Binocular disparity

Main article: Stereopsis § Binocular disparity

Binocular disparity is the difference between the images as seen by the left and right eyes. The difference can have one or more of the following components:

• Horizontal disparity which is associated with the horizontal separation of 6.5 cm between the two eyes;
• Vertical disparity, which is associated with vertical misalignments and tilting the head; and
• Cyclodisparity which is associated with unequal rotations of the two eyes around their visual axes.

Horizontal disparity of P relative to the fixation point = α - β

Horizontal disparity is generally expressed as the difference between the visual directions as seen by the left and right eye: in the figure, the difference between angles α and β. In stereoscopy horizontal disparity is also expressed in terms of the number of associated pixels in the stereogram pictures. Horizontal disparity is also called binocular parallax.

The horopter Point C has a crossed disparity. P has parallel disparity.

The horopter has been used to describe the relation between disparity and stereopsis, and between disparity and double images. It depicts points with zero disparity relative to the fixation point (α = β).

Horizontal disparity, and in some cases also vertical disparity,^[1] can contribute to stereopsis, but only if horizontal, vertical and cyclo disparities are limited in size.

Horizontal disparity is also associated with the separation perceived between so-called double images. Zero disparities and small disparities are associated with seeing fused images in direction vision.

Binocular disparity and motion parallax are geometrically similar and can elicit a similar sensation of stereopsis in the binocular and monocular systems. As an example, the image below alternates between the left and right eyes' stereoscopic images which creates a 3D sensation in the perception system for motion.

• 
  Binocular disparity as motion parallax.

Application

Wheatstone invented the stereoscope in 1838 and proved that horizontal disparity is sufficient to experience stereopsis. Since then many applications have been realized, which vary from instruments like the binocular microscope to aids for stereoscopy.

In medicine disparity is used to detect and correct disorders in binocular vision.

Knowledge of disparity can be used in extraction of information from stereo images. One case in which disparity is most useful is for depth/distance calculation. Disparity and distance from the cameras are inversely related. As the distance from the cameras increases, the disparity decreases. This allows for depth perception in stereo images. Using geometry and algebra, the points that appear in the 2D stereo images can be mapped as coordinates in 3D space.

This concept is particularly useful for navigation. For example, the Mars Exploration Rover uses a similar method for scanning the terrain for obstacles.^[2] The Rover captures a pair of images with its stereoscopic navigation cameras and disparity calculations are performed in order to detect elevated objects (such as boulders).^[3] Additionally, location and speed data can be extracted from subsequent stereo images by measuring the displacement of objects relative to the Rover. In some cases, this is the best source of this type of information, as the encoder sensors in the wheels may be inaccurate due to tire slippage.

Depth information based on disparity is not always clear-cut (correspondence problem). In humans, this leads to the double-nail illusion.

See also

• Binocular vision
• Directional vision
• Stereopsis
• Stereopsis#Binocular disparity
• Cyclodisparity
• Epipolar geometry