Alignment of multiple non-overlapping axially symmetric 3D datasets

An axially-symmetric surface is broken into disjoint pieces along a set of break-curves, i.e., the curves along which the surface locally breaks into two pieces. A subset of the pieces is available and for each of them we obtain noisy 3D measurements of its surface and break-curves. Using the piece measurements and knowledge of which pieces share a common break-curve, we propose a stochastic method for automatically estimating the unknown axially-symmetric global surface. Surface and break-curve estimation is then an alignment problem where we must estimate the unknown axially-symmetric surface and break-curves while simultaneously estimating the Euclidean transformation that positions each measured piece with respect to the a-priori unknown surface. Parameter estimation is implemented as maximum likelihood estimation where we seek the global pot geometry which best explains the measured fragment data. This new approach is robust, fast, and accurate. Experimental results are presented which solves an application of interest, specifically the reconstruction of archaeological pots from subsets of their surface pieces.