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Discrete Laplace-Beltrami operators for shape analysis and segmentation

机译：离散Laplace-Beltrami运算符，用于形状分析和分割

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摘要

Shape analysis plays a pivotal role in a large number of applications, ranging from traditional geometry processing to more recent 3D content management. In this scenario, spectral methods are extremely promising as they provide a natural library of tools for shape analysis, intrinsically defined by the shape itself. In particular, the eigenfunctions of the Laplace-Beltrami operator yield a set of real-valued functions that provide interesting insights in the structure and morphology of the shape. In this paper, we first analyze different discretizations of the Laplace-Beltrami operator (geometric Laplacians, linear and cubic FEM operators) in terms of the correctness of their eigenfunctions with respect to the continuous case. We then present the family of segmentations induced by the nodal sets of the eigenfunctions, discussing its meaningfulness for shape understanding.
机译：从传统的几何处理到最新的3D内容管理，形状分析在许多应用中都起着关键作用。在这种情况下，光谱方法极有希望，因为它们为形状分析提供了自然的工具库，这些工具由形状本身固有地定义。特别是，Laplace-Beltrami运算符的本征函数产生了一组实值函数，这些函数提供了有关形状的结构和形态的有趣见解。在本文中，我们首先根据其本征函数相对于连续情况的正确性，分析了Laplace-Beltrami算符（几何拉普拉斯算子，线性和三次FEM算子）的不同离散化。然后，我们介绍由特征函数的节点集引起的分割族，讨论其对于形状理解的意义。

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  • 来源
    《Computers & Graphics》 |2009年第3期|381-390|共10页
  • 作者

    Martin Reuter; Silvia Biasotti; Daniela Giorgi; Giuseppe Patane; Michela Spagnuolo;

  • 作者单位

    Massachusetts Institute of Technology, Cambridge, MA, USA AA, Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA;

    Istituto di Matematica Applicata e Tecnologie Informatiche - Consiglio Nazionale delle Ricerche, Genova, Italy;

    Istituto di Matematica Applicata e Tecnologie Informatiche - Consiglio Nazionale delle Ricerche, Genova, Italy;

    Istituto di Matematica Applicata e Tecnologie Informatiche - Consiglio Nazionale delle Ricerche, Genova, Italy;

    Istituto di Matematica Applicata e Tecnologie Informatiche - Consiglio Nazionale delle Ricerche, Genova, Italy;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    laplace-Beltrami operator; eigenfunctions; nodal sets; nodal domains; shape analysis; shape segmentation;

    机译：laplace-Beltrami运算符;本征函数;节点集节点域;形状分析;形状分割;

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