BINOCULAR DEPTH INVERSION

Binocular Depth Inversion Sometimes a solid object seen with both eyes can seem to reverse perspective. A study of this geometrically irrational experience suggests that ordinary depth perception is somewhat precarious by John A Visitor to the Haunted Mansion at Disneyland in California sees among other things a pair of hu­ man faces that appear to rotate in a mys­ terious and sinister way as he walks by. They are in fact inside-out relief masks, but because of the lighting and the way they are mounted the visitor unwittingly reverses their depth, perceiving them in­ correctly as normal faces. This uncon­ scious reversal of perspective gives rise to the apparent rotation. Besides mystifying visitors to the Haunted Mansion this illusion pre­ sents a problem for theories on the per­ ception of visual form. The problem is not the apparent rotation of the fac­ es; psychologists have known for some time that whenever a three-dimensional object is perceived in reverse perspec­ tive, it will seem to rotate as the observ­ er's head moves. What is puzzling is the perspective reversal itself. Ordinarily people see the three-dimensional forms of things correctly, and reversals of per­ spective occur only in special circum­ stances that deny the brain its normal visual cues to depth. One such circum­ stance is viewing the three-dimensional form with one eye closed, so that the depth cues provided by binocular vision are eliminated. The masks at Disney­ land, however, show that sometimes ob­ jects are routinely perceived inside out in spite of the availability of all the nor­ mal depth cues, including those due to binocular vision. How can such a ma­ jor perceptual mistake occur? And giv­ en that it does happen sometimes, why is it so rare? In this article I draw a distinction be­ tween the kind of perspective reversals produced by ambiguous pictures such as the famous Necker cube and those experienced in viewing actual three­ dimensional objects, such as the masks in the Haunted Mansion. I shall refer to the latter type of illusion as depth inversion. Reversible-perspective pic­ tures and their perceptual consequences are quite well known; drawings such as the Necker cube have illustrated countc less psychology textbooks since the 19th r. Yellott,Jr. century, and artists have explored the same theme for much longer. Depth inversion of solid objects also has a long scientific history. References to the phenomenon date from the 18th century, and in the 19th century it was studied by such notable figures as Her­ mann von Helmholtz and Ernst Mach. In this century, however, it seems to have been neglected until 1970, when the British psychologist Richard L. Gregory drew attention to it again in his book The Intelligent Eye. Gregory's dis­ cussion stimulated my interest and led me to devise several experiments to de­ termine whether objects can be seen in reverse perspective when the brain is truly in full possession of all the depth information available in normal vision, including in particular the information provided by binocular vision, which according to classical accounts should make the illusion impossible. The re­ sults of these experiments indicate that under appropriate conditions the brain is prepared to override all its sensory cues to depth and create an inside-out visual world that defies geometrical analysis but nonetheless seems just as realistic as normal visual experience. T hese experiments on binocular depth inversion are the subject of this arti­ cle, but to put them in context it will be helpful to first consider monocular in­ version, which is much easier to explain. Depth inversion of a three-dimensional object viewed with one eye can be un­ derstood if one thinks of visual experi­ ence as the outcome of a process in which the brain tests hypotheses about the three-dimensional shapes of objects against the evidence provided by their retinal images. With one eye alone the only potential source of unequivocal in- formation about depth is accommoda­ tion, or change of focus, and the brain normally gives this cue little or no weight in its judgment of distance. Ac­ commodation therefore presents no bar­ rier to the acceptance of an inside-out shape as being real. All the other mon­ ocular cues to depth are intrinsically ambiguous. The evidence they provide cannot exclude inside-out hypotheses, although they can render such hypothe­ ses statistically unlikely in the sense that, say, a tree rotating in synchrony with movements of the head is an improbable object. Apparently this is normally enough to enable the brain to guess correcrtly about the shapes of things seen monocularly. If sensory evidence becomes sufficiently impoverished, however, the brain may accept an inside-out hypothesis that is compatible with the retinal image. In such a case visual experience is totally transformed to agree with the hypothe­ sis, intellectual knowledge of the correct form notwithstanding. Yet the inverted object now seen still incorporates all the information available on the retina, just as in normal vision. The only difference is that now every depth cue is visually reinterpreted in order to agree with a false premise. Now consider the situation in binoc­ ular vision. The key to my explanation of monocular inversion (an explanation borrowed from Helmholtz, Mach and Gregory) is the fact that all the monocu­ lar cues to depth can be consistently rec­ onciled with an inverted-object hypoth­ esis. When both eyes view an object, however, no such reconciliation is possi­ ble. Binocular vision provides depth in­ formation that is geometrically incom­ patible with depth inversion, in other words information that should enable INSIDE-OUT FACE, made as the mold of a bust, is showu iu side and front views on the oppo­ site page. Looked at from the front it is more easily seen as a normal face because the brain overrides th'e depth cues that suggest an object as improbable as an inside-out face. (The rever­ sal is made easier when, as in the front view here, the lighting eliminates shadows that might aid the brain in making the correct interpretation.) A three-dimensional inside-out face seen in reversed perspective seems to rotate and to follow an observer who is moving laterally past it. © 1981 SCIENTIFIC AMERICAN, INC


Binocular Depth Inversion
Sometimes a solid object seen with both eyes can seem to reverse perspective.A study of this geometrically irrational experience suggests that ordinary depth perception is somewhat precarious A Visitor to the "Haunted Mansion" at Disneyland in California sees among other things a pair of hu man faces that appear to rotate in a mys terious and sinister way as he walks by.They are in fact inside-out relief masks, but because of the lighting and the way they are mounted the visitor unwittingly reverses their depth, perceiving them in correctly as normal faces.This uncon scious reversal of perspective gives rise to the apparent rotation.
Besides mystifying visitors to the "Haunted Mansion" this illusion pre sents a problem for theories on the per ception of visual form.The problem is not the apparent rotation of the fac es; psychologists have known for some time that whenever a three-dimensional object is perceived in reverse perspec tive, it will seem to rotate as the observ er's head moves.What is puzzling is the perspective reversal itself.Ordinarily people see the three-dimensional forms of things correctly, and reversals of per spective occur only in special circum stances that deny the brain its normal visual cues to depth.One such circum stance is viewing the three-dimensional form with one eye closed, so that the depth cues provided by binocular vision are eliminated.The masks at Disney land, however, show that sometimes ob jects are routinely perceived inside out in spite of the availability of all the nor mal depth cues, including those due to binocular vision.How can such a ma jor perceptual mistake occur?And giv en that it does happen sometimes, why is it so rare?
In this article I draw a distinction be tween the kind of perspective reversals produced by ambiguous pictures such as the famous Necker cube and those experienced in viewing actual three dimensional objects, such as the masks in the "Haunted Mansion."I shall refer to the latter type of illusion as "depth inversion."Reversible-perspective pic tures and their perceptual consequences are quite well known; drawings such as the Necker cube have illustrated countc less psychology textbooks since the 19th 148 by John r.Yellott,Jr.
century, and artists have explored the same theme for much longer.
Depth inversion of solid objects also has a long scientific history.References to the phenomenon date from the 18th century, and in the 19th century it was studied by such notable figures as Her mann von Helmholtz and Ernst Mach.In this century, however, it seems to have been neglected until 1970, when the British psychologist Richard L. Gregory drew attention to it again in his book The Intelligent Eye.Gregory's dis cussion stimulated my interest and led me to devise several experiments to de termine whether objects can be seen in reverse perspective when the brain is truly in full possession of all the depth information available in normal vision, including in particular the information provided by binocular vision, which according to classical accounts should make the illusion impossible.The re sults of these experiments indicate that under appropriate conditions the brain is prepared to override all its sensory cues to depth and create an inside-out visual world that defies geometrical analysis but nonetheless seems just as realistic as normal visual experience.
T hese experiments on binocular depth inversion are the subject of this arti cle, but to put them in context it will be helpful to first consider monocular in version, which is much easier to explain.Depth inversion of a three-dimensional object viewed with one eye can be un derstood if one thinks of visual experi ence as the outcome of a process in which the brain tests hypotheses about the three-dimensional shapes of objects against the evidence provided by their retinal images.With one eye alone the only potential source of unequivocal in-formation about depth is accommoda tion, or change of focus, and the brain normally gives this cue little or no weight in its judgment of distance.Ac commodation therefore presents no bar rier to the acceptance of an inside-out shape as being real.All the other mon ocular cues to depth are intrinsically ambiguous.The evidence they provide cannot exclude inside-out hypotheses, although they can render such hypothe ses statistically unlikely in the sense that, say, a tree rotating in synchrony with movements of the head is an improbable object.
