Binocular vision#Ghost images

File:Disparity depth and distance.jpg

When the left eye (LE) and the right eye (RE) observe two objects X and Y, the following concepts are important:Krol J.D.(1982),"Perceptual ghosts in stereopsis, a ghosly problem in binocular vision", PhD thesis ISBN 90-9000382-7.Koenderink J.J.;van Doorn A.J. (1976) "Geometry of binocular vision and a model of stereopsis", Biol. Cybern. 21, 29-35.

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

The accommodation distance of an eye is the egocentric distance at which the lens has focused.

The line of sight of an eye is the line that runs through the center of the fovea and the center of the lens/pupil.

The direction of gaze is the angle between the line of sight and the connecting line between both eyes.

The (con)vergence point of both eyes is the point in space at which the line of sights of both eyes cross.

The (con)vergence distance is the egocentric distance to the vergence point.

The fixation point is the point at which attention is focused, with the result that the eyes converge and focus on this point (vergence distance = accommodation distance).

The monocular visual direction of point X is the direction of point X relative to the line of sight.

The relative direction of point X with respect to point Y is the angle between the line to X and the line to Y. In the figure:

• Angle αXY is the direction of X with respect to Y in the left eye.
• Angle βXY is the direction of X with respect to Y in the right eye.

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

Binocular disparity refers to the horizontal difference in image location of similar features seen by the left and right eyes resulting from the eyes' horizontal separation (parallax). Vertical disparity refers to height differences.

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.

File:Binocular vision.svg 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.

Binocular direction is the way in which the brain merges the images from both eyes into one, combined image (cyclopean image). In this composite image, some objects are seen single (in one direction) and others are seen double (in two directions).

Keep the thumb of your left hand about 30 cm away, straight ahead, and look with both eyes at the tip of your thumb. While doing this, hold your right thumb behind your left thumb, but slightly higher so that you can see both thumbs. You now see what you already knew, one thumb (your right thumb) behind your left thumb. Now move your right thumb away from you while continuing to look at, and focus on, your left thumb. At a certain distance, you see your right thumb not once but twice, in two directions (double images). If you alternately close your left and right eye, you can see which of these images comes from your left and right eye. Note that as you move your thumbs apart in depth, these two images move apart sideways, so that the latter distance is a measure of the depth between the two thumbs. This is referred to as disparity below.

File:Cyclopean image.jpg

Hering(1861)Zum Lehre von Ortsinne der Netzhaut. E. Hering (1861), Leipzig: Engelmann, p.37. 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.

File:Hering midsagittal line.jpg

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.

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 fusion area and are seen in an intermediate direction (allelotropia). The binocular direction of monocular images is slightly influenced by neighbouring fused images.Hariharan-Vilupurua, S.l Bedella H (2008), The perceived visual direction of monocular objects in random-dot stereograms is influenced by perceived depth and allelotropia”, Vision Research 49 (2009) 190–201 In the cyclopean image, under certain conditions it can be recognized which eye is stimulated monocularly (intraocular discrimination).{{cite journal | last1 = Blake | first1 = R. | last2 = Cormack | first2 = R. H. | year = 1979 | title = On utrocular discrimination | journal = Perception & Psychophysics | volume = 26 | pages = 53–68 | doi = 10.3758/BF03199861 |doi-access=free}}

‘’’Allelotropia’’’ is the mixing of the visual directions in the left and right eye to one fused direction in the cyclopean image which essentially is the average of the two monocular visual directions.

File:Gebied van binoculair dieptezien.jpgPanum's fusion area is the area in space where fused images occur. This area is located around the horopter, see the figure.

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

Binocular rivalry is the alternating sight of the left and right eyes, more....{{cite journal|last1=Blake|first1=Randolph|last2=Logothetis|first2=Nikos K.|title=Visual rivalry|journal=Nature Reviews Neuroscience|date=January 1, 2002|volume=3|issue=1|pages=13–21|doi=10.1038/nrn701|pmid=11823801|s2cid=8410171}}

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).

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.

