A Geometric Theory Integrating Human Binocular Vision With Eye Movement

Area of Science:

• Vision Science
• Computational Neuroscience
• Robotics

Background:

• The classic model of empirical horopters, introduced by Ogle in 1932, used conic sections in an ad hoc manner.
• Existing theories do not fully account for the global asymmetry of the eyeball, including foveal displacement and crystalline lens tilt, which contribute to optical aberrations.

Purpose of the Study:

• To develop a new theory of the binocular system incorporating asymmetric eyes (AEs) within bicentric perspective projections.
• To propose a neurophysiologically meaningful definition for the eyes' primary position.
• To advance the understanding of horopter curves and retinal correspondence.

Main Methods:

• Development of a theory based on bicentric perspective projections for asymmetric eyes.
• Mathematical modeling of horopter curves as conic sections derived from anatomical eye asymmetries.
• Computer simulation to visualize transformations of horopteric conics with varying AE positions.

Main Results:

• Horopter curves are described as conic sections that resemble empirical horopters and are anatomically supported.
• The derived horopteric conics vary with the position of asymmetric eyes in the visual plane during bifoveal fixations.
• The theory allows for dynamic changes in retinal correspondence, challenging the notion of it being preformed and stable.

Conclusions:

• The new theory provides an anatomically grounded explanation for horopter curves and retinal correspondence in asymmetric eyes.
• This framework offers potential applications in designing stable perceptual systems for mobile robots.
• A novel, neurophysiologically relevant definition for the eyes' primary position is proposed.