Horopter

The concept of horopter can then be extended as a geometrical locus of points in space where a specific condition is met: As other quantities that describe the functional principles of the visual system, it is possible to provide a theoretical description of the phenomenon.

[1][2] The horopter as a special set of points of single vision was first mentioned in the eleventh century by Ibn al-Haytham, known to the west as "Alhazen".

Thus Alhazen noticed the importance of some points in the visual field but did not work out the exact shape of the horopter and used singleness of vision as a criterion.

[5] In 1818, Gerhard Vieth argued from Euclidean geometry that the horopter must be a circle passing through the fixation-point and the nodal point of the two eyes.

Recently, plausible explanation has been provided to this deviation, showing that the empirical horopter is adapted to the statistics of retinal disparities normally experienced in natural environments.

[9] (Under no conditions does the horopter become either a cylinder through the Vieth-Müller circle or a torus centered on the nodal points of the two eyes, as is often popularly assumed.)

These statements follow from the Central Angle Theorem and the fact that three non-collinear points give a unique circle.

When the eyes are in tertiary position away from the two basic horopter lines, the vertical disparities due to the differential magnification of the distance above or below the Vieth-Müller circle have to be taken into account, as was calculated by Helmholtz.

Moreover the vertical horopter have been consistently found to have a backward tilt of about 2 degrees relative to its predicted orientation (perpendicular to the fixation plane).

The theory underlying these deviations is that the binocular visual system is adapted to the irregularities that can be encountered in natural environments.

[1][2] 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.