This paper addresses how to automatically reconstruct pottery vessels from a collection of sherds using a variety of features and their comparisons. We present a computational framework that is founded on the primitive operations of "match" proposal and evaluation, where a match defines the geometric relationship between a pair of sherds. This framework affords a natural decomposition of the computation required by an automatic assembly process and provides a concrete basis to evaluate the utility of different features and feature comparisons for assembly. Our framework paves the way for a system to automatically reconstruct pottery vessels. We demonstrate a greedy assembly strategy that predicts likely pairs and triples of sherds using a handful of proposal and evaluation modules.