The existence of stereopsis based on horizontal disparity was first described by Charles Wheatstone in 1838.[http://www.stereoscopy.com/library/wheatstone-paper1838.html Contributions to the Physiology of Vision. – Part 1. On Some Remarkable and Hitherto Unnoticed Phenomena of Binocular Vision. By CHARLES WHEATSTONE, F.R.S., Professor of Experimental Philosophy in King's College, London.] According to Hering (1864){{citation needed|date=June 2025}} 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)Julesz B. (1971) “Foundations of cyclopean perception”, U. Chicago Press. confirmed with random dot stereograms that disparity detection precedes shape detection.

File:Gebied van binoculair dieptezien.jpg

Depth differences are only directly perceived in a narrow area around the distance of the horopter and this occurs with three qualities. Ogle K.N. (1952a) "On the limits of stereoscopic vision" K, J. Exp. Psychol. 44, 253 -259.Ogle K.N. (1952b) "Disparity limits of stereopsis", A.M.A. Ophtalm. 48, 50- 60.

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

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

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

Image:Relation disparity depth Ogle.jpg

Measurements by Ogle (1950)Ogle K. N. (1950),

"Researches in binocular vision", Philadelphia: Saunders. 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 is a height or size difference between images in both eyes. In some cases, these can also evoke a sense of depth.Matthews N;Meng X.; Xu P; Qian Q.(2003) “A physiological theory of depth perception from vertical disparity”, Vision Research. Volume 43, Issue 1, January 2003, Pages 85-99.

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.

Wheatstone (1838) demonstrated with his invention of the pseudoscope that perceived binocular depth and monocular depth can influence each other. 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 (double-nail illusion). 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

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).

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. 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.

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.

{{Anchor|Pulfrich_pendulum effect}}

[[File:Pulfrich_effect_pendulum.svg|thumb|

A denotes the actual position of the pendule, A′ its previous position (as perceived by the darkened eye) and A* its apparent position; similarly for B and C.]]

When viewing the swinging movement of the rain wiper of a car, and holding a grey filter or dark sunglass in front of one of the eyes, the pendulum appears to make an elliptical movement in depth. It even appears to move through the glass.

This illusion was first described by (Pulfrich in 1922). It suggests that signals of the covered eye are processed with a delay.

Stereopsis has a positive effect on practicing practical tasks such as threading a needle and catching balls (especially in fast ball games).{{cite journal |title=The contribution of stereo vision to one-handed catching |url=https://research.vu.nl/ws/files/2022889/173426.pdf |journal=Experimental Brain Research |date=August 2004 |volume=157 |issue=3 |pages=383–90 |pmid=15221161 |doi=10.1007/s00221-004-1926-x |vauthors=Mazyn LI, Lenoir M, Montagne G, Savelsbergh GJ |hdl=1871/29156 |s2cid=6615928}}), 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.){{cite journal |title=Wiley Post, Around the World Without Stereopsis |journal=Survey of Ophthalmology |date=2014 |volume=59 |issue=3 |pages=365–72 |pmid=24359807 |doi=10.1016/j.survophthal.2013.08.001 |vauthors=Elshatory YM, Siatkowski RM}} Also surgeons{{cite journal |title=An Evaluation of Stereoacuity (3D Vision) in Practicing Surgeons in various surgical specialties |journal=De Chirurg |date=February 2014 |volume=12 |issue=1 |pages=7–10 |pmid=23764432 |doi=10.1016/j.surge.2013.05.002 |vauthors=Biddle M, Hamid S, Ali N}} normally show high stereoacuity. Regarding driving, one study found a positive effect of stereopsis in specific situations, only at intermediate distances.{{cite journal |title=The relevance of stereopsis for drivers: a pilot study |journal=Graefe's Archive for Clinical and Experimental Ophthalmology |date=July 2001 |volume=239 |pages=400–6 |pmid=11561786 |doi=10.1007/s004170100273 |vauthors=Bauer A, Dietz K, Kolling G, Hart W, Schiefer U |issue=6 |s2cid=6288004}} 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.{{cite journal |vauthors=Rubin GS, Ng ES, Bandeen-Roche K, Keyl PM, Freeman EE, West SK |title=A prospective, population-based study of the role of visual impairment in traffic crashes among older drivers: the SEE study |journal=Investigative Ophthalmology & Visual Science |volume=48 |issue=4 |pages=1483–91 |date=April 2007 |pmid=17389475 |doi=10.1167/iovs.06-0474 |doi-access=free}}

