Binocular Disparity - Definition

Definition

Human eyes are horizontally separated by about 50–75 mm (interpupillary distance) depending on each individual. Thus, each eye has a slightly different view of the world. This can be easily seen when alternately closing one eye while looking at a vertical edge. The binocular disparity can be observed from apparent horizontal shift of the vertical edge between both views.

At any given moment, the line of sight of the two eyes meet at a point in space. This point in space projects to the same location (i.e. the center) on the retinae of the two eyes. Because of the different viewpoints observed by the left and right eye however, many other points in space do not fall on corresponding retinal locations. Visual binocular disparity is defined as the difference between the point of projection in the two eyes and is usually expressed in degrees as the visual angle.

The term "binocular disparity" refers to geometric measurements made external to the eye. The disparity of the images on the actual retina depends on factors internal to the eye, especially the location of the nodal points, even if the cross section of the retina is a perfect circle. Disparity on retina conforms to binocular disparity when measured as degrees, while much different if measured as distance due to the complicated structure inside eye.

Figure 1: The full black circle is the point of fixation. The blue object lies nearer to the observer. Therefore it has a "near" disparity d_n. Objects lying more far away (green) correspondingly have a "far" disparity d_f. Binocular disparity is the angle between two lines of projection in one eye(Mathematically,d_n-d_f, with sign, measured counterclockwise). One of which is the real projection from the object to the actual point of projection. The other one is the imaginary projection running through the nodal point of the lens of the one eye to the point corresponding to the actual point of projection in the other eye. For simplicity reasons here both objects lie on the line of fixation for one eye such that the imaginary projection ends directly on the fovea of the other eye, but in general the fovea acts at most as a reference. Note that far disparities are smaller than near disparities for objects having the same distance from the fixation point.

In computer vision, binocular disparity is calculated from stereo images taken from a set of stereo cameras. The variable distance between these cameras, called the baseline, can affect the disparity of a specific point on their respective image plane. As the baseline increases, the disparity increases due to the greater angle needed to align the sight on the point. However, in computer vision, binocular disparity is referenced as coordinate differences of the point between the right and left images instead of a visual angle. The units are usually measured in pixels.