A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification under the Fréchet Distance
Identifieur interne : 003541 ( Istex/Corpus ); précédent : 003540; suivant : 003542A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification under the Fréchet Distance
Auteurs : Isabelle SivignonSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Given a digital curve and a maximum error, we propose an algorithm that computes a simplification of the curve such that the Fréchet distance between the original and the simplified curve is less than the error. The algorithm uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in $\mathcal{O}(n\log(n))$ , experiments show a linear behaviour in practice.
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DOI: 10.1007/978-3-642-19867-0_28
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Bern</OrgName><OrgAddress><City>Bern</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgName>Indian Institute of Technology</OrgName><OrgAddress><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgName>University of Dortmund</OrgName><OrgAddress><City>Dortmund</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgName>Massachusetts Institute of Technology</OrgName><OrgAddress><State>MA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgName>University of California</OrgName><OrgAddress><City>Los Angeles</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgName>University of California</OrgName><OrgAddress><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff14"><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgName>Max-Planck Institute of Computer Science</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingDepth="2" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-3-642-19867-0</BookID><BookTitle>Discrete Geometry for Computer Imagery</BookTitle><BookSubTitle>16th IAPR International Conference, DGCI 2011, Nancy, France, April 6-8, 2011. Proceedings</BookSubTitle><BookVolumeNumber>6607</BookVolumeNumber><BookSequenceNumber>6607</BookSequenceNumber><BookDOI>10.1007/978-3-642-19867-0</BookDOI><BookTitleID>217662</BookTitleID><BookPrintISBN>978-3-642-19866-3</BookPrintISBN><BookElectronicISBN>978-3-642-19867-0</BookElectronicISBN><BookChapterCount>43</BookChapterCount><BookCopyright><CopyrightHolderName>Springer Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2011</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I22013" Priority="1" Type="Secondary">Computer Graphics</BookSubject><BookSubject Code="I22021" Priority="2" Type="Secondary">Image Processing and Computer Vision</BookSubject><BookSubject Code="I22005" Priority="3" Type="Secondary">Computer Imaging, Vision, Pattern Recognition and Graphics</BookSubject><BookSubject Code="I2203X" Priority="4" Type="Secondary">Pattern Recognition</BookSubject><BookSubject Code="I17028" Priority="5" Type="Secondary">Discrete Mathematics in Computer Science</BookSubject><BookSubject Code="I16021" Priority="6" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Isabelle</GivenName><FamilyName>Debled-Rennesson</FamilyName></EditorName><Contact><Email>isabelle.debled-rennesson@loria.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Eric</GivenName><FamilyName>Domenjoud</FamilyName></EditorName><Contact><Email>eric.domenjoud@loria.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Bertrand</GivenName><FamilyName>Kerautret</FamilyName></EditorName><Contact><Email>bertrand.kerautret@loria.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Philippe</GivenName><FamilyName>Even</FamilyName></EditorName><Contact><Email>philippe.even@loria.fr</Email></Contact></Editor><Affiliation ID="Aff16"><OrgName>LORIA, Equipe ADAGIo</OrgName><OrgAddress><Street>Campus Scientifique, BP 239</Street><Postcode>54506</Postcode><City>Vandœuvre-lès-Nancy Cedex</City><Country>France</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part5"><PartInfo TocLevels="0"><PartID>5</PartID><PartSequenceNumber>5</PartSequenceNumber><PartTitle>Discrete Shape Representation, Recognition and Analysis</PartTitle><PartChapterCount>12</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Discrete Geometry for Computer Imagery</BookTitle></PartContext></PartInfo><Chapter ID="Chap28" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>28</ChapterID><ChapterDOI>10.1007/978-3-642-19867-0_28</ChapterDOI><ChapterSequenceNumber>28</ChapterSequenceNumber><ChapterTitle Language="En">A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification under the Fréchet Distance</ChapterTitle><ChapterFirstPage>333</ChapterFirstPage><ChapterLastPage>345</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2011</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><PartID>5</PartID><BookID>978-3-642-19867-0</BookID><BookTitle>Discrete Geometry for Computer Imagery</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff17"><AuthorName DisplayOrder="Western"><GivenName>Isabelle</GivenName><FamilyName>Sivignon</FamilyName></AuthorName><Contact><Email>isabelle.sivignon@gipsa-lab.grenoble-inp.fr</Email></Contact></Author><Affiliation ID="Aff17"><OrgName>gipsa-lab, CNRS, UMR 5216</OrgName><OrgAddress><Postcode>F-38420</Postcode><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Given a digital curve and a maximum error, we propose an algorithm that computes a simplification of the curve such that the Fréchet distance between the original and the simplified curve is less than the error. The algorithm uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject FileRef="978-3-642-19867-0_28_Chapter_TeX2GIF_IEq1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{O}(n\log(n))$</EquationSource></InlineEquation>, experiments show a linear behaviour in practice.