Repositorio Institucional Universidad EAFIT ::Examinando por Autor "Cadavid, C."

Examinando por Autor "Cadavid, C."

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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.
Ellipse-based Principal Component Analysis for Self-intersecting Curve Reconstruction from Noisy Point Sets
(Springer Berlin Heidelberg, 2011) Ruíz, 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 1manifold for the surface reconstruction to proceed -- This article describes an implemented algorithm for the reconstruction of planar curves (1manifolds) out of noisy point samples of a sel-fintersecting or nearly sel-fintersecting planar curve C -- C:[a,b]⊂R→R 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 sel fintersect -- Existing algorithms for curve reconstruction out of either noisy point samples or pixel data, do not produce a (possibly disconnected) Piecewise Linear 1manifold approaching the whole point sample -- The algorithm implemented in this work uses Principal Component Analysis (PCA) with elliptic support regions near the selfintersections -- 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 noncorrelation at the self-intersections(nonmanifold neighborhoods) but also to occasional high noise at the nonselfintersecting (1manifold) neighborhoods
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.
Erratum: Ellipse-based principal component analysis for self-intersecting curve reconstruction from noisy point sets (Visual Computer DOI: 10.1007/s00371-010-0527-x)
(SPRINGER, 2011-01-01) Ruiz, O.; Vanegas, C.; Cadavid, C.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
[No abstract available]
Erratum: Ellipse-based principal component analysis for self-intersecting curve reconstruction from noisy point sets (Visual Computer DOI: 10.1007/s00371-010-0527-x)
(SPRINGER, 2011-01-01) Ruiz, O.; Vanegas, C.; Cadavid, C.; Ruiz, O.; Vanegas, C.; Cadavid, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
[No abstract available]
Gabriel-constrained Parametric Surface Triangulation
(InTech, 2009-11-01) Ruiz OE; Externo Otras Dependencias; Cadavid, C.; Lalinde Pulido, J.G.; Externo Otras Dependencias; Beatriz Defez-Garcia; Ricardo Serrano; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
The Boundary Representation of a 3D manifold contains FACES (connected subsets of a parametric surface S( ): R2 -> R3). In many science and engineering applications it is cumbersome and algebraically difficult to deal with the polynomial
Gabriel-constrained Parametric Surface Triangulation
(InTech, 2009-11-01) Ruiz OE; Externo Otras Dependencias; Cadavid, C.; Lalinde Pulido, J.G.; Externo Otras Dependencias; Beatriz Defez-Garcia; Ricardo Serrano
The Boundary Representation of a 3D manifold contains FACES (connected subsets of a parametric surface S( ): R2 -> R3). In many science and engineering applications it is cumbersome and algebraically difficult to deal with the polynomial
Gabriel-constrained Parametric Surface Triangulation
(InTech, 2009-11-01) Ruiz OE; Externo Otras Dependencias; Cadavid, C.; Lalinde Pulido, J.G.; Externo Otras Dependencias; Beatriz Defez-Garcia; Ricardo Serrano; Ruiz OE; Externo Otras Dependencias; Cadavid, C.; Lalinde Pulido, J.G.; Externo Otras Dependencias; Beatriz Defez-Garcia; Ricardo Serrano; Universidad EAFIT. Departamento de Ingeniería de Sistemas; I+D+I en Tecnologías de la Información y las Comunicaciones
The Boundary Representation of a 3D manifold contains FACES (connected subsets of a parametric surface S( ): R2 -> R3). In many science and engineering applications it is cumbersome and algebraically difficult to deal with the polynomial
Geodesic-based manifold learning for parameterization of triangular meshes
(Springer-Verlag France, 2016-11-01) Acosta, D.A.; Ruiz, O.E.; Arroyave, S.; Ebratt, R.; Cadavid, C.; Londono, J.J.; Acosta, Diego A.; Acosta, D.A.; Ruiz, O.E.; Arroyave, S.; Ebratt, R.; Cadavid, C.; Londono, J.J.; Acosta, Diego A.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Procesos Ambientales (GIPAB)
Reverse 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.
Geodesic-based manifold learning for parameterization of triangular meshes
(Springer-Verlag France, 2016-11-01) Acosta, D.A.; Ruiz, O.E.; Arroyave, S.; Ebratt, R.; Cadavid, C.; Londono, J.J.; Acosta, Diego A.; Universidad EAFIT. Departamento de Ingeniería de Procesos; Desarrollo y Diseño de Procesos
Reverse 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.
Geodesic-based manifold learning for parameterization of triangular meshes
(Springer-Verlag France, 2016-11-01) Acosta, D.A.; Ruiz, O.E.; Arroyave, S.; Ebratt, R.; Cadavid, C.; Londono, J.J.; Acosta, Diego A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Reverse 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.
Geodesic-based manifold learning for parameterization of triangular meshes
