An Algebraic-Geometric Model of the Receptive Field Properties of the Macaque Striate Cortex

Proc. Aust. Neuroscience Soc. Vol 8, 1997

David M. Alexander 1, Phil Sheridan 2, Paul D. Bourke 3
(Introduced by Daniele Farnbach-Pralong)
1 School of Biophysical Sciences and Electrical Engineering, Swinburne University of Technology, Hawthorn 3122
2 School of Information Technology, Charles Sturt University, Bathurst 2795
3 Brain Dynamics Laboratory, Mental Health Research Institute of Victoria, Parkville 3052

We provide a model of the Macaque striate cortex which predicts the relationship between the global retinotopic mapping of the visual field and the local receptive field mappings. We assumed that the geometry of the striate cortex can be approximated by a hexagonal lattice, with each hexagon representing a cortical column approximately 200um wide. An addressing system for bijective mappings on this lattice was developed, and the address space interpreted in terms of a Lie Algebra. Simple arithmetric operations such as addition and multiplication were defined, and shown to correspond to geometric operations such as translation, rotation and scaling. A unique multiplication was shown to predict various local (i.e. columnar) receptive field properties from the global (complex logarithmic) retinotopic mapping of the striate cortex, The predictions of the model include:
1) general statistical properties of receptive fields for orientation selectivity, including iso- orientation bands, density and ratio of singularity types, and presence of fractures;
2) position of ocular dominance bands, correct ratio between width and length of hypercolumns, singularities arranged over centres of ocular dominance bands, and orientation bands crossing ocular dominance borders at right angles;
3) position of cytochrome oxidase blobs, and explanation of their selectivity for lower spatial frequencies, contrast sensitivity and colour;
and 4) projection of lateral connections to columns with similar receptive fields. The model does not require the multiple free parameters found in other models of striate receptive field maps (1). The geometric-algebraic model has the additional advantage that it provides a functional explanation for the architecture of the Macaque striate cortex; i.e. cortical manipulation of visual images through rotation and scaling.

1. Swindale, N.V. (1996) Network 7, 161-247