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＜電子ブック＞
Neuromathematics of Vision / edited by Giovanna Citti, Alessandro Sarti
(Lecture Notes in Morphogenesis. ISSN:21951942)

版	1st ed. 2014.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XVIII, 367 p. 114 illus., 69 illus. in color : online resource
著者標目	Citti, Giovanna editor Sarti, Alessandro editor SpringerLink (Online service)
件　名	LCSH:Neural networks (Computer science)  LCSH:Computer vision LCSH:Cognitive psychology LCSH:Biomedical engineering FREE:Mathematical Models of Cognitive Processes and Neural Networks FREE:Computer Vision FREE:Cognitive Psychology FREE:Biomedical Engineering and Bioengineering
一般注記	Landmarks for Neurogeometry -- Shape, Shading, Brain and Awareness -- From functional architectures to percepts: a neuro mathematical Approach -- Cuspless Sub-Riemannian Geodesics within the Euclidean Motion Group SE(d) -- Psychophysics, Gestalts and Games -- Remarks on invariance in the primary visual systems of mammals -- Hebbian Learning of the Statistical and Geometrical Structure of Visual Input This book is devoted to the study of the functional architecture of the visual cortex. Its geometrical structure is the differential geometry of the connectivity between neural cells. This connectivity is building and  shaping the hidden brain structures underlying visual perception. The story of the problem runs over the last 30 years, since the discovery of Hubel and Wiesel of the modular structure of the primary visual cortex, and slowly cams towards a theoretical understanding of the experimental data on what we now know as functional architecture of the primary visual cortex. Experimental data comes from several domains:  neurophysiology, phenomenology of perception and neurocognitive imaging. Imaging techniques like functional MRI and diffusion tensor MRI allow to deepen the study of cortical structures.  Due to this variety of experimental data, neuromathematematics deals with modelling  both cortical structures and perceptual spaces. From the mathematical point of view, neuromathematical call for new instruments of pure mathematics: sub-Riemannian geometry models horizontal connectivity, harmonic analysis in non commutative groups allows to understand pinwheels structure, as well as non-linear dimensionality reduction is at the base of many neural morphologies and  possibly of the emergence of  perceptual units. But  at the center of the  neurogeometry is the problem of harmonizing contemporary mathematical instruments with neurophysiological findings and phenomenological experiments in an unitary science of vision. The contributions to this book come from the very founders of the discipline HTTP:URL=https://doi.org/10.1007/978-3-642-34444-2

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