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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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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DOI: https://doi.org/10.1023/A:1008304909717