A Metric Model for the Functional Architecture of the Visual Cortex
| Autor: | Noemi Montobbio, Alessandro Sarti, Giovanna Citti |
|---|---|
| Přispěvatelé: | Centre d'Analyse et de Mathématique sociales (CAMS), École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS), Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Montobbio N., Sarti A., Citti G. |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Computer science
Space (mathematics) 01 natural sciences Measure (mathematics) 03 medical and health sciences [SCCO]Cognitive science 0302 clinical medicine Mathematics - Metric Geometry FOS: Mathematics medicine Visual cortex 0101 mathematics [MATH]Mathematics [math] Diffusion processe ComputingMilieux_MISCELLANEOUS Structure (mathematical logic) business.industry Applied Mathematics [SCCO.NEUR]Cognitive science/Neuroscience 010102 general mathematics Metric Geometry (math.MG) Pattern recognition Neurogeometry Construct (python library) Metric space medicine.anatomical_structure FOS: Biological sciences Quantitative Biology - Neurons and Cognition Metric (mathematics) Neurons and Cognition (q-bio.NC) Artificial intelligence business 030217 neurology & neurosurgery |
| Zdroj: | SIAM Journal on Applied Mathematics SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2020, 80 (2), pp.1057-1081. ⟨10.1137/18M120141X⟩ |
| ISSN: | 0036-1399 |
| DOI: | 10.1137/18M120141X⟩ |
| Popis: | The purpose of this work is to construct a model for the functional architecture of the primary visual cortex (V1), based on a structure of metric measure space induced by the underlying organization of receptive profiles (RPs) of visual cells. In order to account for the horizontal connectivity of V1 in such a context, a diffusion process compatible with the geometry of the space is defined following the classical approach of K.-T. Sturm. The construction of our distance function does neither require any group parameterization of the family of RPs, nor involve any differential structure. As such, it adapts to non-parameterized sets of RPs, possibly obtained through numerical procedures; it also allows to model the lateral connectivity arising from non-differential metrics such as the one induced on a pinwheel surface by a family of filters of vanishing scale. On the other hand, when applied to the classical framework of Gabor filters, this construction yields a distance approximating the sub-Riemannian structure proposed as a model for V1 by G. Citti and A. Sarti [J Math Imaging Vis 24: 307 (2006)], thus showing itself to be consistent with existing cortex models. 21 pages, 9 figures. Added acknowledgements |
| Databáze: | OpenAIRE |
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