Abstract

A theory of the binocular system with asymmetric eyes (AEs) is developed in the framework of bicentric perspective projections. The AE accounts for the eyeball's global asymmetry produced by the foveal displacement from the posterior pole, the main source of the eye's optical aberrations, and the crystalline lens' tilt countering some of these aberrations. In this theory, the horopter curves, which specify retinal correspondence of binocular single vision, are conic sections resembling empirical horopters. This advances the classic model of empirical horopters as conic sections introduced in an ad hoc way by Ogle in 1932. In contrast to Ogle's theory, here, anatomically supported horopteric conics vary with the AEs' position in the visual plane of bifoveal fixations and their transformations are visualized in a computer simulation. Integrating horopteric conics with eye movements can help design algorithms for maintaining a stable perceptual world from visual information captured by a mobile robot's camera head. Further, this paper proposes a neurophysiologically meaningful definition for the eyes' primary position, a concept which has remained elusive despite its theoretical importance to oculomotor research. Finally, because the horopteric conic's shape is dependent on the AE's parameters, this theory allows for changes in retinal correspondence, which is usually considered preformed and stable.

Highlights

  • Our eyes receive two disparate perspective projections of a scene due to their bilateral separation

  • The tilt of the effective lens is represented in my geometrical model of the binocular system with asymmetric eyes (AEs) by the image plane passing through the eye’s rotation center that is parallel to the equatorial plane of the effective lens

  • The horopteric conic sections resembling empirical horopters were numerically studied in Turski (2018) in the binocular system with AEs

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Summary

A Geometric Theory Integrating Human Binocular Vision With Eye Movement

The AE accounts for the eyeball’s global asymmetry produced by the foveal displacement from the posterior pole, the main source of the eye’s optical aberrations, and the crystalline lens’ tilt countering some of these aberrations. In this theory, the horopter curves, which specify retinal correspondence of binocular single vision, are conic sections resembling empirical horopters. The horopter curves, which specify retinal correspondence of binocular single vision, are conic sections resembling empirical horopters This advances the classic model of empirical horopters as conic sections introduced in an ad hoc way by Ogle in 1932.

INTRODUCTION
ASYMMETRIC EYE
BINOCULAR SYSTEM WITH AES
THE GEOMETRIC CONSTRUCTION OF BINOCULAR CONICS
RETINAL CORRESPONDENCE
ANTHROPOMORPHIC BINOCULAR CONICS
BINOCULAR CONICS IN VISUAL PLANE
Parabola containing F3
DISCUSSION
Retinal Correspondence and Geometric Horopters
Binocular Conics and Eye Movement
DATA AVAILABILITY STATEMENT
Full Text
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