Accurately Estimating Sherd 3D Surface Geometry with Application to Pot Reconstruction

Abstract

Archaeological ContextIn antiquity, pots and vases were mass-produced by civilizations for use in a variety of contexts. Hence, pieces of pots and vases, hereafter referred to as sherds, are prevalent artifacts uncovered in many archaeological excavation sites. By studying these fragments, archaeologists obtain great amounts of information about ancient civilizations. This paper provides a highly accurate solution to the difficult problem of extracting a geometric model of the unknown pot structure in the region associated with 3D measurements obtained from a sherd. The model extracted may be used in a variety of applications. Some examples are:shape-based searching of 3D sherd databases; sherd classification; and pot reconstruction. In §7, we touch on the specific application of our models to pot reconstruction. Surfaces of RevolutionThe notation and terminology adopted for surfaces in this paper is that used in classic texts such as [10,7]. A surface of revolution S ∈ 3 is obtained by revolving a planar curve C ∈ 2 about a line l ∈ 3. α is called the profile (or generating) curve and l the axis of S. When the Z-axis is taken as the axis of revolution with profile curve α(z), the surface S may be represented parametrically asWith this parametrization, the curves z = constant are parallels of S and the curves θ = constant are meridians of S. The profile curve characterizes how the radius and height of the surface change for a fixed meridian, see Fig (1). In the literature, [14], an axially symmetric surface is a special case of a Simple Homogeneous Generalized Cylinder, SHGC, one which has circular cross section. In (1), the radius function, r = α(z), is a single-valued function of z. In the case of archaeological sherds, there often occur multiple radius values for a specific height z. Examples include sherds which come from pot bases and rims, see Fig. 3 for

On the mathematical formulation of the problem of reassembling fragmented objects: two new theorems

“…have been made so far in order to tackle this problem [2][3][4] and [5]. The authors have developed a novel methodology that has succeeded in reassembling fragmented archaeological objects and not only.…”

Optimization for automated assembly of puzzles

“…More general partial curve matching algorithms that solve the global 2D and 3D assembly problems based on geometrical properties were presented in (Kong 2001;Radack 1982;Willis 2003). The problem of 3D curves is addressed by (Ucoluk 1999).…”

“…This method detects candidate fractured faces, matches fragments one by one and assembles fragments into complete or partially complete entities. The Shape Lab at Brown University presents an approach to automatic estimation of mathematical models of axially symmetric pots made on a wheel (Willis 2002(Willis , 2003. This technique is based on matching break curves, estimated axis and profile curves, a number of features of groups of break-curves.…”

Bayesian assembly of 3D axially symmetric shapes from fragments

“…In [17] fast and robust methods are provided for the difficult problem of estimating (l, α), the axis/profile-curve pairs from small patches of noisy 3D data measurements of axially-symmetric surfaces which is the case for archaeological pot fragment data. We have parameterized the pot axis of symmetry using the standard parametric equation of a 3D line as shown in (1).…”

“…In addition, a number of insights are given which have not previously been discussed and significantly reduce computation. A working implementation of the Bayesian framework introduced in [17,15,16] and further developed in [14] is presented for the purpose of assembling pots from 3D measurements of their fragments which we refer to as sherds.…”