Skip to main content
SpringerLink
Log in

Scale-time

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

A conceptually simple and logically consistent version of “scale-space” for the temporal domain is proposed. The method does not violate temporal causality, yet conserves causality in the resolution domain at any given moment in time. The filter kernels are not Gaussians (that would certainly lead to a violation of temporal causality) but are related to the Gaussians via a simple transformation of the time axis. They depend on a pair of parameters, one that has the character of a temporal delay and one that specifies the temporal resolution. In the limit for long delays (but fixed resolution) these kernels asymptotically approach the Gaussian again. Extensions of the theory towards a scale space-time are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Babaud JA, Witkin AP, Baudin M, Duda RO (1986) Uniqueness of the Gaussian kernel for scale-space filtering. IEEE PAMI 8:26–33

    Google Scholar 

  • Jaynes ET (1968) Prior probabilities. IEEE SSC-4:227–241

    Google Scholar 

  • Koenderink JJ (1984) The structure of images. Biol Cybern 50:363–370

    Google Scholar 

  • Koenderink JJ, van Doorn AJ (1978) Visual detection of spatial contrast: influence of location in the visual field, target extent and illuminance level. Biol Cybern 30:157–167

    Google Scholar 

  • Koenderink JJ, van Doorn AJ (1987) Representation of local geometry in the visual system. Biol Cybern 55:367–375

    Google Scholar 

  • Reichardt W (1961) Autocorrelation, a principle for the evaluation of sensory information by the central nervous system. In: Sensory communication. Rosenblith, WA (ed). MIT Press, Cambridge Mass, pp 303–317

    Google Scholar 

  • Witkin A (1983) Scale-space filtering. Proc IJCAI, Karlsruhe, pp 1019–1021

  • Young RA (1986) Simulation of human retinal function with the Gaussian derivative model. Proc IEEE CCVP, pp 564–569

  • Yuille AL, Poggio T (1986) Scaling theorems for zero crossings. IEEE PAMI 8:15–25

    Google Scholar 

  • Zucker SW Hummel RA (1986) Receptive fields and the representation of visual information. Hum Neurobiol 5:121–128

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Science, University of Oxford, Oxford, United Kingdom

    J. J. Koenderink

  2. The Physics Laboratory, MFF Utrecht University, P.O. Box 80000, NL-3508 TA, Utrecht, The Netherlands

    J. J. Koenderink

Authors
  1. J. J. Koenderink
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The Physics Laboratory, MFF, P.O. Box 80000, NL-3508 TA Utrecht, The Netherlands

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koenderink, J.J. Scale-time. Biol. Cybern. 58, 159–162 (1988). https://doi.org/10.1007/BF00364135

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00364135

Keywords

Search

Navigation