# Space Perception and Binocular Vision

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Space Perception and Binocular Vision
(Organized as suggested presentation slides; text in italics is commentary directed to the instructor. This commentary is in a conversational tone and provides information that goes beyond the slides. It is also meant to help guide a lecture and tie into other topics in the course.)

Chapter 6 Space Perception and Binocular Vision
Monocular Cues to Three-Dimensional Space Binocular Vision and Stereopsis Combining Depth Cues Development of Binocular Vision and Stereopsis

Realism: The external world exists.
Introduction Realism: The external world exists. Positivists: The world depends on the evidence of the senses; it could be a hallucination! This is an interesting philosophical position, but for the purposes of this course, let’s just assume the world exists.

Objects maintain the same size and shape as they move around in space.
Introduction Euclidian geometry: Parallel lines remain parallel as they are extended in space. Objects maintain the same size and shape as they move around in space. Internal angles of a triangle always add up to 180 degrees, etc.

Notice that images projected onto the retina are non-Euclidean!
Introduction Notice that images projected onto the retina are non-Euclidean! Therefore, our brains work with non-Euclidean geometry all the time, even though we are not aware of it.

Figure 6.1 The Euclidean geometry of the three-dimensional world turns into something quite different on the curved, two-dimensional retina SensationPerception4e-Fig jpg

One of the advantages of having two eyes that face forward.
Introduction Probability summation: The increased probability of detecting a stimulus from having two or more samples. One of the advantages of having two eyes that face forward.

The two retinal images of a three- dimensional world are not the same!
Introduction Binocular summation: The combination (or “summation”) of signals from each eye in ways that make performance on many tasks better with both eyes than with either eye alone. The two retinal images of a three- dimensional world are not the same!

Figure 6.2 The two retinal images of a three-dimensional world are not the same
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Introduction Binocular disparity: The differences between the two retinal images of the same scene. Disparity is the basis for stereopsis, a vivid perception of the three- dimensionality of the world that is not available with monocular vision.

Introduction Depth cue: Information about the third dimension (depth) of visual space. Monocular depth cue: A depth cue that is available even when the world is viewed with one eye alone. Binocular depth cue: A depth cue that relies on information from both eyes.

Figure 6.3 Comparing rabbit and human visual fields (Part 1)
Rabbits have a very wide field of view, both in front and above them. Very little of their visual field is seen by both eyes, so they must use mostly monocular depth cues.

Figure 6.3 Comparing rabbit and human visual fields (Part 2)
Humans have a narrower field of view, but much of our visual field is seen by both eyes, allowing us to use binocular depth cues.

Figure 6.4 M. C. Escher, Relativity, 1953
The depth relations in this picture don’t add up! The three-dimensional world is projected onto our two-dimensional retinas and then our brain must reconstruct the lost dimension of depth. Our brain uses many cues to determine depth, but they are not foolproof, as this picture demonstrates. Next, we are going to learn about the cues our brains uses to perceive depth.

Monocular Cues to Three-Dimensional Space
Occlusion: A cue to relative depth order in which, for example, one object partially obstructs the view of another object.

Figure 6.5 Occlusion makes it easy to infer relative position in depth
Figure 6.5 depicts three shapes that, we typically assume, are stratified in depth with the triangle being farthest away and the circle being closest

Figure 6.6 Figure 6.5 could be an “accidental” view of the pieces shown here in (a). It is much more likely, however, that it is a generic view of circle, square, and triangle, as shown in (b) In Figure 6.6 we see two possible interpretations of the situation: (a) It’s possible that the square and triangle are actually the same distance away as the circle but that they have pieces cut out of them. (b) The other, more likely possibility, is that the three shapes are whole figures that are stratified in depth.

Monocular Cues to Three-Dimensional Space
Metrical depth cue: A depth cue that provides quantitative information about distance in the third dimension. Nonmetrical depth cue: A depth cue that provides information about the depth order (relative depth) but not depth magnitude. Based on metrical depth cues, you know exactly how far away something is. This might be useful if you are trying to catch a baseball, for example. Nonmetrical depth cues tell you which object is in front of or behind other objects, but you don’t necessarily know how far away the object is from you.

Monocular Cues to Three-Dimensional Space
Relative size: A comparison of size between items without knowing the absolute size of either one. All things being equal, we assume that smaller objects are farther away from us than larger objects.

