Neuromathématiques

Présentation et informations pratiques pour le séminaire 2020/2021 : voir ici

Organisateurs : Giovanna Citti (University of Bologna), Jean-Pierre Nadal (CAMS – EHESS/CNRS & LPENS – ENS/CNRS/SU/Univ. de Paris, PSL), Jean Petitot (CAMS – EHESS),  Jérôme Ribot (Collège de France), Alessandro Sarti (CAMS – EHESS/CNRS)

1er mardi du mois de 14h à 16h (Collège de France, 11 Place Marcelin Berthelot 75005 Paris), du 1er décembre 2020 au 1er juin 2021 .

Programme – année 2020-2021

  • Mardi 1er décembre, Jonathan Touboul (Brandeis University, Boston) and Jérôme Ribot (Collège de France)
  • Mardi 2 février, Marcelo Bertalmio (Universitat Pompeu Fabra)
  • Mardi 2 mars, 14h30-16h30 en visio-conférence exclusivement
    Inscription obligatoire sur https://listsem.ehess.fr/ (pour sélectionner le bon séminaire, saisir UE 225 – avec un espace entre UE et 225).

    Emre Baspinar
    Inria Sophia Antipolis Méditerranée, MathNeuro Team

    « Biologically-inspired modeling for Poggendorff type illusions and frequency-phase sensitive cortical behavior applied to image enhancement »

    Abstract: In this talk, we will see a geometric approach for cortical modeling which is in the same alignment following [1], [2] and [3]. In the first part, we will see a new biologically-inspired sub-Riemannian model employing Wilson-Cowan type mean field equations described in the model geometry proposed in [3], and in a similar fashion as in [4]. The model is applied to reproducing orientation-dependent Poggendorff-type illusions. The novelty of the model is that it embeds sub-Riemannian diffusion into the neuronal interaction term appearing in the mean field equations. This tunes the neuronal interactions in agreement with the functional architecture of the visual cortex. In the second part, we start with the sub-Riemannian model geometry proposed in [3], which is only orientation sensitive. We extend this model and provide a novel sub-Riemannian model of V1 which models orientation-frequency selective, phase shifted cortical cell behavior and the associated neural connectivity [5]. We develop an image enhancement algorithm using a multi-frequency Laplace-Beltrami procedure in this extended sub-Riemannian model framework.

    References
    [1] W. C. Hoffman, “The visual cortex is a contact bundle,”Applied Mathemat-ics and Computation, vol. 32, no. 2-3, pp. 137–167, 1989.
    [2] J. Petitot and Y. Tondut, “Vers une neurogeometrie. Fibrations corticales,structures de contact et contours subjectifs modaux,”Math ́ematiques et Sciences Humaines, vol. 145, pp. 5–101, 1999.
    [3] G. Citti and A. Sarti, “A cortical based model of perceptual completion in the roto-translation space,”Journal of Mathematical Imaging and Vision,vol. 24, no. 3, pp. 307–326, 2006.
    [4] M. Bertalmio, L. Calatroni, V. Franceschi, B. Franceschiello, and D. Prandi, “Cortical-inspired Wilson–Cowan type equations for orientation-dependent contrast perception modelling,”Journal of Mathematical Imaging and Vision, pp. 1–19, 2020.
    [5] E.Baspinar, G.Citti, A.Sarti, A sub-Riemannian model of the visual cortex with frequency and phase, Journal of mathematical neuroscience, 2020.

  • Mardi 6 avril, Ugo Boscain


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