We present a complete system for the purpose of automatically assembling 3D pots given 3D measurements of their fragments commonly called sherds. A Bayesian approach formulated which, at present, models the data given a set sherd geometric parameters. Dense sherd measurement is obtained by scanning the outside surface of each with a laser scanner. Mathematical models, specified by a set of geometric parameters, represent the sherd surface and break curves on the outer surface (where sherds have broken apart). Optimal alignment of assemblies sherds, called configurations, is implemented as maximum likelihood estimation (MLE) of the surface and curve parameters given the measured sherd data for sherds in a configuration.