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Wenping Wang - One of the best experts on this subject based on the ideXlab platform.

  • Medial Meshes – A Compact and Accurate Representation of Medial Axis Transform
    IEEE Transactions on Visualization and Computer Graphics, 2016
    Co-Authors: Feng Sun, Yi King Choi, Wenping Wang
    Abstract:

    The Medial Axis transform has long been known as an intrinsic shape representation supporting a variety of shape analysis and synthesis tasks. However, for a given shape, it is hard to obtain its faithful, concise and stable Medial Axis, which hinders the application of the Medial Axis. In this paper, we introduce the Medial mesh , a new discrete representation of the Medial Axis. A Medial mesh is a 2D simplicial complex coupled with a radius function that provides a piecewise linear approximation to the Medial Axis. We further present an effective algorithm for computing a concise and stable Medial mesh for a given shape. Our algorithm is quantitatively driven by a shape approximation error metric, and progressively simplifies an initial Medial mesh by iteratively contracting edges until the approximation error reaches a predefined threshold. We further demonstrate the superior efficiency and accuracy of our method over existing methods for Medial Axis simplification.

  • Medial Meshes-A Compact and Accurate Representation of Medial Axis Transform
    IEEE Transactions on Visualization and Computer Graphics, 2016
    Co-Authors: Feng Sun, Yi King Choi, Yizhou Yu, Wenping Wang
    Abstract:

    The Medial Axis transform has long been known as an intrinsic shape representation supporting a variety of shape analysis and synthesis tasks. However, for a given shape, it is hard to obtain its faithful, concise and stable Medial Axis, which hinders the application of the Medial Axis. In this paper, we introduce the Medial mesh, a new discrete representation of the Medial Axis. A Medial mesh is a 2D simplicial complex coupled with a radius function that provides a piecewise linear approximation to the Medial Axis. We further present an effective algorithm for computing a concise and stable Medial mesh for a given shape. Our algorithm is quantitatively driven by a shape approximation error metric, and progressively simplifies an initial Medial mesh by iteratively contracting edges until the approximation error reaches a predefined threshold. We further demonstrate the superior efficiency and accuracy of our method over existing methods for Medial Axis simplification.

  • A 3D shape descriptor based on spectral analysis of Medial Axis
    Computer Aided Geometric Design, 2015
    Co-Authors: Yi King Choi, Yanwen Guo, Xiaohu Guo, Wenping Wang
    Abstract:

    The Medial Axis of a 3D shape is widely known for its ability as a compact and complete shape representation. However, there is still lack of a generative description defined over the Medial Axis directly which limits its actual application to 3D shape analysis such as shape matching and retrieval. In this paper, we propose a new spectral shape descriptor that directly applies spectral analysis to the Medial Axis of a 3D shape, which we call the Medial Axis spectrum for a 3D shape. We develop a newly defined Minkowski-Euclidean ratio inspired by the Minkowski inner product to characterize the geometry of the Medial Axis of a 3D mesh. We then generalize the Laplace-Beltrami operator to the Medial Axis, and take the solution to a Laplacian eigenvalue problem defined on it as the Medial Axis spectrum. The Medial Axis spectrum is invariant under rigid transformation and isometry of the Medial Axis, and is robust to shape boundary noise as shown by our experiments. The Medial Axis spectrum is finally used for 3D shape retrieval, and its superiority over previous work is shown by extensive comparisons.

  • Spectral Analysis on Medial Axis of 2D Shapes
    Computer Graphics Forum, 2014
    Co-Authors: Yi King Choi, Yanwen Guo, Wenping Wang
    Abstract:

    Shape analysis finds many important applications in shape understanding, matching and retrieval. Among the various shape analysis methods, spectral shape analysis aims to study the spectrum of the Laplace-Beltrami operator of some well-designed shape-dependent equations and obtain a spectral shape descriptor that can in turn be used for shape analysis purposes. The success of such approaches depends greatly on the discriminating power of a shape descriptor. On the other hand, the Medial Axis of a shape is widely known for its complete shape representation. It is sensitive to small perturbation of the boundary of a shape which often poses difficulty in its effective use for shape analysis. In this paper, we propose a new spectral shape descriptor, called the Medial Axis spectrum for 2D shapes, which directly applies spectral analysis to the Medial axes of the shapes. We extend the Laplace-Beltrami operator onto the Medial Axis, and take the solution to an extended Laplacian eigenvalue problem defined on the Axis as the Medial Axis spectrum. The Medial Axis spectrum is robust in the presence of shape boundary noise, and is invariant under rigid transformations, uniform scaling and isometry of the Medial Axis. We demonstrate these benefits of such a Medial Axis spectrum representation through extensive experiments. The Medial Axis spectrum is further used for 2D shape retrieval, and its superiority over previous work is shown by comparison.