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.{{cite journal |title=Functional workload of strabismus: reduced binocular summation and binocular inhibition |journal=JAMA Ophthalmology |date=November 2013 |volume=131 |pages=1413–9 |pmid=24052160 |doi=10.1001/jamaophthalmol.2013.4484 |pmc=4136417 |vauthors=Pineles SL, Velez FG, Isenberg SJ, Fenoglio Z, Birch E, Nusinowitz S, Demer JL |issue=11}}{{cite news |author=Damian McNamara |title=Studie of Strabismus Reveals Visual Function Deficits |date=2013-09-23 |journal=Medscape Medical News}}

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

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.

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.

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 ===

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 and more..._ The first stereoscope was invented by Wheatstone in 1838.

File:VL sterogram.jpg

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.

File:Vergence Lock stereoscope.jpgNow 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 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.

Stereograms can be created by hand, by drawing with a computer program, or by taking photographs with a stereo camera or one or two photo or video cameras.International Stereoscopic Union, [https://isu3d.org/] The geometry used to design the correct disparities for these images is described in epipolar geometry and computer stereo vision.

For natural scenes, the images for a stereogram are usually taken from positions as far apart as the distance between the two eyes. For macro photography, this distance should be smaller to achieve a natural depth effect, and for a reconnaissance stereogram it should be larger. Another special stereogram is based on the motion of the moon relative to the sun (moon stereogram).

File:Moon stereogram.jpg

In 1860 Whipple invented taking a photo of the moon on two different days and viewing the photos in a stereoscope. In the stereoscope, the wobbling of the moon (lunar libration) and the shifting of the shadows make the mountains and craters clearly visible in depth. (Krol, 1982, p. 2-3).

Stereograms have been used since World War I during reconnaissance flights. During the flight, photographs of the terrain are taken at regular time intervals. Consecutive photographs are viewed in pairs in a stereoscope. Camouflaged objects can now be clearly seen in depth. (Krol, 1982, p. 2-3).

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....

Binocular summation is the process by which the detection threshold for a stimulus is lower with two eyes than with one.{{cite journal | last1 = Pardhan | first1 = S. | last2 = Whitaker | first2 = A. | year = 2000 | title = Binocular summation in the fovea and peripheral field of anisometropicamblyopes | journal = Current Eye Research | volume = 20 | issue = 1| pages = 35–44 | doi=10.1076/0271-3683(200001)20:1;1-h;ft035| pmid = 10611713}} There are various types of possibilities when comparing binocular performance to monocular. 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. 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. Other factors that can affect binocular summation include, spatial frequency, stimulated retinal points, and temporal separation.

{{Main|Ocular dominance}}

When each eye has its own image of objects, it becomes impossible to align images outside Panum's fusional area with an image inside that area.{{cite journal | last1 = Bingushi | first1 = K. | last2 = Yukumatsu | first2 = S. | year = 2005 | title = Disappearance of a monocular image in Panum's limiting case | journal = Japanese Psychological Research | volume = 47 | issue = 3| pages = 223–229 | doi = 10.1111/j.1468-5884.2005.00291.x | doi-access = free }} This occurs when one has to point a finger at a distant object. When looking at the fingertip, it is single, but there are two images of the distant object. When looking at the distant object, it is single, but there are two images of the fingertip. In order to point successfully, one of the dual images must be prioritized and one must be ignored or suppressed (also called "eye dominance"). The eye that can both move to the object more quickly and remain fixated on it is more likely to be called the dominant eye.

