4. Can quantave analysis produce data useful for the automac classificaon of archaeological material? To help the reply to the defined archaeological quesons, we idenfied several measures. 1. The experse of the arsan can be quanfied analyzing: a. The variance of thickness of the material in the tubular part of a statuee; b. A measure of how much the tubular part is circular (circularity); c. A straightness measure for the tubular part (distance from the principal axis). These measures are more meaningful for specific type of statues (e.g., straightness is not very meaningful for wheel- made objects - the result is almost always prey straight, because it is done with an external tool - while it express very well the arsan ability for hand-made ones, while the opposite holds for the variance of thickness). 2. Fixed measures that can be analyzed to find similaries are: a. Total size; b. Posion and length of the arms; c. Rao between the body parts measures; d. Clay amount (volume ). 3. Defined some descriptors for the shape of the heads, it is possible to cluster them. Then we can count the number of clu- sters and the number of artefacts produced with a specific cluster. We can even further analyze heads produced with the same mould (same cluster) to see if the total volume is different (higher volume can suggest deterioraon of the mould) or if some parts of the head had changed in shape (e.g., a smoother surface or a crooked nose can suggest that the corre- sponding part of the mould had changed) and this could suggest a chronological sequence; 4. Different experiments can be performed to search for meaningful descriptors for allowing a clustering of the statuees. Bibliography [1] Gjerstad, E., Lindros, J., Sjöqvist, E., Westholm, A. The Swedish Cyprus Expedion II (SCE II). Finds and results of the excavaons in Cyprus 1927-1931, Stockholm 1935, 642-824. [2] Vassallo V. 2016. A 3D digital approach to study, analyse and (re)interpret cultural heritage: the case study of Ayia Irini (Cyprus and Sweden). In S. Campana, R. Scopigno, G. Carpenero and M. Cirillo (eds), Keep The Revoluon Going. Proceedings of the 43rd Annual Conference on Computer Applicaons and Quantave Methods in Archaeology. Archaeopress, 227-232. [3] Vassallo, V. 2017. The archaeological collecon of Ayia Irini (Cyprus). A 3D digital approach to analyse and reinterpret a 20th century study. Ancient Cyprus, an unexpected journey. Communies in Connuity and Transion. Luca Bombardieri, Ma- rialucia Amadio and Francesca Dolce (Eds.), Artemide: Roma. [4] Toussaint, Godfried T. (1983). "Solving geometric problems with the rotang calipers". Proc. MELECON '83, Athens. [5] Coope, Ian D. (1993). "Circle fing by linear and nonlinear least squares". Journal of Opmizaon Theory and Applicaons 76, 2, 381–388. 2 [6] hp://clb.demon.fi/MathGeoLib/nightly/ [7] Jukka, Jylanki (2015). "An Exact Algorithm for Finding Minimum Oriented Bounding Boxes ". Type 7 “conical helmet” “long pointed hat” “long curved helmet” “short pointed hat” “truncated coni- cal helmet” “turbant hat” “short conical helmet” Type 5 “long squared helmet” Type 6  Manufacturing  Head: hand-made vs moulded  Body: hand-made vs wheel-made  Measurements and proporons (only total height and weight of statues available)  Presence, posion and shape of features: Base, Body Parts (arms, nose, ears, eyes), Garments (hat or helmet, mantle, …), Accessories (musical instruments, animals, weapons ) Slices similarity: some quite similar slices (in pairs) with the corresponding approxi- mate skeleton Minimal volume bounding box Thickness Eccentricity Roundness Straightness Handmade statuee Wheel-made statuee Best fing circle on a slice of the tubular part Curvature on the mesh surface Parametric template: the quantave analysis of the collecon is likely to reveal new classificaons into subgroups having homoge- neous properes (proporons, relave posion of features, etc.). We plan to define a parametric template for each subgroup. The template will be an abstract representave of a class of similar statues, encoding the geometric variability and structural properes of the class instan- ces and retaining semanc relaonships among the statue feature and parts. Applicaons of the template will be: the classificaon of statues based on a measure of deviaon from templates; the deformaon of statues constrained by the structural and semanc “rules” encoded in the template; the fing of fragments on a proper template to make hypotheses about the original shape. Roundness Eccentricity Precision 0.8167 0.7353 Recall 0.8167 0.6667 F1-score 0.8167 0.6993 0 10 20 30 40 50 60 70 80 Wheel-made statuettes Handmade statuettes A handmade/wheel-made classification based on eccentricity and roundness data Correct classification Eccentricity classification Roundness classification View publication stats View publication stats