Although mature technologies exist for acquiring images, geometry, and normals of small objects, they remain cumbersome and time-consuming for non-experts to employ on a large scale. In an archaeological setting, a practical acquisition system for routine use on every artifact and fragment would open new possibilities for archiving, analysis, and dissemination. We present an inexpensive system for acquiring all three types of information, and associated metadata, for small objects such as fragments of wall paintings. The acquisition system requires minimal supervision, so that a single, non-expert user can scan at least 10 fragments per hour. To achieve this performance, we introduce new algorithms to robustly and automatically align range scans, register 2-D scans to 3-D geometry, and compute normals from 2-D scans. As an illustrative application, we present a novel 3-D matching algorithm that efficiently searches for matching fragments using the scanned geometry.

In this paper, an original general methodology is introduced to establish whether a handmade shape corresponds to a given geometrical prototype. Using this methodology, one can decide if an artist had the intention of drawing a specific mathematical prototype or not. This analysis is applied to the 1650 B.C. wall paintings from the prehistoric settlement on Thera, and inferences of great archaeological and historical importance are made. In particular, strong evidence is obtained suggesting that the spirals depicted on the wall paintings correspond to linear (Archimedes) spirals, certain shapes correspond to canonical 48-gon and 32-gon, while other shapes correspond to parts of ellipses. It seems that the presented wall paintings constitute the earliest archaeological findings on which these geometrical patterns appear with such remarkable accuracy.