Abstract
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.
Highlights
Primates must explore the environment with saccades and smooth pursuit eye movements because acuity in primate foveate vision is limited to a visual angle of a mere two degrees
To model the eye with both the tilt and decentration of the natural crystalline lens, we present the asymmetric conformal camera
We identified the semisimple group SL(2, C) as the group of image transformations during the conformal camera’s gaze rotations
Summary
Primates must explore the environment with saccades and smooth pursuit eye movements because acuity in primate foveate vision is limited to a visual angle of a mere two degrees. Most of the neurons processing visual information encode the position of objects in gaze-centered coordinates, that is in the frame attached at the fovea in retino-cortical maps. This retinotopic information is constantly changing due to the eye’s incessant movements, our perception appears stable. By modeling the external scene projected on the retina of a rotating eye with the correspondingly updated retino-cortical maps, it can provide us with efficient algorithms capable of maintaining visual stability when imaging with an anthropomorphic camera head mounted on a moving platform replicating human eye movements [4,5,6]. Symmetry 2016, 8, 88 framework to a model of stereo vision that conforms to the physiological data of primate eyes. We divide the presented material into the prior and recent work and the original contributions
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