Advertisement

Abstract

A geometric model is proposed for an artificial foveal vision system, and its plausibility in the context of biological vision is explored. The model is based on an isotropic, scale invariant two-form that describes the spatial layout of receptive fields in the the visual sensorium (in the biological context roughly corresponding to retina, LGN, and V1). It overcomes the limitation of the familiar log-polar model by handling its singularity in a graceful way. The log-polar singularity arises as a result of ignoring the physical resolution limitation inherent in any real (artificial or biological) visual system. The incorporation of such a limitation requires the introduction of a physical constant, measuring the radius of the geometric foveola (a central region characterized by maximal resolving power). The proposed model admits a description in singularity-free canonical coordinates that generalize the well-established log-polar coordinates, and that reduce to these in the asymptotic case of negligibly sized geometric foveola (or, equivalently, at peripheral locations in the visual field). Biological plausibility of the model is demonstrated by comparison with known facts on human vision.

Keywords

Generalized log-polar map foveal vision cortical magnification scale invariance receptive field scaling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Duits, R., et al.: On the axioms of scale space theory. Journal of Mathematical Imaging and Vision 20(3), 267–298 (2004)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Florack, L.M.J., et al.: Linear scale-space. Journal of Mathematical Imaging and Vision 4(4), 325–351 (1994)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Iijima, T.: Basic theory on normalization of a pattern (in case of typical one-dimensional pattern) (in Japanese). Bulletin of Electrical Laboratory 26, 368–388 (1962)Google Scholar
  4. 4.
    Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363–370 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Koenderink, J.J., van Doorn, A.J.: Representation of local geometry in the visual system. Biological Cybernetics 55, 367–375 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Koenderink, J.J., van Doorn, A.J.: Operational significance of receptive field assemblies. Biological Cybernetics 58, 163–171 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Koenderink, J.J., van Doorn, A.J.: Receptive field families. Biological Cybernetics 63, 291–298 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Koenderink, J.J.: The brain a geometry engine. Psychological Research 52, 122–127 (1990)CrossRefGoogle Scholar
  9. 9.
    Weickert, J.A., Ishikawa, S., Imiya, A.: Linear scale-space has first been proposed in Japan. Journal of Mathematical Imaging and Vision 10(3), 237–252 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Witkin, A.P.: Scale-space filtering. In: Proceedings of the International Joint Conference on Artificial Intelligence, Karlsruhe, Germany, pp. 1019–1022 (1983)Google Scholar
  11. 11.
    Rodieck, R.W.: The First Steps in Seeing. Sinauer Associates, Inc., Sunderland (1998)Google Scholar
  12. 12.
    Florack, L.M.J.: A geometric model for cortical magnification. In: Bülthoff, H.H., Poggio, T.A., Lee, S.-W. (eds.) BMCV 2000. LNCS, vol. 1811, pp. 574–583. Springer, Heidelberg (2000)Google Scholar
  13. 13.
    Tistarelli, M., Sandini, G.: On the advantages of polar and log-polar mapping for direct estimation of time-to-impact from optical flow. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(4), 401–416 (1993)CrossRefGoogle Scholar
  14. 14.
    Jost, J.: Riemannian Geometry and Geometric Analysis, 4th edn. Springer, Berlin (2005)zbMATHGoogle Scholar
  15. 15.
    Koenderink, J.J.: Solid Shape. MIT Press, Cambridge (1990)Google Scholar
  16. 16.
    Wandell, B.A.: Foundations of Vision. Sinauer Associates, Inc., Sunderland (1995)Google Scholar
  17. 17.
    Hartridge, H.: The limit to peripheral vision. Journal of Physiology 53(17) (1919)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Luc Florack
    • 1
  1. 1.Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, NL-5600 MB  EindhovenThe Netherlands

Personalised recommendations