Stereopsis (from stereo- meaning "solid" or "three-dimensional", and opsis meaning appearance or sight) is the impression of depth that is perceived when a scene is viewed with both eyes by someone with normal binocular vision. Binocular viewing of a scene creates two slightly different images of the scene in the two eyes due to the eyes' different positions on the head. These differences, referred to as binocular disparity, provide information that the brain can use to calculate depth in the visual scene, providing a major means of depth perception. The term stereopsis is often used as shorthand for 'binocular vision', 'binocular depth perception' or 'stereoscopic depth perception', though strictly speaking, the impression of depth associated with stereopsis can also be obtained under other conditions, such as when an observer views a scene with only one eye while moving. Observer motion creates differences in the single retinal image over time similar to binocular disparity; this is referred to as motion parallax. Importantly, stereopsis is not usually present when viewing a scene with one eye, when viewing a picture of a scene with both eyes, or when someone with abnormal binocular vision (strabismus) views a scene with both eyes. This is despite the fact that in all these three cases humans can still perceive depth relations.
History of stereopsis
Stereopsis was first explained by Charles Wheatstone in 1838: “… the mind perceives an object of three dimensions by means of the two dissimilar pictures projected by it on the two retinæ …”. He recognized that because each eye views the visual world from slightly different horizontal positions, each eye's image differs from the other. Objects at different distances from the eyes project images in the two eyes that differ in their horizontal positions, giving the depth cue of horizontal disparity, also known as retinal disparity and as binocular disparity. Wheatstone showed that this was an effective depth cue by creating the illusion of depth from flat pictures that differed only in horizontal disparity. To display his pictures separately to the two eyes, Wheatstone invented the stereoscope.
Leonardo da Vinci had also realized that objects at different distances from the eyes project images in the two eyes that differ in their horizontal positions, but had concluded only that this made it impossible for a painter to portray a realistic depiction of the depth in a scene from a single canvas. Leonardo chose for his near object a column with a circular cross section and for his far object a flat wall. Had he chosen any other near object, he might have discovered horizontal disparity of its features. His column was one of the few objects that projects identical images of itself in the two eyes.
Stereoscopy became popular during Victorian times with the invention of the prism stereoscope by David Brewster. This, combined with photography, meant that tens of thousands of stereograms were produced.
Until about the 1960s, research into stereopsis was dedicated to exploring its limits and its relationship to singleness of vision. Researchers included Peter Ludvig Panum, Ewald Hering, Adelbert Ames Jr., and Kenneth N. Ogle.
In the 1960s, Bela Julesz invented random-dot stereograms. Unlike previous stereograms, in which each half image showed recognizable objects, each half image of the first random-dot stereograms showed a square matrix of about 10,000 small dots, with each dot having a 50% probability of being black or white. No recognizable objects could be seen in either half image. The two half images of a random-dot stereogram were essentially identical, except that one had a square area of dots shifted horizontally by one or two dot diameters, giving horizontal disparity. The gap left by the shifting was filled in with new random dots, hiding the shifted square. Nevertheless, when the two half images were viewed one to each eye, the square area was almost immediately visible by being closer or farther than the background. Julesz whimsically called the square a Cyclopean image after the mythical Cyclops who had only one eye. This was because it was as though we have a cyclopean eye inside our brains that can see cyclopean stimuli hidden to each of our actual eyes. Random-dot stereograms highlighted a problem for stereopsis, the correspondence problem. This is that any dot in one half image can realistically be paired with many same-coloured dots in the other half image. Our visual systems clearly solve the correspondence problem, in that we see the intended depth instead of a fog of false matches. Research began to understand how.
Also in the 1960s, Horace Barlow, Colin Blakemore, and Jack Pettigrew found neurons in the cat visual cortex that had their receptive fields in different horizontal positions in the two eyes. This established the neural basis for stereopsis. Their findings were disputed by David Hubel and Torsten Wiesel, although they eventually conceded when they found similar neurons in the monkey visual cortex. In the 1980s, Gian Poggio and others found neurons in V2 of the monkey brain that responded to the depth of random-dot stereograms.
In 1989 Medina demonstrated with photographs that retinal images with no parallax disparity but with different shadows are fused stereoscopically, imparting depth perception to the imaged scene. He named the phenomenon "shadow stereopsis." Shadows are therefore an important, stereoscopic cue for depth perception. He showed how effective the phenomenon is by taking two photographs of the Moon at different times, and therefore with different shadows, making the Moon to appear in 3D stereoscopically, despite the absence of any other stereoscopic cue.
