Linear scale-space

  • Florack L
  • ter Haar Romeny B
  • Koenderink J
 et al. 
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Abstract

The formulation of afront-end orearly vision system is addressed, and its connection with scale-space is shown. A front-end vision system is designed to establish a convenient format of some sampled scalar field, which is suited for postprocessing by various dedicated routines. The emphasis is on the motivations and implications of symmetries of the environment; they pose natural, a priori constraints on the design of a front-end. The focus is on static images, defined on a multidimensional spatial domain, for which it is assumed that there are no a priori preferred points, directions, or scales. In addition, the front-end is required to be linear. These requirements are independent of any particular image geometry and express the front-end's pure syntactical, bottom up nature. It is shown that these symmetries suffice to establish the functionality properties of a front-end. For each location in the visual field and each inner scale it comprises a hierarchical family of tensorial apertures, known as the Gaussian family, the lowest order of which is the normalised Gaussian. The family can be truncated at any given order in a consistent way. The resulting set constitutes a basis for alocal jet bundle. Note that scale-space theory shows up here without any call upon the prohibition of spurious detail, which, in some way or another, usually forms the basic starting point for diffusion-like scale-space theories.

Author-supplied keywords

  • Gaussian family
  • front-end vision
  • local jet bundle
  • scale invariance
  • scale-space
  • scaled differential operators

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Authors

  • L. M.J. Florack

  • B. M. ter Haar Romeny

  • J. J. Koenderink

  • M. A. Viergever

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