Scale-space for 1-D discrete signals

  • Tony Lindeberg
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 256)

Abstract

The scale-space theory has been developed and well-established for continuous signals and images. However, it does not tell anything about how the implementation should be performed computationally in real-life problems, i.e., for discrete signals and images. In principle, there are two possible approaches:
  • Apply the results from the continuous scale-space theory by discretizing the occurring equations. For example, the convolution integral (1.3) can be approximated by a sum using standard numerical methods. Or, the diffusion equation (1.5) can be discretized in space with the ordinary five-point operator forming a set of coupled ordinary differential equations, which can be further discretized in scale. If the numerical methods are chosen with care, reasonable approximations to the continuous numerical values can certainly be expected. But it is not guaranteed that the original scale-space conditions, however formulated in a discrete situation, will be preserved.

  • Formulate a genuinely discrete theory by postulating suitable axioms.

Keywords

Gaussian Kernel Local Extremum Filter Coefficient Coarse Level Discrete Analogue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Tony Lindeberg
    • 1
  1. 1.Royal Institute of TechnologyStockholmSweden

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