Spectral Mesh Simplification

Thibault Lescoat, Hsueh-Ti Derek Liu, Jean-Marc Thiery, Alec Jacobson, Tamy Boubekeur, Maks Ovsjanikov

Research output: Contribution to journalArticlepeer-review

Abstract

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 languageEnglish (US)
Pages (from-to)315-324
Number of pages10
JournalComputer Graphics Forum
Volume39
Issue number2
DOIs
StatePublished - Jul 13 2020
Externally publishedYes

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