Modeling Foveal Vision

A geometric model is proposed for an artificial foveal vision system, and its plausibility in the context of biological vision is explored. The model is based on an isotropic, scale invariant two-form that describes the spatial layout of receptive fields in the the visual sensorium (in the biological context roughly corresponding to retina, LGN, and V1). It overcomes the limitation of the familiar log-polar model by handling its singularity in a graceful way. The log-polar singularity arises as a result of ignoring the physical resolution limitation inherent in any real (artificial or biological) visual system. The incorporation of such a limitation requires the introduction of a physical constant, measuring the radius of the geometric foveola (a central region characterized by maximal resolving power). The proposed model admits a description in singularity-free canonical coordinates that generalize the well-established log-polar coordinates, and that reduce to these in the asymptotic case of negligibly sized geometric foveola (or, equivalently, at peripheral locations in the visual field). Biological plausibility of the model is demonstrated by comparison with known facts on human vision.