Apparently this is normally enough to enable the brain to guess correcrtly about the shapes of things seen monocularly.If sensory evidence becomes sufficiently impoverished, however, the brain may accept an inside-out hypothesis that is compatible with the retinal image.In such a case visual experience is totally transformed to agree with the hypothe sis, intellectual knowledge of the correct form notwithstanding. Yet the inverted object now seen still incorporates all the information available on the retina, just as in normal vision.The only difference is that now every depth cue is visually reinterpreted in order to agree with a false premise.Now consider the situation in binoc ular vision.The key to my explanation of monocular inversion (an explanation borrowed from Helmholtz, Mach and Gregory) is the fact that all the monocu lar cues to depth can be consistently rec onciled with an inverted-object hypoth esis.When both eyes view an object, however, no such reconciliation is possi ble.Binocular vision provides depth in formation that is geometrically incom patible with depth inversion, in other words information that should enable INSIDE-OUT FACE, made as the mold of a bust, is showu iu side and front views on the oppo site page.Looked at from the front it is more easily seen as a normal face because the brain overrides th' e depth cues that suggest an object as improbable as an inside-out face.(The rever sal is made easier when, as in the front view here, the lighting eliminates shadows that might aid the brain in making the correct interpretation.)A three-dimensional inside-out face seen in reversed perspective seems to rotate and to follow an observer who is moving laterally past it.
the brain to categorically reject invert ed-object hypotheses.
That information stems from the dif ference between simultaneous retinal images of an object in the left and right eyes, a depth cue termed binocular dis parity.Its effect is that none of the in verted-depth hypotheses consistent with the left eye's view can simultaneously be consistent with the right eye's view.If the key to depth inversion is geometrical compatibility between retinal evidence and inverted-object hypotheses, binocu lar depth inversion should be impossi ble, or at least a most unnatural visual experience, quite unlike monocular in version.
Binocular vision actually provides not one new cue to depth but two cues.One is the muscular cue produced by the act of convergence, that is, the action of the eye muscles in aiming both eyes at a common fixation point.This action gives the brain information on the con vergence angle of the line from each eye to the fixation point, and the angle gives a cue to the distance of that point.At a given instant, however, this muscular cue does not provide any information on the depth of other points that are not being fixated.
That information is supplied by the second binocular cue to depth: binocu lar disparity.When the eyes converge on a point, the images of the point fall on corresponding places on the two retinas, namely the center of each fovea (the small area that affords the sharpest vi sion).Points nearer or farther than the fixation point necessarily fall on noncor responding places on the two retinas.The magnitude of this positional dispar ity is conventionally measured in angu lar units.The binocular disparity of any nontargeted point X is the difference be tween the convergence angle and the an gle formed by the lines of sight to X.
This angular measure is proportional to the absolute distances between the reti nal locations of the two images of the point; one minute of binocular disparity corresponds to a six-micrometer differ ence in the retinal positions.
Although convergence is a better cue to depth than accommodation, it still provides rather uncertain distance in formation.Binocular disparity, how ever, is an extremely powerful cue to depth.Under experimental conditions normal observers can detect depth dif ferences that give rise to disparities of about 10 seconds of arc, equivalent to a one-micrometer difference in retinal po sition.In other words, the brain can reli-A NECKER CUBE is a reversible-perspective drawing named for tbe Swiss naturalist Louis Necker, wbo in 1832 described tbe perceptual consequences of ambiguous perspective in pic tures.Tbe perspective of tbe cube binds to reverse back and fortb as one stares at tbe picture.
150 ably detect disparities that are substan tially smaller than the diameter of the smallest photoreceptors (about two mi crometers).Cues furnished by binocu lar disparity therefore seem sufficient in principle to rule out hypotheses of depth-inverted objects.
T he foregoing arguments make it plausible a priori that binocular depth inversion should not occur be cause the brain cannot construct an in verted visual model consistent with all its retinal evidence.Both Helmholtz and Mach apparently believed binocu lar depth inversion is impossible.Greg ory, studying the binocular inversions of a three-dimensional wire cube, noted that they are rare and brief, and that when an inversion does occur, the cube looks unnatural.Historically it seems to have been generally accepted that binocular depth inversion simply does not happen, at least in any stable way compared with monocular inversion.