Figure 6.7 This is a photograph of a collection of Plasticine balls that are resting on the same surface at the same distance from the camera These balls seem to be stratified in depth because of the cue of relative size. Notice that it is possible that these are just different-sized balls all sitting on the same surface. Indeed, since this is a picture, these balls are in fact on the same surface and different sizes. If we see any 3D structure in this picture, it is because of relative size.

Monocular Cues to Three-Dimensional Space
Relative height: For objects touching the ground, those higher in the visual field appear to be farther away. In the sky above the horizon, objects lower in the visual field appear to be farther away.

Monocular Cues to Three-Dimensional Space
Texture gradient: A depth cue based on the geometric fact that items of the same size form smaller, closer spaced images the farther away they get. Texture gradients result from a combination of the cues of relative size and relative height.

Figure 6.8 This rabbit texture gradient shows that the size cue is more effective when size changes systematically The rabbits in the top of the image appear to be farther away than the rabbits at the bottom of the image. This is because of the cues of relative height and relative size.

Figure 6.9 Organized differently, this illustration of the same rabbits as those shown in Figure 6.8 does not produce the same sense of depth The rabbits in this image get smaller as you move from left to right and the sense of depth stratification is much weaker than in the previous image.

Figure 6.11 The rabbit image at the top far left is the same size as the one at the bottom far right
The rabbits in the upper left and bottom right are exactly the same size on the screen, yet the rabbit in the lower right looks smaller. Why? The texture gradient makes that rabbit in the upper left look farther away, so it must be bigger to project the same visual angle on your retina as the rabbit in the lower right.

Monocular Cues to Three-Dimensional Space
Familiar size: A cue based on knowledge of the typical size of objects. When you know the typical size of an object, you can guess how far away it is based on how small or large it appears. The cue of familiar size often works in conjunction with the cue of relative size.

Figure 6.12 The cue of familiar size
The hand on the left looks closer than the hand on the right because it is larger and because we know how large hands should appear, relative to the size of the woman’s body.

Monocular Cues to Three-Dimensional Space
Relative size and relative height both provide some metrical information. Relative metrical depth cue: A depth cue that could specify, for example, that object A is twice as far away as object B without providing information about the absolute distance to either A or B.

Monocular Cues to Three-Dimensional Space
Familiar size can provide precise metrical information if your visual system knows the actual size of the object and the visual angle it takes up on the retina. Absolute metrical depth cue: A depth cue that provides quantifiable information about distance in the third dimension.

Figure The metrical cues of relative size and height can give the visual system more information than a nonmetrical cue like occlusion can If you imagine that all three spheres are touching the ground, then the green one is farthest away. If you imagine that the three spheres are floating, then the green one appears to be the same distance as the blue and red ones, but appears to be smaller.

Monocular Cues to Three-Dimensional Space
Aerial perspective: A depth cue based on the implicit understanding that light is scattered by the atmosphere. More light is scattered when we look through more atmosphere. Thus, more distant objects appear fainter, bluer, and less distinct.

Figure 6.14 The triangles seem to recede into depth more in (b) than in (a)
The triangles near the top appear to be farther away because they are hazier, bluer, and have less contrast.

Figure 6.15 A real-world example of aerial perspective
A real-world scene with the cue of aerial perspective. Ask the class what other depth cues they can name.

Monocular Cues to Three-Dimensional Space
Linear perspective: Lines that are parallel in the three-dimensional world will appear to converge in a two-dimensional image as they extend into the distance. Vanishing point: The apparent point at which parallel lines receding in depth converge.

Figure 6.16 Linear perspective
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Figure Architectural View by Francesco di Giorgio Martini (1477), a very clear example of linear perspective Notice that the vanishing point appears to be in the very center of the image. Also notice that all of the edges on the ground and in the buildings angle towards the vanishing point.

Monocular Cues to Three-Dimensional Space
Pictorial depth cue: A cue to distance or depth used by artists to depict three- dimensional depth in two-dimensional pictures. Anamorphosis (or anamorphic projection): Use of the rules of linear perspective to create a two-dimensional image so distorted that it looks correct only when viewed from a special angle or with a mirror that counters the distortion.

