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Binocular vision

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Binocular vision is seeing with two eyes, which increases the size of the visual field. If the visual fields of the two eyes overlap, binocular depth can be seen. This allows objects to be recognized more quickly, camouflage to be detected, spatial relationships to be perceived more quickly and accurately (stereopsis) and perception to be less susceptible to optical illusions.

In chapter medical attention is paid to the occurrence, defects and sharpness of binocular vision. In chapter biological the occurrence of binocular vision in animals is described.

Geometric terms

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The relationship between geometric disparity, geometric depth and egocentric distance.

When the left eye (LE) and the right eye (RE) observe two objects X and Y, the following concepts are important:[citation needed]

Egocentric distance

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The egocentric distance to object X is the distance from the observer to X. In the figure: Dx.

Metric depth

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The metric depth between two objects X and Y is the difference of the egocentric distances to X and Y. In the figure: dXY.

Direction in the left eye

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Direction αXY is the direction of X relative to Y in the left eye. In the figure Angle αXY. If Y is the fixation point, then αX is also called the direction of X.

Direction in the right eye

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Direction βXY is the direction of X relative to Y in the right eye. In the figure Angle βXY. If Y is the fixation point, then βX is also called the direction of X in the right eye.

Disparity

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The binocular disparity between two points X and Y is the difference between angle αXY and angle βXY. In the figure: δXY. The disparity of point X means the disparity of X relative to the horopter.

Horopter

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Principle of binocular vision with horopter shown

The horopter is the set of points with disparity = 0 relative to the fixation point. These points lie on a circle through the fixation point and both eyes (Vieth-Műller circle).

There is also an empirical vertical horopter, which is effectively tilted away from the eyes above the fixation point and towards the eyes below the fixation point.

Direction

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Binocular direction is the way in which the brain merges the images from both eyes into one, combined image (cyclopean image). In the cyclopean image, the original images of both eyes can be recognized for some objects (double image). Sometimes the image from one of the two eyes is not visible (eye dominance). For other objects, the images in both eyes are fused into one, fused image (Panum's fusion area).

Cyclopean image

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Cyclopean projection according to Hering

Hering(1861)[1] describes that the images from the two eyes are merged into one cyclopean image (after the Cyclopes in Greek mythology) by apparently projecting them onto each other, with the fixation point (vergence point) as the center. He illustrates this with a pencil pointed away from the observer. This is a graphic way of saying that in the binocular cyclopean image, corresponding points in both eyes appear to coincide. In depth, the "two" pencils would cross at the fixation point, possibly due to the monocular perspective being opposite for both pencils.

Hering's midsagittal rod

Hering also performed this experiment with a thin rod where the perspective is less visible. In that case, the images from both eyes coincide and merge into one image. This situation is a special case of the midsagittal-strip illusion. This illusion explains that and why the fused image is seen perpendicular to the direction of view.

If the rod is viewed slightly from above so that the images do not completely merge, then the part that is in Panum's fusion area is seen "single" and the part that is outside it is seen "double" and receding in depth. See the different images at different fixation points in the figure.

In the cyclopean image, ghost images can be observed which are a side effect of the functioning of the binocular system, such as in the double-nail illusion.

Fused image

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A fused image is a cyclopean image in which the projections of both eyes are not separately visible, even if the projections have different directions (disparity). Fused images occur in Panum's fudie area.

Panum's fusion area

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Single vision (fusion) in binocular space, after Ogle.

Panum's fusion area is the area in space where fused images occur. This area is located around the horopter, see the figure.

Double image

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A double image or diplopia is a cyclopian image in which the projections of the left and right eyes are visible separately.

Binocular rivalry

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Binocular rivalry is the alternating sight of the left and right eyes, more....[2]

Depth

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Binocular depth is the metric depth perceived when the images from the two eyes contain small differences (disparities) due to the distance between the two eyes. The quality, precision and accuracy of depth perception depend on several factors. The perceived depth differs depending on the distance from the horopter (types_of_stereopsis) and the distance at which the eyes converge (depth scaling).

Stereopsis

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The word stereopsis comes from the Ancient Greek στερεός (stereós) 'solid' and ὄψις (ópsis) 'appearance, sight'. The word thus indicates seeing the outside of three-dimensional ("solid") objects. The word stereopsis is used as a synonym for binocular depth perception.

