Cortical origins of MacKay-type visual illusions: A case for the non-linearity

TL;DR

This paper investigates the cortical mechanisms behind MacKay-type visual illusions, demonstrating that some illusions are linear phenomena while others depend critically on nonlinear cortical responses, using a mathematical modeling approach.

Contribution

It introduces a controllability framework based on neuronal field equations to distinguish between linear and nonlinear cortical responses in visual illusions.

Findings

MacKay effect is primarily a linear phenomenon.

Billock and Tsou's phenomena are nonlinear and shape-dependent.

The nonlinear response function plays a crucial role in certain visual illusions.

Abstract

To study the interaction between retinal stimulation by redundant geometrical patterns and the cortical response in the primary visual cortex (V1), we focus on the MacKay effect (Nature, 1957) and Billock and Tsou's experiments (PNAS, 2007). We use a controllability approach to describe these phenomena starting from a classical biological model of neuronal field equations with a non-linear response function. The external input containing a localised control function is interpreted as a cortical representation of the static visual stimuli used in these experiments. We prove that while the MacKay effect is essentially a linear phenomenon (i.e., the nonlinear nature of the activation does not play any role in its reproduction), the phenomena reported by Billock and Tsou are wholly nonlinear and depend strongly on the shape of the nonlinearity used to model the response function.