A Geometric Theory Integrating Human Binocular Vision with Eye movement

Abstract

AO_SCPLOWBSTRACTC_SCPLOWA theory of the binocular system with asymmetric eyes (AEs) is developed in the framework of bicentric perspective projections. The AE accounts for the eyeballs global asymmetry produced by the foveal displacement from the posterior pole, the main source of the eyes 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 Ogles 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 robots 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 conics shape is dependent on the AEs parameters, this theory allows for changes in retinal correspondence which is usually considered preformed and stable.