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.
Complementary training activities:
- [Course] Mathematical database and digital Libraries - a.a. 2015-2016 Bologna, Italy
Local training activities:
- [Seminars] Seminaire Périodique: Neuro-mathématiques de la vision: Organizateurs: G.Citti, A. Destexhe, O. Faujeras, Y. Fregnac, J.P. Nadal, J. Petitot, A. Sarti, EITN - 1° semester 2014-2015 Paris, France
- [Course] Cours avancé en neuroscience théorique, (lecturer J.P. Nadal) within the Master Recherche en Sciences Cognitives - 1° semester 2014-2015 Paris, France
- [Course] The partial differential equations of image processing (and their surprising applications) (lecturer J.M. Morel) - 1° semester 2014-2015 Paris, France
- [Course] Méthodes mathématiques pour les neurosciences (lecturer O. Faugeras) - 1° semester 2014-2015 Paris, France
- [Seminar] Geometric visual hallucinations and the architecture of the visual cortex (lecturer J.Cowan) - October 20, 2014 Paris, France
- [Seminars] Topics in Mathematics - a.a. 2016-2017 Bologna, Italy
Network-wide training activities:
- [Workshop] Thematic day on minimal surfaces in sub-Riemannian geometry - October 13, 2014 Paris, France
- [Workshop] Geometric Analysis in the Heisenberg group - March 4-6, 2015 Bologna, Italy
Outreach:
- [Course] Mathematical Analysis II - a.a. 2015-2016 Bologna. Italy
- [Course] Mathematical Analysis I - a.a. 2016-2017 Paris, France
Talks and Poster Presentations:
- [Poster] Existence of sub-riemannian mean curvature flow for amodal completion at Geometrical Models in Vision - October 22-24, 2014 Paris, France
- [Poster] A neuro-mathematical model for Geometrical Optical illusions at ED3C Roscoff meeting - March 1, 2015 Roscoff, France
- [Talk] A neuro-mathematical model for Geometrical Optical illusions at Mid-term Review Meeting - December 9, 2015 Helsinki, Finland
- [Talk] A neuro-mathematical model for Geometrical Optical illusions at Neuromathematics, Mathematical and Computational neuroscience - September 11-17, 2016 Cortona, Italy
- [Poster] A neuro-mathematical model for Geometrical Optical illusions at ED3C Roscoff meeting - March 20-22, 2017 Roscoff, France
- [Talk] A neuro-mathematical model for Geometrical Optical illusions at Cortona Summer school - July 2-14, 2017 Cortona, Italy
- [Talk] A neuro-mathematical model for Geometrical optical illusions at Sub-Riemannian Geometry Harmonic Analysis, PDE and Applications - January 24-27, 2018 Bologna, Italy
Secondment:
- UNIBO - September 2015 to February 2016 Bologna, Italy
- CNRS Université Paris Descartes - February 1 to April 30, 2017
Publications and Preprints
- G. Citti, B. Franceschiello, G. Sanguinetti, A. Sarti, Sub-Riemannian mean curvature flow for image processing on SIAM Journal on Imaging Sciences Vol 9 Society for Industrial and Applied Mathematics Publications 2016 pp. 212-237 open access version
- B. Franceschiello, A. Mashtakov, G. Citti, A. Sarti, Modelling of the Poggendorff Illusion via sub-Riemannian geodesics in the roto-translation group on Lecture Notes in Computer Science Vol 10590 Springer, Cham 2017 pp. 37-47
- B. Franceschiello, A. Sarti, G. Citti, A neuro-mathematical model for geometrical optical illusions on Journal of Mathematical Imaging and Vision Vol 60 Springer Verlag 2018 pp. 94-108 open access version
- B. Franceschiello, A neurogeometrical model for image completion and visual illusion report
- B. Franceschiello, A neuro-mathematical model for geometrical optical illusions report
- B. Franceschiello, A neuro-mathematical model for Geometrical optical illusions report
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