The Conformal Camera in Modeling Active Binocular Vision

• Main Author: Jacek Turski
• Format: Article
• Language: English
• Published: MDPI AG 2016-08-01
• Series: Symmetry
• Subjects: active vision; the conformal camera; the Riemann sphere; Möbius geometry; complex projective geometry; projective Fourier transform; retinotopy; binocular vision; horopter
• Online Access: http://www.mdpi.com/2073-8994/8/9/88

Primate vision is an active process that constructs a stable internal representation of the 3D world based on 2D sensory inputs that are inherently unstable due to incessant eye movements. We present here a mathematical framework for processing visual information for a biologically-mediated active vision stereo system with asymmetric conformal cameras. This model utilizes the geometric analysis on the Riemann sphere developed in the group-theoretic framework of the conformal camera, thus far only applicable in modeling monocular vision. The asymmetric conformal camera model constructed here includes the fovea’s asymmetric displacement on the retina and the eye’s natural crystalline lens tilt and decentration, as observed in ophthalmological diagnostics. We extend the group-theoretic framework underlying the conformal camera to the stereo system with asymmetric conformal cameras. Our numerical simulation shows that the theoretical horopter curves in this stereo system are conics that well approximate the empirical longitudinal horopters of the primate vision system.