Geometry of Cells Sensible to Curvature and Their Receptive Profiles

2025/04/23 by Vasiliki Liontou, Liontou, Vasiliki
Engineering · #58A17 (Primary) 43A80 (Secondary) #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Differential Geometry (math.DG) #FOS: Biological sciences #FOS: Mathematics #Neurons and Cognition (q-bio.NC)

paper · pdf · doi:10.48550/arxiv.2504.16869

openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We propose a model of the functional architecture of curvature sensible cells in the visual cortex that associates curvature with scale. The feature space of orientation and position is naturally enhanced via its oriented prolongation, yielding a 4-dimensional manifold endowed with a canonical Engel structure. This structure encodes position, orientation, signed curvature, and scale. We associate an open submanifold of the prolongation with the quasi-regular representation of the similitude group SIM (2), and find left-invariant generators for the Engel structure. Finally, we use the generators of the Engel structure to characterize curvature-sensitive receptive profiles .

Citations

• Cortical Functional architectures as contact and sub-Riemannian geometry
• Liouville integrability in a four-dimensional model of the visual cortex
• Left-invariant evolutions of wavelet transforms on the Similitude Group

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