Deep structure from a geometric point of view

  • Authors:
  • Luc Florack

  • Affiliations:
  • Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

  • Venue:
  • DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
  • Year:
  • 2005

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Abstract

The geometry of “empty” scale space is investigated. By virtue of the proposed geometric axioms the generating PDE, the linear isotropic heat equation, can be presented in covariant, or geometrical form. The postulate of a metric for scale space cannot be upheld, as it is incompatible with the generating equation. Two familiar instances of scale spaces consistent with the geometric axioms are considered by way of example, viz. classical, homogeneous scale space, and foveal scale space.