Cortical Functional architectures as contact and sub-Riemannian geometry

2023/10/16 by Giovanna Citti, Citti, Giovanna, Alessandro Sarti +1 · 1 citation
Computer Science · Neuroscience · #Topological and Geometric Data Analysis #Visual perception and processing mechanisms #Digital Image Processing Techniques

paper · pdf · doi:10.48550/arxiv.2310.16056

Abstract

In a joint paper, Jean Petitot together with the authors of the present paper described the functional geometry of the visual cortex as the symplectization of a contact form to describe the family of cells sensitive to position, orientation and scale. In the present paper, as a "homage" to the enormous contribution of Jean Petitot to neurogeometry, we will extend this approach to more complex functional architectures built as a sequence of contactization or a symplectization process, able to extend the dimension of the space. We will also outline a few examples where a sub-Riemannian lifting is needed.

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• Geometry of Cells Sensible to Curvature and Their Receptive Profiles

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