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The Topological Structure of Scale-Space Images

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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.

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Authors and Affiliations

  1. Department of Mathematics, Utrecht University, Budapestlaan 6, NL-3584 CD, Utrecht, The Netherlands

    Luc Florack

  2. Department of Computer Science, Utrecht University, Padualaan 14, NL-3584 CH, Utrecht, The Netherlands

    Arjan Kuijper

Authors
  1. Luc Florack
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  2. Arjan Kuijper
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Florack, L., Kuijper, A. The Topological Structure of Scale-Space Images. Journal of Mathematical Imaging and Vision 12, 65–79 (2000). https://doi.org/10.1023/A:1008304909717

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