Ocular dominance also plays a role when aiming something, even if both eyes are open).{{cite journal | last1 = Miles | first1 = W. R. | year = 1930 | title = Ocular dominance in human adults | journal = Journal of General Psychology | volume = 3 | issue = 3| pages = 412–430 | doi=10.1080/00221309.1930.9918218}}

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.{{cite journal | vauthors = Coutant BE, Westheimer G | title = Population distribution of stereoscopic ability | journal = Ophthalmic & Physiological Optics | volume = 13 | issue = 1 | pages = 3–7 | date = January 1993 | pmid = 8510945 | doi = 10.1111/j.1475-1313.1993.tb00419.x | s2cid = 32340895 }}

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.{{cite journal | vauthors = Bradley A, Barrett BT, Saunders KJ | title = Linking binocular vision neuroscience with clinical practice | journal = Ophthalmic & Physiological Optics | volume = 34 | issue = 2 | pages = 125–8 | date = March 2014 | pmid = 24588530 | doi = 10.1111/opo.12125 | hdl = 10454/10180 | s2cid = 29211166 | url = https://pure.ulster.ac.uk/ws/files/11616855/Bradley_et_al-2014-Ophthalmic_and_Physiological_Optics.pdf | hdl-access = free }}

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.Sandra Blakeslee: [https://www.nytimes.com/2011/06/14/health/views/14vision.html?_r=0 A Defect That May Lead to a Masterpiece], New York Times, New York edition, page D6, 14 June 2011 (online June 13, 2001; downloaded 22 July 2013) In particular, a case has been made that Rembrandt may have been stereoblind.

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.[http://www.allaboutvision.com/conditions/strabismus.htm Strabismus], from All About Vision, Access Media Group LLC See psychosocial effects of strabismus for more information about this.

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

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.[http://one.aao.org/bcscsnippetdetail.aspx?id=0e621c85-dd06-42e2-8e03-e2748de94172 Stereoacuity testing], ONE Network, American Academy of Phthalmology (downloaded September 2, 2014)

{{Main|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.[http://medical-dictionary.thefreedictionary.com/Lang+stereotest Language stereotest] in Farlex medical dictionary. Referring to: Millodot: Dictionary of Optometry and Visual Science, 7th edition. 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). To standardize the results, the image should be viewed at a distance of 40 cm from the eye and exactly in the frontoparallel plane. 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.

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.{{cite book |last=Kalloniatis |first=Michael |chapter=Perception of Depth |year=1995 |chapter-url=http://webvision.med.utah.edu/book/part-viii-gabac-receptors/perception-of-depth/ |title=WEBVISION: The Organization of the Retina and Visual System |publisher=University of Utah |pmid=21413376|access-date=9 April 2012}}

Vision therapy is a controversial treatment to improve stereopsis.

To maintain stereopsis and singleness of vision, the eyes need to be pointed accurately. The position of each eye 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.{{Cite book|last=Evans, Bruce J. W.|url=https://www.worldcat.org/oclc/785829294|title=Pickwell's binocular vision anomalies|publisher=Elsevier Butterworth Heinemann|others=Pickwell, David.|year=2007|isbn=978-0-7020-3925-6|edition=5th|location=Edinburgh|chapter=Detecting binocular vision anomalies in primary eye care practice|oclc=785829294}}

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. 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. 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.{{cite journal | last1 = Hamed | first1 = M. | last2 = Goss | first2 = D. A. | last3 = Marzieh | first3 = E. | year = 2013 | title = The relationship between binocular vision symptoms and near point of convergence. Indian | journal = Journal of Ophthalmology | volume = 61 | issue = 7| pages = 325–328 | doi = 10.4103/0301-4738.97553 | pmid = 23552348 | pmc = 3759101 | doi-access = free }} About 20% of patients who come to optometry clinics will have binocular vision anomalies. 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).{{Cite journal |last1=Maharjan |first1=Urusha |last2=Rijal |first2=Sujata |last3=Jnawali |first3=Ashutosh |last4=Sitaula |first4=Sanjeeta |last5=Bhattarai |first5=Sanjeev |last6=Shrestha |first6=Gulshan Bahadur |date=2022-04-07 |title=Binocular vision findings in normally-sighted school aged children who used digital devices |journal=PLOS ONE |language=en |volume=17 |issue=4 |pages=e0266068 |doi=10.1371/journal.pone.0266068 |issn=1932-6203 |pmc=8989299 |pmid=35390023 |doi-access=free |bibcode=2022PLoSO..1766068M }} The most effective way to diagnosis vision anomalies is with the near point of convergence test. 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. |language=en |volume=17 |issue=4 |pages=e0266068 |doi=10.1371/journal.pone.0266068 |issn=1932-6203 |pmc=8989299 |pmid=35390023 |doi-access=free |bibcode=2022PLoSO..1766068M }} The most effective way to diagnosis vision anomalies is with the near point of convergence test. 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.

