Families of tuned scale-space kernels

  • L. M. J. Florack
  • B. M. ter Haar Romeny
  • J. J. Koenderink
  • M. A. Viergever
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 588)


We propose a formalism for deriving parametrised ensembles of local neighbourhood operators on the basis of a complete family of scale-space kernels, which are apt for the measurement of a specific physical observable. The parameters are introduced in order to associate a continuum of a priori equivalent kernels with each scale-space kernel, each of which is tuned to a particular parameter value.

Ensemble averages, or other functional operations in parameter space, may provide robust information about the physical observable of interest. The approach gives a possible handle on incorporating multi-valuedness (transparancy) and visual coherence into a single model.

We consider the case of velocity tuning to illustrate the method. The emphasis, however, is on the formalism, which is more generally applicable.


Stimulus Velocity Complete Family Functional Operation Point Stimulus Stereo Disparity 
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.


  1. 1.
    A. Witkin, “Scale space filtering,” in Proc. International Joint Conference on Artificial Intelligence, (Karlsruhe, W. Germany), pp. 1019–1023, 1983.Google Scholar
  2. 2.
    J. J. Koenderink, “The structure of images,” Biol. Cybern., vol. 50, pp. 363–370, 1984.PubMedMathSciNetGoogle Scholar
  3. 3.
    T. Lindeberg, “Scale-space for discrete signals,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 3, pp. 234–245, 1990.CrossRefGoogle Scholar
  4. 4.
    B. M. ter Haar Romeny, L. M. J. Florack, J. J. Koenderink, and M. A. Viergever, “Scalespace: Its natural operators and differential invariants,” in International Conf. on Information Processing in Medical Imaging, vol. 511 of Lecture Notes in Computer Science, (Berlin), pp. 239–255, Springer-Verlag, July 1991.Google Scholar
  5. 5.
    L. Florack, B. ter Haar Romeny, J. Koenderink, and M. Viergever, “Scale-space.” Submitted to IEEE PAMI, November 1991.Google Scholar
  6. 6.
    R. A. Young, “The gaussian derivative model for machine vision: I. retinal mechanisms,” Spatial Vision, vol. 2, no. 4, pp. 273–293, 1987.PubMedGoogle Scholar
  7. 7.
    P. Bijl, Aspects of Visual Contrast Detection. PhD thesis, University of Utrecht, University of Utrecht, Dept. of Med. Phys., Princetonplein 5, Utrecht, the Netherlands, May 1991.Google Scholar
  8. 8.
    J. J. Koenderink and A. J. van Doom, “Representation of local geometry in the visual system,” Biol. Cybern., vol. 55, pp. 367–375, 1987.PubMedGoogle Scholar
  9. 9.
    J. J. Koenderink and A. J. Van Doom, “Operational significance of receptive field assemblies,” Biol. Cybern., vol. 58, pp. 163–171, 1988.PubMedGoogle Scholar
  10. 10.
    J. J. Koenderink and A. J. van Doom, “Receptive field families,” Biol. Cybern., vol. 63, pp. 291–298, 1990.Google Scholar
  11. 11.
    P. Werkhoven, Visual Perception of Successive Order. PhD thesis, University of Utrecht, University of Utrecht, Dept. of Med. Phys., Princetonplein 5, Utrecht, the Netherlands, May 1990.Google Scholar
  12. 12.
    D. J. Heeger, “Model for the extraction of image flow,” Journal of the Optical Society of America-A, vol. 4, no. 8, pp. 1455–1471, 1987.Google Scholar
  13. 13.
    D. Heeger, “Optical flow using spatiotemporal filters,” International Journal of Computer Vision, vol. 1, pp. 279–302, 1988.Google Scholar
  14. 14.
    E. H. Adelson and J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” Journal of the Optical Society of America-A, vol. 2, no. 2, pp. 284–299, 1985.Google Scholar
  15. 15.
    W. E. Reichardt and R. W. Schögl, “A two dimensional field theory for motion computation,” Biol. Cybern., vol. 60, pp. 23–35, 1988.PubMedGoogle Scholar
  16. 16.
    P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics. Springer-Verlag, 1986.Google Scholar
  17. 17.
    J. J. Koenderink, “Scale-time,” Biol. Cybern., vol. 58, pp. 159–162, 1988.Google Scholar
  18. 18.
    A. J. Noest and J. J. Koenderink, “Visual coherence despite transparency or partial occlusion,” Perception, vol. 19, p. 384, 1990. Abstract of poster presented at the ECVP 1990, Paris.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • L. M. J. Florack
    • 1
  • B. M. ter Haar Romeny
    • 1
  • J. J. Koenderink
    • 2
  • M. A. Viergever
    • 1
  1. 1.3D Computer Vision Research GroupUniversity HospitalCX UtrechtThe Netherlands
  2. 2.Dept. of Medical and Physiological PhysicsUniversity of UtrechtCC UtrechtThe Netherlands

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