Disparity detection

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The existence of stereopsis based on horizontal disparity was first described by Charles Wheatstone in 1838.[3] According to Hering (1864)[citation needed] our brains detect the disparity of "edges" and the surfaces between these edges are "filled in". No binocular color mixing occurs (Krol 1982, p. 38-39). Julesz (1971)[4] confirmed with random dot stereograms that disparity detection precedes shape detection.

Types of stereopsis

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Depth perception in binocular space, after Ogle.

Depth differences are only directly perceived in a narrow area around the distance of the horopter and this occurs with three qualities..[5][6]

Fine stereopsis

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In the area for fine stereopsis the perceived depth between two objects is proportional to the present disparity. Ogle calls this patent stereopsis.

Coarse stereopsis

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In the area for coarse stereopsis depth is perceived without the amount of depth being accurately indicated. Ogle calls this qualitative stereopsis.

No stereopsis

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In this area, objects without vivid depth sensation, at or around the distance of the horopter, are usually seen as double image.

Depth as a function of horizontal disparity

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Relation between disparity and depth, after Ogle

Measurements by Ogle (1950)[7] show how the horizontal disparity and the perceived depth of two points X and F relate to each other.

If point F is fixed and the other point X is moved in depth, then the perceived depth first increases linearly with the disparity (fine stereopsis), and then the depth decreases again (coarse stereopsis).

If the eyes alternately fixate X and Y, i.e. converge back and forth, then the perceived depth increases linearly over a much larger distance.

Vertical disparity

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Vertical disparity is a height or size difference between images in both eyes. In some cases, these can also evoke a sense of depth.[8]

Depth scaling

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When the observer moves in space, the disparity δXF varies with the egocentric distance, but the perceived depth dXF remains almost the same. This is caused by eye vergence; the visual system uses egocentric distance, measured by eye vergence, to scale perceived depth relative to disparity. This phenomenon is used in stereo photography to increase the perceived depth effect: the images for both eyes are presented in such a way that the viewer is forced to converge further away than the distance at which the original scene was photographed.

Multi-modal information

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Wheatstone (1838) demonstrated with his invention of the pseudoscope that perceived binocular depth and monocular depth can influence each other.[3] Krol (1982) describes that two identical tangible physical objects can appear binocularly at radically different tangible positions, where they are seen with vivid depth, but are not felt (tweespijkerillusie ). Furthermore, when the physical objects are manually moved relative to each other, the perceived objects move in a different way than intended and felt by the motor system: the stereoscopic misperception prevails over tactile, motor and monocular cues.[9]

Ghost images

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A "binocular ghost" or "ghost image" is a perception of a physically present 3-D object at a position that does not correspond to tangible reality. Binocular ghosts are predicted by neural models that explain binocular vision, see ghosts in a neural network. Binocular ghosts occur despite information that multimodal reality differs from perception (multi-modal illusion).

Correspondence problem

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In disparity detection, each dot in the left eye can be matched with a dot or rim of the same color in the other eye. The "correspondence problem" refers to the question of which of these possible disparities (correlations) are perceived and which are not. This problem was investigated by Julesz using random dot stereograms.[4] This research shows, among other things, that the visual system prefers to see surfaces (globality principle) and that shapes are only filled in after disparities have been established.

Binocular interaction

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Apart from binocular summation, the two eyes can influence each other in at least three ways.

  • Pupillary diameter. Light falling in one eye affects the diameter of the pupils in both eyes. One can easily see this by looking at a friend's eye while he or she closes the other: when the other eye is open, the pupil of the first eye is small; when the other eye is closed, the pupil of the first eye is large.
  • Accommodation and vergence. Accommodation is the state of focus of the eye. If one eye is open and the other closed, and one focuses on something close, the accommodation of the closed eye will become the same as that of the open eye. Moreover, the closed eye will tend to converge to point at the object. Accommodation and convergence are linked by a reflex, so that one evokes the other.
  • Interocular transfer. The state of adaptation of one eye can have a small effect on the state of light adaptation of the other. Aftereffects induced through one eye can be measured through the other.


