Structure of Applicable Surfaces from Single Views
Identifieur interne : 000198 ( Istex/Corpus ); précédent : 000197; suivant : 000199Structure of Applicable Surfaces from Single Views
Auteurs : Nail Gumerov ; Ali Zandifar ; Ramani Duraiswami ; S. DavisSource :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2004.
Abstract
Abstract: The deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. A new exact integration of these equations is developed that relates the 3-D structure of the applicable surface to an image. The solution is tested by comparison with particular exact solutions. We present results for both the forward and the inverse 3D structure recovery problem.
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DOI: 10.1007/978-3-540-24672-5_38
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ISTEX:18C104E5BEDF364AC08E9EDF9FA69A98AB12EA93Le document en format XML
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Davis</name><affiliation><mods:affiliation>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: lsd@umiacs.umd.edu</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>2004</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">18C104E5BEDF364AC08E9EDF9FA69A98AB12EA93</idno><idno type="DOI">10.1007/978-3-540-24672-5_38</idno><idno type="ChapterID">38</idno><idno type="ChapterID">Chap38</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. A new exact integration of these equations is developed that relates the 3-D structure of the applicable surface to an image. The solution is tested by comparison with particular exact solutions. We present results for both the forward and the inverse 3D structure recovery problem.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Nail Gumerov</name><affiliations><json:string>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</json:string><json:string>E-mail: gumerov@umiacs.umd.edu</json:string></affiliations></json:item><json:item><name>Ali Zandifar</name><affiliations><json:string>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</json:string><json:string>E-mail: alizand@umiacs.umd.edu</json:string></affiliations></json:item><json:item><name>Ramani Duraiswami</name><affiliations><json:string>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</json:string><json:string>E-mail: ramani@umiacs.umd.edu</json:string></affiliations></json:item><json:item><name>Larry S. Davis</name><affiliations><json:string>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</json:string><json:string>E-mail: lsd@umiacs.umd.edu</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><abstract>Abstract: The deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. 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We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. A new exact integration of these equations is developed that relates the 3-D structure of the applicable surface to an image. The solution is tested by comparison with particular exact solutions. 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California</OrgName><OrgAddress><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgName>Max-Planck Institute of Computer Science</OrgName><OrgAddress><City>Saarbruecken</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>978-3-540-24672-5</BookID><BookTitle>Computer Vision - ECCV 2004</BookTitle><BookSubTitle>8th European Conference on Computer Vision, Prague, Czech Republic, May 11-14, 2004. Proceedings, Part III</BookSubTitle><BookVolumeNumber>3023</BookVolumeNumber><BookSequenceNumber>3023</BookSequenceNumber><BookDOI>10.1007/b97871</BookDOI><BookTitleID>82643</BookTitleID><BookPrintISBN>978-3-540-21982-8</BookPrintISBN><BookElectronicISBN>978-3-540-24672-5</BookElectronicISBN><BookChapterCount>47</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2004</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I22021" Priority="1" Type="Secondary">Image Processing and Computer Vision</BookSubject><BookSubject Code="I2203X" Priority="2" Type="Secondary">Pattern Recognition</BookSubject><BookSubject Code="I22013" Priority="3" Type="Secondary">Computer Graphics</BookSubject><BookSubject Code="I21017" Priority="4" Type="Secondary">Artificial Intelligence (incl. Robotics)</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff14"><EditorName DisplayOrder="Western"><GivenName>Tomáš</GivenName><FamilyName>Pajdla</FamilyName></EditorName><Contact><Email>pajdla@cmp.felk.cvut.cz</Email></Contact></Editor><Editor AffiliationIDS="Aff15"><EditorName DisplayOrder="Western"><GivenName>Jiří</GivenName><FamilyName>Matas</FamilyName></EditorName><Contact><Email>matas@cmp.felk.cvut.cz</Email></Contact></Editor><Affiliation ID="Aff14"><OrgDivision>Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering</OrgDivision><OrgName>Czech Technical University</OrgName><OrgAddress><City>Prague 6</City><Country>Czech Republic</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgDivision>Center for Machine Perception, Dept. of Cybernetics, Faculty of Elec. Eng.</OrgDivision><OrgName>Czech Technical University in Prague</OrgName><OrgAddress><Street>Karlovo nám. 13</Street><Postcode>121 35</Postcode><City>Prague</City><Country>Czech Rep</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part3"><PartInfo TocLevels="0"><PartID>3</PartID><PartSequenceNumber>3</PartSequenceNumber><PartTitle>Posters III</PartTitle><PartChapterCount>38</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Computer Vision - ECCV 2004</BookTitle></PartContext></PartInfo><Chapter ID="Chap38" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>38</ChapterID><ChapterDOI>10.1007/978-3-540-24672-5_38</ChapterDOI><ChapterSequenceNumber>38</ChapterSequenceNumber><ChapterTitle Language="En">Structure of Applicable Surfaces from Single Views</ChapterTitle><ChapterFirstPage>482</ChapterFirstPage><ChapterLastPage>496</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2004</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>3</PartID><BookID>978-3-540-24672-5</BookID><BookTitle>Computer Vision - ECCV 2004</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff16"><AuthorName DisplayOrder="Western"><GivenName>Nail</GivenName><FamilyName>Gumerov</FamilyName></AuthorName><Contact><Email>gumerov@umiacs.umd.edu</Email></Contact></Author><Author AffiliationIDS="Aff16"><AuthorName DisplayOrder="Western"><GivenName>Ali</GivenName><FamilyName>Zandifar</FamilyName></AuthorName><Contact><Email>alizand@umiacs.umd.edu</Email></Contact></Author><Author AffiliationIDS="Aff16"><AuthorName DisplayOrder="Western"><GivenName>Ramani</GivenName><FamilyName>Duraiswami</FamilyName></AuthorName><Contact><Email>ramani@umiacs.umd.edu</Email></Contact></Author><Author AffiliationIDS="Aff16"><AuthorName DisplayOrder="Western"><GivenName>Larry</GivenName><GivenName>S.