Abstract
We propose a mathematical description for the spatial organization of orientation preference in the visual cortex. The theory is derived from the principle of optimal smoothness and predicts the spatial pattern of orientation preference from position and chirality of its singularities (i.e. “pinwheels”). The model exhibits long range order in the sense that, given the configuration of singularities, the specification of orientation preference at a single location fixes the entire map. A comparison with optically recorded images of cortical maps suggests that orientation preference can indeed be predicted over a much larger spatial range than previously estimated on the basis of correlation measurements.
This work has been supported by the Deutsche Forschungsgemeinschaft (Schwerpunktpro-gramm Physiologie und Theorie neuronaler Netze, LA 441/5-1 and SFB 185 Nichtlineare Dynamik).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Grmvald, A., Lieke, E., Frostig, R.D., Gilbert, CD. & Wiesel, T.N., Functional architecture of cortex revealed by optical imaging of intrinsic signals, Nature 324, 361–364 (1986).
Blasdel, G.G., Salama, G., Voltage-sensitive dyes reveal a modular organization in monkey striate cortex, Nature 321, 579–585 (1986).
Bonhoeffer, T., Grinvald, A., Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns, Nature 343,429–431 (1991).
Obermayer, K., Schulten, K., & Blasdel, G.G., A comparison between a neural network model for the formation of brain maps and experimental data, in Neural Information Processing Systems 4, eds. Moody, E.M., Hanson, S.J. & Lippmann, R.P., (Morgan Kaufmann, 1992).
Obermayer, K., Blasdel, G.G., & Schulten, K., Statistical-mechanical analysis of self-organization and pattern formation during the development of visual maps, Phys. Rev. A 45,7568–7589 (1992).
Niebur, E., Wörgötter, F., Orientation columns from first principles, in Com-putation and Neural Systems, eds. Bower, J., Eeckmann, F., (Kluwer, 1993).
Swindale, N.V., Matsubara, J. & Cynader, M.S., Surface organization of orientation and direction selectivity in cat area 18, J. Neurosci. 7, 1414–1427 (1987).
Swindale, N.V., Cynader, M.S. & Matsubara, J., Cortical cartography: A two-dimensional view, in Computational Neuroscience, ed. Schwartz, E.L., (MIT-Press, Cambridge, 1990).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Wolf, F., Pawelzik, K., Geisel, T., Kim, DS., Bonhoeffer, T. (1994). Optimal Smoothness of Orientation Preference Maps. In: Eeckman, F.H. (eds) Computation in Neurons and Neural Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2714-5_16
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2714-5_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6169-5
Online ISBN: 978-1-4615-2714-5
eBook Packages: Springer Book Archive