We propose to employ scale spaces of mathematical morphology to hierarchically simplify fracture surfaces of complementarity fitting archaeological fragments. This representation preserves complementarity and is insensitive to different kinds of abrasion affecting the exact fitting of the original fragments. We present a pipeline for morphologically simplifying fracture surfaces, based on their Lipschitz nature; its core is a new embedding of fracture surfaces to simultaneously compute both closing and opening morphological operations, using distance transforms.
When fitting archaeological artifacts, one would like to have a representation that simplifies fragments while preserving their complementarity. In this paper, we propose to employ the scale-spaces of mathematical morphology to hierarchically simplify potentially fitting fracture surfaces. We study the masking effect when morphological operations are applied to selected subsets of objects. Since fitting locally depends on the complementarity of fractures only, we introduce ‘Boundary Morphology’ on surfaces rather than volumes. Moreover, demonstrating the Lipschitz nature of the terracotta fractures informs our novel extrusion method to compute both closing and opening operations simultaneously. We also show that in this proposed representation the effects of abrasion and uncertainty are naturally bounded, justifying the morphological approach. This work is an extension of our contribution earlier published in the proceedings of ISMM2019 [10].
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.
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