Fiedler trees for multiscale surface analysis

Matt Berger, Luis Gustavo Nonato, Valerio Pascucci, Cludio T. Silva

Research output: Contribution to journalArticle

Abstract

In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the LaplaceBeltrami operator to recursively decompose the surface. For this reason we coin our surface decomposition the Fiedler tree. Using the Fiedler tree ensures a number of attractive properties, including: mesh-independent decomposition, well-formed and nearly equi-areal surface patches, and noise robustness. We show how the evenly distributed patches can be exploited for generating multiresolution high quality uniform meshes. Additionally, our decomposition permits a natural means for carrying out wavelet methods, resulting in an intuitive method for producing feature-sensitive meshes at multiple scales.

Original languageEnglish (US)
Pages (from-to)272-281
Number of pages10
JournalComputers and Graphics (Pergamon)
Volume34
Issue number3
DOIs
StatePublished - Jun 2010

Keywords

  • Multiresolution shape analysis
  • Multiscale representation
  • Surface partition

ASJC Scopus subject areas

  • Engineering(all)
  • Human-Computer Interaction
  • Computer Graphics and Computer-Aided Design

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