Intrinsic Shape Analysis in Archaeology: A Case Study on Ancient Sundials

Author:

Hanik Martin1ORCID,Ducke Benjamin2ORCID,Hege Hans-Christian3ORCID,Fless Friederike2ORCID,Tycowicz Christoph Von1ORCID

Affiliation:

1. Freie Universität Berlin, Germany

2. German Archaeological Institute, Germany

3. Zuse Institute Berlin, Germany

Abstract

The fact that the physical shapes of man-made objects are subject to overlapping influences—such as technological, economic, geographic, and stylistic progressions—holds great information potential. On the other hand, it is also a major analytical challenge to uncover these overlapping trends and to disentagle them in an unbiased way. This article explores a novel mathematical approach to extract archaeological insights from ensembles of similar artifact shapes. We show that by considering all shape information in a find collection , it is possible to identify shape patterns that would be difficult to discern by considering the artifacts individually or by classifying shapes into predefined archaeological types and analyzing the associated distinguishing characteristics. Recently, a series of high-resolution digital representations of artifacts have become available. Such datasets enable the application of extremely sensitive and flexible methods of shape analysis. We explore this potential on a set of 3D models of ancient Greek and Roman sundials, with the aim of providing alternatives to the traditional archaeological method of “trend extraction by ordination” (typology). In the proposed approach, each 3D shape is represented as a point in a shape space —a high-dimensional, curved, non-Euclidean space. Proper consideration of its mathematical properties reduces bias in data analysis and thus improves analytical power. By performing regression in shape space, we find that for Roman sundials, the bend of the shadow-receiving surface of the sundials changes with the latitude of the location. This suggests that, apart from the inscribed hour lines, also a sundial’s shape was adjusted to the place of installation. As an example of more advanced inference, we use the identified trend to infer the latitude at which a sundial, whose location of installation is unknown, was placed. We also derive a novel method for differentiated morphological trend assertion, building upon and extending the theory of geometric statistics and shape analysis. Specifically, we present a regression-based method for statistical normalization of shapes that serves as a means of disentangling parameter-dependent effects (trends) and unexplained variability . In addition, we show that this approach is robust to noise in the digital reconstructions of the artifact shapes.

Funder

Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strateg through MATH+, the Berlin Mathematics Research Center

Bundesministerium für Bildung und Forschung (BMBF) through BIFOLD, the Berlin Institute for the Foundations of Learning and Data

Publisher

Association for Computing Machinery (ACM)

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Information Systems,Conservation

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