Geodesic-based manifold learning for parameterization of triangular meshes

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dc.citation.journalTitleInternational Journal On Interactive Design And Manufacturingeng
dc.contributor.authorAcosta, D.A.
dc.contributor.authorRuiz, O.E.
dc.contributor.authorArroyave, S.
dc.contributor.authorEbratt, R.
dc.contributor.authorCadavid, C.
dc.contributor.authorLondono, J.J.
dc.contributor.authorAcosta, Diego A.
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería de Procesosspa
dc.contributor.researchgroupDesarrollo y Diseño de Procesosspa
dc.date.accessioned2021-04-12T19:06:19Z
dc.date.available2021-04-12T19:06:19Z
dc.date.issued2016-11-01
dc.description.abstractReverse Engineering (RE) requires representing with free forms (NURBS, Spline, B,zier) a real surface which has been point-sampled. To serve this purpose, we have implemented an algorithm that minimizes the accumulated distance between the free form and the (noisy) point sample. We use a dual-distance calculation point to / from surfaces, which discourages the forming of outliers and artifacts. This algorithm seeks a minimum in a function that represents the fitting error, by using as tuning variable the control polyhedron for the free form. The topology (rows, columns) and geometry of the control polyhedron are determined by alternative geodesic-based dimensionality reduction methods: (a) graph-approximated geodesics (Isomap), or (b) PL orthogonal geodesic grids. We assume the existence of a triangular mesh of the point sample (a reasonable expectation in current RE). A bijective composition mapping allows to estimate a size of the control polyhedrons favorable to uniform-speed parameterizations. Our results show that orthogonal geodesic grids is a direct and intuitive parameterization method, which requires more exploration for irregular triangle meshes. Isomap gives a usable initial parameterization whenever the graph approximation of geodesics on be faithful. These initial guesses, in turn, produce efficient free form optimization processes with minimal errors. Future work is required in further exploiting the usual triangular mesh underlying the point sample for (a) enhancing the segmentation of the point set into faces, and (b) using a more accurate approximation of the geodesic distances within , which would benefit its dimensionality reduction.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1709
dc.identifier.doi10.1007/s12008-014-0249-9
dc.identifier.issn19552513
dc.identifier.issn19552505
dc.identifier.otherWOS;000386658600006
dc.identifier.otherSCOPUS;2-s2.0-84908274455
dc.identifier.urihttp://hdl.handle.net/10784/28241
dc.language.isoeng
dc.publisherSpringer-Verlag France
dc.relationDOI;10.1007/s12008-014-0249-9
dc.relationWOS;000386658600006
dc.relationSCOPUS;2-s2.0-84908274455
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84908274455&doi=10.1007%2fs12008-014-0249-9&partnerID=40&md5=b352f375462cb12bd2c58160dae80f89
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/1955-2513
dc.sourceInternational Journal On Interactive Design And Manufacturing
dc.subjectComputational geometryeng
dc.subjectParametric surfaceseng
dc.subjectSurface reconstructioneng
dc.subjectReverse engineeringeng
dc.titleGeodesic-based manifold learning for parameterization of triangular mesheseng
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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