Computing the discrete fréchet distance with imprecise input

Handle URI:
http://hdl.handle.net/10754/564523
Title:
Computing the discrete fréchet distance with imprecise input
Authors:
Ahn, Heekap; Knauer, Christian; Scherfenberg, Marc; Schlipf, Lena; Vigneron, Antoine E. ( 0000-0003-3586-3431 )
Abstract:
We consider the problem of computing the discrete Frechet distance between two polyg- onal curves when their vertices are imprecise. An imprecise point is given by a region and this point could lie anywhere within this region. By modelling imprecise points as balls in dimension d, we present an algorithm for this problem that returns in time 2 O (d 2)m 2n 2 log 2 (mn) the minimum Frechet distance between two imprecise polygonal curves with n and m vertices, respectively. We give an improved algorithm for the pla- nar case with running time O(mnlog 3 (mn)+(m 2 +n 2) log(mn)). In the d-dimensional orthogonal case, where points are modelled as axis-parallel boxes, and we use the L∞ distance, we give an O(dmnlog(dmn))-time algorithm. We also give effcient O(dmn)-time algorithms to approximate the maximum Frechet distance, as well as the minimum and maximum Frechet distance under translation. These algorithms achieve constant factor approximation ratios in \realistic" settings (such as when the radii of the balls modelling the imprecise points are roughly of the same size). © 2012 World Scientific Publishing Company.
KAUST Department:
Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer Science Program; Geometric Algorithms Group
Publisher:
World Scientific Pub Co Pte Lt
Journal:
International Journal of Computational Geometry & Applications
Issue Date:
Feb-2012
DOI:
10.1142/S0218195912600023
Type:
Article
ISSN:
02181959
Appears in Collections:
Articles; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAhn, Heekapen
dc.contributor.authorKnauer, Christianen
dc.contributor.authorScherfenberg, Marcen
dc.contributor.authorSchlipf, Lenaen
dc.contributor.authorVigneron, Antoine E.en
dc.date.accessioned2015-08-04T07:03:10Zen
dc.date.available2015-08-04T07:03:10Zen
dc.date.issued2012-02en
dc.identifier.issn02181959en
dc.identifier.doi10.1142/S0218195912600023en
dc.identifier.urihttp://hdl.handle.net/10754/564523en
dc.description.abstractWe consider the problem of computing the discrete Frechet distance between two polyg- onal curves when their vertices are imprecise. An imprecise point is given by a region and this point could lie anywhere within this region. By modelling imprecise points as balls in dimension d, we present an algorithm for this problem that returns in time 2 O (d 2)m 2n 2 log 2 (mn) the minimum Frechet distance between two imprecise polygonal curves with n and m vertices, respectively. We give an improved algorithm for the pla- nar case with running time O(mnlog 3 (mn)+(m 2 +n 2) log(mn)). In the d-dimensional orthogonal case, where points are modelled as axis-parallel boxes, and we use the L∞ distance, we give an O(dmnlog(dmn))-time algorithm. We also give effcient O(dmn)-time algorithms to approximate the maximum Frechet distance, as well as the minimum and maximum Frechet distance under translation. These algorithms achieve constant factor approximation ratios in \realistic" settings (such as when the radii of the balls modelling the imprecise points are roughly of the same size). © 2012 World Scientific Publishing Company.en
dc.publisherWorld Scientific Pub Co Pte Lten
dc.subjectFréchet distanceen
dc.subjectimprecise inputen
dc.subjectShape matchingen
dc.titleComputing the discrete fréchet distance with imprecise inputen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentComputer Science Programen
dc.contributor.departmentGeometric Algorithms Groupen
dc.identifier.journalInternational Journal of Computational Geometry & Applicationsen
dc.contributor.institutionDepartment of Computer Science and Engineering, POSTECH, Pohang, South Koreaen
dc.contributor.institutionInstitute of Computer Science, Universität Bayreuth, 95440 Bayreuth, Germanyen
dc.contributor.institutionInstitute of Computer Science, Freie Universität Berlin, 14195 Berlin, Germanyen
kaust.authorVigneron, Antoine E.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.