We present a neuro-mathematical model for the well-known Poggendorff illusion, where an illusory contour appears as a geodesic in some given metric, induced in the primary visual cortex V1 by a visual stimulus. Our model extends the cortical based model by Citti and Sarti of perceptual completion in the roto-translation space SE(2), where the functional architecture and neural connectivity of V1 of mammalians is modelled as principal fiber bundle of SE(2) equipped with a sub-Riemannian (SR) metric. We extend the model by taking into account a presence of a visual stimulus (data adaptivity), which is done by including an appropriate external cost modulating the SR-metric. Perceptual curves appear as geodesics, that we compute via SR-Fast Marching.
Catania, Italy