P.C. Bressloff, J.D. Cowan, M. Golubitsky, P.J. Thomas and M.C. Wiener
What geometric visual hallucinations tell us about the visual cortex
Neural Computation.
14 (2002) 473-491.
Geometric visual hallucinations are seen by many observers after
taking hallucinogens such as LSD, cannabis, mescaline or psilocybin,
on viewing bright flickering lights, on waking up or falling asleep,
in "near death" experiences, and in many other syndromes. Kluver
organized the images into four groups called "form constants": (1)
tunnels and funnels, (2) spirals, (3) lattices, including honeycombs
and triangles, and (4) cobwebs. In general the images do not move
with the eyes. We interpret this to mean that they are generated
in the brain. Here we present a theory of their origin in visual
cortex (area V1), based on the assumption that the form of the
retino-cortical map and the architecture of V1 determine their
geometry. We model V1 as the continuum limit of a lattice of
interconnected hypercolumns, each of which itself comprises a number
of interconnected iso-orientation columns. Based on anatomical
evidence we assume that the lateral connectivity between hypercolumns
exhibits symmetries rendering it invariant under the action of the
Euclidean group E(2), composed of reflections and translations in
the plane, and a (novel) shift-twist action. Using this symmetry,
we show that the various patterns of activity that spontaneously
emerge when V1's spatially uniform resting state becomes unstable,
correspond to the form constants when transformed to the visual
field using the retino-cortical map. The results are sensitive to
the detailed specification of the lateral connectivity and suggest
that the cortical mechanisms which generate geometric visual
hallucinations are closely related to those used to process edges,
contours, textures and surfaces.