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Topological Analysis and Characterization of Discrete Scalar Fields

  • Emanuele Danovaro
  • Leila De Floriani
  • Mohammed Mostefa Mesmoudi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2616)

Abstract

In this paper, we address the problem of analyzing the topology of discrete scalar fields defined on triangulated domains. To this aim, we introduce the notions of discrete gradient vector field and of Smalelike decomposition for the domain of a d-dimensional scalar field. We use such notions to extract the most relevant features representing the topology of the field. We describe a decomposition algorithm, which is independent of the dimension of the scalar field, and, based on it, methods for extracting the critical net of a scalar field. A complete classification of the critical points of a 2-dimensional field that corresponds to a piecewise differentiable field is also presented.

Keywords

Saddle Point Simplicial Complex Gradient Vector Decomposition Algorithm Topological Analysis 
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 2003

Authors and Affiliations

  • Emanuele Danovaro
    • 1
  • Leila De Floriani
    • 1
  • Mohammed Mostefa Mesmoudi
    • 1
  1. 1.Department of Computer Science and Information Science (DISI)University of GenovaGenovaItaly

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