Figure In 1533, Hans Holbein painted the double portrait in (a) with an odd object (b) at the feet of the two men SensationPerception4e-Fig jpg

Figure 6.20 Modern-day anamorphic art
TOP RIGHT: The image appears three-dimensional when viewed from the correct position. BOTTOM LEFT: When viewed from the opposite direction, it is clear that the image is massively distorted in reality.

Monocular Cues to Three-Dimensional Space
Motion parallax: Images closer to the observer move faster across the visual field than images farther away. The brain uses this information to calculate the distances of objects in the environment. Head movements and any other relative movements between observers and objects reveal motion parallax cues. The visual system has access to these physical cues and uses them to help infer the distance of objects being fixated.

Figure 6.21 Motion parallax
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Monocular Cues to Three-Dimensional Space
Accommodation: The process by which the eye changes its focus (in which the lens gets fatter as gaze is directed toward nearer objects). Convergence: The ability of the two eyes to turn inward, often used to focus on nearer objects. Divergence: The ability of the two eyes to turn outward, often used to focus on farther objects. The visual system has access to these physical cues and uses them to help infer the distance of objects being fixated.

Binocular Vision and Stereopsis
Corresponding retinal points: A geometric concept stating that points on the retina of each eye where the monocular retinal images of a single object are formed are at the same distance from the fovea in each eye.

Figure This simple visual scene illustrates how geometric regularities are exploited by the visual system to achieve stereopsis from binocular disparity Bob is focusing on the red crayon and the image on the right shows that the image of the red crayon falls on the fovea of both of his eyes.

Figure 6.24 The overlapping portions of the images falling on Bob’s left and right retinas
The images are upside down because of the optics of the eyes. The two red crayons are at corresponding retinal points—the foveas. The purple and brown crayons are not at corresponding retinal points, so they therefore have binocular disparity. The blue crayon also happens to be at a corresponding retinal point in both eyes. Objects do not need to fall on the fovea of each eye to be in corresponding retinal points.

Binocular Vision and Stereopsis
Horopter: The location of objects whose images lie on the corresponding points. The surface of zero disparity. Vieth–Müller circle: The location of objects whose images fall on geometrically corresponding points in the two retinas. The Vieth–Müller circle and the horopter are technically different, but for our purposes you may consider them the same.

Figure 6.25 Bob is still gazing at the red crayon
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Binocular Vision and Stereopsis
Objects on the horopter are seen as single images when viewed with both eyes. Panum’s fusional area: The region of space, in front of and behind the horopter, within which binocular single vision is possible.

Binocular Vision and Stereopsis
Objects significantly closer to or farther away from the horopter fall on noncorresponding points in the two eyes and are seen as two images. Diplopia: Double vision. If visible in both eyes, stimuli falling outside of Panum’s fusional area will appear diplopic.

Figure Superposition of Bob’s left (L) and right (R) retinal images of the crayons in Figure 6.24, showing the relative disparity for each crayon The red and blue crayons appear at the same locations in the two eyes and therefore have zero disparity. The purple and brown crayons, on the other hand, appear at different places in the two eyes and therefore have some disparity in their projected images.

Binocular Vision and Stereopsis
Crossed disparity: The sign of disparity created by objects in front of the plane of the horopter. Images in front of the horopter are displaced to the left in the right eye and to the right in the left eye. A heuristic for remembering this is that you need to cross your eyes to look at something closer than the horopter.

Binocular Vision and Stereopsis
Uncrossed disparity: The sign of disparity created by objects behind the plane of the horopter. Images behind the horopter are displaced to the right in the right eye and to the left in the left eye. A heuristic for remembering this is that you need to uncross your eyes to look at something father away than the horopter.

Figure 6.28 Crossed and uncrossed disparity
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Binocular Vision and Stereopsis
Stereoscope: A device for presenting one image to one eye and another image to the other eye. Stereoscopes were a popular item in the 1900s. Many children in modern days had a ViewMaster, which is also a stereoscope. The Oculus Rift headset is a more modern example of a stereoscope.

Figure 6.29 Wheatstone’s stereoscope
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Figure 6.30 Stereopsis for the masses
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Binocular Vision and Stereopsis
Free fusion: The technique of converging (crossing) or diverging (uncrossing) the eyes in order to view a stereogram without a stereoscope. “Magic Eye” pictures rely on free fusion.

