Geometric Structure Estimation of Axially Symmetric Pots from Small Fragments

The recovery of geometric structure from noisy data poses difficult non-linear statistical estimation problems. This paper describes a novel, robust, low computational cost approach for finding the geometric structure of an axially symmetric pot from a small fragment of it (an unorganized set of 3D points). This problem is of great archaeological importance to the study of the hundreds and thousands of shards found at excavation sites. Our method is based on the following fact: for each point on the surface, the center of the sphere of principal curvature corresponding to the circles of revolution is on the symmetric axis. By finding the line which minimizes the weighted leastsquares distance to the estimated centers, we can find first the symmetric axis and then the profile curve. Because of the special properties of a surface of revolution, we can do this using only first derivatives, hence this method is robust to noisy data. We then use bootstrap methods to find confidence bounds for the axis and the profile curve. These confidence bounds are essential if the estimations are used for the assembly of the full pot from multiple sherds.