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Colored Point Set Matching Under Noise in 3D

Let A and B be two colored points sets in R, 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”. Our algorithm consists of two main stages. In the first one we generate all, up to a certain equivalence, possible motions that bring A close to some subset B′ of B and seek for a matching between sets A and B′. To look for these possible matchings we use a bipartite matching algorithm that uses skip octrees for neighborhood queries. Additionaly, we also present a lossless filtering algorithm to discard those subsets of B where there can not appear any matches and thus, improve the efficiency of our process. This 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 octree 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 octree node.