Function

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Stereopsis has a positive effect on practicing practical tasks such as threading a needle and catching balls (especially in fast ball games).[10]), pouring liquids, and others. Occupational activities may include operating stereoscopic instruments such as a binocular microscope. Although some of these tasks may benefit from compensation of the visual system by means of other depth cues, there are some functions for which stereopsis is necessary. Occupations that require accurate distance judgment sometimes require some degree of stereopsis; aircraft pilots in particular have such a requirement (even if the first pilot to fly solo around the world, Wiley Post, accomplished his feat with only monocular vision.)[11] Also surgeons[12] normally show high stereoacuity. Regarding driving, one study found a positive effect of stereopsis in specific situations, only at intermediate distances.[13] Furthermore, a study among elderly people found that glare, visual field loss and the useful visual field were significantly were predictors of crash involvement, whereas older adults' visual acuity, contrast sensitivity, and stereoacuity scores were not associated with crashes.[14]

Binocular vision has other advantages besides stereopsis, in particular the improvement of the quality of vision by binocular summation; People with strabismus (even those without diplopia) score lower on binocular summation, and this appears to prompt people with strabismus to close one eye in visually demanding situations.[15][16]

Stereopsis is also important for object recognition and for seeing through camouflage.[4]

Stereoscopy

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Stereogram

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A stereogram is a set of two images (pictures, videos or computer-generated images), one for each eye, with which a binocular three-dimensional scene can be evoked.

Vergence and accommodation reflexes

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When looking around in a natural 3D environment, the eyes fixate different spatial points in succession. The eyes automatically focus and converge on the fixated point.

Vergence-accommodation conflict

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When looking at a stereogram, the eyes must focus on the distance of the pictures and not on the distance of the fixation point. The vergence must move with the fixation point to ensure that the area for stereopsis is around the fixation point. This means that the vergence and accommodation reflexes must be decoupled. This can be trained, but can initially cause eye strain or headaches.

Stereoscope

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A stereoscope is a tool to present the two images of a stereogram separately and sharply to both eyes and at a different distance than where the eyes converge.

There are different types of stereoscopes, based on lenses, mirrors, prisms, color filters and polaroid filters. The first stereoscope was invented by Wheatstone in 1838, see more...

Vergence lock stereoscope

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Stereogram to view with crossed eyes

With some practice, the two stereo images of a stereogram can also be viewed without a stereoscope. A common way to do this is with a stereogram where the image for the left eye is on the right and the image for the right eye is on the left.

Vergence Lock stereoscope

Now you have to practice crossing the eye axes at a point in front of the stereogram in such a way that the left eye looks at the center of the right picture and the left eye looks at the center of the left picture. It helps to hold a pencil point at the crossing and focus your attention on this point, and then wait until the image becomes sharp and depth is perceived.

Instead of a pencil, Krol (1982, p.16-17) uses a piece of cardboard with a round or square recess. This allows each eye to see only its own picture. In addition, the hole helps to automatically converge correctly.

Pseudoscopy

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Pseudoscopy is viewing a stereogram of a natural scene in which the pictures for both eyes have been swapped. This reverses the binocular depth (disparity), convex becomes concave and vice versa. The monocular perspective is unchanged, and therefore conflicts with the binocular depth information. This results in nearby objects appearing larger than normal and more distant objects appearing smaller. This gives a surreal feeling.[3]

Medical

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Prevalence of stereopsis

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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.[17]

Stereopsis has a positive impact on exercising practical tasks such as needle-threading, ball-catching (especially in fast ball games[18]), pouring liquids, and others. Professional activity may involve operating stereoscopic instruments such as a binocular microscope. While some of these tasks may profit from compensation of the visual system by means of other depth cues, there are some roles for which stereopsis is imperative. Occupations requiring the precise judgment of distance sometimes include a requirement to demonstrate some level of stereopsis; in particular, there is such a requirement for aeroplane pilots (even if the first pilot to fly around the world alone, Wiley Post, accomplished his feat with monocular vision only.)[19] normally demonstrate high stereo acuity. As to car driving, a study found a positive impact of stereopsis in specific situations at intermediate distances only;[20] furthermore, a study on elderly persons found that glare, visual field loss, and useful field of view were significant predictors of crash involvement, whereas the elderly persons' values of visual acuity, contrast sensitivity, and stereoacuity were not associated with crashes.[21]

Binocular vision has further advantages aside from stereopsis, in particular the enhancement of vision quality through binocular summation; persons with strabismus (even those who have no double vision) have lower scores of binocular summation, and this appears to incite persons with strabismus to close one eye in visually demanding situations.[15][22]

It has long been recognized that full binocular vision, including stereopsis, is an important factor in the stabilization of post-surgical outcome of strabismus corrections. Many persons lacking stereopsis have (or have had) visible strabismus, which is known to have a potential socioeconomic impact on children and adults. In particular, both large-angle and small-angle strabismus can negatively affect self-esteem, as it interferes with normal eye contact, often causing embarrassment, anger, and feelings of awkwardness.[23] For further details on this, see psychosocial effects of strabismus.

