Instructor’s Manual

to accompany

Sensation & Perception,FourthEdition

Chapter 6: Space Perception and Binocular Vision

Chapter Overview

In this chapter we learn how the visual system accomplishes the difficult task of perceiving the spatial layout of the three-dimensional world using only the two-dimensional images formed on the back of our retinas. Monocular depth cues such as occlusion, relative size, and motion parallax allow us to interpret depth relations in paintings, photographs, and films, and also help with depth perception in the real world. But objects really “pop out” in depth when our brains are able to compare the slightly different perspectives of the world offered to us by our two eyes, a depth cue called stereopsis. These depth cues are combined by our brain into a coherent representation of the world, possibly via a Bayesian type of process (a logical process that takes into account the probabilities of certain events in the world). When cues conflict, the result is often a visual illusion. The development of stereopsis normally occurs during a critical period of the first 6–8 months of life, unless the eyes are not aligned due to strabismus.

Chapter Outline

Monocular Cues to Three-Dimensional Space

Occlusion

Size and Position Cues

Aerial Perspective

Linear Perspective

Pictorial Depth Cues and Pictures

Motion Cues

Accommodation and Convergence

Binocular Vision and Stereopsis

Stereoscopes and Stereograms

Random Dot Stereograms

Stereo Movies, TV, and Video Games

Using Binocular Stereopsis

Stereoscopic Correspondence

The Physiological Basis of Stereopsis

Combining Depth Cues

The Bayesian Approach Revisited

Illusions and the Construction of Space

Binocular Rivalry and Suppression

Development of Binocular Vision and Stereopsis

Abnormal Visual Experience Can Disrupt Binocular Vision

Chapter Summary

1. Reconstructing a three-dimensional world from two non-Euclidean, curved,two-dimensional retinal images is one basic problem faced by the brain.

2. A number of monocular cues provide information about three-dimensionalspace. These include occlusion, various size and position cues, aerial perspective,linear perspective, motion cues, accommodation, and convergence.

3. Having two eyes is an advantage for a number of reasons, some of whichhave to do with depth perception. It is important to remember, however,that it is possible to reconstruct the three-dimensional world from a singletwo-dimensional image. Two eyes have other advantages over just one:expanding the visual field, permitting binocular summation, and providingredundancy if one eye is damaged.

4. Having two laterally separated eyes connected to a single brain also providesus with important information about depth through the geometryof the small differences between the images in each eye. These differences,known as binocular disparities, give rise to stereoscopic depth perception.

5. Random dot stereograms show that we don’t need to know what we’reseeing before we see it in stereoscopic depth. Binocular disparity alone cansupport shape perception.

6. Stereopsis has been exploited to add, literally, depth to entertainment—from nineteenth-century photos to twenty-first-century movies. It has alsoserved to enhance the perception of information in military and medicalsettings.

7. The difficulty of matching an image element in one eye with the correct elementin the other eye is known as the correspondence problem. The brainuses several strategies to solve the problem. For example, it reduces the initialcomplexity of the problem by matching large “blobs” in the low-spatialfrequencyinformation before trying to match every high-frequency detail.

8. Single neurons in the primary visual cortex and beyond have receptivefields that cover a region in three-dimensional space, not just the twodimensionalimage plane. Some neurons seem to be concerned with a crudein-front/behind judgment. Other neurons are concerned with more precise,metrical depth perception.

9. When the stimuli on corresponding loci in the two eyes are different, weexperience a continual perceptual competition between the two eyes knownas binocular rivalry. Rivalry is part of the effort to make the best guessabout the current state of the world based on the current state of the input.

10. All of the various monocular and binocular depth cues are combined(unconsciously) according to what prior knowledge tells us about the probabilityof the current event. Making the wrong guess about the cause ofvisual input can lead to illusions. Bayes’ theorem is the basis of one type offormal understanding of the rules of combination.11. Stereopsis emerges suddenly at about 4 months of age in humans, andit can be disrupted through abnormal visual experience during a criticalperiod early in life.

Lecture Outline

(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 lectureand tie into other topics in the course.)

Introduction

[New slide]

  • 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.

[New slide]

  • 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!
  • Therefore, our brains work with non-Euclidean geometry all the time, even though we are not aware of it.

[New slide]

  • Show concept of Euclidian geometry (Figure 6.1).

[New slide]

  • 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.
  • 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!

[New slide]

  • Show concept of different retinal images (Figure 6.2).

[New slide]

  • 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.

[New slide]

  • 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.

[New slide]

  • Show Figure 6.3 depicting the visual fields of rabbits and humans.
  • 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.
  • 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.

Monocular Cues to Three-Dimensional Space

[New slide]

  • Show Figure 6.4 depicting M.C. Escher’s Relativity.
  • 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.

[New slide]

  • Occlusion: A cue to relative depth order in which, for example, one object partially obstructs the view of another object.
  • Show Figures 6.5 and 6.6.
  • 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.
  • 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.

[New slide]

  • Metrical depth cue: A depth cue that provides quantitative information about distance in the third dimension.
  • Based on these depth cues, you know exactly how far away something is. This might be useful if you are trying to catcha baseball, for example.
  • Nonmetrical depth cue: A depth cue that provides information about the depth order (relative depth) but not depth magnitude.
  • These 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.

[New slide]

  • 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.

[New slide]

  • Show Figure 6.7, depicting an arc of Plasticine balls. 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 apicture, these balls arein fact on the same surface and different sizes. If we see any 3D structure in this picture, it is because of relative size.

[New slide]

  • 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.
  • 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.

[New slide]

  • Show Figure 6.8, illustrating a texture gradient of rabbits.
  • 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.

[New slide]

  • Show Figure 6.9, illustrating a different texture gradient of rabbits.
  • 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.

[New slide]

  • Show Figure 6.11, depicting yet another texture gradient of rabbits.
  • 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.

[New slide]

  • 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

[New slide]

  • Show Figure 6.12, depicting 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.

[New slide]

  • 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.
  • 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.

[New slide]

  • Show Figure 6.13, illustrating how relative size and height can give relative metrical depth cue information.
  • 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.

[New slide]

  • 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.

[New slide]

  • Show Figure 6.14, depicting the cue of aerial perspective. The triangles near the top appear to be farther away because they are hazier, bluer, and have less contrast.

[New slide]

  • Show Figure 6.15, depicting a real-world scene with the cue of aerial perspective.
  • Ask the class what other depth cues they can name.

[New slide]

  • 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.

[New slide]

  • Show Figure 6.16, which is the simplest demonstration of the concept of both linear perspective and the vanishing point.

[New slide]

  • Show Figure 6.17, a more realistic depiction of linear perspective and a vanishing point.
  • 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.

[New slide]

  • 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.

[New slide]

  • Show Figure 6.19, demonstrating anamorphosis in a 1533 painting by Hans Holbein.

[New slide]

  • Show Figure 6.20, depicting modern-day anamorphic street 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.

[New slide]

  • 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.

[New slide]

  • Show Figure 6.21, depicting how objects in the visual field would change position as you travel past them in a moving train.

[New slide]

  • 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

[New slide]

  • 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.

[New slide]

  • Show Figure 6.23, depicting Bob looking at four crayons. 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.

[New slide]

  • Show Figure 6.24, showing the retinal images that Bob is seeing from the crayons.
  • 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.

[New slide]