Examinando por Materia "Self-intersecting curves"

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    Ítem
    Ellipse-based principal component analysis for self-intersecting curve reconstruction from noisy point sets
    (SPRINGER, 2011-03-01) Ruiz, O.; Vanegas, C.; Cadavid, C.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    Surface 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.
  • No hay miniatura disponible
    Ítem
    Ellipse-based principal component analysis for self-intersecting curve reconstruction from noisy point sets
    (SPRINGER, 2011-03-01) Ruiz, O.; Vanegas, C.; Cadavid, C.; Ruiz, O.; Vanegas, C.; Cadavid, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    Surface 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.
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    Ítem
    Parametric curve reconstruction from point clouds using minimization techniques
    (2013-01-01) Ruiz, O.E.; Cortés, C.; Aristizábal, M.; Acosta, D.A.; Vanegas, C.A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    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 (C1-, C2-,?) 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 fitting 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.
  • No hay miniatura disponible
    Ítem
    Parametric curve reconstruction from point clouds using minimization techniques
    (2013-01-01) Ruiz, O.E.; Cortés, C.; Aristizábal, M.; Acosta, D.A.; Vanegas, C.A.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
    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 (C1-, C2-,?) 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 fitting 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.