Binocular Vision and Stereopsis
Stereoblindness: An inability to make use of binocular disparity as a depth cue. Can result from a childhood visual disorder, such as strabismus, in which the two eyes are misaligned. Most people who are stereoblind do not even realize it.

Figure Try to converge (cross) or diverge (uncross) your eyes so that you see exactly three big blue squares here, rather than the two on the page SensationPerception4e-Fig jpg

Binocular Vision and Stereopsis
Recovering Stereo Vision Susan Berry had strabismus as an infant and never developed stereo vision. At age 48, began visual therapy to improve coordination between her two eyes. One day she suddenly developed stereo vision! Suggests that binocular vision might possibly be developed outside of the normally accepted “critical period.” Exercises included taping one end of a string to the wall and holding it up to her nose. The string had several beads along its length and Susan practiced focusing on the beads at different distances.

Binocular Vision and Stereopsis
Random dot stereogram (RDS): A stereogram made of a large number of randomly placed dots. RDSs contain no monocular cues to depth. Stimuli visible stereoscopically in RDSs are cyclopean stimuli. Cyclopean: Referring to stimuli that are defined by binocular disparity alone. RDSs are significant because they prove that stereopsis can be achieved without monocular depth cues. Named after the one-eyed Cyclops of Homer’s Odyssey

Figure If you can free-fuse this random dot stereogram you will see two rectangular regions: one in front of the plane of the page, the other behind the page If you can free-fuse, you should be able to see the image, which is one square floating above the surface and a square-shaped hole poking into the surface.

Binocular Vision and Stereopsis
3D movies were popular in the 1950s and 60s and have made a resurgence in recent years.

Binocular Vision and Stereopsis
For movies to appear 3D, each eye must receive a slightly different view of the scene (just like in real life). Early methods for seeing movies in 3D involved “anaglyphic” glasses with a red lens on one eye and a blue lens on the other. Current methods use polarized light and polarizing glasses to ensure that each eye sees a slightly different image.

Figure 6.34 An audience watching a stereo movie in the 1950s
The people in the photo are wearing anaglyphic style 3D glasses

Binocular Vision and Stereopsis
Correspondence problem: In binocular vision, the problem of figuring out which bit of the image in the left eye should be matched with which bit in the right eye. The problem is particularly vexing in images like random dot stereograms.

Figure 6.37 Is this a simple picture or a complicated computational problem?
If the image in Figure 6.37 falls on the eye, what gave rise to it? There are many plausible interpretations, as depicted in Figure 6.38c.

Figure 6.38 Interpreting the visual information from the three circles in Figure 6.37

Binocular Vision and Stereopsis
There are several ways to solve the correspondence problem: Blurring the image: Leaving only the low-spatial frequency information helps.

Binocular Vision and Stereopsis
Uniqueness constraint: The observation that a feature in the world is represented exactly once in each retinal image. Continuity constraint: The observation that, except at the edges of objects, neighboring points in the world lie at similar distances from the viewer.

Figure 6.39 A low-spatial-frequency–filtered version of the stereogram in Figure 6.33
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Binocular Vision and Stereopsis
How is stereopsis implemented in the human brain? Input from two eyes must converge onto the same cell.

Binocular Vision and Stereopsis
Many binocular neurons respond best when the retinal images are on corresponding points in the two retinas: Neural basis for the horopter. However, many other binocular neurons respond best when similar images occupy slightly different positions on the retinas of the two eyes (tuned to particular binocular disparity).

Figure 6.40 Receptive fields for two binocular-disparity–tuned neurons in primary visual cortex
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Binocular Vision and Stereopsis
Stereopsis can be used as both a metrical and nonmetrical depth cue. Some cells just code whether a feature lies in front of or behind the plane of fixation (nonmetrical depth cue). Other cells code the precise distance of a feature from the plane of fixation (metrical depth cue).

The Bayesian Approach, Revisited (first mentioned in Chapter 4).
Combining Depth Cues The Bayesian Approach, Revisited (first mentioned in Chapter 4). Like object recognition, depth perception results from the combination of many different cues..

