Motion Parallax is Asymptotic to Binocular Disparity

TL;DR

This paper demonstrates that retinal motion from lateral translation closely approximates binocular disparity at normal viewing distances, providing a simple algebraic formula to improve analysis of peripheral vision cues.

Contribution

It establishes a strong asymptotic equivalence between motion parallax and binocular disparity, extending previous approximations to peripheral vision with practical implications.

Findings

Retinal motion from lateral translation satisfies an asymptotic approximation to binocular disparity.

The algebraic formula applies at normal viewing distances, enhancing analysis outside central vision.

The approximation extends known central vision models to peripheral vision, reducing quantitative errors.

Abstract

Researchers especially beginning with (Rogers & Graham, 1982) have noticed important psychophysical and experimental similarities between the neurologically different motion parallax and stereopsis cues. Their quantitative analysis relied primarily on the "disparity equivalence" approximation. In this article we show that retinal motion from lateral translation satisfies a strong ("asymptotic") approximation to binocular disparity. This precise mathematical similarity is also practical in the sense that it applies at normal viewing distances. The approximation is an extension to peripheral vision of (Cormac & Fox's 1985) well-known non-trig central vision approximation for binocular disparity. We hope our simple algebraic formula will be useful in analyzing experiments outside central vision where less precise approximations have led to a number of quantitative errors in the vision literature.