Ellipse-based Principal Component Analysis for Self-intersecting Curve Reconstruction from Noisy Point Sets

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dc.citation.epage226spa
dc.citation.issue3spa
dc.citation.journalTitleThe Visual Computer, Collection: Computer Scienceeng
dc.citation.journalTitleThe Visual Computerspa
dc.citation.spage211spa
dc.citation.volume27spa
dc.contributor.authorRuíz, O.
dc.contributor.authorVanegas, C.
dc.contributor.authorCadavid, C.
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.contributor.researchgroupLaboratorio CAD/CAM/CAEspa
dc.date.accessioned2016-11-18T22:14:34Z
dc.date.available2016-11-18T22:14:34Z
dc.date.issued2011
dc.description.abstractSurface reconstruction from cross cuts usually requires curve reconstruction from planar noisy point samples -- The output curves must form a possibly disconnected 1manifold for the surface reconstruction to proceed -- This article describes an implemented algorithm for the reconstruction of planar curves (1manifolds) out of noisy point samples of a sel-fintersecting or nearly sel-fintersecting planar curve C -- C:[a,b]⊂R→R is self-intersecting if C(u)=C(v), u≠v, u,v∈(a,b) (C(u) is the self-intersection point) -- We consider only transversal self-intersections, i.e. those for which the tangents of the intersecting branches at the intersection point do not coincide (C′(u)≠C′(v)) -- In the presence of noise, curves which self-intersect cannot be distinguished from curves which nearly sel fintersect -- Existing algorithms for curve reconstruction out of either noisy point samples or pixel data, do not produce a (possibly disconnected) Piecewise Linear 1manifold approaching the whole point sample -- The algorithm implemented in this work uses Principal Component Analysis (PCA) with elliptic support regions near the selfintersections -- The algorithm was successful in recovering contours out of noisy slice samples of a surface, for the Hand, Pelvis and Skull data sets -- As a test for the correctness of the obtained curves in the slice levels, they were input into an algorithm of surface reconstruction, leading to a reconstructed surface which reproduces the topological and geometrical properties of the original object -- The algorithm robustly reacts not only to statistical noncorrelation at the self-intersections(nonmanifold neighborhoods) but also to occasional high noise at the nonselfintersecting (1manifold) neighborhoodseng
dc.formatapplication/pdfeng
dc.identifier.doi10.1007/s00371-010-0527-x
dc.identifier.issn1432-2315
dc.identifier.urihttp://hdl.handle.net/10784/9681
dc.language.isoengeng
dc.publisherSpringer Berlin Heidelbergspa
dc.relation.ispartofThe Visual Computer, Collection: Computer Science, Volume 27, Issue 3, pp. 211-226spa
dc.relation.urihttp://dx.doi.org/10.1007/s00371-010-0527-x
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightsSpringer-Verlag 2010spa
dc.rights.localAcceso abiertospa
dc.subject.keywordCurves, planespa
dc.subject.keywordTopologyspa
dc.subject.keywordManifolds (Mathematics)spa
dc.subject.keywordCorrelation (statistics)spa
dc.subject.keywordStochastic analysisspa
dc.subject.keywordFunctions, ellipticspa
dc.subject.keywordCurveseng
dc.subject.keywordplaneeng
dc.subject.keywordTopologyeng
dc.subject.keywordManifolds (Mathematics)eng
dc.subject.keywordCorrelation (statistics)eng
dc.subject.keywordStochastic analysiseng
dc.subject.keywordFunctionseng
dc.subject.keywordellipticeng
dc.subject.keywordReconstrucción superficial.keywor
dc.subject.keywordNube de puntos.keywor
dc.subject.lembCURVAS PLANASspa
dc.subject.lembCOLECTORES (INGENIERÍA)spa
dc.subject.lembTOPOLOGÍAspa
dc.subject.lembVARIEDADES (MATEMÁTICAS)spa
dc.subject.lembCORRELACIÓN (ESTADÍSTICA)spa
dc.subject.lembANÁLISIS ESTOCÁSTICOspa
dc.subject.lembFUNCIONES ELÍPTICASspa
dc.titleEllipse-based Principal Component Analysis for Self-intersecting Curve Reconstruction from Noisy Point Setseng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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