</GivenName><FamilyName>Davis</FamilyName></AuthorName><Contact><Email>lsd@umiacs.umd.edu</Email></Contact></Author><Affiliation ID="Aff16"><OrgDivision>Perceptual Interfaces and Reality Lab</OrgDivision><OrgName>University of Maryland</OrgName><OrgAddress><City>College Park</City></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>The deformation of <Emphasis Type="Italic">applicable</Emphasis> surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the <Emphasis Type="Italic">full geometric structure</Emphasis> from <Emphasis Type="Italic">a single image</Emphasis> of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. A new exact integration of these equations is developed that relates the 3-D structure of the applicable surface to an image. The solution is tested by comparison with particular exact solutions. We present results for both the forward and the inverse 3D structure recovery problem.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Surface</Keyword><Keyword>Differential Geometry</Keyword><Keyword>Applicable Surfaces</Keyword><Keyword>Shape from <Emphasis Type="Italic">X</Emphasis></Keyword></KeywordGroup></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Structure of Applicable Surfaces from Single Views</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Structure of Applicable Surfaces from Single Views</title></titleInfo><name type="personal"><namePart type="given">Nail</namePart><namePart type="family">Gumerov</namePart><affiliation>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</affiliation><affiliation>E-mail: gumerov@umiacs.umd.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Ali</namePart><namePart type="family">Zandifar</namePart><affiliation>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</affiliation><affiliation>E-mail: alizand@umiacs.umd.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Ramani</namePart><namePart type="family">Duraiswami</namePart><affiliation>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</affiliation><affiliation>E-mail: ramani@umiacs.umd.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Larry</namePart><namePart type="given">S.</namePart><namePart type="family">Davis</namePart><affiliation>Perceptual Interfaces and Reality Lab, University of Maryland, College Park</affiliation><affiliation>E-mail: lsd@umiacs.umd.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="conference [eBooks]" displayLabel="OriginalPaper"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2004</dateIssued><copyrightDate encoding="w3cdtf">2004</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">Abstract: The deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. A new exact integration of these equations is developed that relates the 3-D structure of the applicable surface to an image. The solution is tested by comparison with particular exact solutions. We present results for both the forward and the inverse 3D structure recovery problem.</abstract><relatedItem type="host"><titleInfo><title>Computer Vision - ECCV 2004</title><subTitle>8th European Conference on Computer Vision, Prague, Czech Republic, May 11-14, 2004. Proceedings, Part III</subTitle></titleInfo><name type="personal"><namePart type="given">Tomáš</namePart><namePart type="family">Pajdla</namePart><affiliation>Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Prague 6, Czech Republic</affiliation><affiliation>E-mail: pajdla@cmp.felk.cvut.cz</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jiří</namePart><namePart type="family">Matas</namePart><affiliation>Center for Machine Perception, Dept. of Cybernetics, Faculty of Elec. Eng., Czech Technical University in Prague, Karlovo nám. 13, 121 35, Prague, Czech Rep</affiliation><affiliation>E-mail: matas@cmp.felk.cvut.cz</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="Book Series" displayLabel="Proceedings"></genre><originInfo><copyrightDate encoding="w3cdtf">2004</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="I22021">Image Processing and Computer Vision</topic><topic authority="SpringerSubjectCodes" authorityURI="I2203X">Pattern Recognition</topic><topic authority="SpringerSubjectCodes" authorityURI="I22013">Computer Graphics</topic><topic authority="SpringerSubjectCodes" authorityURI="I21017">Artificial Intelligence (incl. Robotics)</topic></subject><identifier type="DOI">10.1007/b97871</identifier><identifier type="ISBN">978-3-540-21982-8</identifier><identifier type="eISBN">978-3-540-24672-5</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">82643</identifier><identifier type="BookID">978-3-540-24672-5</identifier><identifier type="BookChapterCount">47</identifier><identifier type="BookVolumeNumber">3023</identifier><identifier type="BookSequenceNumber">3023</identifier><identifier type="PartChapterCount">38</identifier><part><date>2004</date><detail type="part"><title>Posters III</title></detail><detail type="volume"><number>3023</number><caption>vol.</caption></detail><extent unit="pages"><start>482</start><end>496</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2004</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name 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, 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, CA, USA</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, 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, 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>New York University, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Dough</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, Saarbruecken, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><copyrightDate encoding="w3cdtf">2004</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-Verlag Berlin Heidelberg, 2004</recordOrigin></recordInfo></relatedItem><identifier type="istex">18C104E5BEDF364AC08E9EDF9FA69A98AB12EA93</identifier><identifier type="DOI">10.1007/978-3-540-24672-5_38</identifier><identifier type="ChapterID">38</identifier><identifier type="ChapterID">Chap38</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2004</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 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