On the optimality of spectral compression of mesh data

Ben Chen Mirela, Craig Gotsman

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

Spectral compression of the geometry of triangle meshes achieves good results in practice, but there has been little or no theoretical support for the optimality of this compression. We show that, for certain classes of geometric mesh models, spectral decomposition using the eigenvectors of the symmetric Laplacian of the connectivity graph is equivalent to principal component analysis on that class, when equipped with a natural probability distribution. Our proof treats connected one-and two-dimensional meshes with fixed convex boundaries, and is based on an asymptotic approximation of the probability distribution in the two-dimensional case. The key component of the proof is that the Laplacian is identical, up to a constant factor, to the inverse covariance matrix of the distribution of valid mesh geometries. Hence, spectral compression is optimal, in the mean square error sense, for these classes of meshes under some natural assumptions on their distribution.

Original languageEnglish (US)
Pages (from-to)60-80
Number of pages21
JournalACM Transactions on Graphics
Volume24
Issue number1
DOIs
StatePublished - 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design

Keywords

  • Laplacian
  • Spectral decomposition
  • Triangle mesh

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