It is easy to show that things are not so simple.Under appropriate conditions binocular depth inversion can occur quite easily, yielding a stable perception much like the one resulting from mon ocular inversion in spite of binocular disparity cues that would be detected readily in normal vision.The trick is to use an object with an overwhelmingly improbable real form, so that it looks normal only when it is seen inverted in depth.The best example is an inside-out human face like the two in Disneyland.Such a face is the mold of a normal re lief.The inside of an ordinary Hallow een mask will also do.
With a little practice one can easily achieve stable binocular depth inver sions of such a face at a viewing distance of about an arm's length.An excellent stimulus is a plastic mask mounted in side out on a sheet of cardboard and illuminated from behind.This arrange ment eliminates informative shadows that can slow down inversion.
With such a setup monocular inver sion is easy.At first opening the other eye tends to disrupt a monocularly sta ble inversion, just as movements of the head initially disrupt monocular inver sions achieved with the head stationary.With practice, however, one learns to tolerate the new depth information pro vided by binocular vision, and the per ceptual result is a depth-inverted face that appears to be natural and stable.
Trying the illusion for the first time, observers often find that the surface of the inside-ouf face does not invert all at once.Instead inversion begins in one re gion, typically the nose, and then other regions gradually become incorporated into the inverted percept.Thus at early stages one may find that during a move ment of one's own head the inverted nose will seem to wobble on an other wise immobile face.
The fact that binocular inversion can occur with an •inside-out face is not entirely surprising.One can simply say that the brain is prepared to over ride even unequivocal sensory evidence when the evidence supports a highly im probable object hypothesis.Conversely, when past experience is compatible with both an inverted and a noninverted ver sion of an object, binocular-disparity cues tip the scales in favor of the correct hypothesis.This explains why objects such as three-dimensional wire cubes are easy to • invert monocularly but diffi cult to invert binocularly.When binocular inversion does occur, however, there still remains the critical question of what happens to the binocu lar-disparity information that should, if it is properly incorporated into percep tion, prevent inversion altogether.To put the issue another way, how can the retinal images in rhe two eyes be com bined into a single three-dimensional vi sual experience when that experience cannot be geometrically reconciled with both images simultaneously?
Two answers suggest themselves im mediately.The first and simplest one is that a binocular inversion is not truly binocular.Even though both eyes view the object, perhaps the information from only one eye is incorporated into visual experience.This would mean that information from the other eye is sup pressed at some preconscious level.Since this kind of suppression of one eye's view in favor of the other's is rou tine in normal vision, one might suppose it could account for binocular depth in version.If the brain discards the infor mation from one eye, it is then free to construct an inverted object that is en tirely consistent with information from the other eye.On this hypothesis binoc ular inversion would be only monocular inversion coupled with suppression of the information from one eye.
T he other answer I thought of origi nally was that binocular inversion might be truly binocular in the sense that the information from both eyes is incorporated into visual experience but with the signs of all the binocular-dis- If one looks at it long enough with one eye, trying to imagine that it is in the configuration of an upright book open for reading (right), it will appear to reverse and be turned inside out, so that its bend points down and the card seems to perch on one end.This man has forgotten his computer system.
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3.
Through either eye alone one sees only a flat field uniformly speckled with dots.
To present the left and right halves of a random-dot stereogram (or any other stereogram) separately to the two eyes a convenient technique is to print one pic ture in green ink and the other, super posed, in red and to view the composite through glasses equipped with a red fil ter for one eye and a green filter for the other.Through the red filter green dots look black and red dots are invisible; that eye therefore sees only the green half of the stereogram.Conversely, the eye covered by the green filter sees only the red half.This kind of stereogram is called an anaglyph.
The next step is to project an anaglyph version of a random-dot stereogram onto an inside-out face mask and to view the combination through red-green glasses.If the stereogram properly per ceived seems to show a central square region floating in front of a plane back ground, what will it look like when the face is seen in depth inversion?Accord ing to the monocular-suppression hy pothesis, no depth should be seen in the stereogram (that is, the central square should be invisible) because stereopsis requires the integration of the view from both eyes.On the other hand, accord ing to the disparity-reversal hypothesis, depth should be seen in the stereogram but with its direction reversed from the normal perception.The central square should seem to be recessed behind its random-dot surround instead of float ing in front of it.
