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Conformal Model of Hypercolumns in V1 Cortex and the Möbius Group. Application to the Visual Stability Problem

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Geometric Science of Information (GSI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12829))

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Abstract

A conformal spherical model of hypercolumns of primary visual cortex V1 is proposed. It is a modification of the Bressloff-Cowan Riemannian spherical model. The main assumption is that simple neurons of a hypercolumn, considered as Gabor filters, obtained for the mother Gabor filter by transformations from the Möbius group \(Sl(2, \mathbb {C})\). It is shown that in a small neighborhood of a pinwheel, which is responsible for detection of high (resp., low) frequency stimuli, it reduces to the Sarti-Citti-Petitot symplectic model of V1 cortex. Application to the visual stability problem is discussed.

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Correspondence to Dmitri Alekseevsky .

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Alekseevsky, D. (2021). Conformal Model of Hypercolumns in V1 Cortex and the Möbius Group. Application to the Visual Stability Problem. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_8

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  • DOI: https://doi.org/10.1007/978-3-030-80209-7_8

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  • Publisher Name: Springer, Cham

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