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.

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).

Manfred Fahle has stated six specific advantages of having two eyes rather than just one:{{cite journal | last1 = Fahle | first1 = M | year = 1987 | title = Wozu zwei Augen? [Why two eyes?] | journal = Naturwissenschaften | volume = 74 | issue = 8| pages = 383–385 | doi = 10.1007/BF00405466 | pmid = 3657989 | bibcode=1987NW.....74..383F| s2cid = 32015271 }}

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.

Henson, D.B. (1993). Visual Fields. Oxford: Oxford University Press.

1. 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.
2. 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){{cite web |last1=Qayyum |title=Gaze Angle |url=https://huntgearpro.com/what-is-gaze-angle/ |website=Huntgearpro.com |publisher=Asad Qayyum}} to be determined from the images in the two eyes.{{cite journal | last1 = Longuet-Higgins | first1 = H. C. | year = 1982 | title = The role of the vertical dimension in stereoscopic vision | journal = Perception | volume = 11 | issue = 4| pages = 377–386 | doi = 10.1068/p110377 | pmid = 7182797 | s2cid = 24721194 }} These properties are necessary for the third advantage.
3. 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.
4. It gives binocular summation in which the ability to detect faint objects is enhanced.

{{Cite journal|doi=10.3758/BF03198631|first1=Randolph |last1=Blake |first2=Robert |last2=Fox |date=August 1973 |title=The psychophysical inquiry into binocular summation |journal=Perception & Psychophysics |volume=14 |issue=1 |pages=161–85|doi-access=free }}

File:Fieldofview-pigeon-owl.svg

Some animals{{snd}}usually, but not always, prey animals{{snd}}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{{snd}}usually, but not always, predatory animals{{snd}}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|date=April 2023}}{{cite journal|doi=10.1111/j.1748-7692.2002.tb01017.x|title=How do sperm whales catch squids?|year= 2002 |first1= K. M. |last1=Fristrup|first2=G. R.|last2=Harbison |journal= Marine Mammal Science |volume=18|issue=1 |pages=42–54|doi-access=free|bibcode=2002MMamS..18...42F }}

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.

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

File:Grey crowned crane portrait front and side view.jpg, 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.

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 has been found in many vertebrates{{cite book |vauthors=Howard IP, Rogers BJ |year=1995 |title=Binocular vision and stereopsis |location=New York |publisher=Oxford University Press}} including mammals such as horses,{{cite journal |last=Timney |first=Brian |last2=Keil |first2=Kathy |date=1999 |title=Local and global stereopsis in the horse |journal=Vision Research |volume=39 |issue=10 |pages=1861–1867 |doi=10.1016/S0042-6989(98)00276-4}} birds such as falcons{{cite journal |last=Fox |first=Robert |last2=Lehmkuhle |first2=Stephen W. |last3=Bush |first3=Robert C. |date=1977 |title=Stereopsis in the Falcon |journal=Science |volume=197 |issue=4298 |pages=79–81 |doi=10.1126/science.867054 |issn=0036-8075}} and owls,{{cite journal |last=van der Willigen |first=R. F. |date=2011-06-10 |title=Owls see in stereo much like humans do |journal=Journal of Vision |volume=11 |issue=7 |pages=10–10 |doi=10.1167/11.7.10 |issn=1534-7362|doi-access=free }} reptiles, amphibia including toads{{cite journal |last=Collett |first=T. |date=1977 |title=Stereopsis in toads |journal=Nature |volume=267 |issue=5609 |pages=349–351 |doi=10.1038/267349a0 |issn=0028-0836}} and fish. It has also been found in invertebrates including cephalopods like the cuttlefish,{{cite journal |last=Feord |first=R. C. |last2=Sumner |first2=M. E. |last3=Pusdekar |first3=S. |last4=Kalra |first4=L. |last5=Gonzalez-Bellido |first5=P. T. |last6=Wardill |first6=Trevor J. |date=2020-01-10 |title=Cuttlefish use stereopsis to strike at prey |journal=Science Advances |volume=6 |issue=2 |page= |doi=10.1126/sciadv.aay6036 |issn=2375-2548 |pmc=6949036 |pmid=31934631}} crustaceans, spiders, and insects such as mantis.{{cite journal |last=Rossel |first=Samuel |date=1983 |title=Binocular stereopsis in an insect |journal=Nature |volume=302 |issue=5911 |pages=821–822 |doi=10.1038/302821a0 |issn=0028-0836}} Stomatopods even have stereopsis with just one eye.{{cite web |last=Fox |first=Helen|title=The better to see you with... |website=University of California Museum of Paleontology |year=2001|url=https://ucmp.berkeley.edu/aquarius/oneeye.html |access-date=2 March 2021}}

