Elements of Neurogeometry: Functional Architectures of Vision

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. Front Matter ....Pages i-xv Preface (Jean Petitot)....Pages 1-20 Introduction (Jean Petitot)....Pages 21-43 Receptive Fields and Profiles, and Wavelet Analysis (Jean Petitot)....Pages 45-111 Functional Architecture I: The Pinwheels of V1 (Jean Petitot)....Pages 113-273 Functional Architectures II: Horizontal Connections and Contact Structure (Jean Petitot)....Pages 275-346 Transition to Volume II (Jean Petitot)....Pages 347-366 Back Matter ....Pages 367-379