Ellipse-based principal component analysis for self-intersecting curve reconstruction from noisy point sets

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dc.citation.journalTitleVISUAL COMPUTER
dc.contributor.authorRuiz, O.
dc.contributor.authorVanegas, C.
dc.contributor.authorCadavid, C.
dc.contributor.departmentUniversidad EAFIT. Departamento de Cienciasspa
dc.contributor.researchgroupMatemáticas y Aplicacionesspa
dc.creatorRuiz, O.
dc.creatorVanegas, C.
dc.creatorCadavid, C.
dc.date.accessioned2021-04-12T14:04:17Z
dc.date.available2021-04-12T14:04:17Z
dc.date.issued2011-03-01
dc.description.abstractSurface reconstruction from cross cuts usually requires curve reconstruction from planar noisy point samples. The output curves must form a possibly disconnected 1-manifold for the surface reconstruction to proceed. This article describes an implemented algorithm for the reconstruction of planar curves (1-manifolds) out of noisy point samples of a self-intersecting or nearly self-intersecting planar curve C. C:[a,b]R?R 2 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 self-intersect. Existing algorithms for curve reconstruction out of either noisy point samples or pixel data, do not produce a (possibly disconnected) Piecewise Linear 1-manifold approaching the whole point sample. The algorithm implemented in this work uses Principal Component Analysis (PCA) with elliptic support regions near the self-intersections. 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 non-correlation at the self-intersections (non-manifold neighborhoods) but also to occasional high noise at the non-self-intersecting (1-manifold) neighborhoods. © 2010 Springer-Verlag.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1586
dc.identifier.doi10.1007/s00371-010-0527-x
dc.identifier.issn01782789
dc.identifier.issn14322315
dc.identifier.otherWOS;000287450000004
dc.identifier.otherSCOPUS;2-s2.0-79951958575
dc.identifier.urihttp://hdl.handle.net/10784/27683
dc.language.isoengeng
dc.publisherSPRINGER
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-79951958575&doi=10.1007%2fs00371-010-0527-x&partnerID=40&md5=7d6f1265b6bcdac6362f53372e3d9f29
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0178-2789
dc.sourceVISUAL COMPUTER
dc.subjectCurve reconstructioneng
dc.subjectData setseng
dc.subjectElliptic support regioneng
dc.subjectGeometrical propertyeng
dc.subjectHigh noiseeng
dc.subjectIntersection pointseng
dc.subjectNoisy pointeng
dc.subjectNoisy sampleseng
dc.subjectOutput curveeng
dc.subjectPiecewise lineareng
dc.subjectPlanar curveseng
dc.subjectReconstructed surfaceseng
dc.subjectSelf-intersecting curve reconstructioneng
dc.subjectSelf-intersecting curveseng
dc.subjectSelf-intersectionseng
dc.subjectAlgorithmseng
dc.subjectGeometryeng
dc.subjectPiecewise linear techniqueseng
dc.subjectPrincipal component analysiseng
dc.subjectSurface reconstructioneng
dc.titleEllipse-based principal component analysis for self-intersecting curve reconstruction from noisy point setseng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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