### Abstract

Let A and B be two colored point sets in R^{2}, 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.

Original language | English |
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Title of host publication | Computational Science and Its Applications - ICCSA 2007 - International Conference, Proceedings |

Pages | 26-40 |

Number of pages | 15 |

Edition | PART 1 |

Publication status | Published - 2007 Dec 1 |

Event | International Conference on Computational Science and its Applications, ICCSA 2007 - Kuala Lumpur, Malaysia Duration: 2007 Aug 26 → 2007 Aug 29 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 4705 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | International Conference on Computational Science and its Applications, ICCSA 2007 |
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Country | Malaysia |

City | Kuala Lumpur |

Period | 07/8/26 → 07/8/29 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Computational Science and Its Applications - ICCSA 2007 - International Conference, Proceedings*(PART 1 ed., pp. 26-40). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4705 LNCS, No. PART 1).