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Martin Banks, Kai Schreiber; Are the positions of corresponding points adaptive for natural viewing?. Journal of Vision 2008;8(6):1085. doi: 10.1167/8.6.1085.
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In stereopsis, the visual system must match retinal-image points that correspond to the same point in space. Part of the solution to this matching problem is the existence of corresponding retinal points. These point pairs have special status: matching solutions are biased toward them; the region of single vision straddles them; the precision of binocular depth perception is highest for spatial locations that project to them. Thus, it is important to know the regions in space that stimulate or come closest to stimulating corresponding points. Near the eyes' vertical meridians, corresponding points are sheared horizontally in a pattern called the Helmholtz shear. As a result, the empirical vertical horopter is a top-back slanted line in the mid-sagittal plane. Near the eyes' horizontal meridians, corresponding points are shifted horizontally in a pattern called the Hering-Hillebrand deviation. Because of this, the empirical horizontal horopter in the visual plane is less concave than it would be without the shift. We examined whether the shear and deviation patterns of correspondence place the zone of single vision and finest stereopsis usefully relative to the natural environment. Helmholtz claimed that the vertical horopter's slant is adaptive because it places the horopter close to the ground plane even as the observer fixates different positions along the ground, provided that eye position obeys Listing's Law. We describe modern misinterpretations of Helmholtz's claim that do not consider fixations in the ground at finite distances. We also show that the horizontal extension of the horopter cannot lie in the ground plane: because of the Hering-Hillebrand deviation, the horizontal extension is convex so the sides lie progressively farther below ground. Considering both the shear and deviation, corresponding-point positions are most adaptive for viewing near planar surfaces rather than the ground.
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