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Elements of neurogeometry: functional architectures of vision

This book describes several mathematical models of the primary visual cortex, referring them to a vast ensemble of experimental data and putting forward an original geometrical model for its functional architecture, that is, the highly specific organization of its neural connections. The book spells...

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Detalles Bibliográficos
Autor principal: Petitot, Jean
Lenguaje:eng
Publicado: Springer 2017
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-65591-8
http://cds.cern.ch/record/2296545
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author Petitot, Jean
author_facet Petitot, Jean
author_sort Petitot, Jean
collection CERN
description This book describes several mathematical models of the primary visual cortex, referring them to a vast ensemble of experimental data and putting forward an original geometrical model for its functional architecture, that is, the highly specific organization of its neural connections. The book spells out the geometrical algorithms implemented by this functional architecture, or put another way, the “neurogeometry” immanent in visual perception. Focusing on the neural origins of our spatial representations, it demonstrates three things: firstly, the way the visual neurons filter the optical signal is closely related to a wavelet analysis; secondly, the contact structure of the 1-jets of the curves in the plane (the retinal plane here) is implemented by the cortical functional architecture; and lastly, the visual algorithms for integrating contours from what may be rather incomplete sensory data can be modelled by the sub-Riemannian geometry associated with this contact structure. As such, it provides readers with the first systematic interpretation of a number of important neurophysiological observations in a well-defined mathematical framework. The book’s neuromathematical exploration appeals to graduate students and researchers in integrative-functional-cognitive neuroscience with a good mathematical background, as well as those in applied mathematics with an interest in neurophysiology.
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spelling cern-22965452021-04-21T18:58:58Zdoi:10.1007/978-3-319-65591-8http://cds.cern.ch/record/2296545engPetitot, JeanElements of neurogeometry: functional architectures of visionMathematical Physics and MathematicsThis book describes several mathematical models of the primary visual cortex, referring them to a vast ensemble of experimental data and putting forward an original geometrical model for its functional architecture, that is, the highly specific organization of its neural connections. The book spells out the geometrical algorithms implemented by this functional architecture, or put another way, the “neurogeometry” immanent in visual perception. Focusing on the neural origins of our spatial representations, it demonstrates three things: firstly, the way the visual neurons filter the optical signal is closely related to a wavelet analysis; secondly, the contact structure of the 1-jets of the curves in the plane (the retinal plane here) is implemented by the cortical functional architecture; and lastly, the visual algorithms for integrating contours from what may be rather incomplete sensory data can be modelled by the sub-Riemannian geometry associated with this contact structure. As such, it provides readers with the first systematic interpretation of a number of important neurophysiological observations in a well-defined mathematical framework. The book’s neuromathematical exploration appeals to graduate students and researchers in integrative-functional-cognitive neuroscience with a good mathematical background, as well as those in applied mathematics with an interest in neurophysiology.Springeroai:cds.cern.ch:22965452017
spellingShingle Mathematical Physics and Mathematics
Petitot, Jean
Elements of neurogeometry: functional architectures of vision
title Elements of neurogeometry: functional architectures of vision
title_full Elements of neurogeometry: functional architectures of vision
title_fullStr Elements of neurogeometry: functional architectures of vision
title_full_unstemmed Elements of neurogeometry: functional architectures of vision
title_short Elements of neurogeometry: functional architectures of vision
title_sort elements of neurogeometry: functional architectures of vision
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-65591-8
http://cds.cern.ch/record/2296545
work_keys_str_mv AT petitotjean elementsofneurogeometryfunctionalarchitecturesofvision