What is the effective resolution of the retinal image of a distant face?

Abstract

We consider the following question: What is the effective resolution of a face image projected on the retina, when the face is at a specified distance from the eye? Though simple to state, this is a surprisingly challenging issue to resolve. The mapping between viewing distance and effective resolution cannot be readily derived based on the contrast sensitivity, Snellen acuity, or even the packing density of photoreceptors in the fovea. With initial guidelines derived from theoretical considerations, images of varying resolution were presented across a range of viewing distances. For each distance, participants were required to perform an ‘odd one out’ task. This involved detecting the one that was different from the rest in a 2x2 grid, with image resolution being the only dimension of variation. As the experiment progressed, the viewing distance decreased monotonically, and participants were able to detect increasingly subtle resolution differences between the three standard images and the outlier. The collected data have allowed us to establish the upper/lower bounds on the effective available resolution for typical human vision as a function of viewing distance. Interestingly, we find that humans perform significantly better, particularly at short ranges, than what a theoretical model predicts based on projected image size, cone density, and foveal extent. Accordingly, we suggest that the non-uniform in-fovea density, as well as less sharp fall-off in the acuity density function outside the fovea, need to be integrated into future theoretical models to translate viewing distance to perceived image characteristics. A pragmatic benefit of the <distance : effective-resolution> mapping is that it enables a direct comparison of human face recognition performance as assessed across blur and viewing distance. Additionally, it allows us to systematically compare human performance on face recognition at varying distances with that of machine vision systems using the common axis of resolution.