WheatstoneOn some remarkable and hitherto unobserved phenomena of binocular vision, C. Wheatstone(1838), Philos. Trans. R. Soc. London Part 1,371 – 395. first described in 1838 that the presence of binocular disparity is sufficient to give a sensation of depth.Vom binocularen tiefensehen. E. Hering (1864),In: Beiträge zur Physiologie. Fünftes handle. Wilhelm Engelmann: Leipzig. Erster Band. Leipzig. Thieme, 1931. Panum described in 1858 that with small disparities the images from the two eyes merge into one image, and that with larger disparities the images are seen side by side (double images, diplopia).Physiological Investigations on Seeing with Two Eyes. P.L. Panum(1858), Kiel.Why do double images appear in uneven distances from the observer? Albrecht vom Graefes Arch. Klin. Exp. Ophthalm. 41, 134 157. Ogle and others have made measurements of the depth seen at different disparities, and whether or not the images merge.Precision and validity of stereoscopic depth perception from double images, K.N. Ogle (1953), J. Opt. Soc. Am. 43, 906 – 513.The range and scope of binocular depth discrimination in man, C. Blakemore (1970), J. of Pfysiol. Lond. 211, 599-622. Richards (1970) investigated stereoblindness.Stereopsis and stereoblindness, W. Richards (1970}, Exp. Brain Res. 10, 380 – 388. Foley (1972) investigated the influence of eye movements on the experience of depth.Effects of voluntary eye movement and convergence on the binocular appreciation of depth, J.M. Foley, W. Richards (1972), Perception and Psychophysics 11, 423 – 427. Koenderink (1976) described the geometry of binocular vision. Krol (1982) showed that the disparity of similar "edges" is detected and that the surfaces between these edges are filled in, are an interpretation, and can give rise to ambiguity.On the sufficiency of disparate contours as a stimulus for stereopsis., J.D. Krol W.A. van de Grind (1979), Neurosc. Lit. Suppl. 3 S 304.Fixation disparities and depth vision due to a process of vergence fine-tuning, J.D. Krol W.A. v.d. Gravel (1981), In: Proc. 22nd meeting of the Dutch Federation of Medical Scientific Societies, Utrecht, April 24, No. 248.Krol J.D. ; v.d.Grind W.A. (1982) ,”Depth from dichoptic edges depends on vergence fine-tuning,” In the visual cortex, nerve cells have been found that are tuned to a certain binocular disparity.Neurophysiology of binocular single vision and stereopsis. P.O. Bishop (1973), In: Handbook of sensory physiology, vol. VII/3A: Central processing of visual information. A: Integrative functions and comparative data. These cells form the basis for neural models of binocular depth perception.Binocular vision: a physical and neural theory. G. Sperling(1970), Am. J. of Psychol. 83, 461 – 533.[https://pubmed.ncbi.nlm.nih.gov/7220239/ The double-nail illusion, experiments on binocular vision with nails needles and pins, J.D. Krol , W.A. van de Grind (1980) Perception.1980;9(6):651-69] These models predict so-called binocular ghost images.

