Principal component and Voronoi skeleton alternatives for curve reconstruction from noisy point sets

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dc.citation.epage457spa
dc.citation.issue5spa
dc.citation.journalTitleJournal of Engineering Designeng
dc.citation.journalTitleJournal of Engineering Designspa
dc.citation.spage437spa
dc.citation.volume18spa
dc.contributor.authorRuíz, Óscar
dc.contributor.authorVanegas, Carlos
dc.contributor.authorCadavid, Carlos
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.contributor.researchgroupLaboratorio CAD/CAM/CAEspa
dc.date.accessioned2016-11-18T22:23:37Z
dc.date.available2016-11-18T22:23:37Z
dc.date.issued2007-10
dc.description.abstractSurface reconstruction from noisy point samples must take into consideration the stochastic nature of the sample -- In other words, geometric algorithms reconstructing the surface or curve should not insist in following in a literal way each sampled point -- Instead, they must interpret the sample as a “point cloud” and try to build the surface as passing through the best possible (in the statistical sense) geometric locus that represents the sample -- This work presents two new methods to find a Piecewise Linear approximation from a Nyquist-compliant stochastic sampling of a quasi-planar C1 curve C(u) : R → R3, whose velocity vector never vanishes -- One of the methods articulates in an entirely new way Principal Component Analysis (statistical) and Voronoi-Delaunay (deterministic) approaches -- It uses these two methods to calculate the best possible tape-shaped polygon covering the planarised point set, and then approximates the manifold by the medial axis of such a polygon -- The other method applies Principal Component Analysis to find a direct Piecewise Linear approximation of C(u) -- A complexity comparison of these two methods is presented along with a qualitative comparison with previously developed ones -- It turns out that the method solely based on Principal Component Analysis is simpler and more robust for non self-intersecting curves -- For self-intersecting curves the Voronoi-Delaunay based Medial Axis approach is more robust, at the price of higher computational complexity -- An application is presented in Integration of meshes originated in range images of an art piece -- Such an application reaches the point of complete reconstruction of a unified mesheng
dc.formatapplication/pdfeng
dc.identifier.doi10.1080/09544820701403771
dc.identifier.issn0954-4828
dc.identifier.urihttp://hdl.handle.net/10784/9689
dc.language.isoengeng
dc.publisherTaylor & Francisspa
dc.relation.ispartofJournal of Engineering Design, Volume 18, Issue 5, pp. 437-457spa
dc.relation.urihttp://dx.doi.org/10.1080/09544820701403771
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.localAcceso abiertospa
dc.subject.keywordTopologyspa
dc.subject.keywordComputer graphicsspa
dc.subject.keywordTopologyeng
dc.subject.keywordComputer graphicseng
dc.subject.keywordTriangulación de Delaunay.keywor
dc.subject.keywordIngeniería inversa.keywor
dc.subject.keywordDiagramas de Voronoi.keywor
dc.subject.keywordReconstrucción superficial.keywor
dc.subject.keywordReconstrucción 3D.keywor
dc.subject.lembGRÁFICOS POR COMPUTADORspa
dc.subject.lembTOPOLOGÍAspa
dc.titlePrincipal component and Voronoi skeleton alternatives for 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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