Neural Fields Models of Visual Areas: Principles, Successes, and Caveats

I discuss how the notion of neural fields, a phenomenological averaged description of spatially distributed populations of neurons, can be used to build models of how visual information is represented and processed in the visual areas of primates. I describe one of the basic principles of operation of these neural fields equations which is closely connected to the idea of a bifurcation of their solutions. I then apply this concept to several visual features, edges, textures and motion and show that it can account very simply for a number of experimental facts as well as suggest new experiments.

[1]  Olivier D. Faugeras,et al.  Bifurcation analysis applied to a model of motion integration with a multistable stimulus , 2012, Journal of Computational Neuroscience.

[2]  Olivier P. Faugeras,et al.  Bifurcation of Hyperbolic Planforms , 2010, J. Nonlinear Sci..

[3]  Grégory Faye,et al.  Bifurcation Diagrams and Heteroclinic Networks of Octagonal H-Planforms , 2012, J. Nonlinear Sci..

[4]  Olivier D. Faugeras,et al.  A Constructive Mean-Field Analysis of Multi-Population Neural Networks with Random Synaptic Weights and Stochastic Inputs , 2008, Front. Comput. Neurosci..

[5]  O. Faugeras,et al.  Stability of the stationary solutions of neural field equations with propagation delays , 2011, Journal of mathematical neuroscience.

[6]  Olivier D. Faugeras,et al.  Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations , 2009, SIAM J. Appl. Dyn. Syst..

[7]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[8]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[9]  J. Slotine,et al.  Stability and Synchronization in Neural Fields , 2007 .

[10]  J. Touboul,et al.  Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons , 2012, The Journal of Mathematical Neuroscience.

[11]  R. Veltz.  Nonlinear analysis methods in neural field models , 2011 .

[12]  Pascal Chossat,et al.  Analysis of a hyperbolic geometric model for visual texture perception , 2011, Journal of mathematical neuroscience.

[13]  Olivier P. Faugeras,et al.  Hyperbolic Planforms in Relation to Visual Edges and Textures Perception , 2009, PLoS Comput. Biol..

[14]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[15]  S. Amari,et al.  Characteristics of Random Nets of Analog Neuron-Like Elements , 1972, IEEE Trans. Syst. Man Cybern..