Combining Depth Cues The Bayesian approach: A way of formalizing the idea that our perception is a combination of the current stimulus and our knowledge about the conditions of the world—what is and is not likely to occur. Thus, prior knowledge can influence our estimates of the probability of an event. Example: Imagine that you are visiting a friend in Pennsylvania on a cold winter night. As you are about to fall asleep, you hear your car alarm go off. Do you leave your warm bed to go investigate? Situation 1: Your friend lives in rural Pennsylvania on a farm. Do you investigate? Probably not. The car alarm was probably set off by a squirrel or a breeze. You click off the alarm and go to sleep in your warm bed. Situation 2: Your friend lives in downtown Philadelphia. Do you investigate? YES! The car alarm is much more likely to have been set off because of the higher crime rate in downtown Philadelphia compared to rural Pennsylvania. The difference between these two situations depends on prior knowledge of the likelihood of crime in the area. This is the key insight of the Bayesian approach.

Figure 6.41 Retinal image of a simple visual scene
How you interpret the image in Figure 6.41 depends on the prior probability of the size of pennies.

Figure Three of the infinite number of scenes that could generate the retinal image in Figure 6.41 Pennies are almost always the same size, so the situation in Figure 6.42a is the more likely outcome. These sorts of considerations are taken into account by our visual systems when interpreting ambiguous stimuli.

Illusions and the construction of space
Combining Depth Cues Illusions and the construction of space Our visual systems take into account depth cues when interpreting the size of objects.

Figure 6.43 In which image are the two horizontal lines the same length?
Which of these five images has two horizontal lines that are the same width? Answer: Second from left.

Figure 6.44 The two people lying across these train tracks are the same size in the image
Are these two people the same height? Answer: YES. The images of the two men are the same width on the screen, but they look to be different sizes because the railroad tracks make the man in the upper image look farther away. What cues make the man at the top look farther away? Relative height, linear perspective, and texture gradients. All things being equal, if two images are the same size on the retina and one is farther away than the other, then the farther image must be bigger.

Figure 6.45 All of the red lines in this illustration (a) are the same length, as you can see in (b)
What cues give rise to this illusion? Relative height, linear perspective, and texture gradients This illusion results from the same considerations as those at play in Figures 6.43 and 6.44.

Figure Despite their appearance, the vertical lines are parallel in (a), as are the horizontal lines in (b) Are the lines parallel or not? On the left (a), the vertical lines do not appear to be parallel, but they really are. On the right (b), the horizontal lines do not appear to be parallel, but they really are. These illusions have to do with how tilted lines affect the receptive fields of straight lines in the visual system.

Combining Depth Cues Binocular rivalry: The competition between the two eyes for control of visual perception, which is evident when completely different stimuli are presented to the two eyes.

Figure 6.47 Binocular rivalry
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Figure If blue vertical bars are shown to one eye while orange horizontal bars are shown to the other, the two stimuli will battle for dominance This image schematically illustrates the perceptions that arise from binocular rivalry while free-fusing Figure 6.47.

Development of Binocular Vision and Stereopsis
Stereoacuity: A measure of the smallest binocular disparity that can generate a sensation of depth. Dichoptic: Referring to the presentation of two stimuli, one to each eye. Different from binocular presentation, which could involve both eyes looking at a single stimulus. Stereoacuity is often tested using dichoptic stimuli.

Figure 6.50 The onset of stereopsis
Almost all infants showed stereopsis for the first time between three and five months of age.

Figure 6.51 The development of stereoacuity
Stereoacuity develops to adult levels within the first 6–7 months of life.

Development of Binocular Vision and Stereopsis
Abnormal visual experience can disrupt binocular vision: Critical period: In the study of development, a period of time when the organism is particularly susceptible to developmental change. There are critical periods in the development of binocular vision, human language, and so on.

Development of Binocular Vision and Stereopsis
Strabismus: A misalignment of the two eyes such that a single object in space is imaged on the fovea of one eye, and on the nonfoveal area of the other (turned) eye. Suppression: In vision, the inhibition of an unwanted image. If strabismus is present during the critical period, it can lead to stereoblindness. Suppression occurs frequently in persons with strabismus.

Figure Left esotropia SensationPerception4e-Fig jpg

Development of Binocular Vision and Stereopsis
Esotropia: Strabismus in which one eye deviates inward. Exotropia: Strabismus in which one eye deviates outward.

Figure 6.54 Development of stereopsis in normal infants (red line) and in esotropes (blue)
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