This paper studies matching of fragmented objects to recompose their original geometry. Solving this geometric reassembly problem has direct applications in archaeology and forensic investigation in the computer-aided restoration of damaged artifacts and evidence. We develop a new algorithm to effectively integrate both guidance from a template and from matching of adjacent pieces' fracture-regions. First, we compute partial matchings between fragments and a template, and pairwise matchings among fragments. Many potential matches are obtained and then selected/refined in a multi-piece matching stage to maximize global groupwise matching consistency. This pipeline is effective in composing fragmented thin-shell objects containing small pieces, whose pairwise matching is usually unreliable and ambiguous and hence their reassembly remains challenging to the existing algorithms.

We develop a completion pipeline for fragmented and damaged skulls. The goal of this work is to convert scanned incomplete skull fragments to a complete skull model for subsequent forensic or archeological tasks such as facial reconstruction. The proposed assembly and completion algorithms can also be used to repair other fragmented objects with inherent symmetry. A two-step assembly framework is proposed: (1) rough assembly by an ICP-like template matching algorithm integrated with the slippage features and spin-image descriptors; (2) assembly refinement by a global optimization on least square transformation error (LSTE) of break-curves. The assembled skull is finally repaired by a symmetry-based completion algorithm. Experiments on repairing scanned skull fragments demonstrate the efficacy and robustness of this framework.