Fast Approximation of Laplace-Beltrami Eigenproblems

Ahmad Nasikun, Christopher Brandt, Klaus Hildebrandt

Research output: Contribution to journalConference articleScientificpeer-review

7 Citations (Scopus)
22 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)121-134
Number of pages14
JournalComputer Graphics Forum
Volume37
Issue number5
Publication statusPublished - 2018
EventEurographics Symposium on Geometry Processing , SGP 2018 - Paris, France
Duration: 7 Jul 201811 Jul 2018
https://sgp2018.sciencesconf.org/

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