Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
Paul C BressloffMatthew C Wiener

Abstract

This paper is concerned with a striking visual experience: that of seeing geometric visual hallucinations. Hallucinatory images were classified by Klüver into four groups called form constants comprising (i) gratings, lattices, fretworks, filigrees, honeycombs and chequer-boards, (ii) cobwebs, (iii) tunnels, funnels, alleys, cones and vessels, and (iv) spirals. This paper describes a mathematical investigation of their origin based on the assumption that the patterns of connection between retina and striate cortex (henceforth referred to as V1)-the retinocortical map-and of neuronal circuits in V1, both local and lateral, determine their geometry. In the first part of the paper we show that form constants, when viewed in V1 coordinates, essentially correspond to combinations of plane waves, the wavelengths of which are integral multiples of the width of a human Hubel-Wiesel hypercolumn, ca. 1.33-2 mm. We next introduce a mathematical description of the large-scale dynamics of V1 in terms of the continuum limit of a lattice of interconnected hypercolumns, each of which itself comprises a number of interconnected iso-orientation columns. We then show that the patterns of interconnection in V1 exhibit a very interesting symmetry, ...Continue Reading

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Citations

Jan 16, 2007·Journal of Mathematical Biology·S Coombes
Sep 30, 2005·Biological cybernetics·Paul C Bressloff
Nov 17, 2007·Biological cybernetics·Alessandro SartiJean Petitot
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