TY - GEN

T1 - Efficient colored point set matching under noise

AU - Diez Donoso, Santiago

AU - Sellarès, J. Antoni

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:38049032913

SN - 9783540744689

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 26

EP - 40

BT - Computational Science and Its Applications - ICCSA 2007 - International Conference, Proceedings

T2 - International Conference on Computational Science and its Applications, ICCSA 2007

Y2 - 26 August 2007 through 29 August 2007

ER -