Reassembling 3D Thin Fragments of Unknown Geometry in Cultural Heritage

Abstract. Many fragile antiques had already been broken upon being discovered at archaeology sites. The fragments of these objects cannot be effectively interpreted and studied unless they are successfully reassembled. However, there still exists many problems in the reassembly procedure in existing methods, such as the numerical instabilities of curvature and torsion based methods, the limitation of geometric assumption, and the error accumulation of the pairwise matching approach, etc. Regarding these problems, this paper proposed an approach to match the fragments to each other for their original 3D reconstruction. Instead of the curvatures and torsions, the approach is based on establishing a local Cartesian coordinate at every point of the 3D contour curves. First of all, the 3D meshes of the fragments are acquired by a structure-light based method, with the corresponding 3D contour curves extracted from the outer boundaries. Then, the contour curves are matched and aligned to each other by estimating all the possible 3D rigid transformations of the curve pairs with our defined local Cartesian coordinates, and then the maximum likelihood rigid transformations are selected. Finally, a global refinement is introduced to adjust the alignment errors and improve the final reassembling accuracy. In addition, experiments with two groups of fragments suggest that this approach cannot only match and align fragments effectively, but also improve the accuracy significantly. Comparing with the original 3D model acquired before being broken, the final reassembling accuracy reaches 0.47 mm.