Technical Section: Fiedler trees for multiscale surface analysis

Authors:
Matt Berger;Luis Gustavo Nonato;Valerio Pascucci;Cláudio T. Silva
Affiliations:
Scientific Computing and Imaging Institute, University of Utah, USA and US Air Force Research Laboratory USA;Scientific Computing and Imaging Institute, University of Utah, USA and Departamento de Matemática Aplicada e Estatística, Universidade de São Paulo, Brazil;Scientific Computing and Imaging Institute, University of Utah, USA;Scientific Computing and Imaging Institute, University of Utah, USA
Venue:
Computers and Graphics
Year:
2010

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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 Laplace-Beltrami 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.