Examinando por Materia "Principal component analysis"
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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/CAESurface 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.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 AplicacionesSurface 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.Ítem Formación del precio de las transacciones internacionales de electricidad entre Colombia y Ecuador(Universidad EAFIT, 2012-09-15) García, John J.; Gómez Toro, Catalina; Bohórquez, SantiagoThis article describes the operation of the international electric transactions between Colombia and Ecuador, its principal regulation and the most important characteristics of both markets paying special attention to the price formation. There is also two econometrics exercises, principal component analysis and beta convergence, to see if there has been price convergence between these two countries showing that there is no price convergence between both markets.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/CAECurve 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.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 ProcesosCurve 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.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/CAESurface 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.Ítem Statistical assessment of global and local cylinder wear(IEEE, 2007-01-01) Ruiz, Oscar; Vanegas, Carlos; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAEAssessment of cylindricity has been traditionally performed on the basis of cylindrical crowns containing a set of points that are supposed to belong to a controlled cylinder. As such, all sampled points must lie within a crown. In contrast, the present paper analyzes the cylindricity for wear applications, in which a statistical trend is assessed, rather than to assure that all points fall within a given tolerance. Principal Component Analysis is used to identify the central axis of the sampled cylinder, allowing to And the actual (expected value of the) radius and axis of the cylinder. Application of k-cluster and transitive closure algorithms allow to identify particular areas of the cylinder which are specially deformed. For both, the local areas and the global cylinder, a quantile analysis allows to numerically grade the degree of deformation of the cylinder. The algorithms implemented are part of the CYLWEAR© system and used to assess local and global wear cylinders. © 2007 IEEE.