Pairwise Alignment of Archaeological Fragments Through Morphological Characterization of Fracture Surfaces

We design a computational method to align pairs of counter-fitting fracture surfaces of digitized archaeological artefacts. The challenge is to achieve an accurate fit, even though the data is inherently lacking material through abrasion, missing geometry of the counterparts, and may have been acquired by different scanning practices. We propose to use the non-linear complementarity-preserving properties of Mathematical Morphology to guide the pairwise fitting in a manner inherently insensitive to these aspects. In our approach, the fracture surface is tightly bounded by a concise set of characteristic multi-local morphological features. Such features and their descriptors are computed by analysing the discrete distance transform and its causal scale-space information. This compact morphological representation provides the information required for accurately aligning the fracture surfaces through applying a RANSAC-based algorithm incorporating weighted Procrustes to the morphological features, followed by ICP on morphologically selected ‘flank’ regions. We propose new criteria for evaluating the resulting pairwise alignment quality, taking into consideration both penetration and gap regions. Careful quantitative evaluation on real terracotta fragments confirms the accuracy of our method under the expected archaeological noise. We show that our morphological method outperforms a recent linear pairwise alignment method and briefly discuss our limitations and the effects of variations in digitization and abrasion on our proposed alignment technique.