  • Computing a compact spline representation of the Medial Axis transform of a 2D shape
    Graphical Models, 2014
    Co-Authors: Yanshu Zhu, Yi King Choi, Feng Sun, Bert Jüttler, Wenping Wang
    Abstract:

    We present a full pipeline for computing the Medial Axis transform of an arbitrary 2D shape. The instability of the Medial Axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable Medial Axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the Medial Axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of Medial Axis transforms of 2D shapes.

Bardia Sadri - One of the best experts on this subject based on the ideXlab platform.

  • Medial Axis APPROXIMATION AND UNSTABLE FLOW COMPLEX
    International Journal of Computational Geometry and Applications, 2008
    Co-Authors: Joachim Giesen, Edgar A Ramos, Bardia Sadri
    Abstract:

    The Medial Axis of a shape is known to carry a lot of information about the shape. In particular, a recent result of Lieutier establishes that every bounded open subset of ℝn has the same homotopy type as its Medial Axis. In this paper we provide an algorithm that computes a structure we call the core for the approximation of the Medial Axis of a shape with smooth boundary from a discrete sample of its boundary. The core is a piecewise linear cell complex that is guaranteed to capture the topology of the Medial Axis of the shape provided the sample of its boundary is sufficiently dense but not necessarily uniform. We also present a natural method for augmenting the core in order to extend it geometrically while maintaining the topological guarantees. The definition of the core and its extension are based on the steepest ascent flow map that results from the distance function induced by the sample point set. We also provide a geometric guarantee on the closeness of the core and the actual Medial Axis.

  • Medial Axis approximation and unstable flow complex
    Symposium on Computational Geometry, 2006
    Co-Authors: Joachim Giesen, Edgar A Ramos, Bardia Sadri
    Abstract:

    The Medial Axis of a shape is known to carry a lot of information about it. In particular a recent result of Lieutier establishes that every bounded open subset of Rn has the same homotopy type as its Medial Axis. In this paper we provide an algorithm that, given a sufficiently dense but not necessarily uniform sample from the surface of a shape with smooth boundary, computes a core for its Medial Axis approximation, in form of a piecewise linear cell complex, that captures the topology of the Medial Axis of the shape. We also provide a natural method to freely augment this core in order to enhance it geometrically all the while maintaining its topological guarantees. The definition of the core and its extension method are based on the steepest ascent flow induced by the distance function to the sample. We also provide a geometric guarantee on the closeness of the core and the actual Medial Axis.

  • Symposium on Computational Geometry - Medial Axis approximation and unstable flow complex
    Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06, 2006
    Co-Authors: Joachim Giesen, Edgar A Ramos, Bardia Sadri
    Abstract:

    The Medial Axis of a shape is known to carry a lot of information about it. In particular a recent result of Lieutier establishes that every bounded open subset of Rn has the same homotopy type as its Medial Axis. In this paper we provide an algorithm that, given a sufficiently dense but not necessarily uniform sample from the surface of a shape with smooth boundary, computes a core for its Medial Axis approximation, in form of a piecewise linear cell complex, that captures the topology of the Medial Axis of the shape. We also provide a natural method to freely augment this core in order to enhance it geometrically all the while maintaining its topological guarantees. The definition of the core and its extension method are based on the steepest ascent flow induced by the distance function to the sample. We also provide a geometric guarantee on the closeness of the core and the actual Medial Axis.

Joachim Giesen - One of the best experts on this subject based on the ideXlab platform.

  • Medial Axis APPROXIMATION AND UNSTABLE FLOW COMPLEX
    International Journal of Computational Geometry and Applications, 2008
    Co-Authors: Joachim Giesen, Edgar A Ramos, Bardia Sadri
    Abstract:

    The Medial Axis of a shape is known to carry a lot of information about the shape. In particular, a recent result of Lieutier establishes that every bounded open subset of ℝn has the same homotopy type as its Medial Axis. In this paper we provide an algorithm that computes a structure we call the core for the approximation of the Medial Axis of a shape with smooth boundary from a discrete sample of its boundary. The core is a piecewise linear cell complex that is guaranteed to capture the topology of the Medial Axis of the shape provided the sample of its boundary is sufficiently dense but not necessarily uniform. We also present a natural method for augmenting the core in order to extend it geometrically while maintaining the topological guarantees. The definition of the core and its extension are based on the steepest ascent flow map that results from the distance function induced by the sample point set. We also provide a geometric guarantee on the closeness of the core and the actual Medial Axis.

