Elements of Neurogeometry : Functional Architectures of Vision / by Jean Petitot.

Format:

Book

Author/Creator:

Petitot, Jean., Author.

Series:

Lecture Notes in Morphogenesis, 2195-1934

Language:

English

Subjects (All):

Biomathematics.

Neural networks (Computer science).

Geometry.

Mathematical and Computational Biology.

Mathematical Models of Cognitive Processes and Neural Networks.

Local Subjects:

Mathematical and Computational Biology.

Mathematical Models of Cognitive Processes and Neural Networks.

Geometry.

Physical Description:

1 online resource (XV, 379 p. 257 illus., 186 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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.

Contents:

Preface

Introdcution

Receptive Fields and Profiles, and Wavelet Analysis

Pinwheels of V1 Horizontal Connections and Contact Structure

Transition to Volume II

References.

Notes:

Includes bibliographical references at the end of each chapters and index.

ISBN:

3-319-65591-4