Efficient colored point set matching under noise

Let A and B be two colored point sets in R², with \A\ ≤ \B\. We propose a process for determining matches, in terms of the bottleneck distance, between A and subsets of B under color preserving rigid motion, assuming that the position of all colored points in both sets contains a certain amount of "noise". The process consists of two main stages: a lossless filtering algorithm and a matching algorithm. The first algorithm determines a number of candidate zones which are regions that contain a subset S of B such that A may match one or more subsets B′ of S. We use a compressed quadtree to have easy access to the subsets of B related to candidate zones and store geometric information that is used by the lossless filtering algorithm in each quadtree node. The second algorithm solves the colored point set matching problem: we generate all, up to a certain equivalence, possible motions that bring A close to some subset B′ of every S and seek for a matching between sets A and B′. To detect these possible matchings we use a bipartite matching algorithm that uses Skip Quadtrees for neighborhood queries. We have implemented the proposed algorithms and report results that show the efficiency of our approach.