Geometrical optical illusion via sub-Riemannian geodesics in the roto-translation group

Abstract

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.

A psychophysically-tuned computational model of human primary visual cortex produces geometric optical illusions

“…The cortically inspired computational models introduced in (B. Franceschiello et al, 2019;Benedetta Franceschiello et al, 2017) have proven to be effective in reproducing the qualitative responses of the primary visual cortices in response to geometrical optical illusions. The model, tested in (B.…”

“…The model, tested in (B. Franceschiello et al, 2019;Benedetta Franceschiello et al, 2017) from a purely image processing perspective, takes into account as a first step the orientation selection mechanisms discovered by Hubel and Wiesel (Hubel & Wiesel, 1962) and modelled computationally by Daugman (Daugman, 1985) and Jones and Palmer (Jones & Palmer, 1987). For a full description of the model, we refer readers to (B.…”

“…A stable prediction of the misperception in GOIs could be explained by a model considering three main neurophysiological features (B. Franceschiello, Mashtakov, Citti, & Sarti, 2019;Benedetta Franceschiello, Sarti, & Citti, 2017): 1) orientation selectivity process performed by visual areas V1 and V2 (Hubel & Wiesel, 1962), 2) interference between receptive profiles of simple cells in these areas, and 3) long-range connectivity (Bosking, William H., 1997).…”

“…Among those computational models providing a description for GOIs, we find a statistical-based approach in (Fermüller & Malm, 2004) and a geometrical approach in (Ehm & Wackermann, 2012. The first models interpreting GOIs while having a neural-based approach are those in (Franceschiello, Benedetta, Sarti, Alessandro, Citti, 2017;Franceschiello et al, 2019). These provided a first qualitative reconstruction of the phenomena.…”

“…Second, we establish the practice of tuning the computational models in (B. Franceschiello et al, 2019;Benedetta Franceschiello et al, 2017) using psychophysical data: computational models are strongly dependent on the choice of parameters. A part of them is only computationally driven, while another part represents neurophysiological correlates of the studied processes.…”