Discrete Laplace-Beltrami operators for shape analysis and segmentation

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.

关键词： Laplace-Beltrami operator Eigenfunctions Nodal sets Nodal domains Shape analysis Shape segmentation

作者: Martin Reuter Silvia Biasotti Daniela Giorgi Giuseppe Patanè Michela Spagnuolo

作者单位: Massachusetts Institute of Technology, Cambridge, MA USA AA Martinos Center for Biomedical Imaging.M Istituto di Matematica Applicata e Tecnologie Informatiche-Consiglio Nazionale dells Ricerche, Cenov

会议类型: 国际会议

会议名称: IEEE International Conference on Shape Modeling and Applications (SMI)(2009年形状建模国际会议)

会议地点: 北京

会议语种:英文

页码: 381-390

在线出版日期: 2009-06-26（万方平台首次上网日期，不代表论文的发表时间）