Archaeological Fragment Reconstruction Using Curve-Matching

Abstract

We present a novel approach to the problem of puzzle solving as it relates to archaeological fragment reconstruction. We begin with a set of broken fragments. In the first stage, we compare every pair of fragments and use partial curve matching to find similar portions of their respective boundaries. Partial curve matching is typically a very difficult problem because the specification of the partial curves are highly unconstrained and curve matching is computationally expensive. To address the first problem, we only consider matches which begin at fragment corners and then use curve-matching with normalized energy to determine how far the match extends. We also reduce computational cost by employing a multi-scale approach. This allows us to quickly generate many possible matches at a coarse scale and only keep the best ones to be matched again at a finer scale. In the second stage, we take a rank-ordered list of pairwise matches to search for a globally optimal arrangement. The search is based on a best-first strategy which adds fragments with the highest pairwise affinity first, but then evaluates their confidence as part of the global solution by rewarding the formation of triple junctions which are dominant in archaeological puzzles. To prevent failure due to the inclusion of spurious matches, we employ a standard beam-search to simultaneously expand on multiple solutions. Results on several cases are demonstrated.1

Solving the T-Joint Problem in Reconstructing 2-D Objects

“…Most objects fragment in a way that forms triple junctions, such as T-joints. McBride and Kimia (2003) reported that in samples of broken ceramic tiles, T-joints ranged from 70-89% of the junctions, while other triple junctions ranged from 6-9%, and non-triple junctions ranged from 5-20%. Figure 1 shows a Tjoint.…”

“…These characteristics concern orientation of pieces, whether there are missing pieces, whether the exterior boundary is known beforehand (such as a rectangular grid), whether there is a unique solution, and what types of junctions between pieces are allowed (Kleber, 2009). Some approaches consider image features of the pieces, such as color and texture (Nielsen, Drewsen, & Hansen, 2008) and others consider shape of pieces (Da Gama Leitao & Stolfi, 2002;Freeman & Garder, 1964;Goldberg, Malon, & Bern, 2002;Horst & Beichl, 1996;Krebs et al, 1997;Kong & Kimia, 2001;Lee et al, 2003;McBride & Kimia, 2003;Radack & Badler, 1982;Stringfellow et al, 2008;Zhu, Zhou & Hu, 2008), while (Weiss-Cohen & Halevi, 2005;Yao & Shao, 2003) consider both.…”

“…Most of them compare the boundaries of the objects, represented by some sort of spline curve (Lee, Clark, & Araman, 2003;Krebs, Korn & Wahl, 1997) or polygonal approximation. The algorithms split curves at boundary points and then match sub curves (Freeman & Garder, 1964;Kong & Kimia, 2001;McBride & Kimia, 2003;Radack & Badler, 1982;Stringfellow, Simpson, Bui, Peng, & Hood, 2008;Weiss-Cohen, Halevi, 2005). Many approaches perform local shape analysis first, which results in ambiguous matches and require backtracking to resolve the mismatches (Freeman & Garder, 1964;Kong & Kimia, 2001;Radack & Badler, 1982;Stringfellow, Simpson, Bui, Peng, & Hood, 2008).…”

“…In both, the first step finds likely candidate pairs of pieces by computing affinity measures using polygonal approximation of pieces. In Kong and Kimia (2001) McBride and Kimia (2003) triples that arise from generic junctions (Y-and T-joints) are formed from this rank-ordered list of the top-ten pairings.…”

Parametric Estimation of Affine Deformations without Correspondences

“…The method can be extended to 3D fragments scanned by a laser range nder, where a pair of ridges are matched using a generalization of the 2D curve-matching approach. In [70], the rather high computational complexity of curve matching is reduced by adopting a multiscale technique. Papaioannou et al addressed the problem of 3D object reconstruction by just using the surface geometry of fragments, without assuming anything about the nal model to be reconstructed [80].…”