Fast Approximation of Laplace-Beltrami Eigenproblems
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Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
The spectrum and eigenfunctions of the Laplace-Beltrami operator are at the heart of effective schemes for a variety of problems in geometry processing. A burden attached to these spectral methods is that they need to numerically solve a large-scale eigenvalue problem, which results in costly precomputation. In this paper, we address this problem by proposing a fast approximation algorithm for the lowest part of the spectrum of the Laplace-Beltrami operator. Our experiments indicate that the resulting spectra well-approximate reference spectra, which are computed with state-of-the-art eigensolvers. Moreover, we demonstrate that for different applications that comparable results are produced with the approximate and the reference spectra and eigenfunctions. The benefits of the proposed algorithm are that the cost for computing the approximate spectra is just a fraction of the cost required for numerically solving the eigenvalue problems, the storage requirements are reduced and evaluation times are lower. Our approach can help to substantially reduce the computational burden attached to spectral methods for geometry processing.
Description
@article{10.1111:cgf.13496,
journal = {Computer Graphics Forum},
title = {{Fast Approximation of Laplace-Beltrami Eigenproblems}},
author = {Nasikun, Ahmad and Brandt, Christopher and Hildebrandt, Klaus},
year = {2018},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.13496}
}