It has been noted that with the growing introduction of 3D display technology in entertainment and in medical and scientific imaging, high quality binocular vision including stereopsis may become a key capability for success in modern society.[24]

Nonetheless, there are indications that the lack of stereo vision may lead persons to compensate by other means: in particular, stereo blindness may give people an advantage when depicting a scene using monocular depth cues of all kinds, and among artists there appear to be a disproportionately high number of persons lacking stereopsis.[25] In particular, a case has been made that Rembrandt may have been stereoblind.

Strabismus

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Squint, squint, strabismus, or strabismus is an eye condition in which the eyes do not look in the same direction, more....

It has long been known that full binocular vision, including stereopsis, is an important factor in stabilizing the postoperative outcome of strabismus corrections. Many people with a lack of stereopsis have (or had) visible strabismus, which has a potential socioeconomic impact on children and adults. Both wide-angle and narrow-angle strabismus in particular can negatively impact self-confidence because it disrupts normal eye contact, often leading to embarrassment, anger, and feelings of discomfort.[26] See psychosocial effects of strabismus for more information about this.

Binocular summation

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Binocular summation is the process by which the detection threshold for a stimulus is lower with two eyes than with one.[27] There are various types of possibilities when comparing binocular performance to monocular.[27] Neural binocular summation occurs when the binocular response is greater than the probability summation. Probability summation assumes complete independence between the eyes and predicts a ratio ranging between 9-25%. Binocular inhibition occurs when binocular performance is less than monocular performance. This suggests that a weak eye affects a good eye and causes overall combined vision.[27] Maximum binocular summation occurs when monocular sensitivities are equal. Unequal monocular sensitivities decrease binocular summation. There are unequal sensitivities of vision disorders such as unilateral cataract and amblyopia.[27] Other factors that can affect binocular summation include, spatial frequency, stimulated retinal points, and temporal separation.[27]

Amblyopia

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Amblyopia or lazy eye is a neurovisual developmental disorder. The condition is characterized by underdevelopment of several visual features and skills such as visual acuity, eye movements, eye teamwork, and binocular depth perception, more....

Eye dominance

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Main article: Ocular dominance

When each eye has its own image of objects, it becomes impossible to align images outside of Panum's fusional area with an image inside the area.[28] This happens when one has to point to a distant object with one's finger. When one looks at one's fingertip, it is single but there are two images of the distant object. When one looks at the distant object it is single but there are two images of one's fingertip. To point successfully, one of the double images has to take precedence and one be ignored or suppressed (termed "eye dominance"). The eye that can both move faster to the object and stay fixated on it is more likely to be termed as the dominant eye.[28]

Allelotropia

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Because the eyes are in different positions on the head, any object away from fixation and off the plane of the horopter has a different visual direction in each eye. Yet when the two monocular images of the object are fused, creating a Cyclopean image, the object has a new visual direction, essentially the average of the two monocular visual directions. This is called allelotropia.[29] The origin of the new visual direction is a point approximately between the two eyes, the so-called cyclopean eye. The position of the cyclopean eye is not usually exactly centered between the eyes, but tends to be closer to the dominant eye.

Disorders

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To maintain stereopsis and singleness of vision, the eyes need to be pointed accurately. The position of each eye in its orbit is controlled by six extraocular muscles. Slight differences in the length or insertion position or strength of the same muscles in the two eyes can lead to a tendency for one eye to drift to a different position in its orbit from the other, especially when one is tired. This is known as phoria. One way to reveal it is with the cover-uncover test. To do this test, look at a cooperative person's eyes. Cover one eye of that person with a card. Have the person look at your finger tip. Move the finger around; this is to break the reflex that normally holds a covered eye in the correct vergence position. Hold your finger steady and then uncover the person's eye. Look at the uncovered eye. You may see it flick quickly from being wall-eyed or cross-eyed to its correct position. If the uncovered eye moved from out to in, the person has esophoria. If it moved from in to out, the person has exophoria. If the eye did not move at all, the person has orthophoria. Most people have some amount of exophoria or esophoria; it is quite normal. If the uncovered eye also moved vertically, the person has hyperphoria (if the eye moved from down to up) or hypophoria (if the eye moved from up to down). Such vertical phorias are quite rare. It is also possible for the covered eye to rotate in its orbit, such a condition is known as cyclophoria. They are rarer than vertical phorias. Cover test may be used to determine direction of deviation in cyclophorias also.[30]

