Spectral coarsening of geometric operators

Hsueh Ti Derek Liu, Alec Jacobson, Maks Ovsjanikov

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We introduce a novel approach to measure the behavior of a geometric operator before and after coarsening. By comparing eigenvectors of the input operator and its coarsened counterpart, we can quantitatively and visually analyze how well the spectral properties of the operator are maintained. Using this measure, we show that standard mesh simplification and algebraic coarsening techniques fail to maintain spectral properties. In response, we introduce a novel approach for spectral coarsening. We show that it is possible to significantly reduce the sampling density of an operator derived from a 3D shape without affecting the low-frequency eigenvectors. By marrying techniques developed within the algebraic multigrid and the functional maps literatures, we successfully coarsen a variety of isotropic and anisotropic operators while maintaining sparsity and positive semi-definiteness. We demonstrate the utility of this approach for applications including operator-sensitive sampling, shape matching, and graph pooling for convolutional neural networks.
Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalACM Transactions on Graphics
Volume38
Issue number4
DOIs
StatePublished - Jul 12 2019
Externally publishedYes

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