Cyclopean Geometry of Binocular Vision

TL;DR

This paper analyzes the geometric principles of binocular vision in primates, introducing a new oculomotor parameterization and constructing a Cyclopean depth-map to better understand depth perception from retinal images.

Contribution

It introduces a novel oculomotor parameterization and constructs a Cyclopean depth-map, advancing the geometric understanding of binocular vision and depth recovery.

Findings

Identification of the midline horopter and its role in epipolar geometry

Derivation of the Essential matrix from epipoles and horopter projection

Development of a symmetric disparity parameterization for scene depth

Abstract

The geometry of binocular projection is analyzed, with reference to the primate visual system. In particular, the effects of coordinated eye movements on the retinal images are investigated. An appropriate oculomotor parameterization is defined, and is shown to complement the classical version and vergence angles. The midline horopter is identified, and subsequently used to construct the epipolar geometry of the system. It is shown that the Essential matrix can be obtained by combining the epipoles with the projection of the midline horopter. A local model of the scene is adopted, in which depth is measured relative to a plane containing the fixation point. The binocular disparity field is given a symmetric parameterization, in which the unknown scene-depths determine the location of corresponding image-features. The resulting Cyclopean depth-map can be combined with the estimated oculomotor parameters, to produce a local representation of the scene. The recovery of visual direction and depth from retinal images is discussed, with reference to the relevant psychophysical and neurophysiological literature.