Cyclopean Geometry of Binocular Vision
This work provides a more complete geometric model of binocular vision for researchers in computational vision and neuroscience, incrementally improving the understanding of how visual direction and depth are recovered.
This paper analyzes the geometry of binocular projection in the primate visual system, focusing on how coordinated eye movements affect retinal images. It defines a new oculomotor parameterization that complements classical angles and uses it to construct the epipolar geometry, showing the Essential matrix can be derived from epipoles and the midline horopter.
The geometry of binocular projection is analyzed, with reference to the primate visual system. In particular, the effects of coordinated eye movements on the retinal images are investigated. An appropriate oculomotor parameterization is defined, and is shown to complement the classical version and vergence angles. The midline horopter is identified, and subsequently used to construct the epipolar geometry of the system. It is shown that the Essential matrix can be obtained by combining the epipoles with the projection of the midline horopter. A local model of the scene is adopted, in which depth is measured relative to a plane containing the fixation point. The binocular disparity field is given a symmetric parameterization, in which the unknown scene-depths determine the location of corresponding image-features. The resulting Cyclopean depth-map can be combined with the estimated oculomotor parameters, to produce a local representation of the scene. The recovery of visual direction and depth from retinal images is discussed, with reference to the relevant psychophysical and neurophysiological literature.