  • Medial Axis approximation and unstable flow complex
    Symposium on Computational Geometry, 2006
    Co-Authors: Joachim Giesen, Edgar A Ramos, Bardia Sadri
    Abstract:

    The Medial Axis of a shape is known to carry a lot of information about it. In particular a recent result of Lieutier establishes that every bounded open subset of Rn has the same homotopy type as its Medial Axis. In this paper we provide an algorithm that, given a sufficiently dense but not necessarily uniform sample from the surface of a shape with smooth boundary, computes a core for its Medial Axis approximation, in form of a piecewise linear cell complex, that captures the topology of the Medial Axis of the shape. We also provide a natural method to freely augment this core in order to enhance it geometrically all the while maintaining its topological guarantees. The definition of the core and its extension method are based on the steepest ascent flow induced by the distance function to the sample. We also provide a geometric guarantee on the closeness of the core and the actual Medial Axis.

  • Symposium on Computational Geometry - Medial Axis approximation and unstable flow complex
    Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06, 2006
    Co-Authors: Joachim Giesen, Edgar A Ramos, Bardia Sadri
    Abstract:

    The Medial Axis of a shape is known to carry a lot of information about it. In particular a recent result of Lieutier establishes that every bounded open subset of Rn has the same homotopy type as its Medial Axis. In this paper we provide an algorithm that, given a sufficiently dense but not necessarily uniform sample from the surface of a shape with smooth boundary, computes a core for its Medial Axis approximation, in form of a piecewise linear cell complex, that captures the topology of the Medial Axis of the shape. We also provide a natural method to freely augment this core in order to enhance it geometrically all the while maintaining its topological guarantees. The definition of the core and its extension method are based on the steepest ascent flow induced by the distance function to the sample. We also provide a geometric guarantee on the closeness of the core and the actual Medial Axis.

Yi King Choi - One of the best experts on this subject based on the ideXlab platform.

  • Medial Meshes – A Compact and Accurate Representation of Medial Axis Transform
    IEEE Transactions on Visualization and Computer Graphics, 2016
    Co-Authors: Feng Sun, Yi King Choi, Wenping Wang
    Abstract:

    The Medial Axis transform has long been known as an intrinsic shape representation supporting a variety of shape analysis and synthesis tasks. However, for a given shape, it is hard to obtain its faithful, concise and stable Medial Axis, which hinders the application of the Medial Axis. In this paper, we introduce the Medial mesh , a new discrete representation of the Medial Axis. A Medial mesh is a 2D simplicial complex coupled with a radius function that provides a piecewise linear approximation to the Medial Axis. We further present an effective algorithm for computing a concise and stable Medial mesh for a given shape. Our algorithm is quantitatively driven by a shape approximation error metric, and progressively simplifies an initial Medial mesh by iteratively contracting edges until the approximation error reaches a predefined threshold. We further demonstrate the superior efficiency and accuracy of our method over existing methods for Medial Axis simplification.

  • Medial Meshes-A Compact and Accurate Representation of Medial Axis Transform
    IEEE Transactions on Visualization and Computer Graphics, 2016
    Co-Authors: Feng Sun, Yi King Choi, Yizhou Yu, Wenping Wang
    Abstract:

    The Medial Axis transform has long been known as an intrinsic shape representation supporting a variety of shape analysis and synthesis tasks. However, for a given shape, it is hard to obtain its faithful, concise and stable Medial Axis, which hinders the application of the Medial Axis. In this paper, we introduce the Medial mesh, a new discrete representation of the Medial Axis. A Medial mesh is a 2D simplicial complex coupled with a radius function that provides a piecewise linear approximation to the Medial Axis. We further present an effective algorithm for computing a concise and stable Medial mesh for a given shape. Our algorithm is quantitatively driven by a shape approximation error metric, and progressively simplifies an initial Medial mesh by iteratively contracting edges until the approximation error reaches a predefined threshold. We further demonstrate the superior efficiency and accuracy of our method over existing methods for Medial Axis simplification.

