Does vision extract absolute distance from vergence?

Abstract

Since Kepler (1604) and Descartes (1637), 'vergence' (the angular rotation of the eyes) has been thought of as one of our most important absolute distance cues. But vergence has never been tested as an absolute distance cue divorced from obvious confounding cues such as binocular disparity. In this article, we control for these confounding cues for the first time by gradually manipulating vergence and find that observers fail to accurately judge distance from vergence. We consider several different interpretations of these results and argue that the most principled response to these results is to question the general effectiveness of vergence as an absolute distance cue. Given that other absolute distance cues (such as motion parallax and vertical disparities) are limited in application, this poses a real challenge to our contemporary understanding of visual scale.

Keywords: 3D vision; Accommodation; Distance perception; Vergence; Visual scale.

Fig. 1

Distance from vergence. The left panel illustrates how the vergence angle changes with fixation distance and the right panel illustrates the results of absolute distance from vergence in Mon-Williams and Tresilian (1999) (in red), and Viguier, Clément, and Trotter (2001) (in blue), compared to veridical performance (black dotted line)

Fig. 2

Apparatus for experiment. Laser projector (in grey) projects two stimuli onto a black metal plate at the end of the apparatus (grey lines). Occluders either side of the head ensure left eye only sees right stimulus, and right eye sees left stimulus (red lines). Vergence specified distance (indicated by red arrow) is manipulated by increasing/decreasing the distance between the two stimuli (compare the upper and lower panels)

Fig. 3

Fixation targets for Experiment 1 (top) and Experiment 2 (bottom). The fixation target is seen between trials (while vergence is gradually changing). Note that the actual stimulus that subjects point to during each trial (once vergence is stationary) is a dot

Fig. 4

Individual results for 12 subjects in Experiment 1. Grey dots and grey line indicate performance in full-cue condition. Black dots and black line indicate performance in vergence-only condition. Colored dots and red line for subjects KR and EA indicate revised performance in Experiment 2 (the color of the dots indicates accommodative demand: = – 4.15D, = – 3.15D, and = – 2.15D). Bottom panels: Results best fit with two populations with equal variance (△E), with Gaussian mixture model plotted on histogram of the slopes

Fig. 5

Summary of results from Experiment 2 when vergence and accommodation are the only cues to distance. On the x-axis is the vergence-specified distance, and on the y-axis the pointed distance. The left panel illustrates averaged results. The error bars represent bootstrapped 95% confidence intervals across observers. The error band represents the bootstrapped 95% confidence interval of the linear mixed-effects model. The right panel plots the raw trial data across observers as a jitter plot

Fig. 6

Individual results for 12 subjects in Experiment 2. Grey dots and grey line indicate performance in full-cue condition. Colored dots and black line indicate performance in vergence and accommodation-only condition (color of the dots indicates accommodative demand: = – 4.15D, = – 3.15D, and = – 2.15D). Bottom panels Results best fit with a single population, with Gaussian mixture model plotted on histogram of the slopes