Chordal decomposition for spectral coarsening

Honglin Chen, Hsueh TI Derek Liu, Alec Jacobson, David I.W. Levin

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows the user to control the operator sparsity pattern. This allows for a trade-off between the spectral accuracy of the operator and the cost of its application. We efficiently minimize the energy with a change of variables and achieve state-of-the-art results on spectral coarsening. Our solver further enables novel applications including volume-to-surface approximation and detaching the operator from the mesh, i.e., one can produce a mesh tailor-made for visualization and optimize an operator separately for computation.

Original languageEnglish
Article number265
JournalACM Transactions on Graphics
Volume39
Issue number6
DOIs
StatePublished - 26 Nov 2020
Externally publishedYes

Keywords

  • chordal decomposition
  • geometry processing
  • numerical coarsening
  • spectral geometry

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