Investigation of the neural origin of non-Euclidean visual space and analysis of visual phenomena using information geometry

TL;DR

This paper develops a mathematical model linking neural mechanisms to the non-Euclidean geometry of visual space, using information geometry and Fisher information to explain visual phenomena.

Contribution

It explicitly connects neural population coding and Fisher information to the emergence of non-Euclidean visual space in the brain.

Findings

Neural Fisher information acts as an energy-momentum tensor creating a curved space.

The model predicts curved manifolds in neural processing of spatial information.

Visual phenomena can be explained using non-Euclidean geometry and Fisher-Rao metric.

Abstract

The present paper aims to develop a mathematical model concerning the visual perception of spatial information. It is a challenging problem in theoretical neuroscience to investigate how the spatial information of the objects in the physical space is encoded and decoded in the neural processes in the brain. In the past, researchers conjectured the existence of an abstract visual space where spatial information processing takes place. Based on several experimental data it was conjectured that the said psychological manifold is non-Euclidean. However, the consideration of the neural origin of the non-Euclidean character of the visual space was not explicit in the models. In the present paper, we showed that the neural mechanism and specifically the Fisher information contained in the neural population code plays the role of energy-momentum tensor to create the space-dependent metric tensor resulting in a curved space described by a curvature tensor. The theoretical prediction of information geometry regarding the emergence of curved manifolds in the presence of the Fisher information is verified in the present work in the domain of neural processing of spatial information at mid-level vision. Several well-known phenomena of visual optics are analyzed using the notion of non-Euclidean visual space, the geodesics of the space, and the Fisher-Rao metric as the suitable psychometric distance.