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Benedetta Franceschiello

Ph.D. student @ Centre National de la Recherche Scientifique (CNRS)

joint supervision with Alma Mater Studiorum Università di Bologna - Dipartimento di Matematica (UNIBO)

since 10/1/2014 for 3 years.

under the supervision of Prof. Giovanna Citti, Prof. Alessandro Sarti

Ph.D. Thesis

“Cortical Based mathematical models of geometric optical illusions” on September 28, 2017

Research

In the mentioned period I concentrated on the study of the behaviour of the primary visual cortex (V1) in presence of geometric optical illusions. Starting from the cortical based model developed by Citti and Sarti, in which V1 is modelled as principal fiber bundle of SE(2) equipped with a sub-Riemannian metric, the main idea is that the presence of the ground of the image and the activation of the orientations induced by it are responsible for the deformation perceived in presence of this kind of illusion. I focused on the study of this process from the phenomenological point of view and also on the study of infinite strain theory and metric tensors, which have been used as model for these phenomena. In order to test it numerical simulations in Matlab have been made. The process passes first through the detection of the orientation to which the image is sensitive, then through the calculation of the metric which takes into account the cortical response and finally through the solution of PDEs used as model for the deformation. In the mean time I partecipated to the submission and revision of the first paper 'Sub-Riemannian' mean curvature flow for image processing.

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