Geometrical Optical Illusion via Sub-Riemannian Geodesics in the Roto-Translation Group
| Autor: | Giovanna Citti, Alexey Mashtakov, Benedetta Franceschiello, Alessandro Sarti |
|---|---|
| Přispěvatelé: | Franceschiello B., Mashtakov A., Citti G., Sarti A. |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Geodesic Stimulus (physiology) 01 natural sciences Poggendorff 0103 physical sciences FOS: Mathematics Geometrical-optical illusions Illusory contours 0101 mathematics Geometry and topology Mathematics Quantitative Biology::Neurons and Cognition Subriemannian geodesics and PDE Optical illusion 010102 general mathematics Mathematical analysis Lie group Visual cortex-neurogeometry Geometrical optical illusion Differential Geometry (math.DG) Computational Theory and Mathematics FOS: Biological sciences Quantitative Biology - Neurons and Cognition Neurons and Cognition (q-bio.NC) Mathematical modeling 010307 mathematical physics Geometry and Topology Percept Analysis |
| Popis: | 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. 26 pages, 10 figures |
| Databáze: | OpenAIRE |
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