The experiment therefore provides a straightforward test of both hypothe ses, and both turn out to be wrong.Ev ery observer reports that depth can be seen in the stereogram while the face is perceived as being depth-inverted.Thus monocular suppression cannot be a fac tor.Every observer also reports that the direction of depth in the stereogram is the one implied by the actual disparities of the dots, not the opposite as predicted by the disparity-reversal hypothesis.
The second experiment exploits an il lusion of depth known as the Pulfrich effect (after the German physicist Carl Pulfrich, who described it in 1922).To demonstrate the illusion one needs a pendulum that swings in a plane arc.A weighted yardstick swinging on a nail works well enough.The observer stands in front of the pendulum and views it binocularly with one eye covered by a light-attenuating filter, such as one lens from a pair of dark sunglasses.
Seen with either eye alone the end of the pendulum appears correctly to be swinging back and forth in a plane.Viewed with both eyes, however, the end of the pendulum appears distinctly to be swinging back and forth in an el-TEST OF HYPOTHESES was made by the author with a setup in which an anaglyph version of a random-dot stereogram (in which the left and right pictures are superposed, with one print ed in green and one in red, and viewed through a hand-held filter that is green for one eye and red for the other) is projected onto an inside-out face mask.Because of the color each eye sees only half of the stereogram.According to the monocular-suppression hypothesis, no depth should be seen; according to the binocular-disparity hypothesis, depth should be seen but with its direction reversed.Observers do see the depth, however, and its direction is not reversed.
lipse.If the filter covers the observer's right eye, the pendulum seems to swing outward toward him as it moves from left to right and away from him as it moves in the opposite direction.If the filter is placed over the other eye, the direction of this apparently elliptical movement is reversed.The magnitude of the illusion (the bulge of the ellipse) increases with viewing distance and also as the filter is made darker, provided that the observer can still see through it.
The accepted explanation for the Pulfrich illusion was proposed initial ly by Pulfrich himself, apparently fol lowing a suggestion from an associate.(Pulfrich was blind in one eye and there fore could not see his own illusion.)The explanation is that the eye covered by the filter has a slower response time than the uncovered eye and that the delay gives rise to what is in effect a binocular disparity between the left and right reti nal images as registered at some high er level in the brain.As the pendulum moves across the visual field its momen tary position on each retina is the same, but the signal sent to the brain from the covered eye indicating the presence of the pendulum at any given retinal loca tion lags behind the corresponding sig nal from the uncovered eye.Hence at the level of the brain where simulta neous left and right retinal images are compared it seems there is a disparity between the two eyes' images of the swinging end of the pendulum, and the "disparity" is interpreted in the usual way to signify depth.Pulfrich's original explanation has subsequently been con firmed by many experiments.
My variation was to mount an inside- out face mask on the end of a pendulum and then carry out Pulfrich's demon stration in the usual way.Here again the basic question is whether binocular depth inversion of the face can occur at the same time as stereopsis.According to the monocular-suppression hypothe sis, the Pulfrich effect should be absent when the face is seen as being invert ed, because that effect depends on the brain's registering binocular-disparity cues and incorporating them into visual experience.On the other hand, the dis parity-reversal hypothesis implies that the Pulfrich effect should arise during a depth inversion of the face but that the apparent direction of the illusory ellipti cal arc should be reversed, as though the filter had been shifted to the other eye.
Neither prediction stands up.Instead one finds that the face can be seen as depth-inverted and can still appear to swing in an elliptical arc.The monocu lar-suppression hypothesis is therefore ruled out.And since the direction of the movement is the one normally seen, the disparity-reversal hypothesis can be ruled out too.

W
hat do these experiments reveal about depth perception and about the perception of form in general?The central result is that inversion can oc cur even when the brain mechanism re sponsible for constructing visual expe r ' ience has demonstrably registered all the depth information available in nor mal vision, including the geometrically unambiguous information provided by binocular disparity.On this point, then, Helmholtz and Mach were wrong; mon-158 ocular vision, with its inherent three dimensional ambiguity, is not a prereq uisite for seeing things inside out.Evi dently binocular vision can be equally precarious when the stimulus offers suf ficient provocation.
