A Bayesian model of distance perception from ocular convergence

Ocular convergence is one of the critical cues from which to estimate the absolute distance to objects in the world, because unlike most other distance cues a one-to-one mapping exists between absolute distance and ocular convergence. However, even when accurately converging their eyes on an object, humans tend to underestimate its distance, particularly for more distant objects. This systematic bias in distance perception has yet to be explained and questions the utility of vergence as an absolute distance cue. Here we present a probabilistic geometric model that shows how distance underestimation can be explained by the visual system estimating the most likely distance in the world to have caused an accurate, but noisy, ocular convergence signal. Furthermore, we find that the noise in the vergence signal needed to account for human distance underestimation is comparable to that experimentally measured. Critically, our results depend on the formulation of a likelihood function that takes account of the generative function relating distance to ocular convergence.Author summary: Since at least the time of Descartes the ocular convergence state of the eyes has been considered one of the most important cues to distance in the world. However, despite accurate fixation, humans underestimate distance from ocular convergence, particularly for more distant objects. This questions the utility of one of the primary cues from which distance could be estimated. Here we present a rigorous probabilistic analysis of how humans might estimate distance from ocular convergence. This analysis shows that the experimentally observed distance underestimation can be explained by observers estimating the most likely distance in the world to have caused the accurate but uncertain measurement of the convergence state of the eyes. The level of uncertainty needed to account for observed distance underestimation is consistent with that experimentally measured.