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Now showing 1 - 4 of 4
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    Detection of Salient Curvature Features on Polygonal Surfaces
    (Blackwell Publishers Ltd and the Eurographics Association, 2001) Watanabe, Kouki; Belyaev, Alexander G.
    We develop an approach for stable detection of perceptually salient curvature features on surfaces approximated by dense triangle meshes. The approach explores an "area degenerating" effect of the focal surface near its singularities and combines together a new approximations of the mean and Gaussian curvatures, nonlinear averaging of curvature maps, histogram-based curvature extrema filtering, and an image processing skeletonization procedure adapted for triangular meshes. Finally we use perceptually significant curvature extrema triangles to enhance the Garland-Heckbert mesh decimation method.
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    A Skeleton-based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces
    (Blackwell Publishers, Inc and the Eurographics Association, 2002) Hisada, Masayuki; Belyaev, Alexander G.; Kunii, Tosiyasu L.
    The paper presents a skeleton-based approach for robust detection of perceptually salient shape features. Given ashape approximated by a polygonal surface, its skeleton is extracted using a three-dimensional Voronoi diagramtechnique proposed recently by Amenta et al. [3]. Shape creases, ridges and ravines, are detected as curvescorresponding to skeletal edges. Salient shape regions are extracted via skeleton decomposition into patches.The approach explores the singularity theory for ridge and ravine detection, combines several filtering methodsfor skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysisof the skeleton for detection of salient shape regions.ACM CSS: I.3.5 Computational Geometry and Object Modeling
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    Mesh Optimization for Polygonized Isosurfaces
    (Blackwell Publishers Ltd and the Eurographics Association, 2001) Ohtake, Yutaka; Belyaev, Alexander G.
    In this paper, we propose a method for improvement of isosurface polygonizations. Given an initial polygonization of an isosurface, we introduce a mesh evolution process initialized by the polygonization. The evolving mesh converges quickly to its limit mesh which provides with a high quality approximation of the isosurface even if the isosurface has sharp features, boundary, complex topology. To analyze how close the evolving mesh approaches its destined isosurface, we introduce error estimators measuring the deviations of the mesh vertices from the isosurface and mesh normals from the isosurface normals. A new technique for mesh editing with isosurfaces is also proposed. In particular, it can be used for creating carving effects.
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    On Variational and PDE‐Based Distance Function Approximations
    (Copyright © 2015 The Eurographics Association and John Wiley & Sons Ltd., 2015) Belyaev, Alexander G.; Fayolle, Pierre‐Alain; Deussen, Oliver and Zhang, Hao (Richard)
    In this paper, we deal with the problem of computing the distance to a surface (a curve in two dimensional) and consider several distance function approximation methods which are based on solving partial differential equations (PDEs) and finding solutions to variational problems. In particular, we deal with distance function estimation methods related to the Poisson‐like equations and generalized double‐layer potentials. Our numerical experiments are backed by novel theoretical results and demonstrate efficiency of the considered PDE‐based distance function approximations.In this paper, we deal with the problem of computing the distance to a surface (a curve in two dimensional) and consider several distance function approximation methods which are based on solving partial differential equations (PDEs) and finding solutions to variational problems. In particular, we deal with distance function estimation methods related to the Poisson‐like equations and generalized double‐layer potentials. Our numerical experiments are backed by novel theoretical results and demonstrate efficiency of the considered PDE‐based distance function approximations.