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Journal of Mathematical Imaging and Vision

, Volume 12, Issue 1, pp 65–79 | Cite as

The Topological Structure of Scale-Space Images

  • Luc Florack
  • Arjan Kuijper
Article

Abstract

We investigate the “deep structure” of a scale-space image. The emphasis is on topology, i.e. we concentrate on critical points—points with vanishing gradient—and top-points—critical points with degenerate Hessian—and monitor their displacements, respectively generic morsifications in scale-space. Relevant parts of catastrophe theory in the context of the scale-space paradigm are briefly reviewed, and subsequently rewritten into coordinate independent form. This enables one to implement topological descriptors using a conveniently defined coordinate system.

scale-space catastrophe theory critical points deep structure image topology 

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Luc Florack
    • 1
  • Arjan Kuijper
    • 2
  1. 1.Department of MathematicsUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands

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