A Critical Study in Stereopsis and Listing's Law

The brain uses slightly different 2D retinal images to enhance our vision with stereopsis: spatial depth and 3D shape. Stereopsis is organized by pairs of corresponding retinal elements of zero disparity: a small retinal area in one eye and the corresponding unique area in the other share one subjective visual direction. This organization results in retinal disparitys spatial coordinates. The study presented here extends the 2D setting of the authors geometric modeling of the disparitys spatial coordination in the binocular system with the asymmetric eye (AE) to the 3D framework. The AE models the healthy human eyes asymmetry of optical components. In GeoGebras dynamic geometry simulations, the 3D spatial coordinates of retinal disparity integrated with the eyes posture are visualized, and longitudinal and vertical disparities of distal visual stimuli are computed, contributing to stereopsis and visual space geometry study. Further, the torsional disparity is computed in the framework of Eulers rotation theorem. It can assess the geometric and neural or ocular motor plant constraints to Listings law. Finally, epipolar geometry in the binocular system with AEs is discussed. Although this study enhances the geometric description of stereopsis and oculomotor control of eyes 3D orientations, it also simplifies their analyses.