This finding raises two questions.How is the apparent three-dimensional form of a binocularly depth-inverted object related to the two retinal images that give rise to it?What prevents inver sion in ordinary vision?
The first question is perplexing be cause, according to the standard geome try of binocular vision, depth inversion creates an impossible object.What one sees in the mind's eye cannot be geo metrically reconciled with the retinal images.The brain appears to ignore this paradox, presenting consciousness with a seemingly coherent visual object.Apparently depth-inverted percepts are constructed from sensory evidence ac cording to definite perceptual rules, but it is not obvious what the rules are.
Initially I was inclined to look for the rules among variations on the disparity reversal theme.That idea now seems to me to be increasingly implausible.For one thing the theme's geometrical impli cations for the apparent shapes of bin ocularly inverted objects do not seem to agree well with what one actually sees in the illusion.
Moreover, the brain appears not to reverse disparity readily, even when the provocation is strong.Mark Georgeson of the University of Bristol has tested this point by creating reliefs of human faces in which the depth is given entire ly by binocular disparity; they are fac-es sculptured by the three-dimensional surfaces seen in random-dot stereo grams.Depending on which eye sees which half of such a stereogram, the dis parities may create a face that is either normal or inside out.
When the stereogram actually depicts an inside-out face, one might expect per ceptual depth inversion to develop easi ly if the brain is geared to create invert ed percepts by reversing binocular dis parities.This does not happen.George son finds that these purely stereoscopic faces are always s.een in correct depth (that is, inside out, as is implied by their actual disparities), notwithstanding the normal human bias for seeing faces the other way.The finding suggests that dis parity reversal is not a trick the brain performs easily, and so it seems to be an unlikely basis for understanding the per ceptual geometry of binocular depth in version.The architectural key to this novel visual world remains to be found.
The second question raised by binoc ular depth inversion is more general.If one can sometimes see objects as being inverted in spite of the availability of every possible cue to depth, why is the mistake so uncommon in normal vision?One thought might be that binocular in version is an anomaly confined to the special case of inside-out human faces.Perhaps the perception of faces invokes unique mechanisms that do not apply to the perception of other objects.
This idea is easily disposed of, be cause one can achieve binocular inver sion with a broad range of familiar ob jects.The critical factor seems to be not "faceness" but rather a lifelong habit of seeing certain classes of objects in stan dard three-dimensional configurations.Thus to explain why inversion is rare one can only say that most of the time the object hypotheses favored by per ceptual biases turn out to be correct.
To say that is to say not enough.The basic problem is to understand precisely how mental preconceptions mesh with immediate sensory input to create visual experience.The metaphor of the brain as a tester of hypotheses does not carry one very far.
For example, it is clear that before the visual system can decide to interpret its sensory data according to some specif ic object hypothesis it must be guided to a roughly appropriate class of hy potheses, otherwise each new object would present an impossible problem in searching.(One could spend a lifetime testing cow-shaped hypotheses against retinal trees.)This guidance must come primarily from immediate sensory evi dence, and so the key problem in percep tion is how the visual system manages so successfully to pull itself up by its own bootstraps.
The question of how much of what a person sees is forced on him by immedi ate sensory stimulation and how much is Such suppression occurs regularly in normal vision when the two eyes are exposed to quite different stimuli.The phenomenon is known as binocular ri valry.It is easily demonstrated.With both eyes open hold your right hand about six inches in front of your right eye and look across the room at, say, a lighted lamp, making sure the lamp is visible to the left eye but not to the right eye.Closing your left eye, you see your hand, and closing your right eye, you see the lamp: two irreconcilable views of the same region of visual space.Yet when both eyes are open, you see only the lamp.Your hand is suppressed, at least in the region of the visual field where the two stimuli are in conflict.Indeed, you can see the lamp "through" your hand.
. ....I L,..... '...J MONOCULAR INVERSION is readily achieved with an experiment devised by Ernst Mach.A blank card snch as an index card is folded in half lengthwise and placed on a flat surface with the bend upward (left).