  • A 3D shape descriptor based on spectral analysis of Medial Axis
    Computer Aided Geometric Design, 2015
    Co-Authors: Yi King Choi, Yanwen Guo, Xiaohu Guo, Wenping Wang
    Abstract:

    The Medial Axis of a 3D shape is widely known for its ability as a compact and complete shape representation. However, there is still lack of a generative description defined over the Medial Axis directly which limits its actual application to 3D shape analysis such as shape matching and retrieval. In this paper, we propose a new spectral shape descriptor that directly applies spectral analysis to the Medial Axis of a 3D shape, which we call the Medial Axis spectrum for a 3D shape. We develop a newly defined Minkowski-Euclidean ratio inspired by the Minkowski inner product to characterize the geometry of the Medial Axis of a 3D mesh. We then generalize the Laplace-Beltrami operator to the Medial Axis, and take the solution to a Laplacian eigenvalue problem defined on it as the Medial Axis spectrum. The Medial Axis spectrum is invariant under rigid transformation and isometry of the Medial Axis, and is robust to shape boundary noise as shown by our experiments. The Medial Axis spectrum is finally used for 3D shape retrieval, and its superiority over previous work is shown by extensive comparisons.

  • Spectral Analysis on Medial Axis of 2D Shapes
    Computer Graphics Forum, 2014
    Co-Authors: Yi King Choi, Yanwen Guo, Wenping Wang
    Abstract:

    Shape analysis finds many important applications in shape understanding, matching and retrieval. Among the various shape analysis methods, spectral shape analysis aims to study the spectrum of the Laplace-Beltrami operator of some well-designed shape-dependent equations and obtain a spectral shape descriptor that can in turn be used for shape analysis purposes. The success of such approaches depends greatly on the discriminating power of a shape descriptor. On the other hand, the Medial Axis of a shape is widely known for its complete shape representation. It is sensitive to small perturbation of the boundary of a shape which often poses difficulty in its effective use for shape analysis. In this paper, we propose a new spectral shape descriptor, called the Medial Axis spectrum for 2D shapes, which directly applies spectral analysis to the Medial axes of the shapes. We extend the Laplace-Beltrami operator onto the Medial Axis, and take the solution to an extended Laplacian eigenvalue problem defined on the Axis as the Medial Axis spectrum. The Medial Axis spectrum is robust in the presence of shape boundary noise, and is invariant under rigid transformations, uniform scaling and isometry of the Medial Axis. We demonstrate these benefits of such a Medial Axis spectrum representation through extensive experiments. The Medial Axis spectrum is further used for 2D shape retrieval, and its superiority over previous work is shown by comparison.

  • Computing a compact spline representation of the Medial Axis transform of a 2D shape
    Graphical Models, 2014
    Co-Authors: Yanshu Zhu, Yi King Choi, Feng Sun, Bert Jüttler, Wenping Wang
    Abstract:

    We present a full pipeline for computing the Medial Axis transform of an arbitrary 2D shape. The instability of the Medial Axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable Medial Axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the Medial Axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of Medial Axis transforms of 2D shapes.

O. Brock - One of the best experts on this subject based on the ideXlab platform.

  • Adapting the sampling distribution in PRM planners based on an approximated Medial Axis
    IEEE International Conference on Robotics and Automation 2004. Proceedings. ICRA '04. 2004, 2004
    Co-Authors: Yuandong Yang, O. Brock
    Abstract:

    Probabilistic roadmap planners have proven to be effective in solving complex path planning problems. These planners sample the configuration space to compute a representation of its free space connectivity. One of the major difficulties for this approach is the planning of a path through narrow configuration space passages, since samples are placed inside narrow passages only with small probability. To address this problem, approaches have been devised that rely on the Medial Axis of the workspace to bias sampling in configuration space such that the probability of generating samples inside narrow passages is increased. This paper introduces a novel algorithm for computing an approximation to the Medial Axis, which can be computed more efficiently than the exact or discretized Medial Axis. We demonstrate that, compared to the true Medial Axis, this approximation is equally well suited to bias the sampling in probabilistic roadmap planners. Furthermore, we present a novel sampling strategy based on the approximated Medial Axis. This strategy results in high sampling density in narrow passages, while sampling open spaces sparsely. Experiments demonstrate the effectiveness of the Medial Axis approximation and its application to motion planning based on the proposed sampling scheme.