The functional architecture of the early vision and neurogeometric models

TL;DR

This paper provides a concise, mathematically oriented overview of the functional architecture of early vision, focusing on neurogeometric models of the primary visual cortex and their unification in a conformal model.

Contribution

It offers an accessible introduction to neurogeometry and surveys key neurogeometric models, including a synthesis through the conformal model for hypercolumns.

Findings

Summarizes the basic facts of early vision architecture.

Reviews three major neurogeometric models of V1.

Discusses the conformal model as a synthesis of previous models.

Abstract

The initial sections of the paper give a concise presentation, specially designed for a mathematically oriented audience, of some of the most basic facts on the functional architecture of early vision. Such information is usually scattered in a variety of papers and books, which are not easily accessible by non-specialists. Our goal is thus to offer a handy and short introduction to this topics, which might be helpful for researchers willing to enter the area of the applications of modern Differential Geometry in studies on the visual systems, baptized neurogeometry by J. Petitot. We then offer a survey of three of the most important neurogeometric models: Petitot's contact model of the primary visual cortex, its extension to A. Sarti, G. Citti and J. Petitot's symplectic model, and P. C. Bressloff and J. D. Cowan's spherical model of hypercolumns. We finally discuss the main points of the so-called ``conformal model'' for hypercolumns (a model that was briefly presented in [D. V. Alekseevsky, Conformal model of hypercolumns in V1 cortex and the Moebius group, in ``Geometric science of information'', pp. 65--72, Springer, 2021] and given in detail in [D. V. Alekseevsky and A. Spiro, Conformal models for hypercolumns in the primary visual cortex V1, arXiv 2024]), which can be considered as a synthesis of the symplectic and the spherical models.