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＜電子ブック＞
Elements of Neurogeometry : Functional Architectures of Vision / by Jean Petitot
(Lecture Notes in Morphogenesis. ISSN:21951942)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
大きさ	XV, 379 p. 257 illus., 186 illus. in color : online resource
著者標目	*Petitot, Jean author SpringerLink (Online service)
件　名	LCSH:Biomathematics LCSH:Neural networks (Computer science)  LCSH:Geometry FREE:Mathematical and Computational Biology FREE:Mathematical Models of Cognitive Processes and Neural Networks FREE:Geometry
一般注記	Preface -- Introdcution -- Receptive Fields and Profiles, and Wavelet Analysis -- Pinwheels of V1  Horizontal Connections and Contact Structure -- Transition to Volume II --  References 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 HTTP:URL=https://doi.org/10.1007/978-3-319-65591-8

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