On the scaling law for cortical magnification factor

TL;DR

This paper derives a scaling law for how the primate visual system samples the visual scene away from the eye center, optimizing saccadic movements under biological constraints and explaining observed mappings.

Contribution

It introduces a new theoretical model for the sampling density in the visual system based on evolutionary optimization principles.

Findings

Derives the scaling law for sampling density as a function of eccentricity.

Identifies logarithmic conformal mapping as optimal for small eye centers.

Provides corrections to the model for larger eye centers and compares with experimental data.

Abstract

Primate visual system samples different parts of the world unevenly. The part of the visual scene corresponding to the eye center is represented densely, while away from the center the sampling becomes progressively sparser. Such distribution allows a more effective use of the limited transfer rate of the optic nerve, since animals can aim area centralis (AC) at the relevant position in the scene by performing saccadic eye movements. To locate a new saccade target the animal has to sample the corresponding region of the visual scene, away from AC. In this work we derive the sampling density away from AC, which optimizes the trajectory of saccadic eye movements. We obtain the scaling law for the sampling density as a function of eccentricity, which results from the evolutionary pressure to locate the target in the shortest time under the constraint of limited transfer rate of the optic nerve. In case of very small AC the visual scene is optimally represented by logarithmic conformal mapping, in which geometrically similar circular bands around AC are equally represented by the visual system. We also obtain corrections to the logarithmic scaling for the case of a larger AC and compare them to experimental findings.