Geometric–optical illusions and Riemannian geometry

Abstract

Geometric–optical illusions (goi) are a subclass of a vast variety of visual illusions. A special class of gois originates from the superposition of a simple geometric figure (“target”) with an array of non-intersecting curvilinear elements (“context”) that elicits a perceptual distortion of the target element. Here we specifically deal with the case of circular targets. Starting from the fact that (half)circles are geodesics in a model of hyperbolic geometry, we conceive of the deformations of the target as resulting from a context-induced perturbation of that “base” geometry. We present computational methods for predicting distorted shapes of the target in different contexts, and we report the results of a psychophysical pilot experiment with eight subjects and four contexts to test the predictions. Finally, we propose a common scheme for modeling gois associated with more general types of target curves, subsuming those studied previously.