Canonical Coordinates for Retino-Cortical Magnification

A geometric model for a biologically-inspired visual front-end is proposed, based on an isotropic, scale-invariant two-form field. The model incorporates a foveal property typical of biological visual systems, with an approximately linear decrease of resolution as a function of eccentricity, and by a physical size constant that measures the radius of the geometric foveola, the central region characterized by maximal resolving power. It admits a description in singularity-free canonical coordinates generalizing the familiar log-polar coordinates and reducing to these in the asymptotic case of negligibly-sized geometric foveola or, equivalently, at peripheral locations in the visual field. It has predictive power to the extent that quantitative geometric relationships pertaining to retino-cortical magnification along the primary visual pathway, such as receptive field size distribution and spatial arrangement in retina and striate cortex, can be deduced in a principled manner. The biological plausibility of the model is demonstrated by comparison with known facts of human vision.