The cover-uncover test can also be used for more problematic disorders of binocular vision, the tropias. In the cover part of the test, the examiner looks at the first eye as he or she covers the second. If the eye moves from in to out, the person has exotropia. If it moved from out to in, the person has esotropia. People with exotropia or esotropia are wall-eyed or cross-eyed respectively. These are forms of strabismus that can be accompanied by amblyopia. There are numerous definitions of amblyopia.[27] A definition that incorporates all of these defines amblyopia as a unilateral condition in which vision is worse than 20/20 in the absence of any obvious structural or pathologic anomalies, but with one or more of the following conditions occurring before the age of six: amblyogenic anisometropia, constant unilateral esotropia or exotropia, amblyogenic bilateral isometropia, amblyogenic unilateral or bilateral astigmatism, image degradation.[27] When the covered eye is the non-amblyopic eye, the amblyopic eye suddenly becomes the person's only means of seeing. The strabismus is revealed by the movement of that eye to fixate on the examiner's finger. There are also vertical tropias (hypertropia and hypotropia) and cyclotropias.

Binocular vision anomalies include: diplopia (double vision), visual confusion (the perception of two different images superimposed onto the same space), suppression (where the brain ignores all or part of one eye's visual field), horror fusionis (an active avoidance of fusion by eye misalignment), and anomalous retinal correspondence (where the brain associates the fovea of one eye with an extrafoveal area of the other eye).

Binocular vision anomalies are among the most common visual disorders. They are usually associated with symptoms such as headaches, asthenopia, eye pain, blurred vision, and occasional diplopia.[31] About 20% of patients who come to optometry clinics will have binocular vision anomalies.[31] As digital device use has become more common, many children are using digital devices for a significant period of time. This could lead to various binocular vision anomalies (such as reduced amplitudes of accommodation, accommodative facility, and positive fusional vergence both at near and distance).[32] The most effective way to diagnosis vision anomalies is with the near point of convergence test.[31] During the NPC test, a target, such as a finger, is brought towards the face until the examiner notices that one eye has turned outward and/or the person has experienced diplopia or doubled vision.[31]

Up to a certain extent, binocular disparities can be compensated for by adjustments of the visual system. If, however, defects of binocular vision are too great – for example if they would require the visual system to adapt to overly large horizontal, vertical, torsional or aniseikonic deviations – the eyes tend to avoid binocular vision, ultimately causing or worsening a condition of strabismus.

Stereoblindness

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Stereoblindness is the inability to perceive binocular depth (3D), more....

Stereopsis tests

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In stereopsis testing (abbreviated to stereotesting), stereograms are used to measure the presence and sharpness of binocular depth perception (stereopsis).

There are two types of common clinical tests: random dot stereotesting and contour stereotesting. Random-dot stereotesting uses images of stereo figures embedded in a background of random dots. Contour stereo tests use images in which the targets presented to each eye are separated horizontally.[33]

Random-dot stereo tests

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Main article: w:en:Random dot stereogram § Random dot stereo tests

For example, stereopsis ability can be tested with the Lang Stereo Test, which consists of a random-dot stereogram on which a series of parallel strips cylindrical lenses are printed in certain shapes, which represent the images which each eye sees in these areas, separate from each other.[34] similar to a hologram. Without stereopsis, the image appears as a field of random dots, but the shapes become visible with increasing stereopsis and generally consist of a cat (indicating that a stereopsis of 1200 arc seconds of retinal disparity is possible), a star (600 arc seconds), and a car (550 arc seconds).[34] To standardize the results, the image should be viewed at a distance of 40 cm from the eye and exactly in the frontoparallel plane.[34] While most random dot stereotests, such as the Random Dot "E" stereotest or the TNO stereotest, require special glasses (i.e., polarized or red-green lenses), the Lang stereotest works without special glasses, making it easier to use with young children.[34]

Contour stereotests

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Examples of contour stereotests include the Titmus stereotests, of which the Titmus fly stereotest is the best-known example, in which an image of a fly is shown with deviations at the edges. The patient uses 3D glasses to look at the image and determine whether a 3D figure can be seen. The degree of deviation in the images varies, for example 400-100 arc seconds and 800-40 arc seconds.[35]

Defect and treatment

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Main articles: w:en:Stereoblindness and w:en:Stereopsis recovery

Defect of stereopsis can be complete ( stereoblindness ) or more or less limited. Causes include blindness in one eye, amblyopia and strabismus.

