Parametric Curve Reconstruction from Point Clouds using Minimization Techniques

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dc.contributor.authorRuíz, Óscar E.
dc.contributor.authorCortés, C.
dc.contributor.authorAristizábal, M.
dc.contributor.authorAcosta, Diego A.
dc.contributor.authorVanegas, Carlos A.
dc.contributor.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.contributor.researchgroupLaboratorio CAD/CAM/CAEspa
dc.date.accessioned2016-11-18T22:45:51Z
dc.date.available2016-11-18T22:45:51Z
dc.date.issued2013
dc.description.abstractSmooth (C1-, C2-,...) curve reconstruction from noisy point samples is central to reverse engineering, medical imaging, etc -- Unresolved issues in this problem are (1) high computational expenses, (2) presence of artifacts and outlier curls, (3) erratic behavior at self-intersections and sharp corners -- Some of these issues are related to non-Nyquist (i.e. sparse) samples -- Our work reconstructs curves by minimizing the accumulative distance curve cs. point sample -- We address the open issues above by using (a) Principal Component Analysis (PCA) pre-processing to obtain a topologically correct approximation of the sampled curve -- (b) Numerical, instead of algebraic, calculation of roots in point-to-curve distances -- (c) Penalties for curve excursions by using point cloud to - curve and curve to point cloud -- (d) Objective functions which are economic to minimize -- The implemented algorithms successfully deal with self - intersecting and / or non-Nyquist samples -- Ongoing research includes self-tuning of the algorithms and decimation of the point cloud and the control polygoneng
dc.description.sponsorshipINSTICCspa
dc.formatapplication/pdfeng
dc.identifier.citation@inproceedings{oruiz2013parametric, author ={Oscar E. Ruiz and C. Cortes and M. Aristizabal and Diego A. Acosta and Carlos A. Vanegas}, title ={Parametric Curve Reconstruction from Point Clouds using Minimization Techniques}, booktitle ={Proceedings of the International Conference on Computer Graphics Theory (GRAPP2013) and Applications and International Conference on Information Visualization Theory and Applications (IVAPP2013)}, year ={2013}, editor ={Sabine Coquillart and Carlos Andujar and Robert S. Laramee and Andreas Kerren and Jose Braz}, month ={February 21-24}, address ={Barcelona, Spain}, keys ={Parametric Curve Reconstruction, Noisy Point Cloud, Principal Component Analysis, Minimization}, organization ={INSTICC}, pages ={35--48}, publisher ={SCITEPRESS}, abstract ={Curve reconstruction from noisy point samples is central to surface reconstruction and therefore to reverse engineering, medical imaging, etc. Although Piecewise Linear (PL) curve reconstruction plays an important role, smooth (C^1-, C^2-,...) curves are needed for many applications. In reconstruction of parametric curves from noisy point samples there remain unsolved issues such as (1) high computational expenses, (2) presence of artifacts and outlier curls, (3) erratic behavior of self-intersecting curves, and (4) erratic excursions at sharp corners. Some of these issues are related to non-Nyquist (i.e. sparse) samples. In response to these shortcomings, this article reports the minimization-based �tting of parametric curves for noisy point clouds. Our approach features: (a) Principal Component Analysis (PCA) pre-processing to obtain a topologically correct approximation of the sampled curve. (b) Numerical, instead of algebraic, calculation of roots in point- to-curve distances. (c) Penalties for curve excursions by using point cloud to - curve and curve to point cloud. (d) Objective functions which are economic to minimize. The implemented algorithms successfully deal with self - intersecting and / or non-Nyquist samples. Ongoing research includes self-tuning of the algorithms and decimation of the point cloud and the control polygon}, isbn ={978-989-8565-46-4}, }spa
dc.identifier.isbn978-989-8565-46-4
dc.identifier.urihttp://hdl.handle.net/10784/9715
dc.language.isoengspa
dc.publisherSCITEPRESSspa
dc.relation.ispartofProceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications, vol.1, pp.35,48, 2013spa
dc.relation.isversionofhttp://www.scitepress.org/DigitalLibrary/PublicationsDetail.aspx?ID=KumbOOOFkhU=&t=1spa
dc.rights.accessrightsinfo:eu-repo/semantics/closedAccesseng
dc.rights.localAcceso cerradospa
dc.subject.keywordComputer visioneng
dc.subject.keywordStochastic processeseng
dc.subject.keywordMathematical optimizationeng
dc.subject.keywordComputer-aided Designeng
dc.subject.keywordEuclidean geometryeng
dc.subject.keywordNube de puntosspa
dc.subject.keywordReducción de ruidospa
dc.subject.keywordIngeniería inversaspa
dc.subject.keywordReconstrucción 3Dspa
dc.subject.keywordMatriz Hessianaspa
dc.subject.lembVISIÓN POR COMPUTADORspa
dc.subject.lembPROCESOS ESTOCÁSTICOSspa
dc.subject.lembOPTIMIZACIÓN MATEMÁTICAspa
dc.subject.lembDISEÑO CON AYUDA DE COMPUTADORspa
dc.subject.lembGEOMETRÍA EUCLIDIANAspa
dc.titleParametric Curve Reconstruction from Point Clouds using Minimization Techniqueseng
dc.typeinfo:eu-repo/semantics/conferencePapereng
dc.typeconferencePapereng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localDocumento de conferenciaspa

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