Examinando por Materia "Curve reconstruction"

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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.
  • 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 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.
  • No hay miniatura disponible
    Ítem
    Principal component and Voronoi skeleton alternatives for curve reconstruction from noisy point sets
    (Taylor and Francis Ltd., 2007-01-01) Ruiz, O.; Vanegas, C.; Cadavid, C.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    Surface 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 on matching each sampled point precisely. 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 combines principal component analysis (PCA) (statistical) and Voronoi-Delaunay (deterministic) approaches in an entirely new way. It uses these two methods to calculate the best possible tape-shaped polygon covering the flattened point set, and then approximates the manifold using the medial axis of such a polygon. The other method applies PCA 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. The results show that the method solely based on PCA is both 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 the integration of meshes created from range images of a sculpture to form a complete unified mesh.
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    Ítem
    Sensitivity analysis in optimized parametric curve fitting
    (EMERALD GROUP PUBLISHING LIMITED, 2015-03-02) Ruiz, Oscar E.; Cortes, Camilo; Acosta, Diego A.; Aristizabal, Mauricio; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    Purpose-Curve fitting from unordered noisy point samples is needed for surface reconstruction in many applications. In the literature, several approaches have been proposed to solve this problem. However, previous works lack formal characterization of the curve fitting problem and assessment on the effect of several parameters (i.e. scalars that remain constant in the optimization problem), such as control points number (m), curve degree (b), knot vector composition (U), norm degree (k ), and point sample size (r) on the optimized curve reconstruction measured by a penalty function ( f ). The paper aims to discuss these issues. Design/methodology/approach-A numerical sensitivity analysis of the effect of m, b, k and r on f and a characterization of the fitting procedure from the mathematical viewpoint are performed. Also, the spectral (frequency) analysis of the derivative of the angle of the fitted curve with respect to u as a means to detect spurious curls and peaks is explored. Findings-It is more effective to find optimum values for m than k or b in order to obtain good results because the topological faithfulness of the resulting curve strongly depends on m. Furthermore, when an exaggerate number of control points is used the resulting curve presents spurious curls and peaks. The authors were able to detect the presence of such spurious features with spectral analysis. Also, the authors found that the method for curve fitting is robust to significant decimation of the point sample. Research limitations/implications-The authors have addressed important voids of previous works in this field. The authors determined, among the curve fitting parameters m, b and k, which of them influenced the most the results and how. Also, the authors performed a characterization of the curve fitting problem from the optimization perspective. And finally, the authors devised a method to detect spurious features in the fitting curve. Practical implications-This paper provides a methodology to select the important tuning parameters in a formal manner. Originality/value-Up to the best of the knowledge, no previous work has been conducted in the formal mathematical evaluation of the sensitivity of the goodness of the curve fit with respect to different possible tuning parameters (curve degree, number of control points, norm degree, etc.). © Emerald Group Publishing Limited.
  • No hay miniatura disponible
    Ítem
    Sensitivity analysis in optimized parametric curve fitting
    (EMERALD GROUP PUBLISHING LIMITED, 2015-03-02) Ruiz, Oscar E.; Cortes, Camilo; Acosta, Diego A.; Aristizabal, Mauricio; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
    Purpose-Curve fitting from unordered noisy point samples is needed for surface reconstruction in many applications. In the literature, several approaches have been proposed to solve this problem. However, previous works lack formal characterization of the curve fitting problem and assessment on the effect of several parameters (i.e. scalars that remain constant in the optimization problem), such as control points number (m), curve degree (b), knot vector composition (U), norm degree (k ), and point sample size (r) on the optimized curve reconstruction measured by a penalty function ( f ). The paper aims to discuss these issues. Design/methodology/approach-A numerical sensitivity analysis of the effect of m, b, k and r on f and a characterization of the fitting procedure from the mathematical viewpoint are performed. Also, the spectral (frequency) analysis of the derivative of the angle of the fitted curve with respect to u as a means to detect spurious curls and peaks is explored. Findings-It is more effective to find optimum values for m than k or b in order to obtain good results because the topological faithfulness of the resulting curve strongly depends on m. Furthermore, when an exaggerate number of control points is used the resulting curve presents spurious curls and peaks. The authors were able to detect the presence of such spurious features with spectral analysis. Also, the authors found that the method for curve fitting is robust to significant decimation of the point sample. Research limitations/implications-The authors have addressed important voids of previous works in this field. The authors determined, among the curve fitting parameters m, b and k, which of them influenced the most the results and how. Also, the authors performed a characterization of the curve fitting problem from the optimization perspective. And finally, the authors devised a method to detect spurious features in the fitting curve. Practical implications-This paper provides a methodology to select the important tuning parameters in a formal manner. Originality/value-Up to the best of the knowledge, no previous work has been conducted in the formal mathematical evaluation of the sensitivity of the goodness of the curve fit with respect to different possible tuning parameters (curve degree, number of control points, norm degree, etc.). © Emerald Group Publishing Limited.