Luneburg14 concluded that the metric of the space of binocular perception may be formulated in terms of negative Riemannian curvature, the curvature being constant. That is to say, he maintained the position that binocular space is hyperbolic in the sense of the geometry of Bolyai and Lobachevsky.Luneburg developed his equations principally upon the basis of the Blumenfeld3 alleys. Blumenfeld discovered that in addition to the well-known phenomenally parallel alleys studied by Hillebrand10 and Poppelreuter16 there is another alley, called by Blumenfeld the equidistance alley. The latter alley consists in this fact: If two rows of point-like lights are set up in a darkroom so as to appear straight, and parallel to each other, the various pairs of lights do not appear to be the same transverse distance apart throughout the alley's extent.If binocular space were Euclidean, the parallel and equidistance alleys would coincide
SQUIRES PC. Luneburg Theory of Visual Geodesics in Binocular Space Perception: An Experimental Investigation. AMA Arch Ophthalmol. 1956;56(2):288–297. doi:10.1001/archopht.1956.00930040296013
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