Fiedler Trees for Multiscale Surface Analysis

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 Fielder 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 featuresensitive meshes at multiple scales.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 2011
Accession Number
ADA548747

Entities

People

  • Claudio T. Silva
  • Luís Gustavo Nonato
  • Matt Berger
  • Valerio Pascucci

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Engineered Resilient Systems

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Coefficients
  • Computational Fluid Dynamics
  • Computations
  • Curvature
  • Eigenvectors
  • Frequency
  • Geometric Processing
  • Geometry
  • Graph Theory
  • Heuristic Methods
  • Hierarchies
  • Surface Analysis
  • Topology
  • Triangles
  • Triangulation

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Computer Vision.
  • Graph Algorithms and Convex Optimization.