(Springer-Verlag France, 2016-11-01) Acosta, D.A.; Ruiz, O.E.; Arroyave, S.; Ebratt, R.; Cadavid, C.; Londono, J.J.; Acosta, Diego A.; Acosta, D.A.; Ruiz, O.E.; Arroyave, S.; Ebratt, R.; Cadavid, C.; Londono, J.J.; Acosta, Diego A.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Reverse 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.
Geometric functions in computer aided geometric design
(Fondo Editorial Universidad EAFIT, 2008-01-01) Ruíz, O.; Cadavid, C.
El libro da una visión valiosa en principios para robótica, visión por computador, diseño, manufactura, cinemática y dinámica desde un punto de vista práctico. Al mismo tiempo, mantiene un contacto con las propiedades matemáticas decisivas.
Geometry and Topology-based Segmentation of 2-Manifold Triangular Meshes in R3
(SCIENCEDOMAIN international (SDI), 2017-05-23) Orozco, Stella; Formella, Arno; Cadavid, C.; Ruiz, O.; Osorno, Maria; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Geometry and Topology-based Segmentation of 2-Manifold Triangular Meshes in R3
(SCIENCEDOMAIN international (SDI), 2017-05-23) Orozco, Stella; Formella, Arno; Cadavid, C.; Ruiz, O.; Osorno, Maria; Orozco, Stella; Formella, Arno; Cadavid, C.; Ruiz, O.; Osorno, Maria; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Hessian eigenfunctions for triangular mesh parameterization
(SciTePress, 2016-02-27) Mejia, D.; Ruiz OE; Cadavid, C.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional H for Dimensionality Reduction (DR) of a sampled manifold M. This article presents a variation of classic HLLE for parameterization of 3D triangular meshes. Contrary to classic HLLE which estimates local Hessian nullspaces, the proposed approach follows intuitive ideas from Differential Geometry where the local Hessian is estimated by quadratic interpolation and a partition of unity is used to join all neighborhoods. In addition, local average triangle normals are used to estimate the tangent plane TxM at x ? M instead of PCA, resulting in local parameterizations which reflect better the geometry of the surface and perform better when the mesh presents sharp features. A high frequency dataset (Brain) is used to test our algorithm resulting in a higher rate of success (96.63%) compared to classic HLLE (76.4%). © Copyright 2016 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.
Hessian eigenfunctions for triangular mesh parameterization
(SciTePress, 2016-02-27) Mejia, D.; Ruiz OE; Cadavid, C.; Mejia, D.; Ruiz OE; Cadavid, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional H for Dimensionality Reduction (DR) of a sampled manifold M. This article presents a variation of classic HLLE for parameterization of 3D triangular meshes. Contrary to classic HLLE which estimates local Hessian nullspaces, the proposed approach follows intuitive ideas from Differential Geometry where the local Hessian is estimated by quadratic interpolation and a partition of unity is used to join all neighborhoods. In addition, local average triangle normals are used to estimate the tangent plane TxM at x ? M instead of PCA, resulting in local parameterizations which reflect better the geometry of the surface and perform better when the mesh presents sharp features. A high frequency dataset (Brain) is used to test our algorithm resulting in a higher rate of success (96.63%) compared to classic HLLE (76.4%). © Copyright 2016 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.
Implementation and Visualization of Discrete Computational Geometry Using Database Managers
(Engg Journals Publications, 2019-06-30) Orozco Ochoa, Stella; Ruiz, O.; Cadavid, C.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Implementation and Visualization of Discrete Computational Geometry Using Database Managers
(Engg Journals Publications, 2019-06-30) Orozco Ochoa, Stella; Ruiz, O.; Cadavid, C.; Orozco Ochoa, Stella; Ruiz, O.; Cadavid, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Limits of quotients of bivariate real analytic functions
(ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2013-03-01) Cadavid, C.; Molina, S.; Velez, J. D.; Cadavid, C.; Molina, S.; Velez, J. D.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
Necessary and sufficient conditions for the existence of limits of the form lim (x,y)?(a,b)f(x, y)/g(x, y) are given, under the hypothesis that f and g are real analytic functions near the point (a, b), and g has an isolated zero at (a, b). The given criterion uses a constructive version of Hensel's Lemma which could be implemented in a computer algebra system in the case where f and g are polynomials with rational coefficients, or more generally, with coefficients in a real finite extension of the rationals. A high level description of an algorithm for determining the existence of the limit as well as its computation is provided. © 2012 Elsevier B.V.

Examinando por Autor "Cadavid, C."

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