There is strong evidence that the stereoscopic mechanism consists of at least two perceptual mechanisms,{{cite journal | vauthors = Wilcox LM, Allison RS | title = Coarse-fine dichotomies in human stereopsis | journal = Vision Research | volume = 49 | issue = 22 | pages = 2653–65 | date = November 2009 | pmid = 19520102 | doi = 10.1016/j.visres.2009.06.004 | s2cid = 11575053 | doi-access =}} possibly three.{{cite journal | vauthors = Tyler CW | title = A stereoscopic view of visual processing streams | journal = Vision Research | volume = 30 | issue = 11 | pages = 1877–95 | year = 1990 | pmid = 2288096 | doi = 10.1016/0042-6989(90)90165-H | s2cid = 23713665}} 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. 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.{{cite book | first1 = David | last1 = Stidwill | first2 = Robert | last2 = Fletcher | name-list-style = vanc |title=Normal Binocular Vision: Theory, Research, and Practical Aspects|url=https://books.google.com/books?id=cGTz58hxLqEC&pg=PA164|date=November 8, 2010|publisher=John Wiley & Sons|isbn=978-1-4051-9250-7|page=164}} The coarse stereoscopic system appears to be able to provide residual binocular depth information in some individuals who do not have fine stereopsis.See the interpretation of statements by Bela Julesz in: Leonard J. Press: [http://visionhelp.wordpress.com/2011/06/21/the-dual-nature-of-stereopsis-part-6/ The Dual Nature of Stereopsis – Part 6] (downloaded September 8, 2014) It has been found that individuals different stimuli, such as stereoscopic cues and motion occlusion, are processed differently.{{cite journal | vauthors = Hildreth EC, Royden CS | title = Integrating multiple cues into depth order at object boundaries | journal = Attention, Perception & Psychophysics | volume = 73 | issue = 7 | pages = 2218–35 | date = October 2011 | pmid = 21725706 | doi = 10.3758/s13414-011-0172-0 | doi-access = free}}

For dynamic disparity processing, see also{{cite journal | vauthors = Patterson R | title = Unsolved problems in stereopsis: dynamic disparity processing | magazine = Spatial Vision | volume = 22 | edition = 1 | pages = 83–90 | year = 2009 | pmid = 19055888 | doi = 10.1163/156856809786618510}}{{cite journal | vauthors = Ban H, Preston TJ, Meeson A, Welchman AE | title = The integration of motion and disparity signals with depth in the dorsal visual cortex | journal = Nature Neuroscience | volume = 15 | issue = 4 | pages=636–43 | date = February 2012 | pmid = 22327475 | pmc = 3378632 | doi = 10.1038/nn.3046}}{{cite journal | vauthors = Fine I, Jacobs RA | title = Modeling the combination of motion, stereo, and vergence angle signals with visual depth | journal = Neural Computation | volume = 11 | issue = 6 | pages = 1297–330 | date = August 1999 | pmid = 10423497 | doi = 10.1162/089976699300016250 | citeseerx = 10.1.1.24.284 | s2cid = 1397246}}

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.{{cite book | vauthors = Beck J |year=1979 |title=Leonardo's rules of painting |location=Oxford |publisher=Phaidon Press |isbn=978-0-7148-2056-9}} 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.{{cite journal | vauthors = Wade NJ | title = On the late invention of the stereoscope | journal = Perception | volume = 16 | issue = 6 | pages = 785–818 | year = 1987 | pmid = 3331425 | doi = 10.1068/p160785 | s2cid = 24998020}} 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.{{cite journal |last=Julesz |first=B. |year=1960 |title=Binocular depth perception of computer-generated images |journal=Bell System Technical Journal |volume=39 |issue=5 |pages=1125–1163 |doi=10.1002/j.1538-7305.1960.tb03954.x}} 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.{{cite journal | vauthors = Barlow HB, Blakemore C, Pettigrew JD | title = The neural mechanism of binocular depth discrimination | journal = The Journal of Physiology | volume = 193 | issue = 2 | pages = 327–42 | date = November 1967 | pmid = 6065881 | pmc = 1365600 | doi = 10.1113/jphysiol.1967.sp008360}} 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.{{cite journal | vauthors = Hubel DH, Wiesel TN | title = Stereoscopic vision in macaque monkey. Cells sensitive to binocular depth in area 18 of the macaque monkey cortex | journal = Nature | volume = 225 | issue = 5227 | pages = 41–2 | date = January 1970 | pmid = 4983026 | doi = 10.1038/225041a0 | bibcode = 1970Natur.225...41H | s2cid = 4265895 }} In the 1980s, Gian Poggio and others found neurons in V2 of the monkey brain that responded to the depth of random-dot stereograms.{{cite journal | vauthors = Poggio GF, Motter BC, Squatrito S, Trotter Y | title = Responses of neurons in visual cortex (V1 and V2) of the alert macaque to dynamic random-dot stereograms | journal = Vision Research | volume = 25 | issue = 3 | pages = 397–406 | year = 1985 | pmid = 4024459 | doi = 10.1016/0042-6989(85)90065-3 | s2cid = 43335583}}