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification under the Fréchet Distance</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification under the Fréchet Distance</title></titleInfo><name type="personal"><namePart type="given">Isabelle</namePart><namePart type="family">Sivignon</namePart><affiliation>gipsa-lab, CNRS, UMR 5216, F-38420, France</affiliation><affiliation>E-mail: isabelle.sivignon@gipsa-lab.grenoble-inp.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2011</dateIssued><copyrightDate encoding="w3cdtf">2011</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: Given a digital curve and a maximum error, we propose an algorithm that computes a simplification of the curve such that the Fréchet distance between the original and the simplified curve is less than the error. The algorithm uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in $\mathcal{O}(n\log(n))$ , experiments show a linear behaviour in practice.</abstract><relatedItem type="host"><titleInfo><title>Discrete Geometry for Computer Imagery</title><subTitle>16th IAPR International Conference, DGCI 2011, Nancy, France, April 6-8, 2011. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Isabelle</namePart><namePart type="family">Debled-Rennesson</namePart><affiliation>LORIA, Equipe ADAGIo, Campus Scientifique, BP 239, 54506, Vandœuvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: isabelle.debled-rennesson@loria.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Eric</namePart><namePart type="family">Domenjoud</namePart><affiliation>LORIA, Equipe ADAGIo, Campus Scientifique, BP 239, 54506, Vandœuvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: eric.domenjoud@loria.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bertrand</namePart><namePart type="family">Kerautret</namePart><affiliation>LORIA, Equipe ADAGIo, Campus Scientifique, BP 239, 54506, Vandœuvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: bertrand.kerautret@loria.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Philippe</namePart><namePart type="family">Even</namePart><affiliation>LORIA, Equipe ADAGIo, Campus Scientifique, BP 239, 54506, Vandœuvre-lès-Nancy Cedex, France</affiliation><affiliation>E-mail: philippe.even@loria.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2011</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I22013">Computer Graphics</topic><topic authority="SpringerSubjectCodes" authorityURI="I22021">Image Processing and Computer Vision</topic><topic authority="SpringerSubjectCodes" authorityURI="I22005">Computer Imaging, Vision, Pattern Recognition and Graphics</topic><topic authority="SpringerSubjectCodes" authorityURI="I2203X">Pattern Recognition</topic><topic authority="SpringerSubjectCodes" authorityURI="I17028">Discrete Mathematics in Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic></subject><identifier type="DOI">10.1007/978-3-642-19867-0</identifier><identifier type="ISBN">978-3-642-19866-3</identifier><identifier type="eISBN">978-3-642-19867-0</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier 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type="personal"><namePart type="given">Takeo</namePart><namePart type="family">Kanade</namePart><affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Josef</namePart><namePart type="family">Kittler</namePart><affiliation>University of Surrey, Guildford, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jon</namePart><namePart type="given">M.</namePart><namePart type="family">Kleinberg</namePart><affiliation>Cornell University, Ithaca, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH Zurich, Zurich, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart type="given">C.</namePart><namePart type="family">Mitchell</namePart><affiliation>Stanford University, Stanford, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moni</namePart><namePart type="family">Naor</namePart><affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Oscar</namePart><namePart type="family">Nierstrasz</namePart><affiliation>University of Bern, Bern, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Pandu Rangan</namePart><affiliation>Indian Institute of Technology, Madras, India</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bernhard</namePart><namePart type="family">Steffen</namePart><affiliation>University of Dortmund, Dortmund, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Madhu</namePart><namePart type="family">Sudan</namePart><affiliation>Massachusetts Institute of Technology, MA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Demetri</namePart><namePart type="family">Terzopoulos</namePart><affiliation>University of California, Los Angeles, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Doug</namePart><namePart type="family">Tygar</namePart><affiliation>University of California, Berkeley, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moshe</namePart><namePart type="given">Y.</namePart><namePart type="family">Vardi</namePart><affiliation>Rice University, Houston, TX, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Weikum</namePart><affiliation>Max-Planck Institute of Computer Science, Saarbrücken, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2011</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer Berlin Heidelberg, 2011</recordOrigin></recordInfo></relatedItem><identifier type="istex">E01BD109B54D992FCC2DDB56CCEA0963431BD1C8</identifier><identifier type="ark">ark:/67375/HCB-4CN4ZZ9K-F</identifier><identifier type="DOI">10.1007/978-3-642-19867-0_28</identifier><identifier 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