Horopter

In studies of binocular vision the horopter is a 3-dimensional curve that can be defined as the set of points in space from which the light falls on the corresponding points in the two retinas, that is, on anatomically identical points. The corresponding points define identical viewing directions for the two eyes, so along the horopter curve, no stereopsis can be detected by the eyes.

The term was introduced by Franciscus Aguilonius in the second of his six books in optics in 1613, however in a different meaning

The projection of the horopter in the horizontal plane across the fovea is the Vieth-Muller circle, a circle that passes through the focal points of both eyes and the fixating point.

In computer vision, the horopter is defined as the curve of points in 3D space having identical coordinates projections with respect to two cameras with the same intrinsic parameters. It is given generally by a twisted cubic, i.e., a curve of the form x = x(&theta;), y = y(&theta;), z = z(&theta;) where x(&theta;), y(&theta;), z(&theta;) are three independent third-degree polynomials. In some degenerate configurations, the horopter reduces to a line plus a circle.

Horopter