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Seminario: “Problem of stability in vision and conformal geometry of sphere”

Lunedì 29 Gennaio 2018, ore 12:00 - Aula 2AB40 - Dmitri V. Alekseevsky

ARGOMENTI: Seminari

Lunedì 29 Gennaio 2018 alle ore 12:00 in Aula 2AB40, Dmitri V. Alekseevsky (Emeritus Professor of the Institute for Information Transmission Problems Moscow) terrà un seminario di carattere geometrico-applicativo dal titolo “Problem of stability in vision and conformal geometry of sphere”.

Abstract
The eye projects objects of external world (e.g. a curve on a screen) onto the retina by means of the central projection. Even when the gaze is fixed, the eye participates in different types of movements: tremor, drift and microsaccades. Due to this, the image of the object on retina continuosly changes its position. However, stable external object are perceived by the brain as stable inspite of the movements of its image on retina. The problem of stability in vision consists in the description of the mechanisms of compensation of such transformation of the images caused by the eye rotations. We will show that, under some assumptions, the changes of the image on retina is described by conformal transformations and that the problem of stability can be formulated as the following classical problem of conformal geometry of the 2-sphere: characterize a curve on the conformal sphere up to conformal transformations (Conformal Frenet Problem). In this talk, we will discuss the spherical model of hypercolumns in primary visual cortex VI, proposed by Paul Bressloff and Jack Cowan in 2002 and we will show how a modification of such model, inspired by the contact Petitot model of cortex VI and its symplectic generalization, proposed by Petitot-Citti-Sarti can be applied to the stability problem.