Vision therapy (Vision therapy) is one of the treatments for people with stereopsis deficiency. Vision therapy allows people to improve their vision through various

Biological

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Stereopsis requires that the visual fields of both eyes overlap (eyes in front) and therefore comes at the expense of the width of the visual field (eyes at the sides).

Advantages of two eyes

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Manfred Fahle has stated six specific advantages of having two eyes rather than just one:[36]

  1. It gives a creature a "spare eye" in case one is damaged.
  2. It gives a wider field of view. For example, humans have a maximum horizontal field of view of approximately 190 degrees with two eyes, approximately 120 degrees of which makes up the binocular field of view (seen by both eyes) flanked by two uniocular fields (seen by only one eye) of approximately 40 degrees.[37]
  3. It can give stereopsis in which binocular disparity (or parallax) provided by the two eyes' different positions on the head gives precise depth perception. This also allows a creature to break the camouflage of another creature.
  4. It allows the angles of the eyes' lines of sight, relative to each other (vergence), and those lines relative to a particular object (gaze angle)[38] to be determined from the images in the two eyes.[39] These properties are necessary for the third advantage.
  5. It allows a creature to see more of, or all of, an object behind an obstacle. This advantage was pointed out by Leonardo da Vinci, who noted that a vertical column closer to the eyes than an object at which a creature is looking might block some of the object from the left eye but that part of the object might be visible to the right eye.
  6. It gives binocular summation in which the ability to detect faint objects is enhanced.[40]

Other phenomena of binocular vision include utrocular discrimination (the ability to tell which of two eyes has been stimulated by light),[41] eye dominance (the habit of using one eye when aiming something, even if both eyes are open),[42] allelotropia (the averaging of the visual direction of objects viewed by each eye when both eyes are open),[29] binocular fusion or singleness of vision (seeing one object with both eyes despite each eye having its own image of the object),[43] and binocular rivalry (seeing one eye's image alternating randomly with the other when each eye views images that are so different they cannot be fused).[44]

Field of view and eye movements

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The field of view of a pigeon compared to that of an owl

Some animals – usually, but not always, prey animals – have their two eyes positioned on opposite sides of their heads to give the widest possible field of view. Examples include rabbits, buffalo, and antelopes. In such animals, the eyes often move independently to increase the field of view. Even without moving their eyes, some birds have a 360-degree field of view.

Some other animals – usually, but not always, predatory animals – have their two eyes positioned on the front of their heads, thereby allowing for binocular vision and reducing their field of view in favor of stereopsis. However, front-facing eyes are a highly evolved trait in vertebrates, and there are only three extant groups of vertebrates with truly forward-facing eyes: primates, carnivorous mammals, and birds of prey.

Some predatory animals, particularly large ones such as sperm whales and killer whales, have their two eyes positioned on opposite sides of their heads, although it is possible they have some binocular visual field.[how?][45] Other animals that are not necessarily predators, such as fruit bats and a number of primates, also have forward-facing eyes. These are usually animals that need fine depth discrimination/perception; for instance, binocular vision improves the ability to pick a chosen fruit or to find and grasp a particular branch.

The direction of a point relative to the head (the angle between the straight ahead position and the apparent position of the point, from the egocenter) is called visual direction, or version. The angle between the line of sight of the two eyes when fixating a point is called the absolute disparity, binocular parallax, or vergence demand (usually just vergence). The relation between the position of the two eyes, version and vergence is described by Hering's law of visual direction.

In animals with forward-facing eyes, the eyes usually move together.

The grey crowned crane, an animal that has laterally-placed eyes which can also face forward

Eye movements are either conjunctive (in the same direction), version eye movements, usually described by their type: saccades or smooth pursuit (also nystagmus and vestibulo-ocular reflex). Or they are disjunctive (in opposite direction), vergence eye movements. The relation between version and vergence eye movements in humans (and most animals) is described by Hering's law of equal innervation.

