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International Journal of Computer Vision

, Volume 31, Issue 2–3, pp 247–259 | Cite as

Pseudo-Linear Scale-Space Theory

  • Luc Florack
  • Robert Maas
  • Wiro Niessen
Article

Abstract

It has been observed that linear, Gaussian scale-space, and nonlinear, morphological erosion and dilation scale-spaces generated by a quadratic structuring function have a lot in common. Indeed, far-reaching analogies have been reported, which seems to suggest the existence of an underlying isomorphism. However, an actual mapping appears to be missing.

In the present work a one-parameter isomorphism is constructed in closed-form, which encompasses linear and both types of morphological scale-spaces as (non-uniform) limiting cases. The unfolding of the one-parameter family provides a means to transfer known results from one domain to the other. Moreover, for any fixed and non-degenerate parameter value one obtains a novel type of “pseudo-linear” multiscale representation that is, in a precise way, “in-between” the familiar ones. This is of interest in its own right, as it enables one to balance pros and cons of linear versus morphological scale-space representations in any particular situation.

fuzzy dilation/erosion linear scale-space morphological scale-space reaction-diffusion 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Luc Florack
    • 1
  • Robert Maas
    • 1
  • Wiro Niessen
    • 1
  1. 1.Image Sciences Institute, Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands

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