Geometric–optical illusions and Riemannian geometry

• Geometric–optical illusions arising from target–context stimulus interactions are studied.
• The case of circle targets is treated in a general framework of Riemann geometry.
• Perceptual distortions are modeled as context-induced perturbations of the base geometry.
• Numerical methods to compute the shape of the distorted percept are provided.
• Magnitudes of the distortions are measured in a psychophysical experiment.

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.