In the 1970s, Christopher Tyler invented autostereograms, random-dot stereograms that can be viewed without a stereoscope.{{cite journal | vauthors = Tyler CW, Clarke MB |year=1990 |title=The autostereogram, Stereoscopic Displays and Applications |journal=Proc. SPIE |volume=1258 |pages=182–196 | doi = 10.1117/12.19904 |title-link=Stereoscopic Displays and Applications |bibcode=1990SPIE.1256..182T |s2cid=263894428}} This led to the popular Magic Eye pictures.

In the late 1970s and early 1980s, Jodi Krol attempted to predict the interaction of neighbouring binocular neurons, in order to subsequently test this prediction in research on neurons in the visual cortex of the cat by Wim van de Grind. This led to the discovery of the double-nail illusion and the midsagittal-strip illusion. This has led to a lively discussion with Peter Burt and Bela Julesz, with Hiroshi Ono, and in retrospect with John Foley, about the mechanism behind Panum's fusion region and behind "depth mixing", and about the role of vergence.Burt P.; Julesz B.(1982),"The disparity gradient limit for binocular fusion: an answer to J.D. Krol and W.A. van de Grind.", Perception Volume 11, Issue 5,[https://doi.org/10.1068/p1106]Krol J.D.; van de Grind W.A.(1983),"Depth from dichoptic edges depends on vergence fine-tuning.", Perception 1983;12(4):425-38. doi: 10.1068/p120425. Krol J.D.; van de Grind W.A.(1984)"Exorcising the double-nail confusion: a reply to Ono", Perception 13(6):759-64 [https://pubmed.ncbi.nlm.nih.gov/6543956]Ono H.(1984), "Exorcising the double-nail illusion: giving up the ghosts", Perception 13(6): 753-758 [https://eurekamag.com/research/043/068/043068228.php/]Krol J.D.; van de Grind W.A.(1986),“Binocular depth mixture: An artefact of eye vergence?”, Vision Research, Volume 26, Issue 8, p. 1289-1298, ISSN 0042-6989, [https://doi.org/10.1016/0042-6989(86)90110-0].

In 1989, Antonio Medina Puerta described that in stereograms without parallax disparity, but with disparate shadows, depth perception is possible (shadow stereopsis).{{cite journal |title="The power of shadows: shadow stereopsis." |journal=Journal of the Optical Society of America A |date=February 1989 |volume=6 |pages=309–11 |pmid=2926527 |doi=10.1364/JOSAA.6.000309 |vauthors=Medina Puerta A |number=2 |bibcode=1989JOSAA...6..309M}} This resembles the moon stereogram already described and made by Whipple in 1860.

• Binocular illusions
• Opthalmology

{{Reflist|30em}}

• Julesz, B. (1971). [http://psycnet.apa.org/record/1973-26089-000 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 {{Not a typo|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}}

• [http://vision.middlebury.edu/stereo/ Middlebury Stereo Vision Page]
• [http://vip.doc.ic.ac.uk/vision/ VIP Laparoscopic / Endoscopic Video Dataset (stereo medical images)] {{Webarchive|url=https://web.archive.org/web/20110512174240/http://vip.doc.ic.ac.uk/vision/ |date=2011-05-12 }}
• [http://www.vision3d.com/stereo.html What is Stereo Vision?]
• [http://www.easystereogrambuilder.com/HowTheyWork.aspx Learn about Stereograms then make your own Magic Eye]
• [http://www.internationalorthoptics.org/ International Orthoptic Association]

Category:Psychology

Category:Perception

Category:Stereoscopy

Category:Vision

Category:3D imaging