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Colloquia Patavina: A cortical inspired, geometrical model for contour perception and motion integration

Martedì 16 Aprile 2013, ore 16:00 - aula 1A150 - Giovanna Citti

ARGOMENTI: Seminari

Martedì 16 Aprile 2013, alle ore 16:00 in aula 1A/150 della Torre Archimede, Giovanna Citti (Università di Bologna) terrà una conferenza della serie Colloquia Patavina dal titolo:
A cortical inspired, geometrical model for contour perception and motion integration.

Riassunto
We develop a geometrical model of functional architecture for the processing of spatiotemporal visual stimuli. The model arises from the properties of the receptive field, sensible to orientation and speed in the visual cortex. This selectivity property allows to model the cortical as a contact manifold of dimension 5. The fundamental solution of a Fokker Planck equation in this space plays the role of facilitation patterns within a neural activity model, and allows to reproduce some psychophysiological findings about the perception of contours in motion and trajectories of points.

Breve biografia
Education
-1986 - 89 graduated studies in Rome, and in Minneapolis (Minnesota - USA)
-1985 laurea degree in Mathematical analysis from the University of Bologna
Academic position
-1/10/2004 - present Professore ordinario
Other positions
-2006 - 2008 Director of Master in Mathematics and Applications of Math Department, University of Bologna,
-2006 - 2008 Director of the local unit of the group Neuromathematics and Vision It is an interdipartimental group, composed by members Department of Mathematics and Department of Electronics, Information and Systems, of University of Bologna, and of Centre de Recherche en Epistemologie Appliquée of Ecole Polytechnique, Paris.
-2006 - present Member of the scienfic commitee of the PHD school of Mathematics in Bologna.
-2013 - Coordinator of the phd in Mathematics

Coordination activities and Grants
-Coordinator of the project MAnET Metric analysis for Emergent Technologies
-Coordinator of the project AGAPE – Analysis in Lie Groups and Applications to Perceptual Emergences (with members of the math depatment, University of Bologna and the CAMS, EHESS (Paris)
-Coordinator of the Project EU-US CAP – Complex Analysis and PDE mobility - the project promotes mobility in this field, for graduate students in mathematics
-Responsible of a WP within the EU project Fp7 CG-DICE - Dimension Phenomena and Curvature Equations in Carnot Groups
-Coordinator of the European Project GALA – (2006-2008) Geometric analysis in Lie groups and Applications. It is an European Research Project, under the VI programme with the participations of 8 Univeristy, and a total grant of 1.000.000 Euros. The scope of the project is to develop instruments of Subriemannian geometry and Non linear Differential equations in Lie groups, with applications to visual perception, magnetic resonance theory and material theory.
-Coordinator for the math department f the interdipartimental project of "Neuromathematics and Visual Cognition"
-Local coordinator (2004 -2006) of the Alpha -project Computer vision foundations and applications for the Department of Math - Bologna
-Local coordinator of the project Geometrical and Numerical analysis for image processing, of the University of Bologna (2004-2005).

Organization of conferences and workshops
-Coorganizer of the conference Geometric methods in PDE’s Cortona (AR Italy) - May 27-31, 2013
-Coorganzer of the periodic seminar Neuromathematics and vision, IHP Paris, 2011- 12, and 2012- 13
-Coorganzer of the workshop Representation Theory and Vision Bologna, September 20 - 21, 2010
-Coorganzer of the conference Subriemannian geometry and vision, Bologna 2009. August 31- September 4 2009. The scientic committee is composed by G. Citti (Bologna, Italy), P. Koskela (Jyväskylän, Finland), J. Petitot (CREA Paris, France), H. M. Reimann (Bern, Switzerland), A. Sarti (Bologna, Italy ), R. Serapioni (Trento, Italy), J. A. Sethian ( Berkeley, USA), S. Zucker (Yale, USA). The conference will focus on geometrical analysis in Lie groups and computational models of the functional architecture of the visual cortex on the other.
-Coorganizer of the conference Geometric Methods in PDE's: Bologna, May 27-30 2008 Organizing Committee G. Citti A. Montanari, A. Pascucci, S. Policoro (Bologna). Scientific Commitee S.Dragomir (Basilicata), B. Franchi (Bologna), C. Gutierrez (Temple U. Philadelphia).

Scientific profile
The main research themes afforded by the applicant are
-Curvature equation in CR manifolds and Lie groups with a subriemannian metric
-Models of visual perception in Lie goups
In both fields the contribution of the applicant appearead on high level international journals and contributed to open new directions of research.

Short List of recent Pubblications
Preprints
-Barbieri, D. Citti G., Coherent states of the Euclidean Motion Group and CR regularity. Preprint
-Barbieri D., Citti G., Cocci G., Sarti A., A cortical-inspired geometry for contour perception and motion integration. Preprint.
-Capogna, L. Citti G. and Manfredini M., Uniform Gaussian bounds for subelliptic heat kernels and an application to the total variation flow of graphs over Carnot groups, submitted
Papers appeared or accepted on journals with referee
-Capogna L., Citti G. and Senni C., Sub -Riemannian heat kernels and mean curvature flows of graphs,. JFA
-Capogna L., Citti G. and Rea G., A subelliptic analogue of Aronson-Serrin’s Harnack Inequality. Accepted on Math Ann.
-Citti G., Sarti A. Models of the Visual Cortex in Lie Groups, Advanced Courses in Mathematics, Springer, 2013.
-Citti G. Ferrari F., A sharp regularity result of solutions of a transmission problem, Proc. Amer. Math. Soc. 140 (2012) 615-620.
-Citti G., Senni, C., Constant mean curvature graphs on exterior domains of the hyperbolic plane, Math. Zeit, (2012), no. 1-2, 531–550
-Barbieri D., Citti G., Regularity of non charachteristic minimal graphs in Lie groups of step 2 and dimension 3, Journal des Mathématiques Pures et Appliquées 96(3):279-306, 2011.
-Capogna L., Citti G., Manfredini M., Smoothness of lipschitz minimal intrinsic graphs in Heisenberg groups Hn, n > 1,J. Reine Angew. Math. 648 (2010), 75–110.
-Capogna L., Citti G., Generalized mean curvature flow in Carnot groups, Comm. Partial Differential Equations 34 (2009), no. 7-9, 937–956 .
-Capogna L., Citti G., Manfredini M., Regularity of non-characteristic minimal graphs in the Heisenberg group H1 Indiana Univ. Math. J. 58 (2009), no. 5, 2115–2160.
-Citti G., Sarti A., ‘A cortical based model of perceptual completion in the Roto-Translation space’, Journal of Mathematical Imaging and Vision, 2006, vol. 24, pp. 307 - 326
-Citti G., Manfredini M.,.Sarti A., “Neuronal Oscillations in the Visual Cortex: Gamma-convergence to the Riemannian Mumford-Shah Functional”, SIAM Journal Mathematical Analysis, vol. 36, n.6, pag. 1394-1419, 2004

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