This video provides details on custom-designed software that takes as input 3D (x,y,z) measurements of the outer surfaces of a set of broken pottery fragments and outputs the "most likely" pots from which the fragments were generated. For demonstration, a 10-piece puzzle solution is loaded and details regarding the assembly software and how the program works is outlined.
A probabilistic approach is taken which attempts to compute and maximize the joint probability of the fragment data given an assumed set of correspondences between the fragment boundaries and that the collection of all matched fragments share the same central axis and profile curve, i.e., the profile of the pot when viewed from the side is shared by all fragments when they are correctly aligned. The output of the system is a collection of solutions, listed in order of their probability.
Additionally, one can track the assembly process which starts with pairs of fragments that match well and then proceeds by merging a pair with another configuration of fragments, i.e., if fragment pairs (A,B) and (B,C) match well then the triplet (A,B,C) is a triplet formed by merging two pairs. The assembly process continues merging fragment groups (called configurations) until all of the fragments have been merged. At each stage, the algorithm merges a fragment group with a fragment pair that has the highest joint likelihood of being correct prior to computing the exact match.