### Abstract

The Fréchet distance is a metric to compare two curves, which is based on monotone matchings between these curves. We call a matching that results in the Fréchet distance a Fréchet matching. There are often many different Fréchet matchings and not all of these capture the similarity between the curves well. We propose to restrict the set of Fréchet matchings to “natural” matchings and to this end introduce locally correct Fréchet matchings. We prove that at least one such matching exists for two polygonal curves and give an O(N^{3}logN) algorithm to compute it, where N is the number of edges in both curves. We also present an O(N^{2}) algorithm to compute a locally correct discrete Fréchet matching.

Language | English |
---|---|

Pages | 1-18 |

Number of pages | 18 |

Journal | Computational Geometry: Theory and Applications |

Volume | 76 |

DOIs | |

State | Published - 1 Jan 2019 |

### Fingerprint

### Keywords

- Fréchet distance
- Local correctness
- Matching
- Similarity

### Cite this

*Computational Geometry: Theory and Applications*,

*76*, 1-18. DOI: 10.1016/j.comgeo.2018.09.002

}

*Computational Geometry: Theory and Applications*, vol. 76, pp. 1-18. DOI: 10.1016/j.comgeo.2018.09.002

**Locally correct Fréchet matchings.** / Buchin, Kevin; Buchin, Maike; Meulemans, Wouter; Speckmann, Bettina.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Locally correct Fréchet matchings

AU - Buchin,Kevin

AU - Buchin,Maike

AU - Meulemans,Wouter

AU - Speckmann,Bettina

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The Fréchet distance is a metric to compare two curves, which is based on monotone matchings between these curves. We call a matching that results in the Fréchet distance a Fréchet matching. There are often many different Fréchet matchings and not all of these capture the similarity between the curves well. We propose to restrict the set of Fréchet matchings to “natural” matchings and to this end introduce locally correct Fréchet matchings. We prove that at least one such matching exists for two polygonal curves and give an O(N3logN) algorithm to compute it, where N is the number of edges in both curves. We also present an O(N2) algorithm to compute a locally correct discrete Fréchet matching.

AB - The Fréchet distance is a metric to compare two curves, which is based on monotone matchings between these curves. We call a matching that results in the Fréchet distance a Fréchet matching. There are often many different Fréchet matchings and not all of these capture the similarity between the curves well. We propose to restrict the set of Fréchet matchings to “natural” matchings and to this end introduce locally correct Fréchet matchings. We prove that at least one such matching exists for two polygonal curves and give an O(N3logN) algorithm to compute it, where N is the number of edges in both curves. We also present an O(N2) algorithm to compute a locally correct discrete Fréchet matching.

KW - Fréchet distance

KW - Local correctness

KW - Matching

KW - Similarity

UR - http://www.scopus.com/inward/record.url?scp=85053664553&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2018.09.002

DO - 10.1016/j.comgeo.2018.09.002

M3 - Article

VL - 76

SP - 1

EP - 18

JO - Computational Geometry

T2 - Computational Geometry

JF - Computational Geometry

SN - 0925-7721

ER -