Modeling geometric-optical illusions: A variational approach

TL;DR

This paper introduces a variational model for geometric-optical illusions, linking perceptual distortions to a Riemannian geometric framework, supported by psychophysical data.

Contribution

It presents a novel variational approach to modeling GOIs and connects perceptual distortions to Riemannian geometry, providing a new theoretical perspective.

Findings

Model successfully reproduces perceptual distortions for various contexts

The geometric framework explains the nature of target distortions

Psychophysical data supports the model's predictions

Abstract

Visual distortions of perceived lengths, angles, or forms, are generally known as "geometric-optical illusions" (GOI). In the present paper we focus on a class of GOIs where the distortion of a straight line segment (the "target" stimulus) is induced by an array of non-intersecting curvilinear elements ("context" stimulus). Assuming local target-context interactions in a vector field representation of the context, we propose to model the perceptual distortion of the target as the solution to a minimization problem in the calculus of variations. We discuss properties of the solutions and reproduction of the respective form of the perceptual distortion for several types of contexts. Moreover, we draw a connection between the interactionist model of GOIs and Riemannian geometry: the context stimulus is understood as perturbing the geometry of the visual field from which the illusory distortion naturally arises. The approach is illustrated by data from a psychophysical experiment with nine subjects and six different contexts.