[ICMNS] Séminaire Neuromathématiques Davide Barbieri

[Alessandro Sarti]

Séminaire 

Neuromathématiques 




Organisé par 

Giovanna Citti (University of Bologna) 

JP Nadal ( CAMS - EHESS) 

Jean Petitot (CAMS - EHESS) 

Jerome Ribot (Collège de France) 

Alessandro Sarti (CAMS - EHESS/CNRS) (reférent) 




mardi 8 avril 14h30-16h30 




Salle D2.2, Collège de France , 11, Place Marcelin-Berthelot, 75005, Paris 

On se retrouve à l'accueille à 14h15 et on y va à la salle tous ensemble 




Lien Zoom: https://cnrs.zoom.us/j/97625468512?pwd=MwulsVF5QP6THQalI2s0PaaYCbzpYa.1 




______________ 


Davide Barbieri 

Universidad Autonoma de Madrid 



On the completeness of orientation preference maps in primary visual cortex 




We want to consider the model of classical receptive fields of simple cells in primary visual cortex, given by translations and rotations of a two-dimensional modulated gaussian function, with parameters of positions and orientations distributed according to a two-dimensional pinwheel-like orientation preference map, from the point of view of harmonic analysis. 
The aim is to discuss the problem of completeness of the set of receptive fields parametrized by orientation preference maps, the question being: can the visual stimulus be reconstructed in a stable way from such a set of cells, and how can this reconstruction be performed? 
We will start by introducing the model and the basic properties of its linear processing described by a group wavelet transform. 
We will then provide a mathematical proof that completeness can be achieved depending on the relationship between the receptive field size and the correlation length of the pinwheel distribution. The argument makes use of a construction of frames of exponentials from a Fuglede-type theorem for lattices and will be presented in elementary terms as an adaptation of the classical Shannon sampling theorem. 
Finally, we will show an iterative reconstruction algorithm in the form of a classical population dynamics equation, where the iteration kernel contains both the structure of the group wavelet and that of the pinwheel distribution. We will show the results of the reconstruction on natural images, for a properly discretized model. 




[ https://enseignements.ehess.fr/2024-2025/ue/248?fbclid=IwZXh0bgNhZW0CMTAAAR0VCfF-dGa5d-qMex3Niqrdjt8E_JK9HXLWCQ3qxcuxT4PGyY0Dwpv63a8_aem_J065n_5VoHkTgXdejEhJsA | https://enseignements.ehess.fr/2024-2025/ue/248 ] 

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