  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
modelled 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 modelled
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.
