Archaeological objects are often discovered broken into many pieces, and reassembling the original object by solving the three-dimensional puzzle is a time-consuming and expensive task, referred to here as the fragmentation problem. This article describes a methodology that can facilitate the matching of fragments from broken objects, with the use of statistical analysis and three-dimensional computer models. First, the nature of three-dimensional computer models of archaeological objects is explained, emphasizing the benefits of using unit normal vectors to characterize their surfaces. A computer-based model of such an object can be separated into clearly defined and different surfaces through a process called segmentation. The resulting segments are then subjected to a novel statistical analysis, which is based on the calculation of eigenvalues of the unit vectors in Riemannian space. This allows the fragments' surfaces to be characterized, and it is this characterization that leads to fragment matching. As part of the research, a pilot study was undertaken using objects from the Propylaia of Athens and ancient Messini. The results are presented and ways proposed of both improving the methodology and using it in other conservation-related applications.