Geometrical optical illusion via sub-Riemannian geodesics in the roto-translation group. (English) Zbl 1418.53038
Summary: We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual stimulus and its associated percept. They take place in the visual areas V1/V2 whose functional architecture have been modeled in previous works by Citti and Sarti as a Lie group equipped with a sub-Riemannian (SR) metric. Here we extend their model proposing that the metric responsible for the cortical connectivity is modulated by the modeled neuro-physiological response of simple cells to the visual stimulus, hence providing a more biologically plausible model that takes into account a presence of visual stimulus. Illusory contours in our model are described as geodesics in the new metric. The model is confirmed by numerical simulations, where we compute the geodesics via SR-Fast Marching.
MSC:
| 53C17 | Sub-Riemannian geometry |
| 78M99 | Basic methods for problems in optics and electromagnetic theory |
Keywords:
mathematical modeling; geometrical optical illusions; visual cortex-neurogeometry; sub-Riemannian geodesics and PDE; PoggendorffReferences:
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