Elements of Neurogeometry

Elements of Neurogeometry
Author :
Publisher : Springer
Total Pages : 388
Release :
ISBN-10 : 9783319655918
ISBN-13 : 3319655914
Rating : 4/5 (914 Downloads)

Book Synopsis Elements of Neurogeometry by : Jean Petitot

Download or read book Elements of Neurogeometry written by Jean Petitot and published by Springer. This book was released on 2017-11-08 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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