A Geometric Theory Integrating Human Binocular Vision with Eye movement

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.

Riemannian Geometries of Visual Space: Variable Curvature and Horizon

“…For these values, I obtain the distance to the horizon 5.4 m, 33 m, and 83 m, respectively. Thus, the geometric theory of the binocular perception developed in [22] and extended here to iso-disparity curves, unifies in one theory the distances to the horizon reported in the literature, where precise explanations for the differences in these distances were not provided.…”

“…It is not available also from geometrical methods because of the eye's asymmetry: the corresponding points are compressed in the temporal retinae relative to those in the nasal retinae [19]. In the theory of binocular system with AE model [22], the natural asymmetry of eye's optical components is represented in the AE by the fovea's displacement from the posterior pole by α = 5.2 • and the lens' tilt by β that varies between −0.4 • and 4.7 • . The AEs are shown in Figure 1.…”

“…All fixation points are of the distance 75 cm and 150 cm along the Cyclopean ray for the ellipses and hyperbolas, respectively. The direction of the Cyclopean ray specifies the orientation of the horopteric conics [22] and, therefore, the orientations of the iso-disparity conics for a given fixation.…”

“…The horopteric conics simulated in [22] resemble the empirical horopters and are extended in this study to the families of iso-disparity conics. These iso-disparity curves are perceived as the frontal straight lines and are referred to as visual geodesics.…”

A Geometric Theory Integrating Human Binocular Vision With Eye Movement

“…I thank Alice Turski for her editing that has made this manuscript much easier to read. This manuscript has been released as a pre-print at BioRxiv (Turski, 2020 ).…”