The spectrum of the Laplace-Beltrami operator is instrumental for a number of geometric modeling applications, from processing to analysis. Recently, multiple methods were developed to retrieve an approximation of a shape that preserves its eigenvectors as much as possible, but these techniques output a subset of input points with no connectivity, which limits their potential applications. Furthermore, the obtained Laplacian results from an optimization procedure, implying its storage alongside the selected points. Focusing on keeping a mesh instead of an operator would allow to retrieve the latter using the standard cotangent formulation, enabling easier processing afterwards. Instead, we propose to simplify the input mesh using a spectrum-preserving mesh decimation scheme, so that the Laplacian computed on the simplified mesh is spectrally close to the one of the input mesh. We illustrate the benefit of our approach for quickly approximating spectral distances and functional maps on low resolution proxies of potentially high resolution input meshes.
|Original language||English (US)|
|Number of pages||10|
|Journal||Computer Graphics Forum|
|State||Published - Jul 13 2020|
Bibliographical noteKAUST Repository Item: Exported on 2021-02-11
Acknowledged KAUST grant number(s): CRG-2017-3426
Acknowledgements: Research Funding:
KAUST OSR. Grant Number: CRG-2017-3426
This publication acknowledges KAUST support, but has no KAUST affiliated authors.