Repositorio Institucional Universidad EAFIT ::Examinando por Materia "Surface reconstruction"

Examinando por Materia "Surface reconstruction"

Mostrando 1 - 13 de 13

2D shape similarity as a complement for Voronoi-Delone methods in shape reconstruction
(PERGAMON-ELSEVIER SCIENCE LTD, 2005-02-01) Ruiz, O.E.; Cadavid, C.A.; Granados, M.; Peña, S.; Vásquez, E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In surface reconstruction from planar cross sections it is necessary to build surfaces between 2D contours in consecutive cross sections. This problem has been traditionally attacked by (i) direct reconstruction based on local geometric proximity between the contours, and (ii) classification of topological events between the cross sections. These approaches have been separately applied with limited success. In case (i), the resulting surfaces may have overstretched or unnatural branches. These arise from local contour proximity which does not reflect global similarity between the contours. In case (ii), the topological events are identified but are not translated into the actual construction of a surface. This article presents an integration of the approaches (i) and (ii). Similarity between the composite 2D regions bounded by the contours in consecutive cross sections is used to: (a) decide whether a surface should actually relate two composite 2D regions, (b) identify the type and location of topological transitions between cross sections and (c) drive the surface construction for the regions found to be related in step (a). The implemented method avoids overstretched or unnatural branches, rendering a surface which is both geometrically intuitive and topologically faithful to the cross sections of the original object. The presented method is a good alternative in cases in which correct reproduction of the topology of the surface (e.g. simulation of flow in conduits) is more important than its geometry (e.g. assessment of tumor mass in radiation planning). © 2004 Elsevier Ltd. All rights reserved.
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, 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.
Face reconstruction with structured light
(INSTICC-INST SYST TECHNOLOGIES INFORMATION CONTROL & COMMUNICATION, 2011-01-01) Congote, J.; Barandiaran, I.; Barandiaran, J.; Nieto, M.; Ruiz, O.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
This article presents a methodology for reconstruction of 3D faces which is based on stereoscopic images of the scene using active and passive surface reconstruction. A sequence of Gray patterns is generated, which are projected onto the scene and their projection recorded by a pair of stereo cameras. The images are rectified to make coincident their epipolar planes and so to generate a stereo map of the scene. An algorithm for stereo matching is applied, whose result is a bijective mapping between subsets of the pixels of the images. A particular connected subset of the images (e.g. the face) is selected by a segmentation algorithm. The stereo mapping is applied to such a subset and enables the triangulation of the two image readings therefore rendering the (x,y,z) points of the face, which in turn allow the reconstruction of the triangular mesh of the face. Since the surface might have holes, bilateral filters are applied to have the holes filled. The algorithms are tested in real conditions and we evaluate their performance with virtual datasets. Our results show a good reconstruction of the faces and an improvement of the results of passive systems.
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 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.; 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.; 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.
Geometrical degeneracy removal by virtual disturbances - An application to surface reconstruction from point slice samples
(INSTICC-INST SYST TECHNOLOGIES INFORMATION CONTROL & COMMUNICATION, 2008-01-01) Ruiz, Oscar; Vasquez, Eliana; Pena, Sebastian; Granados, Miguel; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In surface reconstruction from slice samples (typical in medical imaging, coordinate measurement machines, stereolithography, etc.) the available methods attack the geometrical and topological properties of the surface. Topological methods classify the transitions occurred in the 2-manifold between two consecutive slices i and i+ 1. Geometrical methods synthesize the surface based on local proximity of the contours in consecutive slices. Superimposed 2D Voronoi Diagrams VDi and VDi+1 for slices i and i + 1, respectively, present topological problems if, for example, a site of VD i lies on an site or an edge of VDi+1. The usual treatment of this problem in literature is to apply a geometrical disturbance to either VDi or VDi+1, thus eliminating the degeneracy. In contrast, this article presents the implementation of a method which identifies the degenerate situation, constructs un-instantiated topological constructs, choses a geometrical instantiation based on a virtual disturbance introduced to the actual configuration. The algorithm was successfully applied to remove non-manifold topologies produced by well known algorithms in surface reconstruction.
Marching cubes in an unsigned distance field for surface reconstruction from unorganized point sets
(INSTICC-INST SYST TECHNOLOGIES INFORMATION CONTROL & COMMUNICATION, 2010-01-01) Congote, J.; Moreno, A.; Barandiaran, I.; Barandiaran, J.; Posada, J.; Ruiz, O.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Surface reconstruction from unorganized point set is a common problem in computer graphics. Generation of the signed distance field from the point set is a common methodology for the surface reconstruction. The reconstruction of implicit surfaces is made with the algorithm of marching cubes, but the distance field of a point set can not be processed with marching cubes because the unsigned nature of the distance. We propose an extension to the marching cubes algorithm allowing the reconstruction of 0-level iso-surfaces in an unsigned distance field. We calculate more information inside each cell of the marching cubes lattice and then we extract the intersection points of the surface within the cell then we identify the marching cubes case for the triangulation. Our algorithm generates good surfaces but the presence of ambiguities in the case selection generates some topological mistakes.
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.
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.
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.

Examinando por Materia "Surface reconstruction"

Resultados por página

Opciones de ordenación