A stereoscope is a device by which each eye can be presented with different images, allowing stereopsis to be stimulated with two pictures, one for each eye. This has led to various crazes for stereopsis, usually prompted by new sorts of stereoscopes. In Victorian times it was the prism stereoscope (allowing stereo photographs to be viewed), in the 1920s it was red-green glasses (allowing stereo movies to be viewed), in the 1950s it was polarizing glasses (allowing coloured movies to be viewed), and in the 1990s it was Magic Eye pictures (autostereograms). Magic Eye pictures did not require a stereoscope, but relied on viewers using a form of free fusion so that each eye views different images.
Not everyone has the same ability to see using stereopsis. One study shows that 97.3% are able to distinguish depth at horizontal disparities of 2.3 minutes of arc or smaller, and at least 80% could distinguish depth at horizontal differences of 30 seconds of arc.
Geometrical basis for stereopsis
Stereopsis appears to be processed in the visual cortex in binocular cells having receptive fields in different horizontal positions in the two eyes. Such a cell is active only when its preferred stimulus is in the correct position in the left eye and in the correct position in the right eye, making it a disparity detector.
When a person stares at an object, the two eyes converge so that the object appears at the center of the retina in both eyes. Other objects around the main object appear shifted in relation to the main object. In the following example, whereas the main object (dolphin) remains in the center of the two images in the two eyes, the cube is shifted to the right in the left eye's image and is shifted to the left when in the right eye's image.
Because each eye is in a different horizontal position, each has a slightly different perspective on a scene yielding different retinal images. Normally two images are not observed, but rather a single view of the scene, a phenomenon known as singleness of vision. Nevertheless, stereopsis is possible with double vision. This form of stereopsis was called qualitative stereopsis by Kenneth Ogle.
Computer stereo vision
Computer stereo vision is a part of the field of computer vision. It is sometimes used in mobile robotics to detect obstacles. Example applications include the ExoMars Rover and surgical robotics.
Two cameras take pictures of the same scene, but they are separated by a distance – exactly like our eyes. A computer compares the images while shifting the two images together over top of each other to find the parts that match. The shifted amount is called the disparity. The disparity at which objects in the image best match is used by the computer to calculate their distance.
For a human, the eyes change their angle according to the distance to the observed object. To a computer this represents significant extra complexity in the geometrical calculations (Epipolar geometry). In fact the simplest geometrical case is when the camera image planes are on the same plane. The images may alternatively be converted by reprojection through a linear transformation to be on the same image plane. This is called Image rectification.
Computer stereo vision with many cameras under fixed lighting is called structure from motion. Techniques using a fixed camera and known lighting are called photometric stereo techniques, or "shape from shading".
Computer stereo display
Many attempts have been made to reproduce human stereo vision on rapidly changing computer displays, and toward this end numerous patents relating to 3D television and cinema have been filed in the USPTO. At least in the US, commercial activity involving those patents has been confined exclusively to the grantees and licensees of the patent holders, whose interests tend to last for twenty years from the time of filing.
Discounting 3D television and cinema (which generally require more than one digital projectors whose moving images are mechanically coupled, in the case of IMAX 3D cinema), several stereoscopic LCDs are going to be offered by Sharp, which has already started shipping a notebook with a built in stereoscopic LCD. Although older technology required the user to don goggles or visors for viewing computer-generated images, or CGI, newer technology tends to employ Fresnel lenses or plates over the liquid crystal displays, freeing the user from the need to put on special glasses or goggles.
The ability of stereopsis can be tested by, for example, the Lang stereotest, which consists of a random-dot stereogram upon which a series of parallel strips of cylindrical lenses are imprinted in certain shapes, which separate the views seen by each eye in these areas, similarly to a hologram. Without stereopsis, the image looks only like a field of random dots, but the shapes become discernible with increasing stereopsis, and generally consists of a cat (indicating that there is ability of stereopsis of 1200 seconds of arc of retinal disparity), a star (600 seconds of arc) and a car (550 seconds of arc). To standardize the results, the image should be viewed at a distance from the eye of 40 cm and exactly in the frontoparallel plane. There is no need to use special spectacles for such tests, thereby facilitating use in young children. Another common clinical test for stereopsis is the contour stereotests. An example of such tests would be the Titmus Fly Stereotest, where a picture of a fly is displayed with disparities on the edges. The patient uses a 3-D glasses to look at the picture and determine whether a 3-D figure can be seen. The amount of disparity in images vary, such as 400-100 sec of arc, and 800-40 sec arc.
Stereopsis deficiency and treatment
Vision therapy is one of the treatments for people lacking in stereopsis. Vision therapy will allow individuals to enhance their vision through several exercises such as by strengthening and improving eye movement. 
- Binocular vision
- Computer stereo vision
- Correspondence problem
- Cyclopean stimuli
- Epipolar geometry
- Interpupillary distance
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- What is Stereo Vision?
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