Chaos on the pseudosphere, Physics Reports, vol.143, issue.3, pp.109-240, 1986. ,
Relationships between orientation-preference pinwheels, cytochrome oxidase blobs, and ocular-dominance columns in primate striate cortex, Proceedings of the National Academy of Sciences, vol.89, pp.11905-11909, 1993. ,
Theory of orientation tuning in visual cortex, Proceedings of the National Academy of Sciences, vol.92, issue.9, pp.3844-3848, 1995. ,
Optimal orientation detection of linear symmetry, Proc. First Int'l Conf. Comput. Vision, pp.433-438, 1987. ,
Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns, Nature, vol.353, issue.6343, p.429, 1991. ,
Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex, Journal of Neuroscience, vol.17, pp.2112-2127, 1997. ,
Dynamical Mechanism for Sharp Orientation Tuning in an Integrate-and-Fire Model of a Cortical Hypercolumn, Neural Computation, vol.12, pp.2473-251, 2000. ,
A spherical model for orientation and spatial frequency tuning in a cortical hypercolumn, Phil. Trans. of the R. Soc. Lond. B, vol.358, pp.1643-1667, 1438. ,
Geometric visual hallucinations, euclidean symmetry and the functional architecture of striate cortex, Phil. Trans. of the R. Soc. Lond. B, vol.306, pp.299-330, 1407. ,
Thomas Scalar and pseudoscalar bifurcations with application to pattern formation on the visual cortex, Nonlinearity, vol.14, pp.739-775, 2001. ,
The Visual Neurosciences, 2003. ,
Hyperbolic planforms in relation to visual edges and textures perception, Plos Comput Biol, vol.5, issue.12, p.1000625, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00807344
Bifurcations of hyperbolic planforms, Journal of Nonlinear Science, vol.21, issue.4, pp.465-498, 2011. ,
Methods in Equivariant Bifurcations and Dynamical Systems, 2000. ,
A cortical based model of perceptual completion in the rototranslation space, Journal of Mathematical Imaging and Visiobn, vol.24, issue.3, pp.307-326, 2006. ,
Neurogeometry of perception: Isotropic and Anisotropic Aspects Axiomathes (First Online, 2019. ,
Waves, bumps, and patterns in neural field theories, Biol. Cybern, vol.93, issue.2, pp.91-108, 2005. ,
, Spatial Vision, 1988.
A mathematical theory of visual hallucination patterns, Biological Cybernetics, vol.22, issue.1, pp.277-326, 2012. ,
Bifurcation diagrams and heteroclinic networks of octagonal h-planforms, Journal of Nonlinear Science, vol.34, pp.137-150, 1979. ,
URL : https://hal.archives-ouvertes.fr/hal-00807364
A spatialized model of visual texture perception using the structure tensor formalism Networks and Heterogeneous Media, vol.8, pp.211-260, 2013. ,
Analysis of a hyperbolic geometric model for visual texture perception, The Journal of Mathematical Neuroscience, vol.1, issue.4, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00784424
Localized states in an unbounded neural field equation with smooth firing rate function : a multi-parameter analysis, Journal of Mathematical Biology, vol.66, pp.1303-1338, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00807366
Localized radial bumps of a neural field equation on the Euclidean plane and the Poincaré disk, Nonlinearity, vol.26, pp.437-478, 2013. ,
The functional organization of local circuits in visual cortex: insights from the study of tree shrew striate cortex, Cerebral cortex, vol.6, pp.329-341, 1996. ,
, Neural Dynamics, 2014.
Singularities and Groups in Bifurcation Theory, 1988. ,
Shiau and A. Török Bifurcation on the Visual Cortex with Weakly Anisotropic Lateral Coupling, SIAM J. Applied Dyn. Systems, vol.2, issue.2, pp.97-143, 2003. ,
Local bifurcations, center manifolds, and normal forms in infinite dimensional systems, EDP Sci, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-01325715
Groups and Geometric Analysis, Mathematical Surveys and Monographs, vol.83, 2000. ,
Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat, Journal of Neurophysiology, vol.28, pp.229-289, 1965. ,
Spectral methods of automorphic forms, AMS Graduate Series in Mathematics, vol.53, 2002. ,
Fuchsian Groups, Chicago Lectures in Mathematics. The University of, 1992. ,
Representing local structure using tensors, Scandinavian Conference on Image Analysis, pp.244-251 ,
PDE Methods for Nonlocal Models, SIAM J. Applied Dyn. Systems, vol.2, issue.3, pp.487-516, 2003. ,
Symmetry Groups and their Applications, 1972. ,
A differential geometric approach to the geometric mean of symmetric positie-definite matrices, SIAM J. Matrix Anal. Appl, vol.26, pp.735-747, 2005. ,
Building maps from maps in primary vi-sual cortex, Curr. Opin. Neurobiol, vol.24, pp.1-6 ,
Ayache A Riemannian Framework for Tensor Computing, Int. J. Computer Vision, vol.66, issue.1, pp.41-66, 2006. ,
Lecture Notes in Morphogesis, 2017. ,
Existence and properties of solutions for neural field equations, Mathematical Methods in the Applied Sciences, vol.33, pp.935-949, 2010. ,
The symplectic structure of the primary visual cortex, Biol Cybern, vol.98, pp.33-48, 2008. ,
Functional geometry of the horizontal connectivity in the primary visual cortex, J. of Physiology-Paris, vol.103, issue.1-2, pp.37-45, 2009. ,
The constitution of visual perceptual units in the functional architecture of V1, J. of Comput Neurosci, vol.38, pp.285-300, 2015. ,
Random waves in the brain: symmetries and defect generation in the visual cortex, Eur. Phys. J. Special Topics, vol.145, pp.137-157, 2007. ,
,
,
Functional anatomy of macaque striate cortex. II. Retinotopic organization, J. Neurosci, vol.8, pp.1531-1568, 1988. ,
Turing The chemical basis of morphogenesis, Phil. Trans. of the Royal Soc. of London. Series B, vol.237, issue.641, pp.37-72, 1952. ,
Excitatory and inhibitory interactions in localized populations of model neurons, Biophys. Journal, vol.12, pp.1-24, 1972. ,
A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Biological Cybernetics, vol.13, issue.2, pp.55-80, 1973. ,