Extended Reeb Graphs for Surface Understanding and Description

  • Silvia Biasotti
  • Bianca Falcidieno
  • Michela Spagnuolo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

Abstract

The aim of this paper is to describe a conceptual model for surface representation based on topological coding, which de.nes a sketch of a surface usable for classi.cation or compression purposes. Theoretical approaches based on di.erential topology and geometry have been used for surface coding, for example Morse theory and Reeb graphs. To use these approaches in discrete geometry, it is necessary to adapt concepts developed for smooth manifolds to discrete surface models, as for example piecewise linear approximations. A typical problem is represented by degenerate critical points, that is non-isolated critical points such as plateaux and .at areas of the surface. Methods proposed in literature either do not consider the problem or propose local adjustments of the surface, which solve the theoretical problem but may lead to a wrong interpretation of the shape by introducing artefacts, which do not correspond to any shape feature. In this paper, an Extended Reeb Graph representation (ERG) is proposed, which can handle degenerate critical points, and an algorithm is presented for its construction.

Keywords

Critical Area Shape Description Digital Terrain Modelling Height Function Morse Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Silvia Biasotti
    • 1
  • Bianca Falcidieno
    • 1
  • Michela Spagnuolo
    • 1
  1. 1.Istituto per la Matematica ApplicataConsiglio Nazionale delle RicercheItaly

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