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 . To appear.
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.