Some animals use both of the above strategies. A starling, for example, has laterally placed eyes to cover a wide field of view, but can also move them together to point to the front so their fields overlap giving stereopsis. A remarkable example is the chameleon, whose eyes appear as if mounted on turrets, each moving independently of the other, up or down, left or right. Nevertheless, the chameleon can bring both of its eyes to bear on a single object when it is hunting, showing vergence and stereopsis.

Stereopsis in animals

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Stereopsis has been found in many vertebrates[46] including mammals such as horses,[47] birds such as falcons[48] and owls,[49] reptiles, amphibia including toads[50] and fish. It has also been found in invertebrates[46] including cephalopods like the cuttlefish,[51] crustaceans, spiders, and insects such as mantis.[52] Stomatopods even have stereopsis with just one eye.[53]

Research

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Wheatstone's mirror stereoscope

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 …".[3] 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.[54] 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.[55] 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.[56] 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.[57] 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.[58] In the 1980s, Gian Poggio and others found neurons in V2 of the monkey brain that responded to the depth of random-dot stereograms.[59]

In the 1970s, Christopher Tyler invented autostereograms, random-dot stereograms that can be viewed without a stereoscope.[60] This led to the popular Magic Eye pictures.

In 1989 Antonio Medina Puerta 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.[61]

Research on Perceptual Mechanisms

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There is strong evidence that the stereoscopic mechanism consists of at least two perceptual mechanisms,[62] possibly three.[63] Coarse and fine stereopsis are processed by two different physiological subsystems, with coarse stereopsis derived from diplopic stimuli (i.e., stimuli with differences far beyond the range of binocular fusion) and yielding only a vague impression of depth.[62] Coarse stereopsis appears to be associated with the magno pathway that processes low spatial frequency differences and motion, and fine stereopsis with the parvo pathway that processes high spatial frequency differences.[64] The coarse stereoscopic system appears to be able to provide residual binocular depth information in some individuals who do not have fine stereopsis.[65] It has been found that individuals different stimuli, such as stereoscopic cues and motion occlusion, are processed differently.[66]

How the brain combines different cues—including stereo, motion, vergenceangle, and monocular cues—to detect motion in depth and the 3D position of objects is an area of active research in science of vision and related disciplines.[67][68][69][70]

Geometrical basis

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Stereopsis appears to be processed in the visual cortex of mammals 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.

The two eyes converge on the object of attention.
The cube is shifted to the right in left eye's image.
The cube is shifted to the left in the right eye's image.
We see a single, Cyclopean, image from the two eyes' images.
The brain gives each point in the Cyclopean image a depth value, represented here by a grayscale depth map.

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.[71]

If the images are very different (such as by going cross-eyed, or by presenting different images in a stereoscope) then one image at a time may be seen, a phenomenon known as binocular rivalry.

There is a hysteresis effect associated with stereopsis.[72] Once fusion and stereopsis have stabilized, fusion and stereopsis can be maintained even if the two images are pulled apart slowly and symmetrically to a certain extent in the horizontal direction. In the vertical direction, there is a similar but smaller effect. This effect, first demonstrated on a random dot stereogram, was initially interpreted as an extension of Panum's fusional area.[73] Later it was shown that the hysteresis effect reaches far beyond Panum's fusional area,[74] and that stereoscopic depth can be perceived in random-line stereograms despite the presence of cyclodisparities of about 15 deg, and this has been interpreted as stereopsis with diplopia.[75]

See also

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Bibliography

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  • Julesz, B. (1971). Foundations of cyclopean perception. Chicago: University of Chicago Press
  • Steinman, Scott B. & Steinman, Barbara A. & Garzia, Ralph Philip (2000). Foundations of Binocular Vision: A Clinical perspective. McGraw-Hill Medical. ISBN 0-8385-2670-5.
  • Howard, I. P., & Rogers, B. J. (2012). Perceiving in depth. Volume 2, Stereoscopic vision. Oxford: Oxford University Press. ISBN 978-0-19-976415-0
  • Cabani, I. (2007). Segmentation et mise en correspondance couleur – Application: étude et conception d'un système de stéréovision couleur pour l'aide à la conduite automobile. ISBN 978-613-1-52103-4
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