GEOMETRY OF BINOCULAR VISION suggests that depth inversion should be difficult or impossible.Here both eyes view points X and Y , with X the nearer one; the respective retinal positions are designated X'L and so on.If the eyes converge on Y , the images of Y fall on the center of the fovea of each retina.The lines of sight projected outward from the images X'L and X'R meet at a unique point in space: the real location of X. Hence the combined retinal images in the eyes cannot be reconciled with hypothesis that X is more distant than Y .parity cues reversed, as though the brain had lost track of which eye is which and had interpreted the retinal image in the left eye as coming from the right (and vice versa).In experiments that present flashes of light randomly to one eye or the other, normal observers often have great difficulty telling which eye has been stimulated.Moreover, in normal vision involving binocular rivalry one is not consciously aware of which eye sees what.(For example, hold a finger a few inches above this page so that some letters are invisible to one eye and some to the other.With both eyes open you can read every letter, but unless you al ternately close one eye and then the oth er you will not be able to tell whether a given letter is seen by the left eye or the right eye.) Hence it seemed possible that the brain might exploit this condition in order to reconcile an overwhelmingly plausible object hypothesis with all the sensory evidence.Such an explanation would at least make binocular inver sion a more or less direct extension of monocular inversion.Visual experi ence would still incorporate all the depth a b TWO HYPOTHESES on binocular deptb inversion are monocular suppression (0) and disparity reversal (b).In each case what is actual ly seen is portrayed at the left and the inversion the hypothesis would explain is shown at the right.In monocular suppression the left eye's view is depicted as being suppressed, so that the inside-out face is seen depth-inverted as it would appear in a monocular inversion when it is viewed by the right eye alone.In disparity reversal point X is real ly nearer the observer than point Y, but the brain treats the retinal image in the right eye as though it came from the left eye and vice versa, with the result that point Yappears to be closer than point X. cues available to the brain, but one cue, namely binocular disparity, would ap pear to be transformed in an unjustifi able way.These two potential explanations of binocular depth inversion can be termed "monocular suppression" and "dispar ity reversal." 1 shall describe two eas ily reproducible experiments, each of which tests both hypotheses simulta neously.Both experiments lead to the same conclusion: neither monocular suppression nor disparity reversal can account for what one sees during binoc ular inversion.a The first experiment makes use of a fascinating class of stimuli known as random-dot stereograms, which were invented in 1959 by Bela J ulesz of Bell Laboratories.(I did the experiment in my laboratory at the University of Cal ifornia at Irvine in collaboration with Jerry Kaiwi, who was then a graduate student.)A stereogram is a pair of pic tures designed to create a sensation of depth when one picture is viewed by the left eye and the other is viewed simulta neously by the right eye.The sense of depth is elicited by discrepancies be tween the left and right pictures that b simulate the binocular disparities a solid object would generate.The process of perceiving depth on the basis of binocu lar-disparity cues is known as stereopsis.Random-dot stereograms provide a definitive test of whether the viewer is achieving stereopsis.Not everyone can; about 2 percent of the population is "stereo blind."To make such a stereo gram one constructs a pair of identical pictures consisting of randomly scat tered dots.Then all the dots in a given region are shifted slightly to the left in one picture and slightly to the right in the other to create a binocular disparity c RANDOM-DOT STEREOGRAM provides a basis for testing the monocular-suppression and disparity-reversal hypotheses.The left and right halves of the stereogram (0, b) are identical except that the dots in a square region in the center are shifted horizontally (to the right in the left-hand picture and to the left in the right-hand picture) to create a binocular disparity.An observer with normal stereoscopic vision, viewing the pictures in a stereoscope or by some other means that presents the pictures separately to the left and right eyes, per ceives the central square as floating above the background (c).Ran dom-dot stereograms were made by Bela Julesz of Bell Laboratories.

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After 46 years in Saudi Arabia, Aramco is still growing fast.So is the number of interesting and rewarding jobs we offer.5.The model airplane took off on the first try.ARAMCO SERVICES COMPANY llOO Milam Building FS • CA Houston:Texas 77002 (713) 750-6965 of binocular depth inversIon of a random-dot stereogram on an inside-out face are depicted.In the panel at the left ab represents the face, cd the stereogram and ef the central square.During depth inversion of the face (a'b') the stereogram appears convex (c'd') and the central square floats in front of it (e'f').Panel at the right shows how the inverted-face-stereogram combination rotates when the observer moves his head to the right.