The Relevance of Non-generic Events in Scale Space Models

  • Arjan Kuijper
  • Luc Florack
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2350)


In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of spatial critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe the behaviour of critical point trajectories when various different types of generic events, viz. annihilations and creations of pairs of spatial critical points, (almost) coincide. Although such events are non-generic in mathematical sense, they are not unlikely to be encountered in practice. Furthermore the behaviour leads to the observation that fine-to-coarse tracking of critical points doesn’t suffice. We apply the theory to an artificial image and a simulated MR image and show the occurrence of the described behaviour.


Critical Path Scale Space Critical Curve Catastrophe Theory Critical Curf 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Arjan Kuijper
    • 1
  • Luc Florack
    • 2
  1. 1.Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Biomedical EngineeringTechnical University EindhovenEindhovenThe Netherlands

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