Abstract
A Riemannian manifold endowed with a conformal metric is proposed as a geometric model for the cortical magnification that characterises foveal systems. The eccentricity scaling of receptive fields, the relative size of the foveola, as well as the fraction of receptive fields involved in foveal vision can all be deduced from it.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P. Bijl. Aspects of Visual Contrast Detection. PhD thesis, University of Utrecht, Department of Physics, Utrecht, The Netherlands, May 8 1991.
Y. Choquet-Bruhat, C. DeWitt-Morette, and M. Dillard-Bleick. Analysis, Manifolds, and Physics. Part I: Basics. Elsevier Science Publishers B.V. (North-Holland), Amsterdam, 1991.
P. M. Daniel and D. Whitteridge. The representation of the visual field on the cerebral cortex in monkeys. Journal of Physiology, 159:203–221, 1961.
B. Fischer and H. U. May. Invarianzen in der Katzenretina: Gesetzmäßige Beziehungen zwischen Empfmdlichkeit, Größe und Lage rezeptiver Felder von Ganglienzellen. Experimental Brain Research, 11:448–464, 1970.
L. M. J. Florack. Image Structure, volume 10 of Computational Imaging and Vision Series. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.
L. M. J. Florack. Non-linear scale-spaces isomorphic to the linear case. In B. K. Ersbøll and P. Johansen, editors, Proceedings of the 11th Scandinavian Conference on Image Analysis (Kangerlussuaq, Greenland, June 7–11 1999), volume 1, pages 229–234, Lyngby, Denmark, 1999.
L. M. J. Florack, R. Maas, and W. J. Niessen. Pseudo-linear scale-space theory. International Journal of Computer Vision, 31(2/3):247–259, April 1999.
L. M. J. Florack, A. H. Salden, B. M. ter Haar Romeny, J. J. Koenderink, and M. A. Viergever. Nonlinear scale-space. In B. M. ter Haar Romeny, editor, Geometry-Driven Diffusion in Computer Vision, volume 1 of Computational Imaging and Vision Series, pages 339–370. Kluwer Academic Publishers, Dordrecht, 1994.
B. M. ter Haar Romeny, L. M. J. Florack, J. J. Koenderink, and M. A. Viergever, editors. Scale-Space Theory in Computer Vision: Proceedings of the First International Conference, Scale-Space’97, Utrecht, The Netherlands, volume 1252 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, July 1997.
J. J. Koenderink. The structure of images. Biological Cybernetics, 50:363–370, 1984.
J. J. Koenderink. The brain a geometry engine. Psychological Research, 52:122–127, 1990.
J. J. Koenderink and A. J. van Doorn. Receptive field families. Biological Cybernetics, 63:291–298, 1990.
T. Lindeberg. Scale-Space Theory in Computer Vision. The Kluwer International Series in Engineering and Computer Science. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.
S. L. Polyak. The Retina. University of Chicago Press, Chicago, 1941.
R. W. Rodieck. The First Steps in Seeing. Sinauer Associates, Inc., Sunderland, Massachusetts, 1998.
M. Spivak. Differential Geometry, volume 1–5. Publish or Perish, Berkeley, 1975.
J. Sporring, M. Nielsen, L. M. J. Florack, and P. Johansen, editors. Gaussian Scale-Space Theory, volume 8 of Computational Imaging and Vision Series. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.
F. W. Weymouth. Visual sensory units and the minimal angle of resolution. American Journal of Ophthalmology, 46:102–113, 1958.
A. P. Witkin. Scale-space filtering. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 1019–1022, Karlsruhe, Germany, 1983.
R. A. Young. The Gaussian derivative model for machine vision: Visual cortex simulation. Journal of the Optical Society of America, July 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Florack, L. (2000). A Geometric Model for Cortical Magnification. In: Lee, SW., Bülthoff, H.H., Poggio, T. (eds) Biologically Motivated Computer Vision. BMCV 2000. Lecture Notes in Computer Science, vol 1811. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45482-9_58
Download citation
DOI: https://doi.org/10.1007/3-540-45482-9_58
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67560-0
Online ISBN: 978-3-540-45482-3
eBook Packages: Springer Book Archive